Microclimate for cultural heritage

Foreword Several books have been written on microclimatology and boundary-layer physics, beginning with Rudolph Geiger's Climate near the Ground (first German Edition in 1927). Until now, however, nobody has produced a book on the effects of small-scale climate variability around and inside buildings, monuments and other cultural objects. So Professor Camuffo's well illustrated account, Microclimate for Cultural Heritage will be greatly welcomed by architects, engineers, preservers and restorers of cultural property, and the wider community of microclimatologists. What has "cultural heritage" to do with microclimatology? Forty years ago, the response from meteorologists would have been: "Very little". Let me cite a personal example. Back in the 1950s while studying engineering meteorology at the University of Michigan, I wrote a term paper on the weathering of exposed surfaces by atmospheric pollution, which was given an A grade, and which was subsequently published (Munn, R.E., 1959: Engineering Meteorology: the Weathering of Exposed Surfaces by Atmospheric Pollution. Bull. Am. Meteorol. Soc. 40, 172-178). But several scientists (including a famous professor of physics at McGill University in Montreal) were alarmed that such a topic should find its way into the meteorological literature, and made their views known. Thirty-five years later, the importance of microclimatological gradients is widely recognized in the preservation and restoration of cultural objects. Credit for this attitude change is largely due to the efforts of a few people like Dario Camuffo, who recognized early on, the importance of micrometeorology in studies of the preservation and restoration of cultural heritages. This monograph contains many practical examples of ways in which micrometeorological knowledge can help in assessments of the deterioration of surfaces that have been exposed to the environment over long periods of time. Not only does the book include interesting outdoor examples from the author's own experience but also indoor cases, like horizontal cross-sections of temperature in the Sistine Chapel and of mixing ratio in the Giotto Room in the Uffizi Gallery in Florence. I know that this book will be widely consulted by specialists in the cultural heritage field, and I am pleased to have been involved in a very small way by contributing this foreword. R.E. Munn

Institute for Environmental Studies

University of Toronto, Toronto, Canada

vii

Preface This book has been designed as a useful microphysics handbook for conservators and specialists in chemistry, architecture, engineering, geology and biology who work in the multidisciplinary field of the environment, and, in particular, in the conservation of works of art. It has been especially written following the continuous d e m a n d to fill a gap in the literature related to this i m p o r t a n t application of atmospheric sciences, i.e. to apply the thermodynamic processes of clouds, or the dynamics of the planetary boundary layer, to a m o n u m e n t surface or to a room of a m u s e u m . The aim is to furnish them with a b a c k g r o u n d familiarity with the u n d e r l y i n g physics behind mathematics, and to give a detailed description and interpretation of the main microphysical p h e n o m e n a which play a fundamental role in practical applications. Correct application of formulae is only possible when all the approximations made in their derivation and the limitations intrinsic to the basic hypotheses are known. In this complex field an effort is m a d e to substitute scientific d e m o n s t r a t i o n s for c o m m o n opinions or popular beliefs. The basis are given for non-destructive diagnostics to evaluate causes of damage and predict outdoor deterioration, determined by meteorological factors, as well as the negative effects in exhibition rooms, due t o u n s o u n d use of technology and mass tourism. To this aim, suggestions are given on the fundamental principles in designing heating, air conditioning, lighting and in reducing the deposition of pollutants on works of art. Theory and experience are coupled to describe the complex condensation mechanisms and the fundamental role played by water in the stone deterioration and the formation of crusts on monuments. Urban meteorology, air-surface interactions, atmospheric stability, dispersion and deposition of airborne pollutants are also key topics of this book, whose main aim has been to make comprehensible to a wider audience a matter that is only familiar to a few specialists. This book combines a theoretical background with m a n y years of accurate laboratory research, field surveys and practice. The first part, devoted to applied theory, is a concise treatise on micro physics, which makes a survey on the basic ideas especially on classical, kinetic and statistical t h e r m o d y n a m i c s which are necessary for e n v i r o n m e n t a l diagnostic and conservation. The second part,

Performing Microclimate Field Surveys, is devoted to the practical utilisation and shows in detail how measurements should be performed, with many suggestions and examples and the indication of some common errors that should be avoided.

viii

Acknowledgments

The book is based on direct experience on a large number of case studies, most of them funded by the European Commission (DG XII: Science Research and Development, Programmes STEP and Environment, Contracts ENV-757-I-SB, EV4V-0051-I-A, STEPCT90-0107-SSMA, ENV4-CT95-0088, ENV4-CT95-0092) and some of them supported by the National Research Council of Italy (CNR), e.g. Finalized Project 'Beni Culturali', ENEL, e.g. project Effects of Air Pollution on Human Health and Cultural Heritage, the Consorzio per la Torre di Pisa and the Consorzio Padova Ricerche. Studies also were made in the occasion of special commissions (e.g. European Union, UNESCO, NAPAP, Vatican, Italian Ministry of Scientific Research). This text utilises also lectures of Atmospheric Physics taken during the last ten years at the Physics Department, University of Padova, as well as those on microclimate and physical weathering of monuments at international schools (e.g. European University Centre for Cultural Heritage of the Council of Europe in Ravello; Community of Mediterranean Universities; UNESCO-ICCROM). A number of original contributions that were published in scientific journals, or presented at international symposia, are here summarised. Special thanks are due to whoever has contributed: all my co-workers, i.e. Dr. A. Bernardi, Mr. A. Ongaro, Dr. G. Sturaro, Dr. A. Valentino and Arch. P. Schenal for their cooperation especially in the field surveys and data analysis; the scientific officers of the European Commission, and particularly Dr. J. Acevedo for her interest, kind encouragement and friend assistance; the good friends and colleagues Prof. A. Arnold (Swiss Federal Institute of Technology, Ziirich), Prof. N.S. Baer (New York University), Dr. E. Bell (Trinity College, Dublin), Prof. P. Brimblecombe (University of East Anglia, Norwich), Dr. L. De Boek (Antwerp University), Prof. M. Del Monte (Bologna University), Prof. B. Fitzner (Technischen Hochschule, Aachen), Dr. P. Bacci (ENEL, Milan), Dr. C. Price (University College, London), Dr. C. Sabbioni (CNR FISBAT, Bologna), Prof. C. Saiz-Jimenes (CSIC, Seville), Prof. R. van Grieken (Antwerp University), Dr. S. Vincenzi (CNR-ISDGM, Venice), Dr. Th. Warscheid (Freie Hansestadt, Bremen) and Prof. F. Zezza (Bari Polytechnic) for having contributed in different ways. For figures, we must acknowledge the following: Fig.l.4, 2.6 and 4.4 are reprinted from European Cultural Heritage Newsletter on Research, and Bollettino Geofisico, joint edition 14, 3, 1-123, Camuffo D. and Bernardi, A.,: The microclimate of Leonardo's "Last Supper" (1991) with kind permission from the European Commission, DG XII, and the Bollettino Geofisico. Fig.l.6 is reprinted from Science of the Total Environment, 46, 243-260, Bernardi, A., Camuffo, D., Del Monte, M., and Sabbioni, C.:. Microclimate and Weathering of an Historical Building: the Ducal Palace in Urbino (1985) with kind permission from Elsevier Science - NL, Sara Burgherharstraat 25, 1055 KV Amsterdam, the Netherlands. Fig.l.13 and Fig.4.5b are reprinted from Bollettino Monumenti Musei Gallerie Pontificie, 6, 211257, Camuffo, D. and Bernardi, A.: Dinamica del microclima e scambi termoigrometrici tra pareti e atmosfera interna nella Cappella Sistina (1986) with kind permission of the Vatican Museums and Galleries. Fig.1.14 is reprinted from Bollettino d'Arte special issue "Giotto a Padova", Camuffo, D. and Schenal, P.: Microclima all'interno della Cappella degli Scrovegni: scambi termodinamici tra gli affreschi e l'ambiente, pp. 107-209 (1982) with kind permission of Ministero dei Beni Culturali ed Ambientali, via di S. Michele 22, Rome and Poligrafico dello Stato, Rome. \ Fig.5.7 has been kindly supplied by Prof. Marco Del Monte, Department of Geology, Bologna University. Fig.5.8a,b is reprinted from Water Soil and Air Pollution 21: 151-159, Camuffo, D.: Condensation-Evaporation Cycles in Pore and Capillary Systems According to the Kelvin Model Fig.2 and 3 pages 154 (1984) with kind permission from Kluwer

ix Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Fig.6.1 is similar to Fig.3 page 44 in Camuffo, D.: Environment and Microclimate; pp. 37-50 in: N. Baer, C. Sabbioni and A. Sors (ed.s): Science Technology and European Cultural Heritage (1991) with kind permission from Butterworth Heinemann, Linacre House, Jordan Hill, Oxford OX2 8DP, UK. Fig.6.2a is reprinted from Atmospheric Environment 18 (19): 2273-2275, Camuffo, D.: The Influence of Run-Off in Weathering of Monuments. Fig.la, page 2274 (1984) with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. Fig.6.4 has been kindly supplied by Dr. Giancarlo Rossi, ENEL, Venezia-Mestre. Fig.6.6 is reprinted from the book Le deposizioni acide - I precursori. L'interazione con l'ambiente e i materiali, (L. Morselli ed.): Camuffo, D., Aspetti Microfisici delle precipitazioni acide in relazione al degrado dei monumenti, Fig. 2 page 348 (1991) by kind permission of Maggioli Editore, Guerrazzi 10, Bologna. Fig.6.10 is reprinted from American Journal of Science, 251, 884-898, Gordon, J. and MacDonald, F.: Anhydrite-Gypsum Equilibrium Relations, Fig. 3 page 892 (1953) with kind permission of American Journal of Science, 217 Kline Geology Laboratory, Yale University, New Haven, CT 06520-8109, USA. Fig.8.8 and Fig.8.9 are reprinted from Museum Management and Curatorship 10, 373-383, Camuffo, D.: Wall Temperature and Soiling of Murals Fig.1 and Fig.2 page 176 (1991) with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. Fig.8.20 is reprinted from Vercelli, F., L'Aria, UTET, Torino (1933). Photo taken on 1920. Fig.11.4 is reprinted from Environmental Monitoring and Assessment 6, 165-170. Camuffo, D. and Valcher, S.: A Dew Point Signaller for Conservation of Works of Art, Fig.1 page 167 (1986) with kind permission from Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. The climatological analyses of meteorological data for the Venice and Rome were based on observations taken by the Meteorological Service of the Italian Air Force. A grateful thought to the memory of two good friends and leading scientists: Prof. O. Vittori, who was specialist of Atmospheric Physics and my Director, and Dr. G. Urbani, who was preserver and Director of the Istituto Centrale del Restauro, Rome, for their unforgettable scientific discussions and for their stimulating contributions to apply atmospheric microphysics theory and environmental survey practice to monument conservation. Finally, special acknowledgements are due to my family for all my missing time.

CHAPTER 1

Microclimate, Air and Temperature

1.1. THE MICROCLIMATE First of all, it m a y be useful to define the w o r d 'microclimate' to which we refer, as in the e v e r y d a y practice some terms such as 'global climate', 'macroclimate',

'mesoclimate', 'climate', 'microclimate', 'nanoclimate' and 'picoclimate' are used by people with different meaning, and the same is done also by specialists. It is clear that all these terms have been utilised to define the climate of a specific area, and the prefix is chosen to indicate the size of the area involved. Of course, we cannot proceed in the apparently most straightforward way, i.e. by stating a scale with the appropriate size unit, e.g. one kilometre in diameter, and then apply the well k n o w n definitions, i.e. milli = 10 -3, micro = 10 -6, nano = 10 -9, pico = 10-12, as in this case the 'micr0climate' w o u l d apply to a site sized only 10 -6 km =1 mm, and this is obviously ridiculous. S o m e b o d y uses the term 'microclimate' for an u r b a n area, 'nanoclimate'

for a

m o n u m e n t and 'picoclimate' for a very small portion of a m o n u m e n t , but this definition has not gained popularity. In principle, the prefix varies with the actual area size, as determined by geographic, topographic or other local factors, e.g. the requirement of reaching a basic homogeneity in some key parameters, but it m a y also vary with reference to the actual interest, in view of a peculiar application, and the list of the subjective elements which intervene in the choice of the appropriate w o r d may continue. In climate research, meteorology and physical geography, the distinction is rather clear and is determined by the field of interest, i.e. the 'global climate' refers to our planet, the 'regional climate' to a geographical homogeneous area, the 'local climate' to a small limited area like a mountain, a valley, a city. Similarly, for conservation, it is useful to use clear terms, derived from the above mentioned sciences, e.g. 'regional

climate' for the main characteristics of the geographic area where the m o n u m e n t is found, 'urban', 'rural', 'mountain', 'valley', 'coastal' and so on for the next dimensional Step, and 'microclimate' relating to the small location, e.g. a corner of street, a square, a

room, where the m o n u m e n t or the object is sited. This definition does not imply a precise size, but focuses the attention on a specific artefact (e.g. a historic building, a statue, a small exhibit) and its surrounding, so that the same term can also apply w h e n studying the interactions between a portion of a m o n u m e n t and the air nearby. In practice, it refers to the whole ambient which is necessary to study in order to know the factors which have a direct influence on the physical state of the monument and the interactions with the air and the surrounding objects. N o w that the prefix 'micro' has been explained, it might be useful to clarify also the w o r d 'climate'. The following definitions can be found: 'climate is the synthesis of the day-to-day weather conditions in a given area', 'climate is the statistical description of weather and atmospheric conditions as exhibited by the patterns of such conditions, in a given region, over a specified period of time long enough to be representative (usually a n u m b e r of decades)', 'climate is the fluctuating aggregate of atmospheric conditions characterised by the states and developments of weather in a given area' (Maunder, 1994). It is evident that in our case the w o r d 'weather' is inappropriate; only in exceptional cases observations exist over a n u m b e r of decades and in general new indicative measurements must be taken in the short term before undertaking restorations; the same definition should be applied either to indoor or outdoor environments. By adapting the previous definitions to our aims, the following interpretation can be given: 'microclimate is the synthesis of the ambient physical conditions (e.g. time and

space distributions, fluctuating values and trends, average and extreme values, space gradients and frequency of oscillations) due to either atmospheric variables (e.g. temperature, humidity, sunshine, airspeed) or exchanges with other bodies (e.g. infrared emission, heating, lighting, ventilating) over a period of time representative of all the conditions determined by the natural and manmade forcing factors'. When a survey cannot continue for a time interval which is statistically representative of all the conditions, it should at least d o c u m e n t one or a few examples of the main different conditions, just to understand the nature of the problem. Another key question is whether meteorological data, taken from a standard w e a t h e r station sited at a few km (or less) from a m o n u m e n t , can be used for the estimation or interpretation of microclimatic situations, or it is always necessary to carry out specific and expensive field tests. It is clear that the acquisition of existing data m a y be helpful for a more complete interpretation of the p h e n o m e n a , but we will see in the following (Chapter 9) that s t a n d a r d w e a t h e r stations operate m e a s u r i n g p a r a m e t e r s with different criteria and methodologies, so that some m e a s u r e m e n t s are useful to our aims, other of scarce relevance and other useless. In addition, several p a r a m e t e r s n e e d e d for the science of conservation are not

considered in w e a t h e r stations. For this reason special field s u r v e y s are indispensable, and only a few parameters, measured by weather stations in a compatible way, appear as a duplicate and could be omitted. However, it is more convenient to record in the same data acquisition system and with the same criteria the whole set of data which is useful for a specific study, and then add or compare further observations, if any.

In the field of conservation or for other particular

e n v i r o n m e n t a l purposes, observations are made to study certain individual problems, so that the instrumental apparatus as well as the operative methodologies are specifically tailored to fit the actual problem. On the other hand, it is evident that weather stations are planned and standardised for meteorological measurements as defined by international protocols, so that they are in principle interchangeable. Not only instruments and methods are generally inappropriate for conservation purposes, but also the free position where the standard weather station is located is not representative of the specific site of the monument, perturbed by nearby buildings, trees or other obstacles. For instance, it is sufficient to consider that, in the wake which forms downstream to a building, the wind direction is opposed to the unperturbed flow measured by the weather station. One of the aims of a field test for cultural heritage is just to describe the complex and 'perturbed' situation originated by the presence of all the obstacles near the monument, whereas the weather station is aimed to monitor the 'unperturbed' situation. It is absolutely restrictive to consider the individual parameters separately, omitting interactions and feed-backs. The microclimate is determined by the complex interaction of several factors and not always an accurate interpretation of what is h a p p e n i n g is possible, or also to forecast the future development of a certain situation. However, our knowledge progresses with small steps and the atmospheric thermodynamics offers a good start. Air and precious surfaces to study and preserve can be found everywhere, either indoors or outdoors. Although traditionally the indoor and the outdoor environments are considered very distinct, in practice they present similar problems: both undergo daily cycles of temperature and humidity, either forced by the solar cycle or by heating, ventilating and air-conditioning systems (HVAC); both are exposed to intense shortwave radiation which may be the direct solar irradiation on the open sky or through window, or artificial light; both are affected by advective air movements, i.e. wind, or air currents, or air infiltration through cracks and openings, or turbulence generated by sources of momentum, e.g. people movements, heat sources, surface roughness in the presence of advective movements. Rainfall and dew are considered typical of outdoor environments, but often rainfall penetrates inside through disconnections, or condensation forms on the

window panes, on the surface of cold objects or inside pores. External pollutants can penetrate through windows and doors and are transported from room to room, and deposit via the same mechanisms, either outside or inside. The same problems can be found outside or inside, although the scale may change as well as the level of complexity. The most important distinction is that the indoor microclimate can be controlled, at least in principle, and it is very important to know how to do it. Although the importance of the indoor microclimate has been stressed for a long time (Benoist, 1960; Camuffo, 1983; De Guichen, 1984; Tomson, 1986; Michalski, 1993; Padfield, 1994; Camuffo and Bernardi, 1995a) very often inappropriate standards of comfort are used, which are based on human well-being and not on the science of material conservation. Are museums oriented towards the well-being of humans or exhibits? Is the main aim of museums to show objects for cultural and educational purposes, or to preserve artefacts in the most appropriate conditions for conservation, to which visitors should adapt? Of course it is necessary to combine the two needs paying attention that the effects on works of art are cumulative and often irreversible. In Europe, the situation was better more than 35 years ago, when Benoist (1960) wrote: 'In winter, museums should be heated not only for visitors and

guardians, but also for works of art. In Europe, visitors are content with 15~ and in America with 21 ~ In Western Europe the above thermal level was appropriate for safely obtaining a correct relative humidity without the need of supplying continually too much moisture to mitigate the exceedingly dry environmental conditions. Unfortunately, Europe is today following the d a n g e r o u s USA temperature standard. In the past, local climate was carefully observed and exploited to the full to adapt buildings and activities to the external ambient and benefit of a natural

microclimate. For example, Hippocrates (De locis), Pliny (Epistulae, II, 17, 7-19), Vitruvious (De Architectura, VI, 4, 1-2) and Palladium (Quattro libri dell'architettura, Book II, Chap. XII), show how a building was constructed with respect to its exposure to the sun, wind and precipitation. Rooms were exploited according to the temperature and type of light that could enter through the windows. Nowadays, the modern technology often induces to think that the climate outside can be ignored, and that a new independent, artificial microclimate can be created inside a building, controlling humidity and temperature with advanced sensors and microprocessors. By maintaining intake air in excess of exhaust of air, commercial buildings and museums are maintained at an indoor pressure higher than the outdoor value, which reduces infiltrations of external air and pollutants, but creates an internal atmosphere, with its artificial microclimate, which is usually not in equilibrium with

walls, floors, ceilings, exhibits, and needs many frequent heat and moisture transfers, to balance the people influence, the air leakage, and the exchanges between air and surfaces. It has been calculated that about 30% of the moisture supplied to a room is absorbed by the room surface (Rosenhow et al., 1985) with the consequence that the benefit in mitigating the air dryness is negatively compensated in moistening surfaces. The excessive confidence on HVAC and their huge use caused in general more damage than advantages. The indoor temperature is regulated on man well-being without keeping into consideration the regional climate and in particular the natural value of the seasonal moisture content (except for calculating the power needed for the HVAC) in order to obtain a reasonable relative humidity. The desired level of temperature is assumed as a primary need, and the concentration of water vapour is increased or decreased accordingly, to create a new artificial microclimate. Several systems which control the humidity level in historical buildings or museums have been analysed with a number of field tests; however, although these systems are good in theory, and the machines operate correctly, the environmental impact has been often found to be disastrous. In fact, a cloud of moist, cool air is generated by these devices that are generally located near the walls where paintings or other precious works of art are positioned. This cloud moves with the internal air motions, and affects all the works with abrupt humidity and temperature changes. The technological limit of HVAC is not in designing new powerful or sophisticated machines, but rather in being able to distribute in a room the new air steadily and homogeneously. The homogeneous distribution of heat and vapour in a room would require too many diffusers, scattered everywhere at short distances. The inflows cause undesired air movements which increase inertial deposition of suspended particles. Unfortunately, present technological research is focused on making more and more sophisticated machines, not in studying and controlling their use. Atmospheric thermodynamics is a precious tool in environmental diagnostics and in the progress of our knowledge on the basic processes of m o n u m e n t deterioration, evidencing causes and effects.

1.2. AIR, WATER VAPOUR AND PERFECT GASES The dry air is composed of a mixture of several gases, mainly nitrogen (N2, 78.084% volume), and oxygen (02, 20.946%), with Argon (Ar, 0.934%), and some

other minor constituents, i.e. carbon dioxide (CO2, 360 ppm, variable), neon (Ne 18.182 ppm), helium (He, 5.24 ppm), methane (CH4, 1.77 ppm), krypton (Kr, 1.14 ppm); hydrogen (H2, 0.5 ppm), Xenon (Xe, 0.09 ppm). Many other trace gases and particles, considered pollutants, are dispersed in the atmosphere, some of them are non-reactive and most of the are reactive, e.g. SO2, NOx. Atmospheric chemistry studies the behaviour and effects of these substances which are reactive especially in association with atmospheric water. For sake of simplicity, the air is often treated as it were an ideal gas, composed of particles having the mass M = 28.96 which is the average weight of the molecules of this mixture. Water vapour is a variable constituent of the atmosphere, whose concentration depends on air temperature and weather vicissitudes, and generally ranges between 0.5 and 4%. This variability is a consequence of the fact that water vapour m a y change state, becoming liquid or solid, and may precipitate or be in different ways transferred from the atmosphere to the earth's surface, or vice-versa. The water molecule itself is far from being a "perfect gas" particle as it is composed of one oxygen and two hydrogen atoms which are 0.95 A far from the oxygen nucleus, and are disposed forming an angle H-O-H equal to 105 ~ This asymmetrical configuration generates an unbalance between positive and negative charges, so that the water molecule is an electric dipole which can orient in an electric field (exerting a strong dielectric action), or may interact with other molecules or bodies exerting van der Waals and electric forces. However, in a first approximation, when the water vapour does not undergo changes of state, for several purposes it can be treated as it were a perfect gas, although some departures may occur and must be considered, as we will see later. Main problems arise w h e n the water vapour approaches saturation, or w h e n a vapour molecule impacts on a surface whose temperature is below the dew point, or which is contaminated with hydrophilic salts. In these conditions, instead of exerting elastic impacts, the vapour molecule will stick on the cold surface, or on the salts (the same holds for condensation nuclei), and the effective number of "free" gaseous molecules decreases. In order to simplify things, the state of a gas is statistically represented by some key p a r a m e t e r s which characterise the average properties of the population of particles. A 'perfect gas' is an ideal reference gas, where the molecules do not exert any force on each other and all impacts are elastic; it is perfectly described by the so called state equation

p V = n .;,r

(1.1)

where p is the pressure, V the volume, n the n u m b e r of moles n = m/M (where m is the actual mass of the gas and M its molar mass),. ~/?~ the universal gas constant, i.e. .~/2~ = 8.3169x107 erg mo1-1 K - l = 1.986 cal mo1-1 K-l; T is the absolute temperature (degree Kelvin, K). For a particular gas X the gas constant is defined as .J2x = .~/2/Mx so that for dry air Ma = 28.965 g mo1-1 and .~/?~a = 0.2870x107 erg g-1 K-1 = 0.06857 cal g-1 K-l; for water v a p o u r Mv = 18 g mo1-1 and .t2v = 0.4615x107 erg g-1 K-1 = 0.1102 cal g-1 K-1. For the gas X the state equation becomes Px V = mx .~/2x T

(1.2)

where Px and mx are the partial pressure and the actual mass. Although a real gas may depart from the perfect gas model, this is, however, the basic equation which will be useful in the following treatment and can also be applied, within certain limits, to the water vapour.

1.3. TEMPERATURE

Temperature is the condition which determines the direction of the net flow of heat between two bodies, i.e. from the w a r m e r to the colder one. For this p r o p e r t y , a t h e r m o m e t e r can be p u t into equilibrium with a b o d y , in o r d e r to read the temperature of the b o d y on the thermometer, if the thermometer does not perturb the original temperature of the body and is not influenced by other factors. From the t h e r m o d y n a m i c point of view, the temperature T represents the average translation

kinetic energy Ec of the gas molecules, according to the principle of equipartition of the energy 3

Ec - -~k T

(1.3)

where k = 1.38x10 -16 erg K -1 is the Boltzmann constant, which represents the ratio .J2/.1J/fvhere ....l / - 0.6023x1024 is the Avogadro number, i.e. the n u m b e r of atoms or molecules which form a mole; the latter is obviously the a m o u n t of substance whose weight (expressed in g) equals the atomic or molecular weight of the substance. As the air is p r e d o m i n a n t l y composed of diatomic molecules characterised by 5 degrees

10 of freedom, the total kinetic energy Et is 5 Et = -2 k T.

(1.4)

For these relationships T is also called molecular temperature. In meteorology it is also called the dry bulb temperature as opposed to the wet bulb temperature which will be seen later. In the following the absolute thermodynamic temperature (K) will be indicated with the capital letter T and the temperature in degrees centigrade (~

with the

lower case t. As t = T-273.16, then AT = At. The value 273.16 is the thermodynamic temperature of the triple point of water, and is usually approximated 273. The concept of temperature can be easily extended from a gas to a liquid or a solid, and a theoretical thermodynamic definition is preferred to the empirical one:

the temperature is the variable measured by a thermometer. As it will be discussed in the following, in the absence of errors, the thermometer measures only the temperature of its bulb, which is not necessarily the same of the object under investigation. In fact, the thermodynamic equilibrium involves a balance between conductivity, convection and radiant heat exchange, which are different for each body. In particular, radiant heat is exchanged with other external bodies either nearby or far away, and this contribution is not included in the definition of temperature. The temperature is a consequence of the present and past energy balance which also includes advective contributions due to the transport of air masses, and only in rare cases is homogeneous in a body or in a room.

1.4. MECHANISMS OF TEMPERATURE DEGRADATION The temperature is a very important factor in conservation of works of art, as changes of this parameter induce differential expansions in the materials and tensile strengths between the surface and the subsurface structure. Temperature cycles induce a n u m b e r of mechanical weathering mechanisms and accelerate fatigue failure in susceptible materials; the faster the cycle, the greater the temperature gradient inside the material, the steeper the front of the thermal wave propagating inside the material, the greater the strength, the faster the ageing and the damage in the surface layer. In fact, the material acts as a low pass filter which attenuates the penetration of the rapid surface temperature changes: the shorter the duration of the

11 fluctuation, the thinner the layer affected by it (Camuffo et al., 1984). However, it must be remembered that the key part of the artistic value of monuments lies in the surface layer. For these reasons daily (or shorter) temperature cycles are much more important than the seasonal ones. Thermal cycles may cause mechanical disgregation of outer part of stones, beginning at the discontinuities included into the rock and the interfaces between the different minerals which form the stone. It is to be noted, however, that the pure thermal effect is an academic abstraction, as in the field the water activity is always superimposed to this variable with synergistic effects. A typical effect is the granular disgregation of magmatic and metamorphic rocks. The thermal anisotropy of the crystalline lattice, the size of the granules and their spatial association determine a system of internal tensions which result in surface disgregation of the granules. The greater the granules, the greater the tensions and the faster the deterioration rate. Sedimentary rocks are characterised by a more regular structure and composition, but the nature of the binding cement between granules acts as a discontinuity factor (Veniale, 1995).

Fig.l.1 The leaning Pisa Tower surrounded by loggias. In the daytime, the solar heating causes the expansion (and compression) of the columns and an additional temporary bending of the Tower which follows the apparent course of the sun.

12 The expansion mechanism may be also important for structural stability. For example, the Pisa Tower (Fig.l.1) is composed of a cylindrical body contoured by six orders of loggias, having thin columns. In the sunny days of the hot season, the stone temperature of the thick central body remains nearly unchanged, but the external parts, and in particular the columns, undergo daily cycles of some 20~

which cause

the expansion of the hot stone (Camuffo et al., 1996). Considering that the expansion coefficient for limestone is 8x10 -6 ~ and that the Tower extends for some 50 m in height, the above daily excursion causes 8 mm vertical expansion of the hot side and temporary bending of the tower. The daily movements of the top, which are forced by solar radiation (and/or wind) have been measured with a pendulum, and the maximum excursion is some 4 seconds of arc from East to West (Jamiolkowski, 1995), which corresponds to about 1 mm of horizontal displacement. The limestone expansion produces a compression of the thin columns and their capitals, most of them are severely damaged or have been substituted in the past. Another consequence of temperature variations are changes in the degree of saturation of the water vapour, and the amount of water adsorbed in the bodies. Several materials, e.g. wood, parchment, ivory, plaster, change their dimension with water content, expanding or contracting, shrinking, micro or macro fissuring and so on. The effects of an external temperature forcing are in general very complex. For instance, wood is characterised by a small heat conductivity, and the internal propagation of a temperature change is preceded by the propagation of a change of relative humidity due to the diffusion of vapour molecules dispersed in air, and this is followed by redistribution of the water absorbed into the grains. As a consequence, delayed differential stresses and shrinking are induced. Again, changes of temperature in porous stones cause changes of relative humidity, which in turn is related to the evaporation of the water in the pores, increasing the concentration of dissolved salts and arriving at the precipitation of them when the solution becomes supersaturated. In sunny days monuments are overheated by the solar radiation and dramatic temperature changes (thermal shocks) occur when the sun appears or disappears; in addition, marked short term (3-15 minutes) temperature fluctuations are a response to variations in wind speed and light cloud cover (Camuffo, 1981; Jenkins and Smith, 1990). Granular disgregation is frequently found on stones with granula r or crystalline texture, e.g. granite or marble, where stresses generated between grains or large crystals with crystallographic axes differently oriented, or having different expansion coefficients, produce fatigue failure along grain or crystal interfaces. For

13 example, calcite crystals expand along the principal axis and contract along the secondary one in the case of a temperature rise. In the long run, heating-cooling cycle will slightly displace crystals from their original position forming a less regular, weaker structure, which will lead to the disgregation and loosing of granules, called

sugaring. The damage is irreversible and cannot be restored (Fig.l.2). In addition to temperature forcing, also wetting-drying cycles cause expansion and contraction cycles in some kinds of stones. However, although disagreement persists over the effectiveness of insolation weathering as a direct cause of rock breakdown, the opinion is that most granular disgregation occurs as a result of a previous weakening of the rock, normally due to chemico-physical weathering mechanisms acting in combination or sequence and involving intrinsic rock properties (e.g. albedo, thermal conductivity and heat capacity, mechanical strength, porosity and specific surface), thermal variations, repeated stressing of the material and role of moisture and dissolved salts (Smith, 1978; Warke and Smith, 1994).

Fig.l.2 Granular disgregation of marble. The restoration had dramatic consequences. Aurelian Column, Rome. Finally, the air temperature is a key factor in determining the habitat for biological life and in controlling metabolisms. At temperatures below 20~ the metabolic processes are reduced and the biodegradation due to bacteria can be often prevented with an appropriate choice of this and other environmental variables (e.g. humidity, light, ventilation). However, although the temperature range from 20 ~ to 35~

generally favours the microbiological activity, the variable response and

adaptability of microorganisms to lower or higher temperatures, as well as to other extreme and stressing environmental conditions (e.g. water activity, pH-value,

14 ionic/osmotic strength), has to be strictly considered when preventive remedies against the microbial attack should be undertaken. Microbial biofilms covering the surface of stones or other materials have several negative consequences: they may enhance the deposition of particles, and the deposited material, as well as the biofilm form a composite layer which changes the albedo of the surface, the porosity and water vapour diffusion inside the material, the thermal conductivity and the water balance, especially in the outer, endangered uppermost layer (Warscheid and Krumbein, 1996). On the other hand, in some cases biofilms exert a protective function with their polymeric matrix, so that it is difficult to formulate an accurate balance between negative impacts and positive factors, especially in view of the variable response of the material contaminating mizroflora (Warscheid and Kuroczkin, 1997). A comparison can be made with the van't Hoff's rule for chemical reactions, which states that the conversion rate is doubled when the temperature is increased by AT = 10~

or is halved for the same drop of temperature. Although this

rule may describe in general the response of biology to temperature, it cannot be simply adapted to all biological reactions.

1.5. THE TEMPERATURE IN A BUILDING, A ROOM In a building, the external forcing (e.g. solar radiation, heat conduction across roof and walls, air exchanges through openings) depends upon the architectural features, and the materials choice. Thin or conductive walls are sensitive to the apparent daily course of the sun; windows may allows for penetration of solar beams and behave as a green-house; in addition they can regulate exchanges of external air. Different exposures in a building have a different heat balance, and not all the rooms have the same temperature. The inner rooms are more shielded and the external forcing is smoothed out; and this is particularly true for the ground floor, where the soil has an enormous heat capacity. The opposite holds for the last floor, being topped by a roof that receives solar radiation during the day and looses infrared (IR) radiation during the night. HVAC or people may completely change the natural equilibrium. Although rooms are often provided with one thermostat for the temperature control, the temperature in a room cannot be described with only one, although timedependent value, but is a four-dimensional function, i.e. of the specific point (x,y,z) and time. As the air is mobile and has a very small specific heat, the inside temperature will be determined by exchanges with floor, ceiling, walls, windows,

15 doors, and all the other sources or sinks of heat, e.g. heaters, air-conditioning systems, solar radiation, lamps, people. If there are open w i n d o w s or doors, or forced flows of air at different temperature, the advection of new air might be the dominant factor. In a closed room hot air rises, but its ascent is stopped by the ceiling: the air distributes according to its density, i.e. the hot and less dense in the top, and the cold and more dense in the bottom. For this reason a stable atmospheric stratification with temperature rising with height tends to form. However, if there are some sources of sinks of heat, or all the surfaces are not exactly in thermal equilibrium with the air at their height, the mass conservation requires that the ascent of warm air is always associated with an equal flow of descending air, and vice-versa. This may happen in several ways, determined by the boundary conditions and room architecture, as we will see with some different examples. (i) Everything is in equilibrium, except for a heat source inside the room. Over the heat source a rising column of hot air will form, it will be stopped and diverge at the ceiling level, will form a new less dense layer on the top, and all the previous ones will remain below, with a general subsidence of the whole volume. If the source is not too hot, the convective motion develops in height up to it finds air less dense, and will be stopped and diverge at this level, leaving unaffected the upper layers. Similarly, if the heat source is not located on the floor but at a middle height, the descending flow stops at the source height, as below it founds colder and denser air. As the mass should remain the same, the ascending and the descending fluxes are equal, so that the ratio between the ascending and the descending velocities equals the ratio between the cross section of the room deprived of the section of the ascending column, and the cross section of the ascending column. (ii) Everything is in equilibrium, except for the floor which is colder (e.g. ground floor in the summertime), o r the ceiling which is warmer than the adjacent air (e.g. metal roof or domes in a sunny day during the hot season). The air-surface exchanges increase the intensity of the atmospheric layering, and the air remains motionless. (iii) Everything is in equilibrium, except for the floor which is warmer (e.g. floor heating), or the ceiling which is colder than the adjacent air (e.g. metal or glass roof in the winter). The air becoming into contactwith a warm floor forms convective rising cells, associated with other descending air, like the convective movements inside a pot of boiling water. Similarly, the air coming into contact with the cold ceiling becomes denser and sinks, forming rivulets of descending cold air associated with convective rise which result in a continuous mixing of the whole atmosphere.

16 (iv) Everything is in equilibrium, except for the walls which are warmer. The heat exchanges form an internal boundary layer of ascending, warm air along the walls; the w a r m air substitutes the previous top layer below the ceiling and slowly displaces downwards the whole mass of stratified layers. If the walls are colder, the internal boundary layer flow is downwards, cold air accumulates above the floor and rises the whole mass of stratified layers. From the above examples it appears that, in general, a natural layering is expected in an inside atmosphere and some air motions may derive from the presence of bodies with different temperature. Thick walls of historical buildings have an enormous heat capacity, tend to maintain the same equilibrium and the typical condition is a steady condition of thermal layering except for the presence of perturbing factors, e.g. HVAC systems, lamps or people. The thick walls of historical buildings are very effective in damping the daily temperature cycles and also, to a minor extent, the seasonal wave, so that internal microclimate is homogeneous, weackly dependent upon the daily cycles and the external weather conditions and the seasonal variability is reduced. The best situation happens when the seasonal time-lag of walls, floor and roof are similar; when they are different the internal stability changes seasonally. For instance, in the case of churches, the ceiling follows the seasonal variations with a shorter time-lag, and the floor based on the ground with a much more longer one, so that in the summertime the relatively warm ceiling and the fresh floor generate an internal layering; in the wintertime the relatively warm floor and fresh roof tend to destroy the air stability with some internal mixing shown by an isothermal vertical profile. An example is given for the Basilica of $. Maria Maggiore, Rome. The external temperature cycle is some 10~

and the internal one order of magnitude less, being

governed by the limited exchanges with the exterior, the walls, the floor and the ceiling, and the heat accumulated (or lost) by these structures in the previous months. In the late summer (Fig.l.3a), the walls have reached equilibrium with the season climate, and the inside temperature is near the average of the external temperature cycle. The external weather conditions have a limited influence on the indoor microclimate, whose changes are mainly governed by the doors and windows openings, and by the nocturnal cooling of the metal domes. The effect of the opening of the two front doors is visible in the early morning, when cold air enters and a lowering of the air temperature is found by the sensor at 3 m level, but not by the sensors at 7 and 11 m. In the autumn (Fig.l.3b), the indoor temperature is greater than the average external values, being close to the daily maxima which equal the temperature of the walls which show a memory of the heat accumulated in

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T i m e (hr) Fig.l.3. External and internal temperature (measured at the heights 3, 7 and 11 m) in the Basilica of S. Maria Maggiore, Rome, in summer (top) and autumn (bottom). The thick walls are very effective in damping out the external daily cycle, and in autumn the heat accumulated during the hot season makes the internal temperature higher than the external average value. Cold air entering through the door is visible at the 3 m level at the opening in the morning (upward arrows in the summer example, 9 to 10 August 1996), and a rise of temperature is visible during the liturgical offices on Saturday evening and Sunday (downward arrows in the autumn example, 19 to 20 Ocober 1996).

18 the hotter months. Peaks of temperature were found in all the seasons during the liturgical offices celebrated Saturday evening and Sunday morning and evening, for the lighting made with incandescence lamps and the massive participation of faithful people. Also interactions between rooms are important. The most common situation is to find consecutive rooms with air flowing through the door and spreading from a room to another (Fig.l.4). The circulation may be forced by HVAC systems or existing pressure differences generated by external winds through w i n d o w s or doors.

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Fig.l.4 Air with a different temperature flowing through the door and spreading in the refectory of the Leonard's Last Supper, Milan (14 November 1982, after Camuffo and Bernardi, 1981a).

Fig.l.5 Interactions between different floors in the S. Rocco Oratory, Padova. In the winter, mild air rises from the cellar through the staircase, spreading in the Oratory. In the bottom of the room (i.e. the right of the map), the wall is milder, being contiguous with another, heated building (18 January 1996).

19 Other important interactions occur between different floors. For example, the San Rocco Oratory (Fig.l.5), Padova, has a staircase which connects the Oratory with an underground cellar. Both are without heating, but the cellar is less sensitive to the daily temperature changes and also attenuates the seasonal temperature wave. In the summertime, and especially during the daytime, the cellar is much colder than the Oratory, so that the cold air remains entrapped in the cellar without any exchange with the upper floor. In the wintertime, and especially during the night and morning hours, the cellar is milder, and this generated a continuous exchange through the staircase: cold air descends and mild air rises with some entrainment and mixing with ambient air up to the lighter air reaches the ceiling, and then spreads horizontally. In addition to the mild area near the staircase, another mild area is found near the opposite wall in the bottom of the room, as this wall is in common with another building which is heated. Another interesting example of interactions between an architectural structure and its surroundings was found at the Ducal Palace in Urbino, Italy (Fig.l.6). This

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Fig.l.6 The microclimate of the curtyard in the Ducal Palace, Urbino, is mainly determined by the daily course of the sun. On the right upper corner, the staircase drains out, as a gigantic chimney, the warm air, determining a cold airstream that invades the staircase (19 December 1982, after Camuffo and Bernardi, 1985, reprinted by permission of Elsevier Science).

20 beautiful Renaissance building has a courtyard which is surrounded by a loggia, and in a corner of the courtyard the staircase of honour connects the court with the upper floors. Particularly damaged are the decorations at the edge of the staircase, which has magnificent bas-reliefs in a local oolithic limestone which is not resistant to weather injuries, especially rainwater. Some field surveys were made to establish the cause of this degradation. In fine days the courtyard and the loggia h a d a t e m p e r a t u r e distribution that followed the apparent course of the sun and the middle of the courtyard was generally colder, for the better ventilation which is found increasing the distance from the architectonic structures, and colder was found also the staircase as the w a r m air was sucked in and drained a w a y as it h a p p e n s inside a gigantic chimney, but this situation was not linked with the damage. Also capillary rise was excluded as well a possible contamination from a back room that in the past was a deposit of sea salt. The cause was found during a rainy day, w h e n a stream of rainwater collected by the roof and gutters was seen to fall d o w n at each corner of the courtyard, being the building without drainpipes. The friction reached with the air after a few metres of free fall, caused the water stream to explode into a myriad of droplets, which were transported by the drainage flow through the staircase and splashed against the decorations. Of course the suggested solution was to apply a drainpipe, but the second hypothesis, i.e. a glass pane to protect the decorations and a glass door to stop the drainage was preferred. Modern buildings made of metal and glass have a conductivity which is higher than traditional brick walls and are more sensitive to the external w e a t h e r conditions. As the thermal capacity of walls and roof is relatively small, the building does not smooth out the seasonal wave. In the wintertime (and during the night) the outer structure cools and generally assumes a temperature which is intermediate between the heated interior and the cold exterior, so that the cold ceiling and walls generate a continuous internal mixing. For example, the Sainsbury Centre for Visual Arts, Norwich, which is built with metal and glass structures with some insulating panels, during a winter survey in a foggy week in December 1996 was found to have the internal air temperature Ti = 19.5~ were ranging between 14.2~

and 15.7~

the metal and glass ceiling panes and walls the outside temperature was To = 7.2~

The continuous mixing of the air masses generated by the contact with the cold structures is also artificially increased, and even in a much more enhanced extent, by the m a n y fans distributed all along the walls, to inject w a r m air in the room. In order to reach the interior of the wide room, and obtain a uniform temperature, the ventilation rate is very high. However, this violent mixing is not sufficient to produce a very uniform temperature (Fig.l.7) and exchanges of heat and moisture

21 are favoured, as well as the deposition of airborne particles. Possibly for this, for safety or other reasons, the main parts of objects is appropriately protected by an individual plexiglas case. On the other hand, in the sunny days of the w a r m season, the ceiling becomes hot forming internal layering, and the glass panes generate some green-house effect.

Fig.l.7 Horizontal cross section of the Sainsbury Centre for Visual Art, Norwich (U.K.), showing the temperature distribution. Modern buildings, made of metal and glass, do not benefit of the inertia of the thick wall, and the microclimate is conditioned by heat exchanges and forced mixing, but fans are not sufficient to obtain a very homogeneous temperature distribution. The 9 December 1996 at 16.30.

1.6. THE TEMPERATURE IN A SHOWCASE We have seen that inside buildings, the 'primary' external heat w a v e is smoothed out by the walls, but abrupt temperature changes are generated by local sources, and the perturbation spreads in different ways within the rooms. For this reason a further natural filter is often useful to smooth out these 'secondary' temperature changes, and show cases accomplish to this aim (Fig.l.8), in addition to protect delicate exhibits from dust deposition and accidental shocks. In this example taken from the Uffizi Gallery, the external daily wave reaches some 20~

and both

the room and the show case have waves with some 4~ amplitude, but the show case has a temperature which is smoothed out with a 2 hr time lag. The exhibits in the case are exposed to a slighly smaller temperature span as the unshielded objects in

22 the room, but are protected against rapid fluctuations or temperature (and humidity) changes. It might be useful to comment that the outside temperature was measured with a sheltered thermometer suspended 30 cm far from the wall, and the thermometer was immersed into the internal boundary layer of hot air which forms and rises along the wall when the latter is hit by solar radiation. This is actually the air which envelops the lighted side of the building, warms the window panes and penetrates through the windows fissures, but is different from the free air, as it would be measured with a standard weather station. 22 20

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Time (hr) Fig.l.8 Comparison between the outdoor temperature, the indoor value and the temperature inside a show-case. Pollaiolo Room, Uffizi Gallery, Florence, 11 to 13 March 1997. The lighting should be obtained with lamps placed outside the case; on the contrary, a lamp inside will act as powerful heater and most of the heat dissipated will remain entrapped inside the case. However, although the light source is external, when a show case is made of a material which is not fully transparent to the IR, it becomes a green-house which causes a dangerous overheating of both the air

and the exhibits preserved inside, as well as a drop of relative humidity. It is popularly known that glass is relatively opaque to the IR radiation, and that more appropriate are plexiglas (i.e. polymethylmethacrylate), polycarbonate, poly-ethylene, polypropylene. However, for all these materials the transmittance in the IR band is neither 1 nor homogeneous, but is generally good except for some narrow absorption bands (Touloukian and DeWitt, 1972; Saint-Gobain, 1977; Michalski et al., 1991) whose relevance changes with the intensity of the spectral band of the IR radiation having the same specific wavelength. For this reason, only

23 looking at the absorption spectra, it is difficult to decide which material is the best one and a laboratory test is much more useful to clarify ideas. Some identical show cases have been built, sized 20 x 10 x 10 cm and with panes 5 m m thick, made one of glass, one of plexiglas and one of polycarbonate, as well as others with panes having twice this thickness. In the bottom of these cases, a black sheet of paper has been placed in order to transform absorbed light into IR radiation, and a thermometer. All these cases have been lighted from outside, with a tungsten incandescence lamp, supplying 500 lux at the top of the boxes in order to obtain a clear effect. The panes, being partially transparent to the IR radiation, absorb part of IR the incoming from the incandescence lamp as well as part of the outgoing radiation, and the heat accumulated in the panes is re-distributed part inside and part outside. The result of this balance is shown in Fig.l.9.

glass 0.5 cm ~3 LJ o

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Time (min) Fig.l.9 Overheating, as a consequence of the green-house effect, of show cases made of: glass, plexiglas, polycarbonate. The cases are lighted with 500 lux from a tungsten incandescence lamp. It is clearly seen that plexiglas and polycarbonate practically behave in the same way, and that their overheating (i.e. 2.9~ 3.5~

is only slightly less than that of glass (i.e.

Making twice the pane thickness a delay is introduced because of the initial

advantage of a greater portion of the IR that is stopped (and accumulated) in the top pane and cannot penetrate inside; after some 2 hr this advantage is lost and the thicker thickness generates a more efficient green-house effect, as expected. After some 6 hr, the overheating is 3.1~

i.e. only 0.2~ more than the box having panes

with half thickness. This experiment clearly shows that, in the case of external

24 lighting with incandescence lamps, the plexiglas is slightly better than glass. A further advantage for short term lighting can be obtained increasing the thickness of the pane. This would reduce and make more gradual the internal overheating and, consequently, the drop in relative humidity. It is thus necessary to avoid the IR radiation, as far as possible, and fluorescent lamps might be a relatively good approach. The same experiment discussed above but with 500 lux generated with a fluorescent lamp led to no detectable overheating. However, these lamps should be controlled for the harmful ultraviolet (UV) emission, but the main drawback is that their irregular spectrum gives an unpleasant tune to colours. The best method consists of using fibre optic lighting, which are, or can be made, practically free of dangerous U V and IR radiation, as it will be discussed in Chapter 4. Showcases, wall display, display tables and so on are useful only if they are suitably built, with use of materials which are inert and no off-gassing, and are appropriately managed. Cases with forced ventilation do not meet the aim of smoothing out room temperature fluctuations. Airtight cases with a closed atmosphere to be dust free should be built with materials that do not release and accumulate noxious substances, or biological infection.

1.7. IS IT POSSIBLE TO COMBINE PEOPLE COMFORT, CONSERVATION NEEDS

AND LOW COST? When a building has a natural microclimate which is not comfortable for people (only rarely the problem is posed whether it is also suitable for conservation), HVAC systems are installed to obtain the desired conditions. Traditional systems are used, e.g. hot water radiators, fan coil convectors, radiant panels, humidifiers) following the everyday practice of keeping a temperature fluctuating around the desired level, or switching on/off the system according to the business times with sudden jumps or drops in temperature (and, consequently, in relative humidity). All these systems are characterised by intermittent use and are located in spot areas, so that they continually generate microclimate perturbations. The use of fans generally worsen the situation, forcing air currents in the rooms. The worst situation is reached in winter, in buildings used only at times, as in the case of churches attended weekly for the Saturday and Sunday liturgy. The first need for conservation is a constant climate, people need a mild climate, and a constant mild microclimate seems the most obvious conclusion, but it is expensive.

25 As it is not easy to combine man comfort, conservation needs and low costs, some different solutions have been attempted, but conservation is more often sacrificed. A compromise solution is to reduce at minimum the heating, warming only pews with electric wires at low temperature, when people is in. This method is aimed at giving a comfortable contact with pews where people seat and rest feet, and is acceptable for heavy dressed people and for a relatively short time. The air should remain unaffected or so. If the temperature is elevated and too much heat is transferred to the air, convective motions are generated, associated with downwards currents of cold air, having the ceiling and wall temperature. These cold flows are very unpleasant to people, and these internal air motions lead to increased deposition rate of candle smoke and other suspended particles. This method is not common in Italy, for the elevated cost of the electric power. Another popular compromise solution is to heat the floor in the pew area, just to mitigate the temperature where people stay. The underfloor heating system uses pipes which carry hot water, placed over an insulating layer and embedded in a conductive layer which constitutes the floor. Heat is transferred from the pipes to the floor and the room is heated by low temperature IR emission from the floor. An advantage of the floor heating is that a large mild temperature heating surface produces comfort at lower air temperature (about 2~

therefore reducing heating

requirement (Porges, 1995). However, when the warm surface is reduced to the pew area, the comfort is diminished, and in addition pews intercept the infrared radiation, leaving people in a relatively cold environment. In any case, floor heating is characterised by low risk for damage to frescoes, paintings, statues and other church decorations, but by high risk to historical pews which undergo enhanced temperature and humidity changes. When such a system is designed for daily use in business buildings, the highest efficiency is obtained with the combined effect of IR radiation and air heating via floor conductivity which generates important convective motions in the air. However, in the case of weekly use in churches, when walls and ceiling are much colder than the air temperature, the air which comes into contact with the cold surfaces sinks, forming down droughts of cold air which are harmful to both people and conservation. In order to avoid dangerous convective motions, the floor should radiate without transferring heat via conductivity to the air. For this reason materials with high IR emissivity and low surface conductivity should be used. Several materials are good emitters e.g. Dolomite which reaches 96% emissivity; granite 93%; brick, 93%; oak 90%, and have a different conductivity, e.g. the above materials have respectively 1.5, 2.9, 1.4, 0.16 W m -1 K -1, so that granite is much more conductive

26 than wood, which is quite an insulator. In most cases inappropriate materials are used for the floor, having a too low conductivity which reduces (or vanishes) the system efficiency or being too much conductive and generating enhanced convective motions, or being poor emitters. For example, the medieval church of Colle S. Lucia in the Italian Alps, 1400 m a.m.s.l., has an underfloor heating just below the pew, but with a w o o d floor. During a field survey in January, with the hot water in the pipe at 30~

the floor was at some 15~ and the air at 1 m was between 8 and 9~

the hot water temperature to 60~ the floor temperature rose to 23~

raising

but the gain in

air temperature was nearly insensitive, being only one degree or so (Fig.l.10). 25 23 ~-21 o

~ t~

19 17 T(floor) ~ 15 ...................................................

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Fig.l.10 Floor and air heating in the church of Colle S. Lucia (Italian Dolomites) from 16 January 1997 at 00.00 to the next day at 9.00. Floor temperature (thick line) and air temperature at 0.1; 0.5 and I m; the measurement at 2 m shown the same temperature found at 1 m. The sharp rise in floor temperature in the afternoon of the 17th is due to the rise of hot water in the underfloor pipe from 30~ to 60~ The air heating from 10.00 to 17.00 of the 16th is due to the external sunshine and warming. Systems based on floor heating need several hours before to w a r m the surface layer and reach the highest efficiency, so that they must be put into operation one or two days before the use, determining dangerous environmental cycles and reducing the spare of money. In practice, in order to abate costs and shorten heating times, these systems are often integrated with other faster systems, e.g. with inflows of hot air w h i c h have the negative consequence of increasing the a m p l i t u d e

of

environmental changes. If costs were neglected, and the floor heating system were continually kept into operation for the whole season, in theory the whole room, walls and ceiling w o u l d reach equilibrium and the problem would be easily solved, at least for the well-being

27 of people, but such a practice is not completely safe for conservation. An example of that was found in the refectory of the Leonard's Last Supper, Milan (Camuffo and Bernardi, 1991a), with a terracotta floor heating. The air, heated from below, was continually mixed by convective motions which led to a heavy deposition of suspended particles and blackening of the painting. The blackening occurred at a so high rate that the restorations works were interrupted for a certain time waiting for an improvement of the ambiental conditions. This obliged tO apply a number of mitigative measures, e.g. to insulate the ceiling to reduce the source of instability aloft, and to forbidden the local traffic which was an important source of soot. However, returning to the problems connected with the heating system, although the floor temperature was kept as low and homogeneous as possible, the temperature distribution inside the room was often characterised by a strong gradient determined by the penetration of w a r m air from the nearby room, where the heating was planned at a higher level for custodians and visitors (as already seen in Fig.l.4). In the general case, the floor heating, which generates air mixing and blackening, is not recommendable in the case of historical buildings with painted walls or ceilings, and exhibits should exposed appropriately protected into show cases. However, although it is not recommendable, in certain cases it might be accepted, with a very soft use, in order to avoid also worse heating systems. A very common system, which is preferred for its low cost, is the hot air heating. Violent airflows of hot air are injected before the people entrance, and are stopped when the people go out. The airflow partially mixes with the indoor atmosphere, generating a wide spectrum of air temperature: hot air forced by its buoyancy reaches the ceiling and forms there a hot layer; on the other hand the dense, cold air originally present" in the room accumulates near the floor; finally, air parcels having intermediate densities find their level of equilibrium, resulting in a strong atmospheric layering. For instance, in a small mediaeval church in the Alps at 1140 m above sea level, in order to reach a benefit of a few degrees rise at the pew level (i.e. 5 ~ at 1 m), a rise of more than 20~

is attained at 3 m and 25~

at 4 m

(Fig.1.11a). These impressive temperature changes in turn generate dramatic drops of relative humidity (Fig.1.11b) with the consequence of forcing internal stress to the canvas paintings and wood statues, which will undergo thermal expansion and moisture shrinking that will destroy the wood artwork in a short time. In addition, the forced inflow generates great atmospheric mixing in the environment with the result of an increased deposition rate of the candle smoke which sticks the cold walls with paintings and frescoes. This is one of the worst heating methods. A mitigative intervention would be to mix vertically air with fans in order to

28 30

rO

25

o

20 r~

15 10

0

10

20

30

40

50

60

40

50

60

T i m e (hr)

90 80 ,.~

,1-1

70

~ i,,,,,i

t~

6o

~

50

9,-, r~

40

~

30 20 0

10

20

30

Time

(hr)

Fig.1.11 (a) Sudden heating and cooling, and strong atmospheric layering, generated by a hot air heating system inside the Church of Rocca Pietore, Italian Alps. The indoor air temperature measurements were taken at the heights 1, 2, 3, 4 m. The measurement at I m is evidenced with a thick line, followed by the others with maximum temperature increasing with height. The values monitored at 3 and 4 m are very similar. The figure reports data from 24 to 26 December 1996, and the peaks correspond to the heating for the Eve and Christmas celebrations. (b) Relative humidity variations caused by the above temperature changes at I m (thick line) and 4 m (thin line).

29 destroy the thermal layering. This would reduce the dramatic temperature rise aloft with the associate humidity drop, but would increase the deposition rate of particles on the surfaces. In order to reduce the room turbulence, the fan can be inserted into a vertical tube, with the lower opening near the floor and the upper near the ceiling. This mounting will generate turbulence only near the two ends of the tube, i.e. in the zones of convergence and divergence of the forced flow. An also worse system, that was especially widespread years ago, was the use of mantle stoves, which burned liquid gas. The chemical reaction of the liquid gas with the atmospheric oxygen generated carbon dioxide and water vapour. In addition to the effects of the hot air discussed above, the most negative consequence originated by the combustion was the enormous production of moisture. Only a small fraction of it was visible when condensed on the cold windows forming rivulets of water, but the main part was absorbed by the porous surfaces of walls and decorations, condensing into the micropores, weakening the stuccoes, shrinking the wood, fading the tissues, favouring the microbial decay and so on. From the above examples it is evident that it is not easy to combine h u m a n comfort, conservation needs and low costs, and that a compromise is required, where the conservation needs should dominate in proportion with the importance of the cultural heritage and the building use. For instance, it could be said that the choice of the microclimate in a museum, which should be aimed at conservation, and where m a n y important items are concentrated, should be more rigorous than in a church which is more oriented to people use. It is also clear that every system presents a number of negative aspects, some of which may have a major impact in certain circumstances, or minor one in others. It this thus important to carry out a careful pros and cons analysis and choose, time by time, the system that provokes the minimum damage. Sometimes a combination of different systems might be considered in order to avoid the excessive impact of specific adverse factors; e.g. in a mountain church the combination of a radiant floor with an electrical pew heating might reach an acceptable comfort with a modest ambient perturbation, and might be better than the more common solution of a radiant floor heating associated with hot air inflows. A general comment, on the ground of the above negative examples, is that it might be preferable to reduce interventions to a m i n i m u m level, in order to also reduce negative effects to a minimum level. It can be argued that many objects have survived till today just because the modern heating was not yet invented and now it constitutes a new challenge. This is true in several cases; nevertheless, it is also possible to use this modern technology to improve natural negative situations, as e.g.

30 w h e n a room temperature is below the dew point and condensation forms everywhere. The conclusion is that heating systems should be installed by experienced engineers, but under the strict directives of experts in conservation science; afterwards, also the use of these thermo-technical devices should be managed under the strict control of experts in conservation. The real problem is that the conservation needs are too often disregarded.

1.8.

MONITORING

AIR

TEMPERATURE

TO

STUDY

AIR-SURFACE

INTERACTIONS AND FOR MICROCLIMATE DIAGNOSTICS The use of a thermohygrograph sited in a corner of a room is very common, but this instrument furnishes data representative only of the point where the sensor is located, not of the whole room, which is generally characterised by spatial gradients continually variable, with fast or slow rates. When the heating or cooling systems are turned on/off, they provoke an abrupt change of temperature, which in general reach few degrees C (Fig.1.12). These frequent and dangerous step changes, when are relatively modest, pass nearly unobserved in the thermograph strip chart records, whose resolution is generally +0.5 ~ or +1~

in that they are smoothed out by the

friction of the pen on the strip chart, or the loose mechanical coupling. Electronic records which are much more accurate and are not affected by mechanical friction, show m u c h better this situation which is c o m m o n to all the most important m u s e u m s and also worse in other situations. Mechanical strip chart recorders can only monitor important changes, as e.g. those induced by hot air heaters, which in the extreme case of churches heated once a week, generate impressive temperature rises,~e.g. 20~ in one or two hours. Measurements of the air temperature and humidity distribution, taken in many points in proximity of surfaces or in horizontal cross sections of rooms, can be used as a diagnostic tool to individuate the air-walls interactions, the causes of microclimate perturbation, the space gradients, the exchanges of heat, the path of the air masses, some deposition mechanisms. Comparing subsequent sections, it is also possible follow the temporal evolution. It is practically impracticable to disseminate a large number of sensors in a room, each having a wire connected with the data logger for two reasons: the wires will form and entangled spider's web in which people cannot move; not all the sensors will exactly have the same transfer function or calibration, and the instrumental response departures will be interpreted as microclimate anomalies.

31 22

20

r"

v

I..i

18

I.,4

~16

T(3)~

[.-, 14

T(O.05)

12

I

I

I

0

I

I

3

I

l

6

9

I

I

I

I

l

I

12

Time

I

I

I

15

l

I

I

18

I

I

21

24

(hr)

30

? t=1

29

I..i

28 [.-

27

9

0

9

I

3

.

9

I

6

.

,

I

9

|

9

I

9

12

,

I

15

|

|

I

18

9

|

I

21

,

.

24

Time (h) Fig.1.12 (a) Abrupt rise and drop of temperature in winter (18 February 1997), w h e n the heating system is turned on in the morning and off in the evening. Measurements respectively taken at 0.05, 1, 2, 3 m from the floor. During the daytime the air is well mixed above 2 m, and the temperture is the same. (b) In summer (11 August 1992), similar step changes are generated by the air conditioning system, but the air is well mixed and the curves at the different heights are practically indistinguishable. For this reason only one has been reported. The Pollaiolo and the Giotto rooms, Uffizi Gallery, Florence.

32 The monitoring is better made moving the same fast-response instrument along a chosen regular grid with points close to the walls as well as inside the room. Repetiting in time these runs, also the time evolution of the temperature distribution is obtained. The method is very effective and has been originally devised for the diagnostic of indoor environments (Camuffo, 1983), in order to find risk areas, causes and effects, and has been applied in many circumstances either indoors or outdoors (Camuffo and Schenal, 1982; Bernardi et al., 1985; 1995a,b; Camuffo, 1986; 1991; 1994; Camuffo and Bernardi, 1988; 1991a,b; 1993; 1995a,b; 1996; 1997). As it is essential to avoid intercalibration errors, the same fast-response instrument is used, i.e. a precision electronic psychrometer (Chapter 11). The spacing between measuring points and hence the number of observations is conditioned by the size of the room and the rate of ambient change. It is essential that in the time employed for the observations the ambient conditions do not change too much. An

uncertainty principle holds:

the greater the spatial resolution, the larger the number of

observation, the longer the time elapsed and the less representative the whole monitoring. In several cases some 40 observations have represented a reasonable compromise solution. The series of measurements can be repeated every 2 or 3 hours d u r i n g the daytime. During the night-time the whole ambient system relaxes without violent perturbing factors, and all the gradients tend to flatten or disappear. The intervals between consecutive measurements can be therefore increased. Ideally, the first observation should be made near sunrise, to monitor the less perturbed situation; then the next observation should be made during the cleaning time, when the windows are open; then two or three hours later and so on, in order to arrive at the end of the visiting time; after the museum closure a few observations are needed. In practice, security reasons limit the possibility of doing measurement outside the m u s e u m business time; fortunately the most important situations are found during the business time. All the cross sections must be monitored exactly following the same order, for two reasons: (i) first of all because if there is a time-lag effect in the monitoring, it repeats identically in all the distributions, and for each point the interval between two successive readings is exactly the same; (ii) then because it is less easy to do errors, and the data must be filed with the same order in the computer. It is also important to repeat for some days the measurements for two reasons: the former is to see whether the results are repetitive, and really representative of the seasonal situation; the latter is that small variations can be found, and their repetition helps to distinguish regular trends from casual fluctuations, i.e. small repetitive variations are not casual.

33 The grid of the measuring points in the horizontal plane is composed of two interconnected series of data: a first series of points at the same height, measured at regular intervals close to the walls, i.e. at 2 mm and at 20 cm from the walls, in order to detect the existing gradients and the exchanges of heat and vapour; the second series (always at the same height) is aimed to show the temperature and humidity distribution inside the room, and is composed of other points, distributed following a regular grid, the points being the vertex of rectangles with the same dimension. All the observations are made exactly at the same level, although the choice of the level is not so important. The height of 1 or 1.5 m from the floor is often preferred for being comfortable for the operator and being representative for the most part of the exhibits. After the observed values of temperature (or humidity) are reported in the cross section, it is possible to use computer graphics or manual interpolation to show the space distribution of the parameter, the anomalies, the intensity and the shape of gradients. Close isolines show gradients. Closed isolines spreading like water waves contain in their centre the source of heat if the temperature value is radially decreasing, or a sink of heat if is increasing. Alternatively, they can show the zone of divergence (or convergence) of air when there is a three dimensional convective motion. In a room, isolines shaped like a tongue which begins from a door or a window show the penetration of external air masses and their path inside. Isolines parallel to the wall surface show that the wall is adsorbing heat if the temperature decreases approaching the wall, or vice-versa. In the same way a gradient of temperature is an index of transport of heat, a gradient of moisture content is an index of transport of vapour and condensation (if the minimum is at the air-surface interface) or evaporation from the surface (the maximum at the interface). Gradients of air temperature are also gradients of air density, and the lighter air gains buoyancy. A thermal minimum along a wall means that the air in contact with it is denser and sinks, a m a x i m u m means that is lighter and is rising up. Therefore, horizontal gradients of temperature may also help to interpret the dynamic state of the air inside a room, the transport and (partially) the deposition of pollutants. An example is shown in Fig.1.13 which reports two horizontal temperature distributions in the Sistine Chapel, first in the early morning when it is open for cleaning, and then a few hours after the entrance of visitors (Camuffo and Bernardi, 1986; 1995a). In the first map, the inside atmosphere was originally in equilibrium with the thick walls, but the opening of three doors (two on the top and one on the right) causes the entrance of cold air: chiefly from the door on the right. The air in the middle of the room, far from the doors, is warmer, but even more warmer is the air

34 close to the walls, which benefits of the heat released from the walls. This air gains buoyancy and forms an uprising current along the walls. This air current tends to increase the deposition rate of airborne pollutants via inertial impaction

(see

Chapter 8), although the positive gradient of temperature tends to partially to counteract it. In the second map, the external atmospheric warming, the presence of visitors and the energy released by the lamps have changed the situation: the air is now w a r m e r than the walls, and a heat island is formed in the central part of the room, where the visitors stay longer. The gradients near the walls are now negative and the heat flows from the air to the walls. The air in proximity of the walls becomes denser and sinks forming a downwards current. The deposition rate is now increased as the negative temperature gradient generates a thermophoretic transport whose effect is added to the contribution of the inertial impaction.

Fig.1.13 Air temperature (~ in a horizontal cross section of the Sistine Chapel when it is opened for cleaning (a) and after the entrance of visitors (b). (7 May 1983, after Camuffo and Bernardi, 1986, reprinted by permission of the Boltettino dei Musei e Gallerie Pontificie).

35 The same method can be applied to investigate the vertical distribution of the air temperature. An example with three different situations found in summer in the Giotto Chapel, Padova, is shown in Fig.1.14 (Camuffo and Schenal, 1982; Camuffo, 1983). In the early morning, when the door is open for cleaning, cold external air enters through the door and fills the lower part of the room up to the height of the door. Above this cold layer, the warm (and less dense) air which was before inside the building remains entrapped there, opposing that new air enters and fills the volume above the height of the door. The isolines are not horizontal, being tilted by the dynamic effect of the external air mass which is entering the room transporting momentum and inducing oscillations in the cold layer. At mid morning, the external air which enters through the door and goes out through some windows in the apse, has a temperature (and a density) which is intermediate between the tongue of cold air which extends from the northern apse as far as the middle nave and the warm air layer which is entrapped below the ceiling. After noon, the solar radiation through the three mullioned window on the facade hits the floor in the front part of the nave, and also heat is released from the hot door. The front part of the nave has the same temperature along the vertical, showing a continuous mixing of the air in the homogeneous region. However, the part of the Chapel near the apse remains unaffected by this perturbation and there the air is thermally stratified (horizontal isotherms), showing a transition zone (curved i s o t h e r m s ) i n the middle of the Chapel. The more vertical the isolines, the more intense the mixing. Sometimes the architectonic features of the rooms are more complicated or the situation is apparently more complex. An interesting example (Fig.1.15) is found in the Cour Marly, Louvre Museum, Paris, which was obtained by closing with a glass roof a courtyard, and the floor is divided into three levels connected with stairs. The top level (on the left) is C shaped and embraces part of the middle level floor; this is Y shaped and surrounds the rectangular bottom level (on the right). Summer air conditioning is accomplished with violent flows of air ejected out of long linear slits sited at the edges of the floor and suction is made with other horizontal slits on walls. The high speed of the airflow facilitates the mixing with the ambient air up to a distance of a few metres from the slits. In addition to the cold air injected by the floor slits, cold air conditioned from some exhibition rooms which face the top level, enters the Cour through open windows and doors. The cold air tends to descend to the lower levels of the Cour flowing along the staircases and jumping over the parapets of the upper floors, and is sucked out by the intake slits. At the bottom level of the Cour, four doors allow free air exchanges between the Cour and the corridor which is connected with the entrance hall. When the corridor is colder, cold air enters

36

24.1

23.7

25.1

26.2

/

/

26.0

Fig.1.14 Vertical cross sections of the Giotto Chapel, in the summertime. (a) In the early morning (8 a.m., the 9 July 1977) cold air penetrates through the door and above the cold layer the warm air remains entrapped. (b) At mid-morning (11.30 a.m., the 8 July 1977) external air penetrates through the door, and has a density intermediate between the cold tongue near the floor on the apse, and the warm air entrapped aloft. (c) In the early afternoon (14.25, the 9 July 1977), the hot floor generates mixing and isothermy in the front part of the nave; after a transition zone in the middle of the Chapel the air in the apse remains unaffected and thermally stratified. (After Camuffo and Schenal, 1982, reprinted by permission of the Bollettino d'Arte).

37 the Cour Marly and forms a cold lake of stable air in the lowest part of the Cour, which is in front of the four doors. When the corridor is warmer (as in this example), the hot air enters, gains buoyancy and rises immediately, forming an uprising flow. This w a r m current rises up to it is stopped at a certain height by w a r m e r air layer stratified below the hot glass roof, or by the roof itself. Whatever is the level aloft where the vertical motion stops, at that level the air flow changes direction and diverges without loosing momentum: it becomes horizontal, crosses the Cour and other colder air sinks, closing the cellar motion. The warmer air found at the bottom layer and the colder one on the top is an index of a very unbalanced situation, and shows that the air is continually moving to reach an equilibrium which is impossible to attain until the forcing factors remain active. In addition, in summer, when the sun is higher on the horizon and solar beams can reach the edge of the floors, hot spots are found which generate a secondary local uprising flow.

21.5

21.9

4-, 21.5

4--

:o' ~ oOoq.

22,3

Fig.1.15 Air temperature (~ measured above each of the three levels of the Cour Marly, Louvre Museum, the 11 August 1993. Hot air enters at the bottom level through the four doors (airflow indicated with arrows) which lead to the entrance hall of the Museum. The hot air rises immediately forming a convective, rotating motion with descent of colder air on the opposite side. Cold air penetrates also through the windows and doors of the exhibition rooms faced to the top floor level, in the opposite side (on the left). The uprising 'bubble' of hot air entering from the four doors (evidenced with arrows) at the bottom level is evidenced with shading.

38 1.9. DRAWING AIR TEMPERATURE AND OTHER ISOLINES Three-dimensional computer graphics give a very elegant visual presentation, but less useful for diagnostic purposes, as several details are masked by the perspective view (Fig.1.16). Two-dimensional maps are much more convenient, as they show with great detail and without distortion the actual distribution and the existing gradients. Computer graphics have been developed to interpolate linearly, quadratically, or with more complex functions, the values between pairs of points.

Fig.1.16 Three-dimensional representation of the temperature distribution at the Sainsbury Centre for Visual Art, Norwich, U.K. (the 9 December 1996 at 16.30, shown in Fig.l.7), and projection of the contour levels in a horizontal plane, which furnishes the two-dimensional diagram. Several details of the 3-D representation are masked by the perspective view. However, this software can be satisfactorily used for a single room with a simple geometry, e.g. a rectangle, but is still unable to well represent the temperature distribution in a complex array of rooms which constitute the floor of a building. In fact, all the data are interpolated in the same way either in the free air or across walls, so that the interpolation is exactly the same for areas in the same room or including walls and different rooms, without considering that the heat flow by advection through an open door is different from the conductive flow across a wall. Computer graphics have not yet reached the level of sophistication which is necessary to equalise the quality of hand drawn isolines in complex architectonic systems. The reason is that this is not only a problem of mathematical interpolation, but of a

39 correct physical interpretation of the data. In the case of building temperature or humidity maps, the distribution is complicated by the presence of sources or sinks of heat or moisture, horizontal advective transports, vertical convective movements, irregular geometry of architectural structures and other perturbation factors. Careful reasoning and experience constitute the best guideline, but some basic directives can be here summarised. A beginner can proceed with successive elementary steps. The first step is to write, on the side of each grid point Ox,y the observed values V(Ox,y). After, one starts by choosing an arbitrary point Ox,y (it is convenient, however, to choose a maximum or a minimum) and drawing the segments which join this point with all the neighbouring points, e.g. the 8 points Ox-l,y-1, Ox-l,y, Ox-l,y+l, Ox,y-1, Ox,y+l, Ox+l,y-1, Ox+l,y, Ox+l,y+l in the case of a regular squared or rectangular grid. Once chosen the map resolution, i.e. the unit step from isoline to isoline (e.g. 0.1~ for air temperature T or dew point spread DPS, 1% for relative humidity RH, 0.1 g kg -1 for specific humidity SH or mixing ratio MR, 0.1 g m -3 for absolute humidity AH) all these segments are divided in equal parts which are determined by the number of times the unit step is included in the difference between the numeric values of the correspondent grid points V(Ox,y) - V(Ox-l,y-1), V(Ox,y) - V(Ox-l,y+l), and so on. For example, if V(Ox,y) = 18.3 and V(Ox-l,y-1) -- 18.7, AV=0.4 and the segment Ox,y Ox-l,y1 is divided into 4 sub-segments which are divided by the equally spaced points 18.4, 18.5 and 18.6. In this way it is possible to note at the extremes of each sub-segment all the values which have been obtained by interpolation. Continuing with this method, it is possible to interpolate the space between all the pairs of points in the grid. Joining by a line all the points having the same value, observed or interpolated, a map is obtained which corresponds to a linear interpolation. All the isolines are closed or end on the walls. This is done in a very short time by several computer programs. However, hand drawn isolines may take into account several other factors. It is possible to distribute more gradually the gradients from flat zones to more perturbed ones instead of using a rude linear interpolation. It is also possible to take into account the presence and location of heat or moisture sources or sinks (e.g. diffusion intakes or suction outlets for hot, cold, humid or dry air) and improve the detail. Even more important is to consider the dynamics of the room, with advective transport from doors or windows, and vertical convection. The dynamics is well represented with analogy to the weather maps and the representation of fronts. In the weather maps a continuity is assumed not only on the values of the parameter, but also in its first and second space derivative. This means that all the isolines and

40 their curvatures (i.e. concavity and convexity) present a progressive and coherent increase or decrease, and that all the points of greatest curvatures are distributed along a line, that in a weather map may represent a front and that has a physical meaning also in a thermal or hygrometric map. In the actual case, when external air masses with different characteristics from the inside air, can penetrate through a door and flow horizontally for a certain path, several successive isolines start from the door, and protrude inside having the m a x i m u m curvature lying on an imaginary line which is the core of the air stream. Two methods are possible: the line oriented point of view, i.e. connecting with an isoline all points having the same value, which is common in topography, and the area oriented criterion, i.e. including between two isolines the belt which has the same

values V(Ox,y) or values which fall within the upper and the lower limit represented by the two contiguous isolines. The field variability obliges to prefer the first or second criterion: line oriented is necessary with a wide range of parameter variability, e.g. climatological maps; the area oriented in the case of a little variability. For instance, if in a room the observed values range in a span of a few tenths of degree, or one degree, the area oriented method is appropriate with resolution 0.1~

if the

span is several degrees, it is practically impossible to keep the same resolution and draw so m a n y lines, and is convenient to choose a larger resolution, e.g. 0.5 ~ or 1~ In this case m a n y data fall within each class and it is preferable to use the line oriented method. The area oriented method is necessary when there are several scattered points having the same value and determining homogeneous areas: e.g. in the case of two contiguous zones characterised by the values 18.3 and 18.4, the band 18.3 includes all the points from 18.30 to 18.39 but not distinguishable because of the truncation at the first decimal, and the separation line ideally joins all the points between 18.39 and 18.40, e.g. 18.399 which of course do not appear in the graph. If we use an accurate psychrometer, whose resolution is 0.1~

but only because the display is truncated

after the first decimal digit, the precision of the transducer being of the order of 0.01~

then the number 18.3 represents any figure from 18.30 and 18.39. This shows

that all the data having the same figures on the display are only apparently identical, being truncated and being directly classified within a class of values. In any case, when a map is drawn, all the space is subdivided with vertical steps and horizontal belts. The line oriented method joins with the vertical steps the few identical values which can determine a line and leaves on the belt the m a n y values between an isoline and the next; the area oriented method groups on the same belt all the m a n y identical values which are scattered over a wider area, where the values are apparently identical, being the result of a truncation, or only slightly

41 different, but fall within the values of two contiguous isolines. The two methods are conceptually the same, if one considers that in the area criterion an isoline instead of separating two areas, ideally connects all the non existing points having a value between the two contiguous classes, as in the example of the truncation. A very practical method for beginners is to facilitate drawing with colours that evidence the maxima and the minima in the map. For example, all the maxima can be evidenced with red, and the minima with blue. All around the maxima the red colour is attenuated (i.e. the saturation of the colour is reduced) as the observed values V(Ox,y) decrease, forming concentric coloured areas with the same pencil but less and less marked. The same can be made with blue, starting from the minima, and leaving untouched the intermediate values. Drawing isolines in a coloured map becomes m u c h easier. After having sketched the first coloured draft, a better and more detailed map can be drawn with a pencil on a new paper sheet. In particular, when all the isolines have been drawn, a very good practice is to colour again the belts, using two different colours for each parameter, one for the upper part of the span of values and one for the lower, and with colour saturation decreasing from the extreme to intermediate levels. The intermediate values can remain white. The visual effect is more immediate making better understandable the microclimate, the forcing factors and the dynamics of the air masses. Finally, it might be useful to compare the practice of the rounding off of a number with that of truncating it, i.e. 16.6 becomes 17 in the first case and 16 in the second one. It is merely illusory to think that the former is more precise, as the figure 17 is in reality 17+0.5, and may indicate any number from 16.5 to 17.4, so that the span of uncertainty is 1. This is exactly the same in the case of truncation, as 16 represents any value from 16.0 to 16.9. The main consequence is that the average of a large population of r a n d o m numbers is different if the numbers are truncated or rounded off, being 0.5 lower for truncated numbers; i.e. truncation makes level to the lowest value of the last digit and rounding off makes level to the middle value of it. In the case of a map of isolines drawn following the former or the latter criterion, the distribution is absolutely the same, but the values (and the isolines) being displaced by 0.5 of the last digit.

42

CHAPTER 2

Humidity

2.1. PARTIAL PRESSURE OF THE WATER VAPOUR The popular term humidity is often used when speaking of the moisture present in the atmosphere; however it is an ambiguous, generic word. Several specific terms exist, each of them represents a different parameter useful to describe a peculiar property. The first hygrometric parameter is the partial pressure of water vapour, conventionally indicated with the letter e. Evaporating new water molecules this pressure increases to a certain limit; when reached, the n u m b e r of molecules escaping from the liquid water is equal to those returning to it from the atmosphere, establishing a dynamic equilibrium between evaporation and condensation. This limit condition is determined by the temperature T, but is irrespective of the dry air pressure according to the Dalton law of the independence of the partial pressures, i.e. the behaviour of any gas in a mechanical mixture is independent of the presence of other gasses and the total pressure is equal to the sum of the partial pressures. The state of being saturated is a characteristic of the vapour, not of the air. The saturation

pressure, also called vapour tension, esat(t), is computed by means of the empirical formula attributed to Magnus or Tetens esat(t) = esat(O) xlOat/(b+t )

(2.1)

where esat(O) = 6.11 hPa (note that in meteorology the mbar unit is more common, and 1 mbar = 1 hPa), a = 7.5, b = 237.3~

The graphical representation of this

equation is shown in Fig.2.1. In the presence of ice, the tension must be calculated with reference to the solid phase with a = 9.5, b = 265.5~

As the tension for ice is

lower than for liquid water, if the two phases coexist, the water molecules will progressively evaporate from the liquid and sublimate on the ice. This equation gives very accurate values at the usual atmospheric temperatures, but is less accurate near the boiling point, where esat(lO0) = 1013 hPa.

43 100 908070c~ v

6050403020100_~, -20

-10

0

10

20

30

40

30

40

Temperature (~ 100

10 c~

0,1 -20

-10

0

10

20

Temperature (~ Fig.2.1 Saturation pressure (esat) of the water vapour (thick line) and partial pressure (e) of the water vapour at different values of relative humidity (RH), i.e. at R H = 90, 80, 70 .... 10%. Of course the thick line is for RH = 100%. The first graph is with linear scales in order to be more immediate to non specialists and present a better resolution of the ordinary vapour partial pressures. The second graph can be better appreciated by specialists: it has the ordinate with logarithmic scale and represents more clearly the physical relationship between vapour partial pressure and air temperature. The lines are not exactly straight, and the departure shows how much the Magnus equation departs from a purely exponential function, giving a clear idea of the approximation made using a such simplified formula.

44 It can be noted that eq.(2.1) is independent of V, so every isothermal compression causes a faster condensation rate until the dynamic equilibrium is established; in the case of an isothermal expansion the evaporation continues until equilibrium; only when all the liquid is evaporated does the water partial pressure decrease, according to eq.(1.2).

2.2. DERIVATION OF THE LATENT HEATS The first law of the thermodynamics states that the increase of the specific energy U of a system that undergoes a change is equal to the mechanical equivalent of the heat absorbed Q plus the work W expended in producing the change.

(Uv-UI ) = Q + W

(2.2)

Gas

P Liq

D A

C B

i i i | |

i

i i t |

gli q

gva p

W

Fig.2.2 Thermodynamic cycle to derive the Clausius Clapeyron equation. Let us consider a liquid in equilibrium with its vapour; Vv is the specific volume V/M of the saturated vapour and Vl the specific volume of the liquid; Pv - Pl

45 are the pressures of the vapour and the liquid (please note that Pv

has been

previously indicated as esat(t), but in this context the new symbol has been introduced for uniformity with the liquid phase, and to make possible the following mathematical treatement); Uv and UI are the two specific energies U/M of the two phases. All these quantities are only functions of the temperature T of the system. In a p versus V diagram, a reversible evaporation-condensation cycle (Fig.2.2) close to the Carnot one can be applied to a sample of water. The cycle is as follows: first the system undergoes an isothermal and isobaric evaporation with increase of V, from A to B; then a little adiabatic heating by compression from T to T + dT from B to C; then an isothermal and isobaric condensation with decrease of V from C to D; finally a cooling by adiabatic expansion to the original state. During the vaporization, the variation of the specific energy of the system is (Uv - UI ) and the external work, negative, is W = Pv (Vv-VI ); the heat Q absorbed in this phase is the latent heat of vaporisation Lv of the liquid, i.e. Q = Lv = (Uv- UI ) + Pv (Vv-V! ).

(2.3)

For the entire cycle, the work is given by the area ABCD between the two isobaric and the two adiabatic transformations, and in the first approximation by the rectangle d W = (Vv -VI) d p . However, the Carnot efficiency is 7/= dT/T = dQ/Q = dW/Q, so that dW = Q dT/T and, combining this with the above equations dT d W - (Vv-Vl ) dp - Q T

(2.4)

i.e.

dp Q = T (Vv-VI) dT

(2.5)

By equating the two values of Q we get dpv (Uv- Ul ) + pv (Vv-VI ) = T (Vv-VI ) dT"

(2.6)

Remembering that Q = Lv the following equation is obtained: dpv Lv = T (Vv-Vl ) dT

(2.7)

46 which was deduced by Clapeyron from Carnot's theory (for this reason it is also called the Clapeyron equation) and proved by Clausius. This equation allows the computation of the value of Lv for every T when the specific volumes are k n o w n as well as the relationship between the increase of saturation pressure and T. For example, for pure water at boiling point T = 373 K and standard pressure Pv = 1013 hPa, Vv = 1674 cm 3, V1 = 1 cm 3, dpv/dT = 36.15 hPa K -1 = 3.62x104 dyne cm -2 K -1 , one obtains Lv = 2260x107 erg gq. The Clapeyron equation shows that the latent heat of vaporisation is due partly to the increase of specific energy and partly to the external work. In order to find a relationship between these two quantities it is necessary to find the ratio between W and Lv

W Pv (Vv- V1)_ P___cvdT Lv Lv - T dpv

(2.8)

and in the above conditions W / L v = 0.075. This means that the external work forms only a small part of the latent heat of vaporisation. A simple approximation of the Clapeyron formula (Fermi, 1958) is obtained by neglecting VI in comparison with Vv (the ratio of the volumes of a molar mass of water in the liquid to the gaseous state is 18:24,000 = 0.75x10 -3) and assuming t h a t the state equation (1.1) for perfect gases is still valid. Under these reasonable assumptions, the formula becomes

Lv = .Jd~vT2 dpv Pv dT

(2.9)

and in the critical case of boiling water the computed value of Lv is Lv = 547.5 cal g-l, slightly greater than the observed value Lv = 538.7 cal g-1. This difference is due to the fact that the specific volume of the saturated vapour at 100~

is less than the

value computed by means of the equation for perfect gases. For usual atmospheric temperatures this approximation is good. The above equation can be rewritten dlnpv Lv dT - . ~ v T2

(2.10)

and, if we assume Lv is constant over a wide temperature interval, this equation can

47 be solved:

Cv

(2.11)

Pv = A e x p ( - . ~ v T)

and this gives the exponential relationship between the saturation pressure and the temperature, theoretically derived. Another approximated formula (Plank, 1926) can be obtained by substituting in eq. (2.6) the formula for the specific energy, Uv = Cv T + constv where Cv is the specific heat at constant volume, which holds for perfect gases in the isothermal processes, when Q +W = 0 and is Cv = 3.~/~v = 0.331 cal g-1 K-1. If for the liquid the specific heat at constant pressure, c! = 1 cal g-1 K-l, is assumed to be constant and the external work is neglected, one gets U! = cl T +constl similar to before, and (Uv - U! ) = (Cv- c! )T. In addition, if the the specific volume of the liquid V! is neglected in comparison with that of the vapour, V v , with the help of the equation for perfect gases (1.1), the following approximations Pv ( V v - V ! ) = ,~/gv T and ( V v - V ! ) = , ~ v T/pv. can be found. By substituting these finding into eq.(2.6), it follows that

(Cv- cl )T + , ~ v

9~ v T2 dpv T +ocnst = - Pv dT

(2.12)

Multiplying both sides by dT/T 2, this equation can be integrated and one obtains Pv = A ' T (Cp-ci ) / . ~ v

A" ) exp(--T-

(2.13)

where A' and A" are positive constants, and Cp = 0.441 cal g-1 K-1 is the specific heat of the vapour at constant pressure. The exponent of T has been obtained considering that . ~ v

Cv - Cl

=

(Cp- Cv ) and, consequently, 1 + .~v

-

Cp - Cv + Cv - Cl

.JZ~v

Cp - Cl

= .~v " This is

another theoretically derived expression. Equation (2.11) can be rewritten in other forms, of wide use, as follows. 9 Lv

esat(T) = e s a t ( ( 2 7 3 K ) e x p ( ~

1

1

( 273 - T- ))

Lv

esat(T) = esat((273K) e x p ( ~ v 2732 (T- 273))

(2.14)

(2,15)

48 0.0318t

esat(T) -~ 6.11x10

(hPa)

(2.16)

where 0.0318 = (Lv/.J?~v 2732) loge (e is the Neper number 2.71828182845904...). From the above formulae the latent heats of vaporisation (or condensation) L v, fusion (or

melting) Lf, and sublimation Ls, can be derived, as follows Lv = 597.3 - 0.57 t,

Lf = 79.7 + 0.52 t,

Ls = 677- 0.05 t

(2.17)

with all the units in cal g-1. Naturally Lv + Lf = Ls.

2.3. MIXING RATIO OF DRY AIR AND WATER VAPOUR The mixing ratio w of moist air (i.e. dry air and water vapour) is the (dimensionless)

ratio of the mass of water vapour mv to the mass of dry air ma, and this ratio represents the ponderal mixture of these two gaseous substances, i.e. mv

w -ma

(g/g)

(2.18)

If e is the partial pressure of water vapour and p the atmospheric pressure, then the partial pressure of dry air is Pa = P - e, and substituting this in the equation of state for perfect gases in the form (1.2), the previous equation can be written in terms of pressure:

w

"

-

-

e .~a p-e.~v

m

e e 0.622 P - e ~0"622p

(2.19)

where 0.622 equals the ratio between the molar masses of the water and the air and, consequently, also .~/~a/.~v. It is e v i d e n t that w is i n d e p e n d e n t of the t e m p e r a t u r e T, v o l u m e V and a t m o s p h e r i c p r e s s u r e of the air parcel and r e m a i n s constant except w h e n condensation, evaporation or mixing with other air masses occur. As a consequence, w can be considered as a characteristic value, which is useful to recognise an air mass and its h y g r o m e t r i c exchanges with the environment, being invariable to either adiabatic (i.e. w i t h o u t exchange of heat) or diabatic (i.e. with exchange of heat), isobaric or non isobaric heating or cooling. For example, in the elevated air masses a

49 decrease of w gives an indication of the amount of water which has been precipitated as rainfall. This parameter, is adimensional as the natural unit is g g-l, representing the fraction of gram of vapour mixed with one gram of dry air, and might also be expressed in percent; however, as the numeric value of w is very small, it is common to multiply this number by 1000 and use the practical unit M R = 1000 w, expressed in g kg -1, which represents the number of grams of vapour mixed with one kilogram of dry air. A plot of this parameter is shown in Fig.2.3. As the atmospheric pressure p is fairly constant (i.e. +4%), a common approximation is to write 1000 hPa instead of p, which simplifies the calculations. At every environmental temperature T the M R increases proportionally to the mass of vapour that is emitted into the atmosphere, until the saturation limit is reached, i.e. when the vapour pressure e equals the upper value esat(t), given by the Magnus eq.(2.1), and the relative humidity RH = 100%. Under saturation conditions, the M R is indicated by MRsat and is computed by means of eq.(2.14), using esat(t) instead of e (for a quantitative evaluation of the error, see the psychrometric chart). Again, as for every T, e is proportional to RH, measuring RH it is possible to calculate MR., i.e. w h e n esat(t) is computed, the saturation value M Rsat is obtained using

eq.(2.14), and the actual M R is: M R = RH x MRsat. By dividing the graph of MRsat versus temperature into fractional parts, one obtains graphically the values of M R at different values of RH. The parameter MRsat is an increasing function of T, with a trend similar to that of esat(t). At usual meteorological conditions, M R <_30 g kg -1. When two different air masses mix together, the final value of the M R depends upon the relative proportion of mixing, and it can be calculated as a weighted mean, i.e. mixing x grams of air having mixing ratio MRx with y grams of air having mixing ratio MRy the resulting M R is

MR =

x MRx +y MRy 9 x +y

(2.20)

In meteorology, this parameter is used to distinguish different air masses, e.g. to evidence the change between the land (dryer) or sea (moister) breeze, or to monitor the evapotranspiration of the soil, or the evaporation over large water bodies. A quantitative evaluation can be made by measuring the vertical gradient of this p a r a m e t e r and the exchange coefficient for the vertical transport in the atmosphere. Similarly, in the conservation science, this parameter can be used to recognise a number of important features and interactions.

50 80 70 60 bO

50

bib "~

40

"~

30 20 10

O-l~ -10

-20

0

10

20

30

40

50

Temperature (~ 1 O0

10bO b~

0,1

/ -20

,

!

-10

|

!

0

|

!

10

~

i

20

|

!

30

|

!

40

|

50

Temperature (~ Fig.2.3 Saturation mixing ratio (MR, thick line) of the vapour in air and actual value of the mixing ratio at different values of relative h u m i d i t y (RH), i.e. at RH = 90, 80, 70 .... 10%. Of course the thick line is for RH = 100%. As in Fig.2.1, the first g r a p h is with linear scales and the second has the ordinate with logarithmic scale.

51 2.4. M O N I T O R I N G MIXING RATIO TO STUDY AIR-SURFACE INTERACTIONS A N D FOR ENVIRONMENTAL DIAGNOSTICS This p a r a m e t e r is very useful for diagnostic purposes, to provide evidence of the action of HVAC systems or air-surface interactions. By m e a s u r i n g this p a r a m e t e r along a horizontal cross section of a room, it is possible to see the advection of external air p e n e t r a t i n g t h r o u g h open (or t h r o u g h fissures of) doors or w i n d o w s (Fig.2.4), or the moisture released by visitors, or where the walls are evaporating or adsorbing moisture. The effects of humidifiers are also pointed out, as they do not generate a h o m o g e n e o u s increase of v a p o u r content, but a cloud of moist air which m a y d a m a g e objects in proximity, or moves into the room along the advective currents b e t w e e n adjacent rooms. A very common, but inappropriate position for a humidifier is near corners or walls where works of art are placed.

5,

,6

Fig.2.4 Mixing ratio (g/kg) in a horizontal cross section of the Giotto Room in the Uffizi Gallery, Florence, showing the penetration of external air masses evidenced with shading (1 February 1993, 4 p.m.). Sometimes the air coming from elsewhere is only a bit different and can be observed as a useful tracer of different air masses. In this case, the emission of moisture in the different rooms is not balanced in comparison with the size and needs of each room. Therefore, the air coming through doors or the vertical slits which have been opened for the passage of paintings, has very different hygrometric characteristics and may perturb the exhibits causing internal stresses. H u m i d i f i e r s generate clouds of moisture which grow in this sheltered space (Fig.2.5). Then these clouds diffuse into the room, or are displaced by local air currents, or are b r o k e n and t r a n s p o r t e d in several directions by the turbulence generated by the motion of visitors. Works of art are alternatively i m m e r s e d into, or emerge from these clouds, or portions of them. The result is a continuous stress and

52

"~ . . . . . . . . 51.7

""~"ii'~i'~i~..!::!ii'..i.i~i."~

53.8

~

9 @

~

~

~

16

~ . ~

8.4

Fig.2.5 Micro-mapping in a horizontal cross section of the Salon CarrY, Louvre Museum, Paris, showing clouds of moisture (evidenced with shading) diffusing into the room, which are generated by humidifiers. Four active humidifiers are placed in corners of the room. Others are in stand-by position. This situation is here described by means of three parameters, in order to gain familiarity with different representations, i.e.: (a) relative humidity (RH, %); (b) mixing ratio (MR, g/kg); (c) dew point spread (DPS, ~ The clouds of moisture appear as local maxima of RH or MR, and minima of DPS. (21 February 1995).

53 fatigue which leads to weakening, microfessuring and flaking the outermost layer or the colour coating. A more appropriate position is far from the exhibits, in the central part of the room, either on the floor (e.g. Kunsthistorishes Museum, Vienna or Uffizi Gallery, Botticelli room) or the ceiling, although the latter position presents a further problem: the suction outlets placed on the lower part of walls d e t e r m i n e a preferential p a t h of the m o i s t u r e into the room, and a non h o m o g e n e o u s distribution. Gradients of the M R close to a surface show that the surface is exchanging vapour with the atmosphere. If the surface is evaporating, the air is locally enriched with water molecules and the M R locally increases; on the other hand, if the surface is adsorbing water molecules or is condensing, the air in proximity to it is depleted of water molecules and the M R locally decreases. Monitoring this parameter near walls directly lighted by solar radiation or artificial lamps, a release of moisture can be seen for a short time during heating, and it stops w h e n the plaster becomes in equilibrium with the hot spots (Fig.2.6).

11,8

11.6

Fig.2.6 Mixing ratio (g/kg) in a vertical cross section in front of the Leonard's Last Supper (Milan) showing the local release of vapour from the area hit by direct artificial lighting (29 July 1982, after Camuffo and Bernardi, 1991). The vapour which is escaped from the wall causes a local enrichment of MR in the air nearby, i.e. the maximum found in the upper part of the wall, on the left. This evaporation is forced by the switching on of the lamps. The radiant energy warms the surface and forces the evaporation. When the equilibrium is reached in the micropores, the evaporation stops and the maximum disappears after a short time.

54 The opposite occurs when the wall cools again after the input of radiant energy has stopped. Daily cycles of direct lighting, which always repeat the same effect on the same areas, may cause severe damages on delicate objects able to adsorb water and change their dimension accordingly. If a cold surface is put in contact with the environmental atmosphere, initially the air in contact with the surface decreases its temperature T, and the M R remains unchanged. This leads RH to rise. As soon as the condensation begins, the M R starts to decrease, and this tends to invert the trend of RH. After some time, the air in the proximity of the surface will be characterised by AMR < 0, and nothing can be said about the final value of RH, which is subjected to two counteracting effects due to T and MR. In general, the thermal effect prevails and ARH > 0. When a wall is hit by direct solar radiation it warms (AT > 0), evaporates (zkMR > 0) and the opposite situation occurs. These obvious facts appear as a paradox w h e n i m p r o p e r l y described: the air is dryer in proximity of a surface where condensation is occurring and more moist near an evaporating surface. This paradox derives from the fact that 'more dry' or 'more moist' are not specified in terms of MR, and people generally associate the concept of dry and moist with that of relative humidity RH which will be analysed later. From the definition, the air is dry or humid in terms of MR as a consequence of its water vapour content only, independently of the temperature T of the system; in terms of R H it means how close the vapour is to saturation, and this depends upon two factors: T and MR. A 'dry' air parcel in terms of MR becomes 'humid' in terms of RH when it is sufficiently cooled; one 'moist' in terms of MR becomes 'dry' in terms of RH when sufficiently warmed.

2.5. SPECIFIC HUMIDITY The specific humidity s of moist air is the (dimensionless) ratio of the mass of water vapour mv to the mass of moist air ma+mv, and this ratio represents the ponderal dilution of the vapour in the atmosphere, i.e. my

s - ma+m--------~

(g/g)

(2.21)

It is also called mass concentration or moisture content of moist air. Substituting eq. (2.21) into (2.18),

55 W S

1+w

t"."z)

and, operating similarly to (2.19)" e

S

0.622 p - 0.378 e

e

0.622 p

w-.~oj

Like the mixing ratio, this parameter is adimensional, the natural unit being g g-1. It might also be expressed in percent; however, in order to avoid the use of small decimal numbers, the practical unit S H = 1000 s, expressed in g kg -1, has been introduced. This represents the n u m b e r of grams of v a p o u r dispersed in one kilogram of moist air. In practice, it can be observed that in the d e n o m i n a t o r of eq.(2.22) w < < l and is therefore negligible; similarly in eq.(2.23) 0.378e can be neglected in comparison with p. As a consequence, the values of w and M R are very similar to s and SH respectively, with differences of the order of 1%. The same properties of the M R can be extended to the SH and the saturation specific humidity

SHsat; also the same graphical representation can be used in a first approximation. Both M R and SH are conservative for adiabatic or diabatic changes of temperature, pressure or volume but are not conservative for evaporation or condensation, as changes of mv are involved.

2.6. ABSOLUTE HUMIDITY The equation of state (1.1) for the water vapour can be written in the form mv~

e = V .... v T = a . J 2 ~ v T

(2.24)

by defining absolute h u m i d i t y a the density of the water vapour, i.e. the mass of vapour contained in the unit volume of moist air mv

a = -~-

(2.25)

From this definition it follows that a is variable with m v, i.e. condensation, evaporation, mixing with other air masses, as well as V, i.e. compression or

56 expansion, d u e to e.g. changing atmospheric pressure or height; from eq. (2.24) it is also e v i d e n t that a is directly p r o p o r t i o n a l to e and inversely p r o p o r t i o n a l to air temperature. Of course, a is e x p r e s s e d in g cm -3, but in o r d e r to avoid the use of small d e c i m a l n u m b e r s , the practical unit A H = 106 a, e x p r e s s e d in g m -3, has b e e n introduced. A H represents the mass of v a p o u r contained in 1 m 3 of moist air. As at s t a n d a r d p r e s s u r e and t e m p e r a t u r e , 1 m 3 of a t m o s p h e r e contains the mass of 1.255 kg of air, the values of A H are numerically similar, but always greater than those of M R or SH. In fact, M R and S H represent the mass of v a p o u r contained in I kg of dry

or moist air, which occupies some 80% of I m 3. The absolute h u m i d i t y can be c o m p u t e d by means of the equation of state (2.24) by considering that the v a p o u r density is the inverse of the specific v o l u m e Vv, i.e. 1

1

e

1

e

a - V v - .~/~v T -.~/?~v 273 (1+ at )

w h e r e the last term comes from the transformation from K to ~

(2.26) i.e. T = 273 (l+c~t)

w h e r e c~ = 1/273 - 0.00366. D e p e n d i n g u p o n the units in which e is expressed, the formula to c o m p u t e A H a s s u m e s one of the following forms. If e is in hPa or mbar (more usual), e

e

1

1+o~t

A H = 220 ; = 0.806 ~ =

0.806e

(2.27)

If e is in d y n e cm-2: e

e

1

l+ott

A H '-- 0.22 ; = 0.806x10 - 3 ~

= 0.806x10 -3 e

(2.28)

or, if e is in m m Hg: e

e

1

1 +o~t

A H = 290 ~ = 1.062 - - =

e

(2.29)

The latter s h o w s that at t = 16.4~ the A H is numerically equal to e m e a s u r e d in m m Hg; at usual meteorological values of t, these two parameters (in the above units) are numerically similar. Using the saturation value esat(t) instead of e, the saturation absolute h u m i d i t y

5? 100

80

~E~

60

,<

40

20

0-~" -20

-10

0

10

20

30

40

50

30

40

50

T e m p e r a t u r e (~

100

10 b~

1

0,1 -20

-10

0

10

20

T e m p e r a t u r e (~

Fig.2.7 Saturation absolute humidity (AH, thick line) and actual values of A H at different levels of relative humidity (RH), i.e. R H = 90, 80, 70 .... 10%. Of course the thick line is for R H = 100%.

58

AHsat is obtained (Fig.2.7). This represents the maximum quantity of vapour that the unit volume of atmosphere can deliver under specified temperature conditions; for this reason it is also called (moisture) capacity. From the above formulae it appears that AHsat is a function of air temperature but not of pressure; in the case of adiabatic compression or expansion the change of AHsat is governed by the change of t (although induced by the change of p), according to the Poisson equation. The value of AHsat allows the computation of the quantity of the liquid that may evaporate or the quantity of vapour which condenses during an adiabatic transformation. As in the previous cases, and the actual AH is: AH = RH x AHsat. By dividing the graph of AHsat versus temperature in fractional parts, the values of AH at different values of RH are graphically obtained.

2.7. RELATIVE HUMIDITY It is useful to state beforehand that in meteorology, for practical purposes, the convention is used of attributing all the properties of the atmosphere to one fictitious gas, called 'air' which behaves as the mixture of the gases and vapours which form the atmosphere. In order to describe particular phenomena, a distinction is made between dry air and moist air. The adjective dry may have two meanings, which are clarified by the context: the former is literal, i.e. without vapour, the latter without

condensation, i.e. the mixture behaves as an ideal gas, without changes of phase; similarly, moist indicates the opposite of these two situations. Under this point of view, the vapour component is formally ignored and it is improperly expressed in terms of relative humidity of the air or degree of saturation of the air instead of the correct form: relative humidity and degree of saturation of the vapour. From the physical point of view, it is meaningless to speak in terms of saturation in the case of a mixing of two (or more) gases, as they are absolutely miscible from 0 to 100%, according to the Dalton law. The saturation arises because one of the components is not a gas but a vapour, and all vapours become saturated when their partial pressure reaches the limiting value determined by the ambient temperature, called saturation tension. In the case of water vapour, this is given by the Magnus formula. It is independent of the presence of other gases and their pressure, and the definition of relative humidity is the same in the presence of air or in absence of it (e.g. for some vapour in a vessel deprived of air). The relative humidity u (popularly termed humidity) was originally defined

59

u =~ esat(t)

(2.30)

i.e. the (non-dimensional) ratio between the actual partial pressure of the vapour and its

saturation vapour pressure. Below 0~

the saturation value esat(t) is c o n v e n t i o n a l l y

c o m p u t e d w i t h refernce to s u p e r c o o l e d water, or to ice if the t e m p e r a t u r e is far below 0~

and this fact introduces ambiguity. The above definition is not any more

rigorous w h e n the s a t u r a t i o n is a p p r o a c h e d . In fact, in this condition the v a p o u r d e p a r t s from the b e h a v i o u r of a perfect gas, in that s o m e m o l e c u l e s a g g r e g a t e f o r m i n g small clusters; the actual n u m b e r of free particles n w h i c h describe the e q u a t i o n of state decreases as well as the partial p r e s s u r e e. N e a r saturation, the partial pressure of a v a p o u r departs from the ideal condition and another unaffected p r o p e r t y should be used. In order to avoid the above problem, the definition of u has been reformulated in t e r m s of the mass mv of the v a p o u r c o n t a i n e d in the air parcel, w h i c h is a conservative property, by substituting e = ( m v / V ) . ~ v T and esat(t) = (mv, sat/V).~/~v T, w h e r e mv, sat is the mass of w a t e r v a p o u r p r e s e n t u n d e r saturation. The relative

h u m i d i t y u is then defined as the (non-dimensional) ratio between the mass of vapour mv actually present in whatever volume of atmosphere, to the greatest amount possible at the same temperature mv, sat, i.e. my

u =~ mv, sat

(2.31)

a n d p h y s i c a l l y r e p r e s e n t s the degree of saturation of the vapour. F r o m the a b o v e definitions it is easy to recognise that

mv mv mv e mv Wv ma av W Sv ma +my u - - - - -esat(t) mv,sat Wv,sat my, sat av,sat my, sat Sv,sat mv, sat ma V ma+ mv,sat

(2.32)

a n d it d e p e n d s u p o n both the a m o u n t of m o i s t u r e w h i c h is actually p r e s e n t mv (to w h i c h it is p r o p o r t i o n a l ) a n d the t e m p e r a t u r e t, w h i c h acts e x p o n e n t i a l l y in the d e n o m i n a t o r mv,sat. The d e p e n d e n c e of u on t is very strong, and at the first sight the d i a g r a m s of u and t seem to be nearly symmetric, as reflecting in a mirror. As u varies b e t w e e n 0 and 1, in order to avoid the use of decimal n u m b e r s , the practical unit R H in p e r c e n t a g e form is used, i.e. RH = 100u. W i t h the help of

60 eq.(2.19), eq.(2.32) and the Magnus equation, it is possible to obtain practical formulae to compute the M R or SH from measurements of t and RH: M R ~-SH ~ 37.95 R H xlO at/'b+t~ P

e = 0.0611RH xlO at/(b+t )

AH =

13.44RH xlO at/(b+t ) 273.3 + t

) 0.03795RH xlO "t/(b+7t'

)

(g/kg)

(2.33)

(hPa)

(2.34)

(g/m3)

(2.35)

The R H can be measured directly (e.g. hair hygrometer) or indirectly. In the following, a very accurate method for the determination of the RH will be described, based on the measure of T and the wet bulb depression; by substituting R H in the above formulae, the values of M R , e and A H can be calculated. It is customary to compute eq.(2.33), eq.(2.34), and eq.(2.35) with the Magnus coefficients a = 7.5 and b = 237.3~ referred to (supercooled) water also when t < 0~ This convention is partially justified as, in mild climates and daytime, ice is covered with a film of liquid water. However, when the wet bulb temperature is below the freezing point, and the sensor is covered with ice, the appropriate coefficient for ice should be used. Climatology requires average values. It might be useful to underline that relative humidity is a parameter derived from other elementary physical variables, e.g. mixing ratio or vapour pressure which is proportional to it, and air temperature. The equations that link the R H to the basic parameters are not linear, and for this reason a mean value obtained as the arithmetic average of a set of R H observations is not physically correct. Mixing two air masses with different R H values, the R H of the final mixture is not the arithmetic average of the two initial R H values, but is determined by the final temperature and mixing ratio. The 24-hour or the monthly averages should be computed after the averages of mixing ratio (or vapour pressure) and air temperature. The common use is to sacrifice correctness to convenience and data are handled in terms of averages; however, in this field the most correct statistical form is to abandon averages and to present data in term of percentiles, which are based on frequency distribution. This parameter constitutes a very useful tool for environmental diagnostic and risk assessment, and the methodology is the same that has been already described for air temperature and mixing ratio.

61

2.8. THE EQUILIBRIUM MOISTURE CONTENT Several materials (e.g. wood, paper, parchment, leather, ivory, bone, paintings, plaster, stucco, stones containing abundant clay minerals) are very sensitive to their water content, and this is in equilibrium with the RH. In materials science a concept similar to the mixing ratio is used in defining the equilibrium moisture content, EMC, i.e. the mass of water per unit mass of anhydrous material. The water molecules can be adsorbed, as in m a n y organic (e.g. wood, paper, parchment, soap) and some inorganic materials, or can be transformed into hydration or crystallisation water, as in some inorganic salts (e.g. sodium sulphate, copper sulphate, barium chloride). The EMC is generally expressed in percent and varies with ambient temperature and relative humidity. It is nearly zero for non porous, non hygroscopic materials; for other materials it vanishes only at zero relative humidity. In some inorganic (e.g. clay minerals) and m a n y natural organic materials, microclimate changes lead to vary the EMC and, consequently, the size of the object. W h e n the deformation is not isotropic, three deformations should be considered. In the case of wood which is characterised by a fibrous structure, the three key directions are: (i) tangent to the tree growing rings, (ii) radial i.e. from the centre of a cross section of a trunk to the exterior, (iii) longitudinal, or parallel to the grain, i.e. along the direction of the trunk. Anisotropic deformations generated by changes of temperature and humidity result in strain and strain-induced stresses. They force internal tensions, deformation, fatigue and often fractures. C o m m o n effects are configurational strain (warping, cupping, bowing etc. or fracture (checking, splitting). The EMC of fresh wood is 30% or more, and for well seasoned wood at ordinary temperature and humidity falls to values typically ranging between 7 and 20%, although important departures can be found for changes of RH. The dependence of wood EMC upon temperature and relative humidity is shown in Fig.2.8, where it is evident that wood is weakly sensitive to a temperature change, but very sensible to humidity changes, especially in moist environments, i.e. for RH > 80%. In the humidity range 10% < RH <70% the plot is a straight line, and at room temperature (i.e. T = 20~

the EMC of the experimental values found by Giordano

(1993) for Italy obey in average to the equation EMC = 5.9 R H - 4.7

(2.36)

but the coefficients may vary with the wood species, seasoning and temperature.

62 35 ,.~

30

o

25

~

20

T = 20~

o

0~

T =

9~

]0

.~..i

T= 40~

.v,=l

~

5 i

a

I

I

l

I

I

I

I

I

0

10

20

30

40

50

60

70

80

90

100

Relative H u m i d i t y (%)

Fig.2.8 Dependence of w o o d equilibrium moisture content (EMC) u p o n ambient temperature (T) and relative humidity (RH). It is evident that wood is very sensible to humidity changes, especially in moist environments. 7 6

5 ~

o r~

r,j

4-

"-,

3

o o

|

0

,

,

|

i

5

,

',

|

,

!

10

,

|

,

|

I

15

,

|

|

|

20

E q u i l i b r i u m M o i s t u r e C o n t e n t (%)

Fig.2.9 Wood size change, expressed as percent of the reference size at EMC = 20%, for oak (thick line) and pine (thin line), and for the two main axes, i.e. the tangential (continuous line) and the radial (broken line) ones. The tangential change is about twice the radial one.

63 When the ambient relative humidity falls, also the EMC drops and the wood shrinks, or vice-versa, with important deformations. For practical purposes, in the EMC range between 0 and 20%, the relationship may be assumed to be linear

(Summit and Slicker, 1980). The shrinkage, expressed as percent of the reference size at EMC = 20%, is shown in Fig.2.9 for two wood species, i.e. oak and pine, and for the two main shrinkage axes: the direction tangent to the tree rings and the radial one. These two figures can be combined in order to express the wood contraction (or expansion) versus the equilibrium relative humidity, and Fig.2.10 shows the response of an aged wood (with initial EMC = 20%) to ambient humidity changes: the w o o d expands in d a m p environments, but severely contracts in drying, especially w h e n this happens with abrupt changes, e.g. originated by s u d d e n warming of hot air heating systems. They may lead to dramatic results in only one or a few cold seasons.

Oak tang

Pine tang ,~-

4

Oak rad 0 r~

I=

3

Pine r a ~ 2

o

1

o

0

0

-1 -2 -8 -4

0

20

40

60

80

100

Relative Humidity (%) Fig.2.10 Wood size change, expressed as percent versus the equilibrium relative humidity (RH). Initial conditions at EMC = 20%. Lines refer to oak (thick line) and pine (thin line), and for the two main axes, i.e. the tangential (continuous line) and the radial ones (broken line). The tangential change is about twice the radial one.

64 From the above figures it is evident that the tangential change is greater than the radial one, and both are greater than the longitudinal one. These coefficients often follow the proportion 1: 1/2: 1/3. The most important expansion or contraction of roof timbers is the longitudinal one, which fortunately is also the smallest one, but the considerable length of the timbers may induce large changes of size. It should be noted that any rise of temperature induces a thermal expansion but also a drop in RH and, consequently, a drop in the EMC and a wood contraction, and vice-versa. By the way, the thermal expansion and the EMC contraction are opposed, so that the shrinkage is partially mitigated by the expansion. However, the shrinkage due to RH changes is largely dominant. Any unbalance caused by the heating, the air conditioning system, or the humidifiers generates severe damage in panels, frames, furniture and so on. Also gradients may generate diffrential expansions in wood structures, which can undergo severe stress and damage (Fig.2.11).

51

56

~

~:

::

...... .~.~i!i~i~i~~il ~i!i~-i-.--i~l~ .~ .t~ . -.~ .....

Fig.2.11 Relative humidity (RH, %) in a horizontal cross section of the Historic Anatomy Theatre of the University of Padova (3 July 1992, 5 p.m.). The most humid corner has been shaded.

2.9. MECHANISMS OF HUMIDITY DEGRADATION It is well known that high humidity levels increase the deterioration rates in several ways. A list of some of the most important phenomena recurrent in conservation has been reported by Thomson (1986), or can be found in special

65 studies. In order to clarify the action operated by moisture, it is useful to summarise some key mechanisms of water into a material; others will be seen in the following. The presence of liquid water favour chemical reactions: the transformation of marble or limestone into gypsum is probably the most popular example (for an extensive discussion of this mechanism see Laurenzi Tabasso and Marabelli, 1992). Gypsum is mainly formed in heterogeneous phase on the monument surface when, in the presence of a film of liquid water, the absorbed sulphur dioxide (SO2) as a primary pollutant is first converted into sulphurous acid (H2SO3) a n d / o r sulphuric acid (H2SO4). The oxidation of S(4) into S(5) is favoured by the presrence of 03, NOx and catalysts such as metals or soot; the reaction with the calcium carbonate (i.e. calcite, CaCO3) forms directly, or as a final product, the hydrated crystal of calcium sulphate, i.e. gypsum (CaSO4-2H20). The chemical reaction is more straight when atmospheric SO2 is dissolved and oxidised to suphuric acid into rain droplets (acid rain), or sulphate aerosols deposit on the marble or limestone surface and, in the presence of water, they are transformed into sulphuric acid and gypsum. Stones, bricks, pottery, plasters, frescoes and other materials having water soluble salts in the pores are sensitive to microclimate changes. Environmental conditions leading to cycles of RH may generate crystallisation and dissolution of salts by means of two key mechanisms: (i) the water evaporation, which is controlled by ambient RH, causes a concentration of the solute, supersaturation and precipitation of salt crystals; (ii) hygroscopic salts, which are in crystalline form only in a dry environment, become deliquescent or precipitate following the ambient RH cycles. These mechanisms generate cumulative mechanical damage, efflorescences, subflorescences, delamination, spalling, flaking etc. Corrosion (Jones, 1996) is the destructive result of a chemical reaction between a metal and its environment, and therefore includes also oxidation which is the first form of metal decay. Metallic corrosion involves transfer of electronic charges in aqueous solutions. For this reason, in presence of water, metals tend to combine with other chemical compounds, and return in a form similar to the natural minerals from which they are extracted, making free the energy required for their extraction. For glass (Newton and Davison, 1989) the situation is complex, as there are several types of glass and deterioration mechanisms. Chemical solutions (and the pH of the attacking solution) may provoke chemical changes on the surface, which may then spread to the whole of the glass. Water originated by condensation or arrived with rainfall, or simply by vapour adsorption, is necessary for the replacement by protons of the diffusing alkali ions and subsequent hydration of the silica network. Water molecules may diffuse inside the glass leaching tiny cracks by acting on

66 sodium and potassium carbonates which are deliquescent and causing ion exchange and alkali extraction. In dry condition, or under the action of solar radiation, the loss of the water absorbed causes dehydration. For this reason humidity cycles are dangerous, also in the absence of pollution. Wood and paper microfibrils (Coped6, 1991; Richardson, 1993) are mainly composed of cellulose chains which are formed from glucose molecules. Each glucose unit possesses three hydroxyl groups which have an affinity for water. When water is absorbed, it will retained between the cellulose chains, displacing them with the first consequence of increasing the size of the material and decreasing its strength for the attenuation of the hydrogen bounds and van der Waals intermolecular forces. The second consequence is that a slow but progressive hydrolysis of cellulose is produced, which breaks the bounds between the glucose units, breaking the cellulose chain into a number of shorter and weaker chains, with a depolymerisation mechanism. The third consequence is oxidation, or chemical degradation, especially in modern paper (i.e. after mid 19th century) which is made from wood pulp and contains several acidic elements. The damage is particularly severe in the presence of atmospheric pollutants and especially ozone. In addition, when paper is stored in a humid environment, it releases sulphuric acid that accelerates the deterioration. The last, but not least, consequence of dampness is biodeterioration. Not only dampness, but also dryness affects the molecular structure. Paper has a structure which is weaker compared to wood and is more sensitive to humidity changes. Moderate cold and dry is better for storage and conservation, but makes paper brittle. Moderate humidity causes the absorption of a number of water molecules which ensure mobility to the cellulose chains, increasing flexibility and this environmental condition is better for use. Therefore, when a book is consulted, it should pass from a cold, dry storage, to an intermediate transition climate, and then to the reading room which should be moister to made paper more elastic and warmer, and to be more comfortable for the reader. For this reason, the choice of the R H may change according to the use. Different humidity limits can be found

suggested in literature, e.g. the interval 45 to 65% RH. Similarly, also the collagen in parchment is arranged with chains of molecules with problems similar to those discussed for cellulose in paper, and extreme dry or wet may irreversibly alter the structural composition. Water can also be absorbed by textiles (cotton, linens, wool and silk) weakening the material and fading their colours. For all materials the microclimate should be especially chosen in order to reduce or eliminate the risk of biologic attack by fungi, bacteria or other parasites.

67 For example, algae and cyanobacteria need high RH, fungi generally prefer RH > 65%, but in already contaminated materials it should be considered that, due to the humidity conserving biofilm, the microorganisms will survive or even act at humidity levels > 50%. High levels of RH, especially when associated with T > 20~ favour biological rotting especially in the case of organic materials whose composition is appreciated by parasites or may offer a good substratum for the development of microbiological life. Besides RH and T, the intensity of microbial attack is basically controlled by the structure and chemistry of the respective substrate (e.g. porosity, inner surface, biosusceptibility of the material) and is secondly determined by air pollution levels (e.g. salts and organic materials) as well as further environmental conditions (e.g. ventilation, light, pH and redoxpotential) (Warscheid and Kuroczkin, 1997). It is should be considered that microflora lives at the interface between a solid substrate and the air: these two media may have a different temperature and moisture content, e.g. with water being adsorbed or trapped into pores. In certain cases, the dynamic situation generated by daily cycles which are transmitted with a phase delay in the two media, may lead to the fortunate circumstance that microorganisms may benefit alternatively from one or the other medium, so that considering only the physical characteristics of the air is analysing only a part of the problem. As far as the atmospheric part is concerned, the appropriate environmental conditions should be carefully chosen as a whole, including not only RH and T, but also ventilation and turbulence (which regulate the deposition and removal of spores), light, pH, air pollution levels, and the relevance of each of these factors may change in the case of indoor or outdoor environments. For instance, in the past when the air pollution was modest, lichens colonised many monuments especially in the Mediterranean belt, where solar radiation and rainfall were most appropriate and many lichens can still found in rather unpolluted zones of Portugal, Spain, Italy, Greece and so on. Later, when the SO2 and sulphates reached elevated levels, the atmosphere became toxic for them, and they disappeared from most cities, leaving on stone monuments typical signs of their past presence, e.g. pitting, oxalates. However, the microflora of stones represents a complex and highly adaptable ecosystem, metabolising inorganic and organic substrates from natural or anthropogenic sources. Because of their metabolic flexibility and remarkable tolerance against osmotic stress (e.g. salts) or toxic compounds, air pollution might cause considerable shifts in the composition of the stone colonising microflora, but will hardly control or stop biodeterioration processes.

68 2.10. WHAT IS THE BEST TYPE OF MICROCLIMATE FOR CONSERVATION? It has been clearly seen that some humidity levels are often associated with specific deterioration mechanisms, or may accelerate them. The water molecules which are absorbed into the material may determine internal stress a n d some deformation to the structure; the amount of absorbed water (and therefore internal stress and deformation) is in equilibrium with the RH and also, to a lesser extent, with T. These deformations tend to be reversible in plastic, new materials, but irreversible and extremely dangerous in aged materials. This is a good reason for suggesting some allowed or non-allowed microclimate conditions. For the materials most frequently used in creating works of art, some recommended values (or spans) of T and RH can be found in the literature, with the aim of determining the conditions of physical well-being, suitable for an appropriate conservation. These values are recommended with the aim of taking advantage from experience, or avoiding the repetition of errors already made by other colleagues, or keeping off from dangerous situations discovered with laboratory tests. However, a fundamental question arises: are microclimate norms and guidelines always useful and should they be always followed? It is useful to underline that recommended values of T and RH which are in principle suitable for materials are not always appropriate for individual artefacts. In fact, specific artefacts which have been kept for centuries under determined T and

RH, have been subjected to internal stresses and eventually have reached a new equilibrium of internal tensions with possible (permanent) deformation of their structure. Now, an old artefact, which has adapted to its environment according to the past internal system of tensions, and has lost its initial elasticity, is unable to adapt again to a new microclimate, and any change is very dangerous. This is a well known problem for wood conservation and when archaeological terracotta or glass is dug up to light. For this reason, an accurate knowledge of the past conditions is needed, and the previous microclimate should be kept untouched, or modified towards a new equilibrium very slowly and with extreme care, only in the case of real need. In addition, once these objects have adapted to some specific values of RH and T, they need very steady conditions as every fluctuation of these parameters works against the durability of the object. For this reason, all the abrupt changes are dangerous (it is common that archaeological pottery breaks when removed from u n d e r g r o u n d due to environmental shock) as well as the daily cycles of these microclimatic parameters. The daily cycles are repetitive and the effect of the stress is

69 of cumulative nature, and soon or later causes mechanical damage (fatigue failure). Seasonal changes, although they have a wider span, are less dangerous, as they occur more slowly, in a time much longer than the relaxation time of the object and with a rate slower than the penetration of heat and moisture in the material, so that there is no significant stress between the external layer and the interior. However, also these changes may be dangerous in the case of non homogeneous materials. It is evident that a furniture, or also a panel built with wood slabs constrained between them and having grains differently oriented, will undergo important internal stress when an element shrinks in a different way. It is obvious that for 'rigid' hygroscopic materials, e.g. aged wood or ivory, need a very constant microclimate, and the risk associated with a rapid change of the physical environment is greater than for more elastic or deformable materials, e.g. paper, parchment, tissues. However, the difference between materials and objects is often substantial: e.g. an old book with paper sheets and parchment cover, bound together with wire, is composed of parts that cannot expand or contract freely, so that microclimate cycles that are harmless to the individual components, may lead rapidly to severe damage of the object. When an object is not irreversibly conditioned by its past microclimate, and it is possible to choose the most appropriate conditions for preservation, these can be found by means of its adsorption isotherm (see Chapter 5). The goal is to avoid the intervals of RH where a small change of RH causes a great change of adsorbed water and to keep the object in one of the intervals where changes of RH do not affect (too much) the amount of adsorbed water and do not provoke new internal tensions. However, it is not always true that the best choice is the one indicated by the physical analysis of the material. In fact, if the experimentally determined 'best' interval is far from the natural local conditions, it might be better to choose a naturally stable microclimate than an artificial one, which is conditioned by the good functioning of complex devices. On this ground, Thomson (1986) suggested 60% RH for m u s e u m in Great Britain, and this value was deduced from the mean natural climatic values of that country. Similarly, in order to avoid shocks to the objects, the National Gallery, London, for reasons of continuity kept the standard 55%, which was the RH value in equilibrium with the moisture content in wood preserved in the Gallery prior the installation of an air conditioning (Padfield, 1994). These values have been acritically transferred to other natural climatic contexts. It is not common to find papers w h o criticise (as Padfield correctly did) the acritical use of microclimate normative or standards, some of them are widely used in everyday practice although without having been scientifically demonstrated.

?0 2.11.

KEEPING

CONSTANT

RELATIVE

HUMIDITY

IN

ROOMS

AND

SHOWCASES Relative humidity is of primary importance in the problem of conservation of works of art, and in exhibition rooms should be kept both homogeneous in space and constant in time. However, in practice several variations exist and dramatic changes occur, especially in the morning when windows and doors are opened d u r i n g cleaning, or when the heating system is switched on. In several cases humidifiers are introduced to mitigate or compensate the effect of the temperature change, but this system is never well balanced and hardly successful (Fig.2.12). Air conditioning systems and humidifiers cause repetitive 'ocal variations which are very dangerous. Active devices which create artificial microclimates are unable to ensure a very homogeneous distribution of the moisture and are very dangerous especially when bad functioning or power supply interruptions cause failure of the system. It is evident that the clouds of moisture generated by humidifiers displaced in rooms produce local perturbations also in terms of RH, with the effects that have been previously discussed.

80

-

t

RH(1)

"~" 7 0 RH(3)

.

~

60

~

50

40 0

3

6

9

12 Time

15

18

21

24

(hr)

Fig.2.12 Change in relative humidity at 1 and 3 m above the floor, i.e. RH(1) and RH(3), when the heating system and the compensating humidifiers are operating during the visiting time (for the temperature change see Fig. 1.13a). The humidifiers are too much powerful and, instead of mitigating the dry air, the net result is a moistening. The Pollaiolo room, Uffizi Gallery, Florence, 18 Febuary 1997.

71 Different systems to control the relative humidity are popularly used. For instance, in the Uffizi Gallery, Florence, a number of different systems can be found and they give the opportunity of very interesting comparisons, as follows. The Giotto room has a system which is based on controlled air introduced from grille diffusers sited in the ceiling above the Madonna d'Ognissanti by Giotto; as an equal flow is removed by intake slits on the wall near the floor level, this system generates a preferential path for the controlled air masses which cross the room and partially mix with the room air. For this reason this system is integrated with some traditional box humidifiers close to the walls. The result is a non homogeneous distribution of the humidity inside the room, and in particular in the summertime the cold flow of air conditioned falls just on the Giotto's painting (Fig.2.13). The Leonard room has a more sophisticated system which is based on the emission aloft of treated air released from line sources, i.e. four pipes hung to the ceiling, which lie parallel to the walls, but at a certain distance, so that the cold air falls far from paintings. In principle, this system is preferable, as the emission is not from a few points but is distributed from lines, and far from the exhibits. However, the treated air is transported by the depression generated by intake slits on the wall near the floor level, and by air currents exixting between a room and another. Although the system is good in principle for a single room, the overall result in the context of a buildings, where rooms are interconnected and air masses are transported from a room to another by internal temperature or pressure differences, the result (Fig.2.14) is not very satisfactory and practically not better than the simpler system in the Giotto room (Bernardi and Camuffo, 1995a). A number of rooms has box humidifiers sited close to walls and paintings, following an incorrect, dangerous practice very frequently found in museums and galleries. More appropriately, the Botticelli room has some humidifiers located in the centre of the room, far from paintings. Also very sophisticated automatic systems which control the ambient relative humidity keeping it in a span between two determined, relatively close, levels, cause continuous fluctuations between the lower and the upper levels (Fig.2.15). Although the range of variability lies within a few percent and the period is relatively short, so that the wave of the hygric perturbation cannot reach deep layers on artefacts, all of these repeated cycles have a very negative impact, especially on objects with small thickness, e.g. canvas paintings. It is easy to imagine the tremendous consequences that hot air heating systems have in churches heated once a week. In the example shown before for the church at Rocca Pietore, Italian Alps (Fig.1.11), the rise of temperature found at I m height, i.e. AT = 7~

causes a humidity drop ARH = 10%; the temperature rise found at 3 and 4

72

~///////////~'////////////////A

~

~'/////////~

5 8______ . 57

Fig.2.13 Relative humidity in the Giotto Room, Uffizi Gallery, Florence. In the hot season, the cold air conditioned released through diffusers in the ceiling, falls generating a perturbed zone. 12 August 1992 at 12.00. 'G' shows where the Giotto's panel is located.

~ ~ / /// / / / / / / / / / / / / / / ~ 62

I, 63

8

~////////////////////~

Fig.2.14 Relative humidity in the.Leonard Room, Uffizi Gallery, Florence. In the hot season, the sophisticated air conditioning system releases treated air from an extended source below the ceiling, but also this system is unable to guarantee ideal conditions. 13 August 1992 at 18.20. 'L' shows where the Leonard's panel is located.

73 m, i.e. AT = 20~

causes a dramatic humidity drop A R H = 50%, so that canvas

paintings, tablets and wood artefacts will contract and shrink, as we have already discussed.

In the long run, the repetition of these cycles has t r e m e n d o u s

consequences. 50 48 46

44 42 40

!

0

I

2

!

I

4

!

I

6

!

I

8

!

I

10

!

I

!

12

I

14

!

I

16

!

I

18

!

I

20

!

I

22

i

24

Time (h)

Fig.2.15. Fluctuations in relative humidity (RH) generated by a sophisticated controlling system, which controls this variable within two stated limits, i.e. the span 45 < RH < 50%. (Private Gallery of Modern Paintings, Parma, February 1996).

Some porous or fibrous materials characterised by large heat capacity maintain constant both T and RH: e.g. a thick wall tends to keep a constant microclimate in its proximity, and paintings hung to it or statues in niches benefit from these conditions; wooden boxes protect small objects against sudden changes of RH. One of the most effective materials, widely used in showcases, is the silica gel, characterised by many fine pores and therefore extremely adsorbent. This material smoothes out abrupt changes of RH, but does not ensure steady, pre-determined conditions. Silica gel is often pre-conditioned at some desired R H levels by keeping it for a sufficient long time at a determined humidity level until equilibrium is reached. At this point the silica gel behaves as a buffering agent, i.e. if the R H drops it will desorb moisture, and if R H rises it will absorb moisture in order to offset changes. However, the silica gel slowly adapts to the new average environmental conditions and the buffering level changes in a rather incontrolled way, so that it is necessary to change often the silica gel in the case with other silica gel, just conditioned at the desired level. This makes complex the management of the case. In addition, the amount of silica gel necessary for good conservation of exhibits in show cases has been calculated to be

74

25 kg per m 3 of air to control (Thomson, 1986). This figure shows clearly that it is e x t r e m e l y difficult to preserve objects at constant R H avoiding fluctuations, disturbances or slow changes. Whenever possible, it is advisable to improve the natural microclimate with the help of all the passive systems which ensure the best stability and reliability. A good method to maintain constant the RH at a desired level inside an airtight case, is to place in the bottom of the case a vessel containing a super-saturated solution of pure water with an excess of a certain solid substance which is in equilibrium with a specific value of RH, a number of these substances being listed in Chapter 11. These super-saturated solutions are characterised by a constant, typical vapour pressure and, consequently, by a constant value of RH. If the R H inside the case lowers, some water evaporates from the vessel to re-establish the equilibrium and, vice-versa, some vapour condenses in the solution if the inside R H increases. The choice can be extended to a large number of buffered RH levels, of course by choosing chemical substances that are not noxious to the exhibits. Sometimes showcases have a humidity level which is controlled by a micro climate generator which adjusts the RH by adding or removing moisture as required. The treated air is continually circulated between the case and the m o i s t u r e controlling unit. The RH sensor which is in the case drives in the control unit a feedback of moisture exchanges and the treatment stops when the desired RH level is reached. If the whole system, i.e. the case and the control unit have exactly the same temperature, there is a good probability that the desired RH is reached in average, i.e. w i t h several dangerous fluctuations around the mean level. H o w e v e r , if temperature differences are found in the system, although the mixing ratio is exactly the same, the relative h u m i d i t y will present d e p a r t u r e s and the r e q u i r e d homogeneity is lost. This happens normally for several reasons, e.g. the case and the control unit m a y have a different temperature, or the exhibit is heated by the lighting system, or the case has not exactly the same temperature everywhere because the most lighted panes w a r m the air near to them or the hot air accumulates in the top part of the box leading to an internal temperature stratification. These active systems are not fully reliable, need continuous control, are rather expensive and expose the works to the risk of dangerous departures in the case of bad control or work.

2.12. DEW POINT: THE TEMPERATURE OF CONDENSATION The dew point temperature, commonly termed dew point, DP is the temperature

75 to which a parcel of moist air must be cooled at constant pressure and constant water vapour content in order for saturation to occur. It can be alternatively defined as the temperature at which the actual pressure of the vapour contained in an air parcel equals the saturation pressure, under constant pressure and mixing ratio. Although it is popularly called dew point of the 'air', it is a property of the vapour that might be extended to the 'air parcel', i.e. the little mass of mixture of dry air and vapour taken into consideration.

From the definition it is a conservative property of the air parcel with respect to isobaric heating or cooling without addition or subtraction of vapour. It is non conservative with respect to adiabatic expansion or compression. Of course, in a completely dry atmosphere there is no any temperature at which water can condense and this parameter does not make sense. This parameter can be easily computed from the relative humidity and air temperature, starting from the consideration that the dew point is reached with an isobaric process, so that the vapour pressure at the original dry bulb temperature equals the saturation pressure at dew point, i.e. e(T) = esat(DP). By substituting this finding in the formula (2.20), one obtains with the help of the Magnus formula: aDP/(b+DP) e(t) esat(DP) esat(O)xl0 [aDP/(b+DP)] - [at/(b+t)] u - esat(t) - esat(t) = at/(b+t ) = 10 esat(O) xl0

(2.37)

hence aDP at logu = b + DP" b + t

(2.38)

and

DP-

b + DP

a

b + DP at b +t logu + ----a--- b +------t--~ logu + t

(2.39)

where the last approximate finding has been obtained substituting t to DP in the right hand side of the first identity. Of course, the first term is negative as u < 1 and logu < 0. Another formula can be deduced considering an air mass over an evaporating surface. The air temperature lowers, while the increase of mixing ratio raises the DP. The air temperature t continues to drop to the temperature of the evaporating surface, called wet bulb temperature, tw, is reached. When the vapour evaporated causes saturation, t = tw. Starting from the Clapeyron equation and the definition of

76 w, and always considering the difference D P - t w , after some laborious steps and approximations the following formula is obtained:

b logu+t logu+at D P = b -al~ - -b l o g u - t ~ gu

(2.40)

where a and b are the Magnus coefficients for vapour in equilibrium with the liquid phase. The eq.(2.39) is a better approximation. The above formulae can be used once the R H is known, and obviously logu = log(RH/lO0) = logRH- 2. The D P < T and D P = T only when R H = 100%. The D P is determined once the air temperature T and the R H are both known, or also when only the M R (or S H or A H ) is known. In particular, maxima of M R correspond to minima of D P and vice-

versa, so that the D P can be used for diagnostic purposes instead of the MR. The d e w p o i n t s p r e a d (also called spread), i.e. the difference A D P = T - D P basically depends upon both the actual air temperature T and the M R . Following the approximation (2.39) it can be expressed as a function of air temperature and relative humidity b+t A D P -- - ----a- logu.

(2.41)

It physically shows how much the air temperature is close to, or far from, the DP. The zones having the smaller A D P are more prone to form condensation and to allow micro biological life and weathering to occur. Useful maps of this parameter can be easily done for diagnostic purposes. However, although the R H is a very different, but related parameter, the areas with maximum R H are the same as those in which the A D P is minimum, and if the critical cooling is not requested, maps of R H are sufficient to give a qualitative description of these micro climatic problems. The d e w has the typical form of droplets and especially forms on leaves during the nocturnal cooling due to the IR emission. The formation of dew on leaves is favoured by the local excess of moisture due to the stomatal transpiration. The surface tension of water tends to displace the larger droplets on the edges of the leaves and in particular on the points of leaves, especially the lance-shaped ones. The u p w a r d IR loss during clear nights is a very effective cooling mechanism. The surfaces on which dew forms are free from any upper shield, and in practice are the same as those which are wet by rainfall. This is the reason that people often believe that dew falls similarly to the drizzle. If a non porous surface cools until it reaches the DP, the environmental vapour

77 begins to condense onto it, forming films of liquid water or droplets. A well known example is the condensation on the window panes during winter, especially in rooms with an elevated M R due to the presence of people, w h e n the glass conductivity cools below the DP the pane surface. Another important example of the same principle, is the condensation which typically occurs in spring in the Mediterranean region, when the air becomes mild and rich of moisture (i.e. with an elevated DP), and especially when the w a r m and humid Sirocco wind blows. Historic buildings have thick walls with high heat capacity and a large thermal inertia, whose temperature keeps a memory of the past cold season. The contrast between the elevated DP of the air, and the low temperature of the thick walls which remain below the DP, causes heavy condensation on the surface (Fig.2.16). If the surface is porous, the effects of the surface tension can favour condensation in the micropores also at temperatures above the DP, as we will see in Chapter 5. For this reason, in spring, thick walls of non heated buildings are very frequently damp. As the dew forms on all the surfaces whose temperature drops below the DP, irrespective of the environmental value of the RH, it is completely useless to insufflate the surface of cold walls or monuments with heated air, which has a lower RH but the same MR and, therefore, the same DP. Due to the large thermal inertia of these structures, the ventilation brings in contact with the cold surface a greater amount of air and vapour, thus increasing the condensation rate. This method was originally proposed by Massari (1959; 1971; 1977) as the windscreen effect, considering the analogy with the method used by cars to remove the misting of the windscreen. However, the vapour mists over the windscreen when the pane temperature T is T < DP of the air, irrespective of the RH of the airflow, but eventually the internal surface of the pane, which is poorly conductive and needs a relatively little amount of heat to warm, rises its temperature above the DP. At this point condensation stops and the misting evaporates. A nice example that the surface condensation is independent of the air temperature is given by a stainless steel pot, half filled with cold water, when this is put over the methane fire. Although the flames lick the pot, the cold pot is immediately covered with dew. A few seconds later, the droplets disappear from the upper half of the pot (i.e. the part which is empty and has a lower thermal capacity) when it is warmed above the DP. The droplets in the lower half of the pot, which is filled of water and has a greater heat capacity, disappear simultaneously several seconds later, when also the water inside the pot is warmed over the DP. For this reason, in some specific cases, condensation on limited surfaces can be eliminated either increasing the surface temperature, e.g. with IR radiation or direct warming, or diminishing the environmental MR. Some results can be also reached by

"/8

Fig.2.16 In spring, the contrast between the air rich of moisture (i.e. with an elevated DP), and the low temperature (below the DP) of the thick walls, causes heavy condensation on the surface, which is damp and fully covered with droplets. In this picture, taken in a room of Castel del Monte (Southern Italy), the 27 March 1996, when the surface is perpendicular to the flash light, the light crosses the droplets which are transparent and invisible, but when the surface is nearly parallel, the light undergoes a multiple reflection inside droplets which appear brilliant, with a silver like appearance. The red colour on the white part of the marble columns is a biopatina.

79 impregnating the surface with hydrorepellent substances which increase the contact angle 0 of the water droplets, as we will see in Chapter 5.

2.13. FROST POINT: THE TEMPERATURE OF FREEZING The frost point FP is defined in the same way as the dew point, but reference is made to ice and in the eq.s (2.39) and (2.40) the Magnus coefficients are a = 9.5 and b = 265.5~

From these equations it follows that FP < T and FP = T only when RH =

100%. In addition, FP - 0~ only in the case that at this temperature RH = 100%. In general, the frost forms at a temperature below 0~

which depends u p o n the

moisture content of the air. The frost (also called hoar, hoar frost, crystalline frost, white frost) is generated by the direct sublimation of the vapour, which forms needle-shaped crystals of ice. It is different from the frozen dew (also called white dew, silver frost) which has the appearance of ice spherules. Similarly to dew, the frost also prevalently covers the horizontal surfaces that loose heat by IR radiation toward the clear sky. Different is soft rime, which is due to the rapid freezing of very small supercooled water droplets in fog or cloud when they impact on (prevalently) vertical surfaces with temperature below 0~

In this way windborne droplets stick

forming a dendritic accretion, and all the trees are white on the side facing the wind, and iceless on the opposite side. The ice is white, porous, and is constituted of very small granules separated by few or many air inclusions. Similar to soft rime, but formed with drizzle droplets of micronic size, is hard rime. In the case that the concretion of ice has been generated by ice needles already formed in the atmosphere, this phenomenon is known as advection hoar frost (or also ice fog, frozen fog, frost fog, air hoar, rime fog). If the drops splashing on the cold surface are even larger, i.e. rain drops, the coating is more homogeneous and translucent, known as glaze (or also glazed frost, clear ice or ground ice for the soil). The windborne droplets and the splashing from them may cover surfaces differently oriented and the branches of trees may break due to excessive weight of the ice.

2.14. WET BULB TEMPERATURE: THE TEMPERATURE OF EVAPORATION The w e t bulb temperature Tw (or tw) or isobaric wet bulb temperature, is the

80

temperature an air parcel would have if cooled adiabatically to saturation at constant pressure by evaporation of water into it, all latent heat being supplied by the parcel. This temperature is directly measured by the wet bulb of a psychrometer, or can be obtained indirectly by means of a psychrometric diagram or formulae, after the dry bulb temperature and one hygrometric value (i.e. e, MR, SH, AH, RH, DP) are known. From the thermodynamic point of view, Tw is the temperature that an air parcel would have when some liquid water is supplied gradually, in very small quantities and at the same temperature as the environmental air, and then this water is evaporated into the air adiabatically (i.e. the latent heat being supplied by the air) at constant pressure, until the saturation is reached. The saturation is reached for the combined action of two factors due to the evaporation: the increase in MR and the drop in T. Consequently, Tw is the lowest temperature that an air parcel would have by evaporating water, the latent heat being subtracted to the air and utilised for the change of state of water from liquid to vapour, until saturation is reached. Tw is also the equilibrium temperature of an evaporating surface of water. Applying the first law of the thermodynamics to an air parcel formed by 1 g of dry air with a mass of vapour mv, i.e. with mixing ratio w = mv, and experiencing the above process, Tz0

mw

f Cpm (l+ mv) d T : T

f Lvdmv

(2.42)

my

where

Cpm

is the isobaric specific heat of the moist air that can be expressed in terms

of isobaric specific heat of dry air Cpd (Cpd = 0.240 cal g-l K-1 = 1.003 Joule g-l K-l), i.e. Cpm = (1+0.8 mv)Cpd and Lv is the latent heat. After integration, by dividing both sides by (Cpd + <w> Cpv), the wet bulb depression ATw = T- Tw is obtained

ATw

(msat,w - m v) Lv =

(2.43)

Cpd + < w > Cpv

where <w> is the average mixing ratio during this process, msat,w is the saturation mixing ratio at the temperature Tw a n d Cpv is the isobaric specific heat for the water vapour (Cpv = 1.81 Joule g-1 K-l). A further approximation of the wet bulb depression is obtained by using the formula (2.19) for w and considering that Cpd + <w> Cpv = Cpd (i.e. <w> <<1), so that the wet bulb depression becomes

81

ZlTw ~-

0.622 Lv (ew - e) Cpd P

(2.44)

where ew is the vapour pressure at Tw. This equation can be solved with successive approximations for every initial set of T, p and e. Graphic solutions are popularly used. Saturation occurs at temperature Tw for the dynamic equilibrium which follows the increase of M R due to the addition of water to the system. From the definition, Tw is conservative with reference to the evaporation of falling rain drops. In the case

of an evaporating porous surface, the evaporation rate is generally modest, so that T tends towards Tw but may not reach it, and the M R increases at the interface, generating a negative gradient of M R (i.e. M R decreasing coming away from the surface) and a positive gradient of T in the air close to the evaporating surface. In the opposite case of evaporation occurring in the internal pores of a wall, the latent heat is supplied by the wall and the air temperature remains unchanged, but the evaporation is still evidenced by the negative gradient of MR. There is an analogy between DP and Tw: both are based on isobaric cooling until saturation is reached, but the DP is reached without changing the MR. On the contrary the Tw is reached with the addition of external water which raises the M R of the air parcel, favouring saturation; for this reason the DP cannot be reached with evaporation forced by ventilation. The DP is the temperature for condensation and the Tw for evaporation and DP < Tw < T

and

ADP >_ATw > 0

(2.45)

where the identity holds only for RH = 100% when DP = Tw = T. It might be noted that in the atmosphere the saturation is usually found on foggy days, especially during night-time. In general, during fog, the RH is 95 < RH <_ 100%. During short rainfalls and showers saturation is not often reached. Summer showers may occur with very low RH, and the fallen water then evaporates in a short time. The Tw can be easily measured by means of a psychrometer, which is constituted by a couple of ventilated thermometers, i.e. a normal one (i.e. the dry bulb) and another having the bulb (i.e. the wet bulb) covered with muslin which supplies water adsorbed for capillarity from a reservoir. The air speed of the ventilation is generally between 3 and 5 m s -1 as will be discussed in Chapter 11. It is evident that, for a given temperature, the greater the M R , the greater the D P as the vapour is less

82 further from saturation. The same can be said for Tw which lies between T and DP. It is also obvious that Tw is also related to the degree of saturation of the air, in that the higher the R H the smaller the amount of water that should be evaporated to reach saturation and, consequently, the cooling ATw caused by the absorption of the latent heat for vaporisation. When the wet bulb is ventilated, it drops in temperature, and the cooling stops at the equilibrium, which is reached when the heat Qv lost by evaporation from the wet bulb e w

Qv = C Lv S ~

- e

(2.46)

P

(where C is a proportionality coefficient, Lv the latent heat of vaporisation, S the surface area of the evaporating surface, e the actual vapour pressure, ew = esat(tw) the saturation vapour pressure at the temperature of the evaporating surface and p the atmospheric pressure) equals the sensible heat Qs transferred from the ambient air to the colder wet bulb (2.47)

Qs = B S ( T - Tw)

where B is another proportionality coefficient and Tw is the wet bulb temperature. By the way, equation (2.46) is the Dalton law of evaporation. Equalling the two previous equations for the heat exchanges equilibrium, the basic psychrometric formula is obtained (2.48)

e = esat - A p ( T - Tw).

where A = ( B / C Lv) is the so-called psychrometer coefficient which is not really a constant and depends, inter alia, on the ventilation rate (see Chapter 11). Substituting in the definition (2.30) of relative humidity, e with the psychrometric formula, esat with the Magnus formula (2.1), and A = 6.667x10 -4 K -1, and dividing numerator and denominator by esat(O) = 6.11 hPa, the very useful equation is derived atw/ (b+tw) 10 - 1.09x10 -4 p (t -tw) R H = 100

at/(b+t)

(2.49)

10 which allows a precise determination of R H after measurements of t and tw and,

83 consequently, precise calculations of M R (eq.(2.33)), e (eq.(2.34)), A H (eq.(2.35)) and DP (eq.(2.28)). This equation has been reported in the form RH vs. ATw in Fig.2.17 for

some values of T. The depression ATw can be also calculated after the readings of T and DP with the following empirical formula ATw = ADP (-1.281x10 -4 t 2 + 0.01786 t + 0.3682) - 0.00889 ADP 2

(2.50)

where the dew point spread can be calculated with the eq. (2.41) in the case of known RH instead of DP. This formula is not commonly used because it obtains values that

are generally measured directly. However, meteorological services furnish the DP instead of the ATw or the RH and for this reason it is useful to calculate from the DP the basic parameters which are then used as input for other formulae.

2.15. THE PSYCHROMETRIC CHART Several thermo-hygrometric parameters can be graphically computed with the help of the psychrometric chart (Fig.2.18) as follows. 9

The abscissa is the actual air temperature T (i.e. the dry bulb temperature) and the

ordinate the MR (or the SH). 9

The vertical lines are isotherms. Ascending, the M R increases (e.g. addition of

external water, e.g. by evaporation); descending, it decreases (e.g. condensation, absorption or adsorption of vapour which is subtracted from the atmosphere; the term 'adsorption' implies the condensation of the vapour on the surface of solids). 9

The horizontal lines are isohume in terms of constant MR:. A displacement to the

right indicates a warming of the system without change in MR, a displacement to the left, a cooling, and according to our previous definition, the final point of this cooling is the DP. 9

The near exponential curve on the left is the saturation curve, and represents

simultaneously the MRsat, the RH = 100%, the DP and the Tw. 9

The (vertical) distance between each point of the saturation curve RH = 100% and

the abscissa can be divided into 100 parts. Each of them, by definition, shows the percentage of MRsat. This is the actual value of the RH of the air parcel characterised by the values of T and M R which are the co-ordinates of that point. The nearly exponential curves with RH = 10, 20, 30..., 100% are generally evidenced. These are isohumes in terms of RH.

84

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Dry Bulb T e m p e r a t u r e (~ Fig.2.18 Psychrometric chart

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86

9

The tilted lines, where both the T decreases and the MR increases, are

characterised by Tw = constant and are nearly isenthalpic. In fact, there is a small departure, being d r a w n for a non perfect gas. The value of T w of each thermodynamic point can be read on the saturation curve. Sometimes, the scale for enthalpy of the system is also added. It can be recalled that the enthalpy,,~ of a system in equilibrium at pressure p and temperature T is defined as

~ ( p , T)= U + pV

(2.51)

where U is the internal energy of the system and V its volume. Therefore, 4 , ~ = dQ + p dV

(2.52)

where dQ is the amount of heat gained or lost. For a process which is isobaric and

reversible = dQ;

(2.53)

and for a perfect gas (i.e. no change of state)

= Cp dT

(2.54)

the enthalpy is a function of T only, i.e. the change in enthalpy measures the heat imparted to the system. In meteorology the enthalpy is considered a synonymous of sensible heat (i.e. heat, in opposition to latent heat) as exchanges of enthalpy coincide with exchanges of heat. Indicating ~ m v the enthalpy per mole of pure water in the vapour phase, and ~ m c in the condensed phase, then

,~mv - ,.~mc = Lv

(2.55)

i.e. the molar heat of evaporation denoting the latent heat of vaporisation for one mole of the associated condensed phase. Therefore, changes of enthalpy always represent transfer of heat, either in the sensible or in the latent form. For an isolated air parcel all the processes that are simultaneously adiabatic and

isobaric are also isenthalpic. A process which is isenthalpic is also adiabatic, as well as isentropic, as the entropy 50 is thermodynamically defined as

81

.5~= ; d ~ 9

(2.56)

In fact, all these processes are characterised by dQ = 0. A process which is adiabatic but not isobaric (e.g. the upward rise of an air parcel) is by definition isentropic (i.e. dQ = 0) but not isenthalpic, due to the work done against the external pressure during the variation of the volume of the air parcel. The sum of enthalpies of the phases of a closed system is conserved in an adiabatic isobaric process. Sometimes, the isochoric lines i.e. the lines with equal specific volume are also reported, expressed in m 3 kg -1. Each point in the chart shows directly, or by interpolation, the complete thermodynamic state of the air parcel: the T, by following d o w n w a r d s the isotherm to the abscissas; the MR, by following the horizontal isohume to the ordinate; the DP, by following the same isohume to the saturation curve; the Tw, by following the iso wet-bulb line (i.e. the isenthalpic) to the saturation curve: the RH, considering on the same vertical the distance between the thermodynamic point and the abscissa and expressing it as a percentage of the whole distance between the abscissa and the saturation curve, or interpolating with the nearly exponential curves with RH = const passing close to the point. A few examples may be useful to clarify the method, first of all becoming familiar with the chart. 1) Let us consider the thermodynamic point (Fig.2.19a) characterised by t = 25~ and RH = 70%; the vertical isotherm and the curve of equal saturation 70% meet at a point where the horizontal isohume shows on the right MR = 14 g kg -1 and on the left DP = 19~

Moisture can be added isothermally to MRsat = 20 g kg -1, or

isenthalpically to MRsat = 15.75 g kg -1, and the corresponding temperature is Tw = 21~ 2) In this example (Fig.2.19b), we want to change the temperature of the air in a room, initially at t = 30~ and RH = 60% in order to arrive at 25~

but with the same

RH. A subtraction of both heat and moisture are necessary, and the moisture can be removed by condensation. The air conditioning system will cool the air; initially the cooling will occur with u n c h a n g e d M R

(i.e. 16.3 g kg -1, with a horizontal

displacement along the isohume to left); at around 21~ the DP will be reached. A further cooling will cause the thermodynamic system to follow the saturation curve RH = 100% with condensation on the refrigerating surface and subtraction of vapour from the air. The system will condense water until the moist air will reach 17~ and the M Rsat = 12 g kg -1. Removing the fraction of liquid water which has been

88 ....

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Fig.2.19 E x a m p l e s cited in the text. (a): Characteristics of a air parcel w i t h t = 25~ a n d RH = 70%. (b)" Thermo, d y n a m i c t r a n s f o r m a t i o n n e e d e d to cool an air m a s s initially at t = 30~ and RH = 60% to t = 25~ but w i t h the s a m e RH. (c): D r y i n g cloths in a b a t h r o o m .

89 condensed and heating the air parcel to 25~

with a horizontal displacement, the

desired temperature and humidity will be reached. 3) Suppose (Fig.2.19c) to hang out the washing in a bathroom, w h e n the external conditions are characterised by t = 0~ and fog, i.e. RH = 100%; consequently, the MR is M R = 3.8 g kg -1. The volume of the bathroom is 25 m 3 and contains the total mass 25 m3x1.255 kg m -3 = 31.4 kg of air. The external air which is penetrated into the house was heated to t = 20~

as there is no subtraction or addition of moisture, the

indoor R H is R H = 25%, i.e. very dry. At this indoor temperature the m a x i m u m allowable M R is MRsat = 14.8 g kg -1, and the amount of water that can evaporate is given by the number of kilograms of air contained in the bathroom, multiplied by the moisture capacity of each air kilogram, minus the initial moisture content, i.e. 31.4 kgx(14.8-3.8) g kg -1 = 345 g, which is a very little amount, corresponding e.g. to one sock. Heating the bathroom to 25~

the MRsat is risen to MRsat = 20 g kg -1, which

allows a further evaporation of 31.4 kgx(20-14.8) g kg q = 163 g, i.e. half a sock. This shows that the critical factor for indoor evaporation is the limited ambient volume, and little help is obtained by overheating. The washing can dry only with the windows open and exchange of the air.

9!

CHAPTER 3

Parameters for Describing Air Masses and Vertical Motions

So far we have observed the air from the Eulerian point of view, i.e. stating a stationary coordinate system linked to the soil or the architecture of a room, where the same air undergoes temperature or humidity changes, or is substituted by other air masses, and we have looked at the variation of a number of parameters in some stated points, isolated or forming a horizontal grid or a vertical profile. It is also useful to consider the thermodynamic transformation of the air masses from a mobile reference frame, which has been linked to the air mass itself, so that the fixed subject is the air, and the changing parts are the locations where the air moves. This is the Lagrangian point of view. Each of these systems presents advantages and disadvantages, and the choice of the more appropriate system depends on the specific problem. However, whatever will be the reference system, it is obvious that, when we are willing to apply a wider analysis, it is always useful to introduce new variables which are better representative of the thermodynamic state of an air mass. In fact, when an air mass is considered not only in a specific location, but in its three dimensional displacement in the atmosphere, it may adiabatically expand or compress, changing in temperature. A temperature drop may lead to saturation and condensation of the vapour, with the release of the latent heat, and vice versa. In addition, also precipitation may occur, which removes liquid water and the possibility of utilising again the latent heat associated to it. All these thermodynamic situations can be appropriately described with new parameters that should be introduced at this point. Although they may seem complex at a first sight, they have the great advantage of being unaffected by some specific thermodynamic processes, so that they may characterise an air mass before and after the happening of the specific transformation to which they are invariable. All of these parameters are well familiar to people working in meteorology and transport of pollutants, and are useful to interpret a specific environmental condition in its more general meteorological context. In addition, they can be applied to better understand the

92 interactions that are happening on a monument surface.

3.1. EQUIVALENT TEMPERATURE The e q u i v a l e n t temperature Te (or te) or isobaric equivalent temperature is the temperature that a moist air parcel would have if all water vapour in it were condensed out at constant pressure and adiabatically, i.e. all the latent heat released in the condensation being used to heat the air. The adjective equivalent implies the sum of the latent and sensible

heat contained in the air parcel. It represents the molecular temperature that would be attained by an air parcel if all the latent heat Lv w potentially present in the parcel were transformed into kinetic energy of the air molecules, and liquid water were removed by the system, e.g. by precipitation. This process is only speculative, as all the forms of condensations that occur in nature do not involve the total a m o u n t of the moisture actually present. This parameter is given by the equation

Lv

Te = T + ~ w Cpd

~ T + 2.5 M R

(3.1)

where the right hand approximation (with constant Lv) shows that 1 g of water vapour raises the temperature of I kg of air by some 2.5~ From this definition this parameter is a conservative property of the air with respect to isenthalpic evaporation or condensation of droplets in the air, e.g. the formation or dissipation of fog or clouds, or condensation or evaporation of water in micropores of non conductive materials. At ground level, considering that at standard conditions, i.e. p = 1013 hPa and t = 0~

1 m 3 of air has the mass of 1.275 kg, and remembering the eq.(2.28), the

previous equation can be approximated also as Te ~ T + 1.95 A H - - T + 2 A H

(3.2)

w h e r e 1.95 = 2.5/1.275. This equation shows that 1 g of v a p o u r raises the temperature of I m 3 of air by some 2~ This parameter, which is a function of both T and M R shows w h e n and where the air exchanges heat (also called sensible heat) or moisture (i.e. latent heat) with an evaporating or absorbing surface, or when two different air masses meet and mix

93 together. In the case of microclimatic studies, this parameter is useful to individuate exchanges between air and surfaces or the penetration and path of external air. When no interactions have occurred, this parameter is the same indoors and outdoors. However, it remains unchanged also if condensation, or evaporation, occurs in micropores of a non conductive material, the heat being supplied or absorbed by the air. If the walls have a low conductivity and a very large heat capacity and all the heat is supplied or absorbed by them, the condensation in the micropores does not affect the room temperature but lowers the room MR and, consequently, the Te; the opposite occurs in the case of evaporation from the micropores. Although this parameter does not describe a realistic process, it presents several diagnostic advantages, and is the first step to arrive to define another parameter, namely the equivalent potential temperature, that is conservative with reference to both adiabatic and non isobaric processes. For instance, the formation or dissipation of a fog (or a cloud) cannot only occur with an isobaric and adiabatic process, and it is necessary to introduce other parameters, which will be conservative before, during and after uplift adiabatic expansions, cloud condensation and precipitation. The next step is to find invariance with respect to adiabatic vertical displacements in the atmosphere.

3.2. ADIABATIC GRADIENT IN THE TROPOSPHERE Following the path and the destiny of an air mass and its moisture in the lower atmosphere is not only of interest for the weather forecast, but also for the transport and dispersion of airborne pollutants. This implies to know how the energy is distributed and transformed within an air mass, its temperature and density. When in the path of an air mass important changes of height are involved, the ambient pressure changes, and the work done to expand an air mass is made with part of the thermal energy of the air molecules, so that the process causes a cooling of the air. This is an example of adiabatic expansion (i.e. without exchange of energy with the external system), and the temperature change which is regulated by this mechanism can be computed with the Poisson equation, as we will see in the following. The convective mixing of the lower atmosphere is the reason why the air temperature is lowering with increasing height in the first 1 0 - 15 km of atmosphere, called

troposphere. Above this layer, up to some 25 km, the air temperature increases again because in this second layer, called stratosphere, the dominant mechanism is the absorption of ultraviolet radiation by oxygen and ozone.

94 In a transformation which is reversible and slow, the internal pressure of an air parcel equals the external one and (3.3)

~)W= p d V .

The condition of reversibility gives (3.4)

5Q=pdV+dU

where the internal energy U = U(T) is a function of T only, as well known for an ideal gas. If an amount of heat 8Q is supplied to the sample of gas having mass m, all the heat is transformed into intcrnal energy and the increase is (3.5)

d U = m Cv d T

and this equation is valid also if the volume is not kept constant. The first principle of thermodynamics can be then written (3.6)

8 Q = p d V + m Cv d T

The equation of state is preferably written in terms of p and T only, as they are easy measurable parameters. The equation of state becomes (3.7)

p dV +V dp = m .J?~a dT.

By definition, for a thermodynamic transformation X the specific heat Cx is given by (SQ)x

mcv

Cx - m d T -

dT+p(dV)x m aT

p dV =Cv+m (d-T-)x

(3.8)

In the case of an isobaric transformation dp = 0 and the (3.7) becomes p dV = m .~a dT and

(3.9)

95

p m,ff/~a Cp = Cv + m

p

(3.10)

- Cv + . ~ a

Substituting this result in the (3.6): 5Q = m Cv d T - V dp + m , ~ a d T = m Cp d T - V

dp

(3.11)

and a further substitution in the equation of the state gives for the unit mass

( S Q )m = 1 = Cp d T - . ~ a T

dp --. P

(3.12)

For an adiabatic process 5Q = 0; if it is also reversible, then

Cp d T = . ~ a T dp P

(3.13)

or

dT = k T

dp P

(3.14)

where k = (Cp- Cv )/Cp = , ~ a / C p = 287/1003 = 0.286, which is valid for small variations of p. By integration the P o i s s o n equation is found for adiabatic and reversible processes, i.e.

T2 (p2k T1 - " ~ - ' "

(3.15)

The atmosphere is called adiabatic when vertical motions occur without any external work, and this happens when the density of the air parcels is always in equilibrium with the ambient air. The atmosphere is characterised by a neutral equilibrium making reference to the vertical adiabatic motions of dry air. It is possible to compute the vertical thermal gradient during neutrality. From the hypsometric equation of the hydrostatics dp = - p g dz where p is the barometric pressure, p the density, g the acceleration of gravity and z

96 the vertical coordinate, remembering that from the equation of the state for perfect gases .~/2~ap T / p = 1, eq.(3.13) can be written dT ,~a P g T g 9.8 d---~- Cp p = - Cp - - 100---3-~ 0.01

(K m -1)

(3.17)

which in practice corresponds to the cooling of 1~ per 100 m of adiabatic uplift. The vertical gradient dT/dz = 1~

m is therefore called adiabatic and is represented

with the symbol 7 (especially in the mathematical formulae) or F (especially for the graphical representation).

3.3. POTENTIAL TEMPERATURE We have seen that the temperature is representative of the average kinetic energy of the molecules in an air parcel, but that this value changes with vertical displacements of the parcel. It is useful to find a parameter which allows for a comparison between the average kinetic energy of the molecules in two air masses, independently of their height, i.e. referring them to a standard level. The p o t e n t i a l temperature 0 is the temperature a parcel of air would have if brought dry adiabatically from its initial state to the standard pressure of 1000 hPa. Note that the round number

1000 is used instead of 1013, in order to make easier calculations. At sea level the potential temperature is very close to the actual air temperature and it is exactly O = T when p = 1000 hPa. The potential temperature of an air parcel is independent of the height, similarly to the temperature of mixed, incompressible liquids. The O is computed with the help of the Poisson equation utilising the initial values of T and p, i.e.

O=T.p.

(1000~ k

(3.18)

where it is clearly shown that O is directly proportional to T. A region of the atmosphere in which O is constant on the vertical is said to be dry adiabatic. A representation in terms of O shows immediately where the

atmosphere is adiabatic, i.e. d O / d z = 0, as there the isotherms are vertical; where d O / d z > 0 the isolines are tilted towards left; where d O /dz < 0 the isolines are tilted towards right (Fig.3.1). Further details will be given in Chapter 7.

97 700 T

//

O

600

500

E~

400

9 ~,,,i

200

100

20

22

24

26

28

30

Temperature (~ Fig.3.1 Vertical profile of the air temperature T (thick line) and potential temperature O (thin line) in the Venice hinterland, the 25 June 1979 at 10 a.m. The first 150 m show a profile superadiabatic, i.e. with a gradient greater (in the absolute value) than the adiabatic one (O profile tilted towards left); from 150 to 280 m substantially adiabatic (O profile vertical); above the air is stable (O profile tilted towards right). In meteorology, weather prediction and pollution transport, the basic equations can be solved more easily if appropriate co-ordinates are used. For this reason, the geopotential, the pressure, the entropy and the potential temperature can be used as a vertical co-ordinate instead of the geometric height (for a discussion see Kasahara, 1974). Potential temperature or isentropic coordinates are especially convenient for description of adiabatic motions. As in the definition of O the a t m o s p h e r e is characterised by adiabatic displacements, in the whole region where O - const, also 5Q = 0 and displacements are isentropic. Therefore, all the surfaces with the same 0 are isentropic and an air parcel having a given value of O will remain within the same

surface of equal potential t e m p e r a t u r e , unless external w o r k is s u p p l i e d to it. Therefore, the isentropic representation of the atmosphere is a very practical tool to forecast where a pollutant can or cannot be transported; whether it will be able to cross m o u n t a i n chains or not (Fig.3.2). In fact, except near the soil w h e r e heat is

98 exchanged and in absence of condensation, an air parcel tends to maintain the same entropy and potential temperature.

Fig.3.2 Surfaces having the same potential temperature are also isoentropes. The vertical cross section of potential temperature shows an example. It is also possible to find a relationship between potential temperature and entropy. Dividing by T both members of eq.(3.12) and integrating, one obtains the

entropy function of the air: dQ = f Cp --~-dT f. ~a --~ dp = Cp lnT-.J?~a lnp .}/~=f --~

(3.19)

This equation holds for unsaturated air, assuming the air and vapour mixture behaves as an ideal gas (unsaturated vapour), but for saturated vapour the equation is identical, but for an additive constant (Goody, 1995). The relationship is easily obtained substituting in the previous equation the definition of O in eq.(3.18) in logarithmic form, i.e. lnO= lnT + -~p (lnl000- lnp)

(3.20)

so that the entropy is immediately found, .~= cp lnO

(3.21)

99 where the additive arbitrary reference constant has been omitted. The Poisson equation can be compared with the assumption that the vertical temperature gradient is constant and given by the eq.(3.17), i.e. dT/dz = y, so that T = To + 7 z

(3.22)

Dividing the hydrostatic equation (3.16) by the equation of state for perfect gases (1.2), and using the previous equation for T, dp

P

.

g dz . . . . . ~ a (To + ~/z )

g d(To + yZ ) - . ~ a 7 To + ~/z

(3.23)

or

dlnp = - g__K__dlnT. 7.~/~a

(3.24)

Integration gives p2 ( ~ ) - g / Y'~-'r Pl -

or

T2 (P2) ~ '~a /g T1 = "P-1-1"

(3.25)

where y. ~Z?a/g = k = 0.286.

3.4. EQUIVALENT-POTENTIAL TEMPERATURE The equivalent-potential temperature Oe is the potential temperature corresponding to the equivalent temperature Te , i.e. (1000}k Lv Oe = T e , p , = O + - -Cpd w

(1000} k , P ,

(3.26)

This p a r a m e t e r is conservative with respect to dry adiabatic processes, e.g. compression or expansion of air parcels due to change of height. The exponent k has been derived for dry air; the moist air, when reduced to the standard pressure of 1000 hPa has a temperature somewhat lower than dry air, and the departure

1 O0

increases with moisture content. However, this departure is in general very small, so that this parameter can be considered quasi-conservative for isenthalpic pseudoadiabatic processes. The adjective 'pseudo-adiabatic' refers to systems in which saturation occurs and the condensed water is removed from the system, e.g. by precipitation. The rising of air masses, which form clouds and rainfall are a meteorological example of a pseudo adiabatic process. Both the dry and the pseudoadiabatic lines are represented in aerological diagrams, e.g. the Strive diagram. This parameter varies for isobaric heating or cooling, or gain of vapour supplied by oceanic waters relatively warmer than the air. The above discussion on the isentropic surfaces can be applied with a wider generality to Oe, as it also includes the possibility of formation of clouds and precipitation. When an air mass is forced to flow over a mountain chain, during the slope rise it may arrive at a height above the cloud condensation level (CCL): the temperature drops below the dew point, the vapour is supersaturated and begins to condense forming cloud droplets and precipitation on the upwind slope. This upslope precipitation is known as stau. This mechanism continues during the cooling associated with the rise and stops when the air is heated by compression when it descends downwards along the other slope. The droplets which remain in the cloud evaporate again. If the equivalent temperature of the uprising and descending streams is measured in the opposite slopes at the same height Zl, the value Te(Zl) is the same for both streams, but is not conservative with changes of level, i.e. Te(Zl) Te(z2). The equivalent-potential temperature Oe of an air parcel which moves adiabatically is independent of the height, and is the same everywhere, so that an air mass can be always individuated by this parameter; when the parcel undergoes non adiabatic transformation, the change AOe gives the gain (or loss) of the thermal energy expressed as the sum of sensible plus latent heat. In the previous example, the temperature T of the air has undergone important changes. During the upwind condensation, the latent heat has warmed the air mass and most of the liquid water has been removed from the system by precipitation. During the descent, the cloud droplets evaporate re-absorbing the heat that they have previously released during the condensation phase, so that this part of the process is reversible; however, the heat supplied by the precipitated water remains in the air, which arrives hotter. This is the well known warm foen wind downslope. In all the stages of upslope cooling and precipitating and downslope warming the equipotential temperature remains unchanged or quasi-unchanged.

101 3.5. VIRTUAL TEMPERATURE A smoke plume, a meteorological balloon, or a cumulus cloud rise whenever their density is lower than the ambient air. However, the density of moist air is determined by two factors: the air temperature, and the moisture content. The molecular weight of water vapour is 18, whereas the average molecular weight of dry air is 28.96. For this reason, the density of a moist air parcel at a given temperature and pressure is equalised by a hotter parcel of dry air at the same pressure. In order to simplify the description atmospheric processes, it is convenient to ignore the presence of moisture and make reference to an ideal dry air with an effective temperature which simulates the effects of moisture in terms of density. The

virtual temperature Tv (or tv) of a parcel of moist air is that temperature at which completely dry air would have the same density and pressure as moist air. Also this parameter is speculative, but is very practical, as it allows to apply to the moist air the equation of state for dry air. This parameter is used w h e n c o m p a r i n g the buoyancy of two different air masses which come into contact, or the vertical uplift of a puff smoke or a meteorological balloon. Using the Dalton law the pressure of the moist air is p = Pa + e where Pa represents the partial pressure of dry air, and the mass is m = ma + mv where the labels 'a' and 'v' are still used to distinguish between dry air and vapour. The equation of state for the moist air becomes:

pV

.161 )

.~v. ~ - + mVm.j?~a ! T = m . ~ a (1 _ _m_Vm (ma.~/P~a+mv.~v) T = m . ~ a ( -ma m

: m . ~ a (1+ 0.61 - ~ ) T-- m.~a (1+ 0.61 m~aaV ) T : m , ~ a (1+ 0.61w)T

= m .~aZv

(3.27)

where Tv is defined as Tv = (1+ 0.61w) T but it is also often expressed as

(3.28)

102 (--,1 TT~

+~3p) T--

T3-------e _

(3.29)

_

8p The derivation of this formula is simple. When w is small, as it is, the reciprocal of (1+0.61w) is to a close approximation (1- 0.61w); substituting to w the approximation (2.19) and considering that 0.61x0.622 = 0.379 -~ 3/8, the latter equation is found. From the formulae it follows that T < T v < Te. Under usual meteorological conditions, the virtual temperature increment is Tv - T < 5~

103

CHAPTER

4

Radiation and Light

4.1. THE EMISSION OF RADIATION FROM BODIES AND THE EFFECTS OF THE ABSORBED ENERGY Each body emits electromagnetic radiation, which propagates in the space in the form of waves of electric and magnetic fields, according to the classic Maxwell's theory of radiation. The radiation frequency v is given by the ratio between the velocity of light c and the wavelength ~ of the radiation, i.e. c V

=

-.

c4.~

X

The intensity I of the flux of energy emitted from a blackbody per unit time, unit wavelength and unit solid angle, depends upon v and the absolute temperature T, according to the P l a n k ' s formula

I(v,T) =

2h

V 3 C2

exp(h vc / KT) - 1

(4.2)

where h = 6.626x10 -27 erg s = 6.626x10 -34 J s is the Plank's constant and K the Boltzman's constant K = 1.3806x10 -16 erg K -1. The same p h e n o m e n o n can be also described in terms of a corpuscular emission (Einstein, 1905), where the radiant energy is transported by photons having the individual energy E = h v,

(4.3)

the intensity of a spectral component being given by the n u m b e r of photons having a given wavelength. Although the two theories are equivalent in several cases, the classical wave representation is more suitable to describe some

104 p h e n o m e n a , e.g. diffraction, interference, polarisation; the q u a n t u m theory for other p h e n o m e n a , e.g. photoelectric effect, emission of cathode rays, gas ionisation by means of ultraviolet radiation. A synthesis of the two points of v i e w has been m a d e to associate with light the dual nature of w a v e and corpuscle. According to the Einstein's theory, w h e n a p h o t o n is absorbed by a molecule, the molecule absorbs its energy and excites, and this provokes a change of the energetic state of its electrons, with a n u m b e r of possible consequences. If the energy hv exceeds the bound energy of an electron, the latter m a y escape (photoelectric effect), or the exited molecule m a y dissociate, or isomerise, or transfer energy to another molecule, or change into a different c o m p o u n d with a photochemical reaction, or undergo other causes of degradation (Wypych, 1995). Ionisation in the u p p e r atmosphere, ozone formation in the stratosphere, and molecular excitation of atmospheric H20, CO2, 03 are well k n o w n mechanisms which absorb some spectral bands of the solar radiation. The solar radiation which arrives at the earth surface is classified as reported in Table 4.1. TABLE 4.1 Wavelength of the solar radiation crossing the atmosphere wavelength

radiation

wavelength

radiation

<10 A 10 A - 0.2 lzm 0.2 - 0.315 ~tm 0.315 - 0.38 ~tm 0.38 - 0.72 ~tm

T rays and X rays far ultraviolet middle ultraviolet near ultraviolet visible

0.72 - 1.5 ~tm 1.5 - 5.6 ~tm 5.6 - 1000 ~tm >1000 ~tm

near infrared middle infrared far infrared micro & radio-waves

The shortest w a v e l e n g t h s are mainly absorbed by the ion- and ozonosphere; the longest ones by atmospheric water vapour and carbon dioxide. The Sun, whose photosphere is at some 5,800 K, emits 99.9 % of its energy within the wavelength interval 0.15 to 40 ~tm, with a peak intensity in the visible, near 0.47 ~tm. A l t h o u g h the ultraviolet (UV) radiation is the most energetic one, it is composed of a small flux of photons and the power emitted is very low; about half of the power lies in the visible light and most of the second half in the near infrared. All bodies can absorb and emit radiation at all w a v e l e n g t h s , and the

'colour', i.e. the distribution of intensity of the spectral lines of the light, depends

105 upon the temperature of the body. This effect is quantitatively described by the

Wien's displacement law, which states that the spectral distribution of the energy density varies with the temperature of the hot body, the peak value being attenuated and displaced towards the infrared with decreasing blackbody temperature. More precisely, the wavelength ~p of the peak intensity for blackbody radiation is inversely proportional to the absolute temperature, i.e.

~P-

const

T

(4.4)

where the proportionality constant is 2897 gm K (Born, 1952). Of course, this finding has been obtained by differentiating the Planck function with respect to the wavelength, and equalising the derivative to zero, i.e. 3I(v,T) /3~ = 0. The highest the body temperature, the shortest the peak wavelength, and the lower the temperature, the longest the peak wavelength. The tungsten filament of a incandescence lamp has a temperature (or, better, the colour temperature i.e. the temperature of a black body having the same strength of colour) around 2800 K; its spectrum falls within the solar spectrum, with a lower spectral radiance, but with the maximum shifted to around 1 gm, in the near IR region. The candle flame has some 1700 K, its spectrum has a lower spectral radiance, begins in the visible and extends into the IR region where the peak value is found at 1.7 gm. At 800 K hot bodies are faint red and below this temperature they emit only invisible radiation in the IR region, with a lower power; at 800 K the peak is at 3.6 gm. At room temperature the spectrum has a still lower power, ranges between 3 and 100 gm, and the peak is near 10 gm. As the power emitted by a body depends upon T, a remote measure of this power can be used to detect the body temperature, which is for this reason called the radiometric temperature,.

4.2. RADIOMETRIC TEMPERATURE The radiometric

temperature Trad is the temperature deduced from the flux of radiant energy, per unit surface and unit time, spontaneously emitted by a body with temperature T by means of the infrared emission, according to the Stefan-Boltzmann law which states that the flux density emitted by a blackbody is proportional to the fourth power of the absolute temperature, i.e.

106 q~ = ~ T 4 where T

(4.5)

=

Zradso

that the temperature can be written in explicit form

Trad = ~ / q)~3

(4.6)

and r~ = 0.286x10 -10 cal cm -2 min -1 K -4 = 5.67 erg cm -2 s -1 K -4 is the Stefan constant. The flux of electromagnetic radiation emitted in the

IR spectral

w i n d o w can

be m e a s u r e d with a radiometer or a bolometer and furnishes an experimental observation of the surface temperature, without mechanical contact with the surface. This aspect is very important especially in the case of delicate surfaces that cannot be touched with contact thermometers (e.g. frescoes, where it is not possible to attach the sensor with glue) or for remote monitoring (e.g. ceilings, vaults) or whenever the contact thermometer m a y alter the surface temperature (e.g. w h e n the surface is lighted, the sensor shields the point of contact and measures the temperature of the surface in the shadow, instead of the lighted one) or the observed object is mobile. The radiometric temperature of a body is a function of several variables, some of intrinsic nature, e.g. the albedo and the thermal diffusivity of the body, and some due to atmospheric forcing, e.g. reflection of long wave radiation, air temperature, humidity, aerosols, cloud cover, heat or moisture accumulated or lost d u r i n g past meteorological conditions. This makes it difficult to obtain accurate observations of

Trad. The

radiometer (see Chapter 10) can be usefully

applied to compare relative temperature levels and to diagnose anomalies in the internal

conductivity

(e.g.

detachment

of frescoes

or

the

presence

of

h e t e r o g e n e o u s materials) especially during dynamic changes of t e m p e r a t u r e . Indoor m e a s u r e m e n t s are m u c h more easy and reliable than outdoor infrared observations. The Stefan-Boltzmann's law in the above form is valid for an ideal black body, w h e n both the absorptivity and emissivity are equal to 1. In practice, real bodies have some departures from this theoretical formulation, and a 'grey' correction should be added, which takes into account for the of the bodies; therefore, the grey emissivity r

relative emissivity

should be explicitly written in the

Stefan Boltzmann equation, i.e. = r r~ T 4.

(4.7)

107 The values of e are in general close to unity for most of the natural materials, but much less for polished metals, as we will see in Chapter 10. As E varies with the physical characteristics of the surface, e.g. wet or dry, attention must be paid in order to distinguish apparent variations of T from changes of e. The flux of radiation arriving from a surface can be divided into two components: one is the radiation emitted by the surface, and the other is the reflected, emitted from other bodies, giving rise to an apparent greater value of ~P. Dividing these quantities by the incident flux, the following identity is found a+R=1

(4.8)

where R is the reflectivity of the surface. This equation shows that good reflectors are bad emitters, and vice-versa; e.g. polished metals are good reflectors but bad emitters; candle smoke has an emissivity close to 1 but a very bad reflectivity.

4.3. ANGULAR DISTRIBUTION OF RADIANT EMISSION OF BODIES The radiant intensity I(0) (i.e. the flux per unit solid angle) emitted in any direction from a unit radiating surface varies as the cosine of the angle 0

between

the normal to the surface and the direction of the radiation ( L a m b e r t law), i.e. I(0) = I(0) cosO.

(4.9)

At the same time, the radiometer sees the observed surface under a given solid angle, determined by the diaphragm which characterises the geometry of its optics. When the instrument is normal to an extended surface, it sees the portion So of it; w h e n it is rotated by the angle 0, it sees a greater portion of surface, i.e. S(O) = S o / c o s O , although tilted by the angle 0. As a consequence, the flux of

radiant energy entering through the diaphragm is

(0) = I(0) S(O) = I(0) cos0

So cos0

= I(O) So = 9 (0)

(4.10)

i.e. the luminance (or radiance) of a radiating surface is independent of direction and appears equally bright at all angles. A surface exactly obeying this law is called

108 Lambertian. The ideal black body is Lambertian, and m a n y bodies are Lambertian,

at least in a first approximation. For this reason the Sun and the Moon have the appearance of a flat disk and not of a three-dimensional sphere, and golden or painted domes appear flat. For this reason Vittori and Mestitz (1975) suggested that in the four brass horses of the Basilica of San Marco in Venice, which are plated with gold and present m a n y narrow scratches, the network of scratches was the result of the delicate work of a skilled engraver to gain the third dimension. However, other surfaces may present some departures from this law. The wings of butterflies which change colour with the angle of sight, and Persian carpets with changeable luminance, are well known examples of non-Lambertian surfaces. It might be useful to remember that radiance (W m -2 sr -1) is a radiometric unit which measures the energy emitted in the unit time (Watts) from the unit surface (square meter) in the unit solid angle (steradians, sr) and luminance (lm m -2 sr -1) is a photometric unit which measures the intensity of the light which is sensible to the eye (lumen) emitted from the unit surface in the unit solid angle; both are a measure of the power radiated from t h e u n i t area into the unit solid angle. A n o t h e r consequence of the Lambert law of emission is that surfaces differently exposed, even if in contact with air at the same temperature, assume different temperatures as a result of the radiative balance. In fact, horizontal surfaces facing the clear sky emit IR radiation receiving back only a small portion of the outcome; on the other hand, vertical surfaces see on the horizon an infinite optical air mass, so that the IR outcome equals the income. For this reason dew forms early on the horizontal top of cars, which faces the sky and cools d o w n more rapidly than the vertical broadsides.

4.4. ATTENUATION OF LIGHT IN THE ATMOSPHERE Corrections to the observed q)should be made also to take into account the attenuation of intensity caused by atmospheric absorption, and in particular by the water v'fipour, CO2 and other gases, smokes and atmospheric aerosols. The atmospheric attenuation is exponential and selective for every w a v e l e n g t h k ( B o u g u e r - L a m b e r t law), i.e. I(k) = Io exp(-~z(k)m)

(4.11)

109 where Io is the intensity of incident radiation (out of the atmosphere), I(;~) the intensity after passing through the optical air mass m, and 0~(~) the absorption coefficient. This law can be expressed also in terms of the optical path length x t h r o u g h the absorbing substance, instead of optical air mass m. This formula shows that a white solar beam, when crossing the atmosphere, has its spectral components attenuated in a diffrent way o~(K), and the final mixture of colours d e p e n d s u p o n the optical air mass m, and the latter is a function of the sun height Ho, or its zenith angle Zo = 90 ~ Ho, i.e. m = secZo.

(4.12)

This is the reason w h y the daylight changes continually colour, from sunrise to sunset. When radiation is incident upon the atmosphere, or a liquid or a solid body, part of it transmitted, part absorbed, and part is reflected. The ratio of each of these quantities to the incident flux, which are respectively called transmissivity

Tr, absorptivity A, and reflectivity R, must add up to unity, i.e. Tr + A + R = 1.

(4.13)

This formula holds in average, as well as for the spectral quantities for any value of wavelength K, included the visible or thermal infrared range.

4.5. DAILY AND SEASONAL CYCLES OF SOLAR RADIATION ON A SURFACE Natural

light falls on external

monuments

and p e n e t r a t e s

through

windows: it is composed of direct radiation, which forms the solar beams, and

diffuse radiation, which is scattered by the sky in every direction. The diffuse component ranges from 20-30% of the total income in clear days, to 100% in overcast ones. The scattering is a function of the wavelength (this is the reason w h y the sky appears blue), and the very energetic photons in the ultraviolet band are the most scattered ones, so that they hit also objects not illuminated by direct light. For every latitude q and day of the year, defined by the solar declination 6o, the direct light can be computed by means of the coordinates of the sun: the

II0 altitude over the horizon (i.e. solar height) Ho and the azimuth Ao i.e. the angular

distance b e t w e e n the vertical circles containing the zenith

and,

respectively, the sun and the south point. The astronomical formulae to compute these coordinates are: sinHo = sin6o sin$ + cos6o cosr cost

(4.14)

cos6o sinz

sin Ao = ~

1- (sint~o sinr + cost~o cosr

(4.15)

cosz)2

where the hour angle T = 180 ~ t/12 is computed from the time t, in hours and tenths of hour, from or to the culmination of the sun, i.e. from or to the true mid-day. This means that t is negative in the morning, vanishes at noon and is positive in the afternoon. The solar declination 3o(j) for the j-th day is found in astronomical ephemerides

tables or, for e n v i r o n m e n t a l p u r p o s e s ,

can be

computed with the simple approximation 2~j

3o(j) = So(0) cos 365

(4.16)

where the j-th day is computed after the winter solstice and 3o(0) = -23 ~ 27' is the declination of the winter solstice. In this formula the earth orbit around the sun is supposed circular. The mean of the Earth orbit eccentricity e~ is ee = 0,0167; the eccentricity is found dividing the distance between the foci by the length of the major axis, and a circle is the limiting case as e~ approches zero. The error of this approximation

is small (some primes) and negligible except for precise

astronomical calculations. From the above formulae it follows that: *

at solar noon, when the hour angle ~: is zero, cost = 1 at any latitude, and the

9

zenith angle Zo (defined as Zo =90 ~ Ho) is Zo = ~ - 6o; at sunrise and sunset (i.e. Ho = 0), at any latitude (except the poles), cosZo=0, and 2~: is the daytime length expressed in hour angle;

9

the daylength DL =2~: can be computed under the condition cos~: = -tanq tan6o, i.e. DL = (24/~:) arccos(tanr t a n ~ ) (hr).

Solar beams are represented by straight lines coming from the sun and passing through a window; their intercepts on the opposite wall represent the light spot. The envelope of these spots describes the areas affected by the direct solar income

111

during the course of the day as discussed below.

intensity Ip of the solar radiation (also irradiation) falling on horizontal, vertical, or arbitrarily inclined planes

The flux density per unit time or called

(Robinson, 1966; K o n d r a t y e v , 1969; Bernardi and Vincenzi, 1994) facing the direction

Ap ( c o m p u t e d from the m o m e n t of the true noon, i.e. the south) and

inclined by the angle ]3 with the plane of the horizon, is

Ip = Io {cos// (sin6o sinq + cos6o cosq cos1:) + + sin]3 {cosAp [tanq (sin6o sinq + cos6o cosq cosr

- sin6o secr ] + (4.17)

+ sinAp cos6o sin~: }} where

Io is the intensity of the solar beam (near the surface) and the irradiation

on a h o r i z o n t a l or vertical plane is o b t a i n e d by setting 13 = 0 ~ or ]3 = 90 ~, respectively. An example of the hourly variation of the flux density of the solar radiation on the h o r i z o n t a l

a n d vertical surfaces w i t h v a r i o u s o r i e n t a t i o n s

is here

discussed for the latitude q = 45 ~ In order to show the influence of the absorption due to the optical mass, first let us s u p p o s e that the a t m o s p h e r e is perfectly transparent. At the winter solstice the sun rises at Ao = 124 ~ i.e. close south-east (135 ~ and sets at Ao = 236 ~ i.e. close south-west (225~

and the vertical surfaces

facing these two directions receive the m a x i m u m flux of energy; at noon the solar height is low, i.e. Ho = 90 ~ Zo = 90 ~ - (~ - ~o) = 22~ and the energy income on the vertical surface facing south is greater than that on the horizontal plane. At the equinoxes, sunrise and sunset occur just at east and west, and w i t h a perfectly transparent a t m o s p h e r e the vertical surfaces facing these two directions receive the m a x i m u m flux of radiation. At this particular latitude, at noon the solar height is Ho = 45 ~ so that the solar energy which falls on the vertical surface facing south equals that on the horizontal plane. At the s u m m e r solstice surprise and sunset occur respectively at Ao = 57 ~ i.e. m i d w a y b e t w e e n north-east and east-north-east and Ao = 303 ~ i.e. m i d w a y b e t w e e n north-west and west-northwest; at noon the sun is high, i.e. Ho = 68 ~ so that the solar energy flux which falls on the vertical surface facing south is less that on the horizontal plane, and at this particular latitude the flux on the horizontal equals the flux at the winter solstice on the vertical surface facing south and vice versa. If the same calculations are m a d e taking into account the attenuation of the solar radiation w h e n it passes t h r o u g h the optical air mass which increases with decreasing solar height according to the above formulae, the results are quite

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T i m e (h) Fig.4.1 Hourly variation of the flux density of the solar irradiation Ip on the horizontal H (dotted line) and vertical surfaces (full lines) with various orientations (principal compass directions, thick lines; secondary, thin lines) for the latitude q~ = 45 ~ (a) Winter solstice; (b) equinoxes; (c) summer solstice.

113 different, as shown in Fig.4.1. At the winter solstice (Fig.4.1a), the declination 3o is at is m i n i m u m and the optical thickness of the atmosphere is so important that w h e n the sun is very low on the horizon (i.e. south-east and south-west), and the light beams perpendicular to the vertical surface, the fraction of energy reaching a vertical surface faced to the sun is less than the energy which arrives at noon, w h e n the beams arrive slant, but after having passed a shorter optical length. The other vertical surfaces receive a smaller flux of energy, which is the combined effect of the atmospheric attenuation and slant incidence of the beam. The vertical surface facing south receives the m a x i m u m flux density, and the horizontal plane a very minor value. At the equinoxes (Fig.4.1b), 3o = 0, and the absorption is less. Near sunrise and sunset the atmosphere causes an important attenuation (but less than in winter) and then the maximum flux density on the vertical surfaces facing the sun remains more or less the same, reaching the m i n i m u m at noon where the geometric effect of the slant beam dominates over the minor atmospheric attenuation. On vertical surfaces not faced to the solar motion (northern sector from west to east) the flux density is much less. The flux density on the vertical surface facing south equals the flux density on the horizontal plane. This is obvious at noon, when the solar altitude is Ho = 45 ~ forming the same angle with the horizontal plane and the vertical surface; on the other hours, for the vertical surface, the advantage of receiving the beam with an angle approaching the normal is substantially compensated for the atmospheric absorption. At the summer solstice (Fig.4.1c), the declination 6o is at is m a x i m u m and the optical thickness of the atmosphere is further reduced. However, the height of the sun over the horizon becomes so important which is the dominant factor, except near sunrise and sunset. In fact, the flux density increases from sunrise as far as east, then decreases and reaches the m i n i m u m at south and continues symmetrically till sunset. The elevated solar altitude makes m a x i m u m the solar income on the horizontal plane. The flux on the south surface is low and at noon is close to the value reached at 6.30 a.m. on the north-north-east or at 17.30 on the north-north-west. A comparison between the plots at the two solstices shows that at noon the summer flux on the vertical south Surface is greater than the winter flux on the horizontal plane at the same hour, and the s u m m e r flux on the horizontal plane at noon is even more greater than the winter flux on the vertical surface facing south. This example shows how the solar income is affected by the atmospheric optical length, although in clear sky. If the atmospheric attenuation originated by the seasonal change of the local climate (e.g. haze persistency, cloud cover) or pollution, the departures are also

114 '~>.~ 35000 30000 ~ , 25000 20000 0

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Sloping Angle Fig.4.2 The daily total income It of the solar radiation on a slant surface oriented in the eight cardinal directions is represented against the sloping angle r for the latitude = 45 ~ (a) Winter solstice; (b) equinoxes; (c) summer solstice.

115 greater. It is also possible to integrate over the whole daytime the flux density of solar radiation for a surface arbitrarily oriented or slant (Fig.4.2). At the winter solstice the dominance of the southern sector is evident. At the equinoxes, the m a x i m u m instantaneous values of irradiation shown in Fig.4.1b were similar for the whole southern sector from east-south-east to west-south-west, with a slight m i n i m u m on south, and the surfaces facing east and west having slightly less than south. However, the daily total solar income on these vertical surfaces (i.e./3 = 90 ~ shows a different situation: the south surface receives the m a x i m u m total and the east and west ones half of it. On the other hand, when ]3 tends to zero, all the slant surfaces tend to the horizontal plane and the differences tend to vanish. For slant surfaces facing south and south-east or south-west, the total income reaches the m a x i m u m respectively at the slopes ]J = 45 ~ and ]J = 40 ~ The whole southern sector has convex plots with the m a x i m u m at a sloping angle which tends to vanish at the east and west orientations. The east and west plots are still convex but close to a straight line. The northern sector has concave plots, with the total income decreasing w h e n the slope increases. The surface exposed to north is no more reached by direct solar radiation when ]3 > 45 ~ At the summer solstice all the integral values, except the northern sector, are quite similar.

4.6. WHAT IS THE COLOUR OF NATURAL LIGHT? Sunlight is optically white, as it is composed of a balanced mixture of all the colours, that is all the wavelengths in the spectrum of incident light. However, w h e n the solar r a d i a t i o n p e n e t r a t e s the a t m o s p h e r e , the w a v e l e n g t h s c o r r e s p o n d i n g to violet and blue resonate with the oxygen and n i t r o g e n molecules which disperse them. Looking at the sky on a clear calm day, the characteristic interstellar blackness of empty space can not be seen, but there is, instead, an intense blue, because the h u m a n eye is much more sensitive to this colour than it is to violet. The lighter blue or the whitish colour of the sky depends upon the presence of minute drops of water of various diameters (which are even more evident w h e n there are clouds), given that the dispersion is not selective but distributed over the whole spectrum. The band of solar radiation is initially white, but when part of the blue has been subtracted from direct sunlight and diffused in all directions by the air molecules, colours slightly change and the white objects which are far away, e.g. the snow-caps of distant mountains, slightly

116 take on a complementary yellow, orange or red. This is what happens every day as the sun changes the height and the light beams cross a variable optical thickness of the atmosphere. The colour change is m i n i m u m when the sun is near its zenith (midday, summer solstice) while it is at its m a x i m u m when the sun is near the horizon (sunrise and sunset, winter solstice), given that the rays are at a grazing angle and cross a thicker atmospheric layer. Pollution increases the opacity and the colour change. The sun itself, which is very white, seems to take these colours that correspond to the progressive detraction of the blue varying from brilliant yellow to purple with the time of day and the season. Not only the light changes colour with the day and the season, but also the eye has a perception of the colour which depends upon the light intensity. When the intensity is high, the objects appear lighted with a w a r m e r spectrum, i.e. displaced towards yellow and red; when the intensity is low, the object appear lighted with a colder light, e.g. objects lighted by the moon appear with a bluer colour. This different response of the eye is called Purkinje effect.

4.7. ARTIFICIAL LIGHTING, OPTICAL FILTERS AND OPTICAL FIBRES The variability of the sunlight colour poses a question, which is very i m p o r t a n t w h e n works of art need artificial lighting 'What kind of lamp will give the same light as the sun?' This question is not a realistic one, in that a lamp does not vary during the day, from red at sunrise to the golden white at noon and red again at sunset. A lamp does not take on the light blue of fog, nor does it d a r k e n as the sky darkens with clouds, neither does a lamp take on the transparency of the drops of water when it rains, nor does it change tone with the various seasonal changes in the vegetation, nor does it reflect the white of the snow. Every lamp, characterised by a different shade can only reproduce one of these particular instantaneous colours, b u t a lamp can never reproduce the same dynamic shades of sunlight. However, in front of a fresco, or in an exhibition room, it is necessary to choose the type of illumination to adopt. Would it be better to choose a light giving the same colour of a candle, a torch, the sun at dawn or at another precise time? This is a static sensation that must be chosen, and once realised, it remains unchanged. For illuminated works of art, however, the choice of the appropriate or inappropriate light depends u p o n two requests: (i) a good reproduction of

117 colours, (ii) the minimum damage to artefacts, either directly or indirectly; e. g. avoiding excessive intensity and especially direct exposure to U V or IR radiation which may provoke alteration or discolouring, while the indirect effects are caused when lamps generate convective cells because of the heat they dissipate, thus leading to deposition of particles which stick on the surface of the work of art. All sources of light have their own emission spectrum, including in different proportions the U V band (which should, therefore, be filtered above all for organic material), and the IR that forms a considerable part of the total light spectrum. The harmful effects of U V and IR radiation vary with the type of material sensible to these wavelengths, and it is virtually impossible to make a universally valid quantitative comparison of the damage resulting from the intensity of the illumination. Any effect would be typical for each material and different source of light. In such cases it is necessary to determine whether it is advisable to substitute one source of light with another, and whether, for example, the situation is improved by substituting partially or wholly the sunlight with artificial light. The answer only depends upon how much U V and IR radiation can be filtered. In terms of conservation, the best lamp is the one

with minor U V and IR bands, i.e. the most dangerous wavelengths, and the less heat dissipation. A comparison of the overheating caused by different kinds of lamps is shown in Fig.4.3 which considers only the IR

component.

With

reference to colour, it must be remembered that the human eye can only visually discern a certain spectral distribution of sunlight, so that the same spectrum should be present in the source of artificial light. Incandescent lamps (i.e. traditional tungsten filament ones and halogen lamps) have a continuous spectrum, with an intensity distribution which is different from sunlight because of the lower emission temperature which favours warm tones. Incandescent lamps are often preferred for their continuous spectrum, with a warm tonality midway between the solar light and the candle, although they have an important IR emission. When a spotlight is switched on, the energy transferred to the illuminated area warms the surface of the artefact (Fig.4.4): part of heat penetrates into the artefact warming it, part is returned back to the air, part forces evaporation, according to the energy balance (see Chapter 7). There is, subsequently, a considerable reduction in the relative humidity both in the air enveloping the object, and in the internal pores. A painted wood tablet looses some vapour and curl up in different directions; flakes of colour drop off the surfaces which is experiencing differential expansion; microfractures appear

118

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2.5

~

2

~

1.5

>

1

0

HL

MMH

0.5 0

10

20

30

40

50

60

70

80

Time (min) Fig.4.3 A comparison of the overheating AT caused by different kinds of lamps, lighting with 500 lux a blackened aluminium target. TIL indicates a tungsten incandescence lamp, HL a halogen lamp, MMH a lamp obtained with a mixture of metal halides. The last has been used to illuminate the Giotto and the Sistine Chapels.

16.8

17.5 17.1

Fig.4.4 Hot spot generated by the incandescence lamps that years ago were used to illuminate the Leonard's Last Supper, Milan. Now the lighting system has been changed with a more diffuse and cold light. Measurement taken the 9 May 1982. (after Camuffo and Bernardi, 1991, reprinted by permission of the Bollettino Geoflsico)

119 on the surfaces as the dehydration continues on the objects which are porous or made of organic material such as ivory. The excitation sources such as fluorescent lamps have a low IR dissipation, and for this reason they are said to give cold light. This is a clear advantage; however, they have a discontinuous spectrum, very different from the solar one, with some chromatic lines missing while others may be excessive with some unbalanced effects which alter colours.

Sometimes they are appreciated for the

absence of IR, more often they are rejected for the colour changes. They have a higher UV emission in comparison with incandescent lamps, which may have negative effects in the oxidation, cross linking and fading. However, now some fluorescent lamps with anti-UV filters incorporated are commercially available, so that this problem is eliminated with an appropriate choice of the lamp characteristics. Joining a cold fluorescent light with a warm one does not mean that this combination will give the same spectrum as sunlight, but will only give a light with a superposition of spectral lines giving excessively w a r m or cold tones with some gaps due to missing lines, so that the overall effect is one that might, in the first instance, trick the h u m a n eye but which does not give the full chromatic picture. It is, however, impossible to add a missing line, although it is always possible to balance a spectrum with an excessively dominant line, toning d o w n the d o m i n a n t colour with a complementary colour. For this reason, the high density discontinuous spectra are preferable, while the ones which have too m a n y missing spectral lines should be discarded. A c o m b i n a t i o n of two complementary lights is unadvisable also because it is very difficult to balance two sources, and the balance changes as the lamps age. Such a combination also creates a double shade in two different colours and, also, the IR emitted and the heat dissipated by conductivity and advection are, on the whole, always greater than those from one source of light having the same luminous efficiency. C o n s i d e r i n g the d a m a g e that excessive illumination can cause in an exhibition room, direct sunlight should be avoided. The daily apparent solar motion induces sunlight spots to describe curved bands on the wall opposed to w i n d o w s (or also in the wall p e r p e n d i c u l a r ) a n d these bands move with the season: they are higher in winter and lower in summer (Fig.4.5). A very common m e t h o d used to intercept the light beams is to apply curtains to w i n d o w s . However, when curtains are hit by solar radiation, their temperature rises: the air coming into contact with them w a r m s and a convective motion is generated. This airflow is responsible for soiling the portion of wall above the windows, or

120

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Fig.4.5a Spots of direct light in the Giotto Chapel, Padova, during the winter solstice. The upper band shows the daily displacement of the sunlight spot through the three-mullioned window on the facade and the lower bands the spots through the first, second and last side windows (the others are shielded by trees). The Chapel is oriented with the facade facing 240 ~ The sunlight has been shaded for a long time with curtains, and now the problem has been solved adding an amber glass outside the old windows. The external pane has been applied at a distance of some 10 cm from the window, leaving a free space on the bottom and the top, to allow a free circulation of air and avoid the green-house effect. The external position helps to protect the stained glass against the adverse meteorological factors.

Fig.4.5b Spots of direct sunlight in the Sistine Chapel calculated for December 15. The windows are in stained glass and the light passing through is partially dispersed. However, as the effect of light is cumulative, a second protective pane, or a polyester film optically treated with the inclusion of metals and other pigments should be applied. (After Camuffo and Bernardi, 1986 reprinted by permission of the Boltettino dei Musei e Gallerie Pontificie)

121 also the ceiling. Another problem with curtains is that dust and bacteria deposit on them; bacteria grow, and when curtains are shaken off for closing windows, they form a dangerous clouds of dust and bacteria. The practice of keeping some areas too much illuminated in order to light up the furthermost parts of the room, is imprudent. Diffuse sunlight should be reduced w h e n it is too intense, or integrated with artificial light in the areas where it is too weak. The goal is to reach everywhere a h o m o g e n e o u s , soft lighting. In the sunlight, the harmful (and optically useless) parts of spectrum outside the optical range should be filtered out. This can be easily done by using optically selective glass panes or applying a filtering film over the panes. However, it may also be necessary to dim the visible light, although this is a particularly delicate problem because it means that, in practice, a reflecting or coloured glass must be used. A reflecting glass is in principle similar to a mirror, but one which has a chromatic tone alters, at least slightly, the tone of sunlight, and the same problem applies to coloured glass. Although everybody appreciates the gothic cathedrals which have large stained glass windows to colour the austere interiors, the use of new coloured glasses is not accepted, especially in an ambient decorated with frescoes or pictures. Several colours exist, but in practice the choice of a coloured pane is necessarily limited to two possibilities: grey and amber. Grey is not properly a colour but a balanced toning down of the whole spectrum, so that none of the single colours dominates in that there is only a light, general attenuation; grey is the first step towards black, which is the total absence of all colour. This choice is probably the less popular, but is certainly the most impartial. It does not alter the colours inside the room but only sunlight intensity coming from the exterior, as if it were covered with a dense layer of clouds; almost a psychological trick played on the weather. Using an amber pane of glass might seem, at first sight, absurd, because this really does alter colours, toning down all of them, except those of the same amber tone which are reinforced. However this is, in reality, the same thing that happens, as described earlier, to the sunlight crossing the atmosphere, i.e. light filtered through an amber pane is similar to sunlight a short time after d a w n or before sunset. An amber glass might be considered, therefore, responsible not for falsifying colours, but rather, for falsifying time, so that in the morning the light inside is similar to that outside a few hours earlier and vice versa in the afternoon. It falsifies the time of the day and, if it is raining outside, it falsifies also the weather. The final choice, however, depends on how adequately the artificial

122 light complements the natural light from windows, so that the overall result is the most pleasant one. Lamps placed inside the exhibition cases turn these into small greenhouses because the panes allow the light in the visible range to pass through but not so the infrared, as we have seen in Chapter 1. Given that the IR emission is considerable, even with the so-called cold lights, heat is trapped in the exhibition case and results in overheating the objects and in dropping the relative humidity. A good method, w h e n e v e r possible, is to place lamps outside the case and transport

light inside with optical fibres, which are m a d e of a glass core

s u r r o u n d e d by a cladding having a lower refraction index. A ray will be transmitted only if the glass is transparent to this wavelength and if the fibre is able to trap the light beam in the core by total internal reflection, which is d e t e r m i n e d by the combination of the refractive indexes of the core and the cladding. Most glasses are opaque to the UV region for some strong absorption bands arising from electron excitation of two types: i.e. when electrons are excited from the valence band to unoccupied states in the exciton or the conduction band, or w h e n electrons are transferred from the shells of one ion to the shells of another ion. The absorption in the IR especially occurs as a result of atomic vibrations in a molecule that has a dipole momentum, which has a fundamental vibration mode in the IR spectrum (Varshneya, 1994), as e.g. the H 2 0 molecule. If the optical waveguide is transparent to the optical b a n d w i d t h and is opaque to both the ultraviolet and infrared edges it acts as a filter which supplies light only in the visible spectrum, otherwise the UV and IR bands can be cut out inserting appropriate filters between the light source (e.g. a halogen lamp) and the fibre. Then the light is concentrated with a lens and supplied to the fibre. This beam, c o m p o s e d of pure light in the visible region, will be transported with the w a v e g u l d e into the show case, and then the beam is opened again with another lens in order to illuminate the object within a desired light cone.

4.8. DETERIORATION TO WORKS OF ART CAUSED BY LIGHT Light causes several mechanisms of degradation, e.g. photo oxidation of gaseous pollutants which form a very aggressive environment, chlorophyll synthesis and possible development of algae (especially in prehistoric caves, Etruscan tombs or other dark rooms) and other forms of vegetation, as well as direct damage to objects. Direct damage severity depends upon several factors:

123 photon energy (i.e. the wavelength of the spectral line), total number of photons as well as material response. This changes with the chemical composition and crystalline structure, type and concentration of the molecules, optical properties of the surface and the subsurface layer, penetration depth, interactions with the molecular structure and electronic state. In the simplest case, absorbed light can be transformed into heat, which affects temperature and relative humidity, and may induce internal stress. Paintings are more intensely illuminated and heated; Fig.4.6 shows the heating of the panel 'the Madonna d'Ognissanti' by Giotto (Uffizi Gallery, Florence), compared with the wall and floor temperature. The wall close to the painting and the floor have a gradual rise of temperature AT which reaches some 1.5~ after 6 hours, with an average heating rate equal to 0.25~ lower thermal capacity, is overheated by a AT = 3~

the panel which has a after 4 hr, with 0.75~

heating rate, i.e. tree times faster. 21 Painting

20 ~ o

v

19 =I ^ _

18

Wall

[..., 17

16

0

3

6

9

12 Time

15

18

.21

24

(h)

Fig.4.6 Heating of the panel painting the Madonna d'Ognissanti by Giotto (Uffizi Gallery, Florence) compared with the wall and floor temperature. The 3 February 1993. Light can alter the crystalline or polymeric structure. Many organic molecules are sensible to this form of degradation, and damage occurs when the amount of energy absorbed by a molecule exceeds the bound energy. For this reason, the sensitiveness of a material increases with the p h o t o n energy, suffering the most severe damage with the shortwave U V light. The most evident effects are polymers ageing, reduction of the plastic and elastic properties, colour fading, textiles yellowing, wood degradation. An extensive presentation of

124 the present day knowledge in this matter has been made by Wypych (1995). A change of colour relates to changes in the chemical composition of the material and discolouring is the main problem of water colours, ink drawings, ancient manuscripts, coloured textiles. Oxidation of keratin exposed to U V radiation is responsible for wool yellowing and decrease in tear and tensile strength and abrasion resistance. Wood is very sensible to UV radiation, and the weathered outer layer increases sensitiveness to abrasion, having loosely connected fibres. Although the UV penetration is limited to a depth of 75 ~tm, the damage progresses in depth and after one year exposure degradation can reach 3 mm, but one century is necessary to double the depth of the deteriorated layer. Surface coating may protect wood, and in the case of painted tablets the problems are substantially two: the degradation of dye, and the stress experienced by the wood after the temperature and the equilibrium humidity change. In special exposition rooms, several attempts have been made to evaluate light levels and types, and some authorities have r e c o m m e n d e d lighting standards between 50 and 200 lux to limit fading, yellowing and breaking of mechanical bonds of dyes. However, there is no known level of lighting which has been proven to be safe for colour change. The real problem is that damage progresses with the cumulative number of photons which have reached the surface (and this involves light intensity, lighting duration, number of repeated cycles) and the energy of individual photons. The energy is associated with the wavelength, and the most obvious conclusion is that the whole visible spectrum should be allowed, but harmful UV and IR should be avoided with the use of appropriate filters. In addition, it should be useful to preserve in the dark artwork which suffer fading (e.g. historical robes, tapestry and other coloured tissues, water coloured drawings, gouache painting) and light them only gently, during the visiting time, as for the Leonard's Virgin and Child with S. Anne and St. John the Baptist in the National Gallery, London. This principle can be usefully extended preserving the whole museum or gallery in the dark and lighting exhibits only when people really want to watch them. This goal can be attained by placing in front of each painting or show-case an IR proximity sensor which detects approaching persons and temporarily switches-on a local gentle lighting, so that light follows paths and stops of visitors. The intermittent use of soft light, when necessary, is different from the dangerous practice of lighting panels or paintings for few minutes with powerful lamps which are turned on every time a visitor introduces a coin. Every painting is composed of a number of different layers (i.e. a colour coating, a preparation

125 base, a canvas, or a wood tablet, or a wall) which are bad conductors, so that the energy of the light beam is not transmitted or dissipated at the same rate in all the layers. When the lamp is turned on, the pictorial coating becomes overheated and expands generating mechanical stress with the base which has not yet been w a r m e d up, causing microfractures and partial detachment of the coating, which is transformed in tiny flakes, raised at the edges like the skin of a snake. After some delay, the heat reaches the preparation base and then the underlying frame, causing a dangerous surface stress every time the light is turned on/off, which tends, in the long run, to detach the coating from the support. This fatigue and ageing are important for painted tablets, paintings on canvas, frescoes, wood, ivory etc., where the mechanical stress is much more dangerous than fading. Flash light is usually forbidden in museums. The principle is theoretically sound, but in practice each flash has a very short duration so that the energy transferred to the objects is so small that its contribution is substantially negligible. For instance, considering that flash light may reach the intensity of daylight and usually has a duration from 1/1000 s to 1/50,000 s, then respectively 1000 or 50,000 flash pictures are equivalent to one second solar lighting as far as photon accumulation is concerned. Regarding heating, their cumulative effect is absolutely negligible, the energy being supplied by means of several very small contributions provided after time intervals which are extremely long compared with the short flashlight duration; consequently, the heat transferred is easily dissipated and never overheating is reached. Flashlight is much more dangerous for the guardians' eyes, and might constitute a real risk only for extremely delicate objects. If some paintings suffer for light accumulation, a much more substantial advantage can be achieved closing curtains and w i n d o w shutters as soon as visiting time is up. The position of the sources of artificial light is very important. In a closed environment the air is naturally stratified into layers with different densities, corresponding to the temperature increase from the ground up to the ceiling. The air heated by lamps starts to rise, forming a convective vertical cell, which develops u p w a r d s up to the warm air reaches the ceiling or another air layer with a lower density. The bottom limit of the cell is determined by air with higher density, and for this reason, in a naturally stable environment, the convective cells cannot develop below the heat source. Therefore, lights placed high up leave the paintings in the underlying space undisturbed. In the case of frescoed ceilings, it is better to keep them slightly warmer than the underlying air, so as to form a kind of cushion against thermophoresis and inertial deposition, as well as

126 putting the lights (which should not dissipate too much energy) fairly low so that the ascending currents do not reach as far as the vaulted ceiling. The energy dissipated by incandescent lamps creates strong convective currents above the sources of light inside the room, thus continually renewing the air near the surface and can, therefore, generate some turbulence, which is further increased by the presence of visitors. This favours inertial deposition of the larger particles. When the inertial force of these particles exceed the viscous force of the air that transports them, the particles deviate from the fluid trajectory and impact on the surface and are thus captured. Even in the event of a moderate laminar flow, the coarseness or roughness of the surface can locally perturb the trajectory of the particles, causing the same type of aerodynamic capture that, in the long run, is very effechve. The difference in temperature between the heated air and the colder surfaces also increase the deposition rate of the particles suspended in the air. This subject will be more widely discussed in Chapter 8. It may be useful to remember that light is not the only responsible for fading: several pigments and traditional colouring materials are also attacked by ozone, or nitrogen oxides associated with photochemical smog. Photochemical reactions involve nitrogen oxides (NO and NO2) and photons to generate ozone (03), the OH- radical and other products including the irritant peroxyacetylnitrate (PAN) (Andrews et al, 1996). Photochemical smog is important not only in the well known cases of Los Angeles and Athens, but in many other sites, especially where the solar radiation is intense and in the proximity of an industrial area. In the Correr Museum, Venice, indoor peaks of some 60 ppb 03 were found in summer, so that simple measures were taken to stop its penetration: 03 concentration was reduced by 2/3 simply by closing windows and stopping other uncontrolled inflows of external air during the hours of photochemical smog generation. Ozone and other photooxidants show a cyclic variability which follows the solar radiation cycle, with the maximum concentration during the heart of the day. However, in coastal areas ozone peaks have been found also during the night-time, and these where loops associated with the return of photochemical smog (formed during the daytime) after the change of the breeze. The practice of filtering the air should be recommended to art galleries with sensitive paintings or textiles, but a substantial advantage can be taken by simply taking into account the cyclic character of this particular kind of pollution as we did in Venice. Finally, a short comment on biodecay induced by light. Phototrophic microorganisms, such as algae and cyanobacteria, use sunlight as energy source

127 for growth, and release oxygen during the photosynthetic process. Their infestation is not limited to carbonatic materials, as their carbon requirement is supplied by the fixation of atmospheric CO2 (Ortega-Calvo et al., 1991). The role of phototrophic algae and cyanobacteria, growing even under low light intensities, needs to be stressed. The photosynthetic microflora causes detrimental aesthetic effects by the accumulation of various pigments (e.g. chlorophyll, carotinoids) and provides in certain cases the nutrient basis for subsequent microbial infections by bacteria and fungi and their biodeteriorating activities. Other details of biogeophysical and biogeochemical impacts of phototrophic microorganisms are discussed by Warscheid and Kuroczkin (1997).

129

CHAPTER 5

Physics of Drop Formation and Micropore Condensation

5.1. H O W A CURVED WATER MENISCUS CHANGES THE EQUILIBRIUM VAPOUR TENSION This Chapter will be devoted to apply the microphysics of clouds to material conservation and discuss an extremely important phenomenon: the condensation in micropores. In reality, this mechanism is complex and rather unfamiliar although the basic equation which controls micropore condensation governs also drop formation in the atmosphere, and the latter subject is well known to meteorologists. However, the application to micropores is not immediate as it involves several differences related to the change of sign of the radius of curvature of the water meniscus and the geometry of the pore. For this reason, it will be useful to discuss the existing formulae and their degree of approximation. To this aim, their derivation is a necessary step. In Chapter 2 it has been seen that, in the atmosphere, the water vapour becomes saturated at relative humidity RH = 100%, when the air temperature (and therefore the moisture dispersed in it) reaches the dew point. However, it is useful to distinguish between the formation of droplets in the free atmosphere and the condensation onto a surface, or inside internal pores. This is because the vapour tension which is in equilibrium with a curved liquid surface varies with the concavity or convexity: it is greater with increasing convexity and lower with increasing concavity. For a concave surface (e.g. condensation into micropores, the meniscus in a wettable capillary) the radius of curvature r of the meniscus is r < 0 ; for a convex surface (e.g. droplets, meniscus in a hydrorepellent capillary) r >0; r = indicates a plane surface, and the physical conditions of the equilibrium with a plane surface of water are well known, which have been previously analysed. The pressure of vapour e(r) in equilibrium with the radius of curvature r of the water meniscus is expressed as a function of r, and for a plane water surface e(~) = esat(t) is computed by means of the Magnus equation. The greater the concavity or the convexity, the

130 greater the d e p a r t u r e from the M a g n u s equation. The s a t u r a t i o n p r e s s u r e in equilibrium with a concave or convex m e n i s c u s w a s calculated by T h o m s o n , later Lord Kelvin,

(e(r )~

2 o Vm

(5.1)

In ~ e ~ ) j = r . ~ T

w h e r e r~ is the surface tension of w a t e r (e.g. c~ = 75.6 erg cm -2 at T = 273 K a n d ~ = 72.2 erg cm -2 at T = 293 K), Vm is the m o l a r v o l u m e of the liquid sorbate (i.e. Vm = 18 cm 3 for p u r e water) a n d .J?~ the gas constant. It is obvious that the ratio e(r)/e(oo) r e p r e s e n t s by d e f i n i t i o n the r e l a t i v e h u m i d i t y R H. The s a m e f o r m u l a can be r e w r i t t e n in terms of the e q u i l i b r i u m RH:

RH(r ) = 100 e x p ( 2r .~~ wm T )

(5.2)

a n d the result is graphically s h o w n in Fig.5.1. The effect is significant only for v e r y small r, i.e. I r I < 0.1 Bm. As the r a d i u s of c u r v a t u r e r is the m a i n p a r a m e t e r , the Kelvin f o r m u l a states that the l o g a r i t h m of the RH in equilibrium w i t h the m e n i s c u s

200 180 t 160~

"~ o~,,I

'~

120

~

100

~.

r>O

140

80

.1==1

9-

60

r
4o-~

I

0 0,001

|

,

|

,

,

, , , i

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|

,

,

,

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,

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,

,

,

,

, , , i

,

1

,

,

,

,

, , ,

10

R a d i u s (~tm) Fig.5.1 Relative Humidity (RH, %) in equilibrium with meniscus of water with radius r (Bm), according to the Kelvin law. r > 0 convex meniscus, e.g. drop; r < 0 concave meniscus, e.g. pore.

131

is inversely proportional to the radius of curvature of the water surface. RH levels higher than the above equilibrium value cause condensation, and lower evaporation. These equations clearly show that for negative radii the argument of the logarithm must be less than 1, and the equilibrium will be with RH(r ) <100%; for positive radii the argument is greater than I and RH(r ) >100%. The Kelvin equation was originally introduced to take into account that in a capillary the tension of the vapour in equilibrium with menisci having different radii of curvature is not the same, and can be derived in two independent ways: one from the Stevin and Laplace laws and one based on the Gibbs and Helmholtz functions of the free energy of a thermodynamic system. A short comment about nomenclature, as the terms micro, macro etc. are not always found to individuate the same class of size, and this generates confusion. For example, Fitzner (1994) reports three classifications: the first one, attributed to De Quervain (1967), is: micropores < 5 ~tm; fine pores 5 - 200 ~tm; coarse pores 200 - 2000 ~tm, large pores > 2000 ~tm; the second one follows the normative DIN 66131 (1973): micropores < 0.002 ~tm, mesopores 0.002 - 0.05 ~tm, macropores > 0.05 ~tm; the third one, attributed to Klopfer (1985), is: micropores <0.1 ~tm, capillarpores 0.1 - 1000 ~tm, macropores > 1000 ~tm. In general, however, the concept of small and large applies related to the consequences of the p h e n o m e n o n under investigation, and in the present case two limiting sizes can be found. The lowest limit is the water molecule which is of the order of 3x10 -4 ~tm; pores with smaller diameter have no relevance on condensation. Another reference size is the interval 0.1- l~tm ; above it the Kelvin effect becomes negligible and the pore size is unimportant, and the term macro can apply. As a consequence, the term micro could apply to the small size interval 10 -3 10 -1

~tm w h e r e the Kelvin effect is dominant. However, there are so m a n y

contradictory definitions that it is not the case of introducing new ones. The only i m p o r t a n t point is to be clear for a better u n d e r s t a n d i n g of the p r o b l e m of (micro)pore condensation.

5.2. DERIVATION OF THE KELVIN EQUATION FOR DROPLETS FORMATION AND MICROPORE CONDENSATION

5.2.1. Derivation of the Kelvin equation from the Stevin and Laplace laws At the liquid-air interface, the molecules of the liquid are more strongly attracted by the molecules of the underlying liquid than by the molecules of the.gas, and this fact can be expressed according to two different points of view: (i) the free

132

liquid surface behaves as an elastic membrane, (ii) some work is needed to change the surface area (or to stretch the surface). Both are described in terms of c~, which respectively represents: (i) the surface tension and is regarded as an elastic force per unit length; (ii) the specific free energy of the surface and is considered an energy per unit area. In fact, the d i m e n s i o n of ~ is expressed in the former case as force/displacement [dyne cm-1]; in the latter as energy/area [erg cm-2]. The surface tension does not comprise the whole surface energy, but it represents the specific

Gibbs free energy of the surface, i.e. the maximum work done for the formation of the unit surface area. If the surface area decreases, also the energy of the system lowers and for this reason free liquid surfaces have a natural tendency to contract, or to assume a spherical shape in the case of free droplets, because the sphere has the smallest surface/volume ratio. The energy oriented point of view is very useful in a n u m b e r of t h e r m o d y n a m i c considerations, but also the 'membrane' model is convenient and immediate, especially when describing a small insect which is walking over the water and the surface is deformed by its weight, or when tea leaves remain motionless on the water surface, apparently kept still by this 'membrane', when the water in a pan is boiling with violent convective motions. Both these points of view play interesting roles although times by times the most appropriate model can be chosen and the other may appear weaker. The Kelvin's law can be derived in different w a y s (membrane, energetic, chemical potentials); here it will be demonstrated following two very different points of view, just to show how distinct approaches can converge. The membrane model has been preferred instead of the energetic one, which seems better in some respects, because the latter is more similar to the second derivation, which will be made in the next section. The physical derivation for the equilibrium of a spherical meniscus in a capillary (Byers, 1965; Mason, 1971; Sedunov, 1974; Kikoin and Kikoin, 1978; Matveev, 1984; Sivuchin, 1986) can be simply derived from the consideration that the pressure of a fluid in a horizontal plane is everywhere the same. Consider a vessel filled of water with a glass capillary partially immersed in it, and all the system in t h e r m o d y n a m i c equilibrium with its atmosphere, which is composed of water vapour only. Consequently, the liquid surface will experience the saturation pressure of water vapour. At the horizontal plane passing for the meniscus, the v a p o u r pressure will be exactly the same, both outside and inside the capillary. The same holds for the horizontal plane of the free liquid surface, so that the pressure exerted by the water column will be compensated by the meniscus effect. Kelvin first derived the equation considering the vapour density constant with height. Under this assumption, the Stevin's law

133 (5.3)

p =p g h

(where p is the fluid density, g the gravity acceleration and h the height) gives the pressure p(O) at the free liquid surface level 0 both for the vapour outside the capillary (5.4)

p (0) = p(h) +Pv g h

and the water inside it 2(~ p (0) = p(h) + 7 +Pw g h

(5.5)

where Pv and Pw are densities of the saturated vapour and liquid water, respectively. In the second equation, the term ap = - 2 ~ / r represents the change of pressure (Laplace formula) due to the surface tension across the curved (spherical) meniscus into the capillary. Equating for p(O) the two eq.s (5.4) and (5.5) the term gh is isolated, which, substituted into eq. (5.4), gives the original Kelvin formula: Pv

p(O) - p(h) = -2c

(5.6)

r (Pw- Pv)

This formula is valid for a small capillary height in which the vapour density can be considered constant, and there is no explicit mention to the wetting angles, i.e. effect of wettability of the surface. A more general derivation can be similarly obtained using the barometric equation for the vapour pressure change with height and introducing the wetting angle. In the capillary tube, the pressure originated by the surface tension c of the meniscus at the top of the water column is caused by the component of force tangential to the capillary Ft, generated by the surface tension all around the circumference 2~r of the capillary, i.e. Ft = - 2~ r~ r cos0

(5.7)

where 0 is the contact angle between the water meniscus and the immersed part of the capillary; cos0 is positive for wettable surfaces and negative for hydrorepellent ones. The Laplace pressure I-[ is obtained dividing Ft by the section of the capillary ~r 2, 2(~

II = - - 7

cosO

(5.8)

134 which considers the effect of the wettability of the surface by means of the correction factor cos0. Equating [I with the hydrostatic pressure p of the liquid into the capillary calculated with the Stevin formula 2($ p g h = - ' - ~ cos0

(5.9)

and the term gh, called geopotential height, is obtained dividing by p the two terms of the above equation and will be used, as before, to derive the Kelvin equation. The next step is to consider the vapour pressure in the horizontal plane at the height of the meniscus. In equilibrium, it can be supposed that the low pressure over the curved meniscus is in equilibrium with the natural barometric decrease of pressure of the vapour with height. The latter can be calculated by substituting into the state equation (1.1) for perfect gases the fundamental equation of the hydrostatics dp = -p g dz.

(5.10)

For a mole of gas, with molar mass M =p V, integration gives

,p(h)

Mgh

In 9(0) ) =- , ~ T

(5.11)

which represents the barometric (or hypsometric) formula which gives the vertical distribution of pressure for the increase of height h = Zl - z2 with vapour density decreasing with height. By operating similarly to the derivation of the simpler Kelvin formula (5.6) and substituting the value formerly derived of the geopotential height, i.e.-2ocos0/pr to gh in the barometric equation (5.11), the general Kelvin formula is obtained, which includes the interaction between water and solid (wettable or hydrorepellent surfaces):

,p(h) Vm (p(O)- p(h) - 2 G cos0] r -" ln~'p(O) ) = - , g g T

(5.12)

The curvature effect can be taken into account substituting the equilibrium vapour pressure over the meniscus of radius r , i.e. e(r), to p(h) in the left hand term, as the two pressures must be equal, being at the same horizontal level. The same holds for

p(O). It should be noted that this more general Kelvin equation can be p(O) -p(h) is very small compared to p(O). More precisely, if the two following conditions are satisfied,

e(oo) and

approximated in a Very practical form if the value of

135

2 ~ cos0

>> I p(O)-p(h)l

Vm ,9~ T I p(O) - p(h) I << 1

(5.~3)

then the Kelvin formula assumes the usual form

(RH(r ) ln~ 100 ) =

2 ~ Vm cos 0 r ~T

(5.14)

where RH(r)/IO0, i.e. the relative humidity in equilibrium with a curved meniscus of radius r has been substituted to the ratio e(r)/e(~,) in accordance with the definition given in Chapter 2. In the case of droplets r > 0 and cos(9 = 1; in the case of menisci of water condensed into micropores, r < 0 and 0 is typical for each material, i.e. 8 < re/2 for wettable surfaces and 8> re/2 for non wettable ones. An interesting ideal experiment was suggested by Kelvin (Thomson, 1870), based on the barometric formula. Let us consider two separate vessels (Fig.5.2) with water, posed at different heights Zl and z2 in a closed box in thermal equilibrium. At both heights the free water surfaces have equilibrium tension e(~,), but inside the box the pressure decreases according to the hypsometric formula. Therefore, the water molecules over the upper water surface will migrate in the box which at the same height z2 has a lower pressure, and redistribute in the box, increasing the pressure at every level. At the lower level zl the pressure is also increased, and condensation occurs in the vessel where the free water surface has the equilibrium pressure e(~,) lower than the new pressure at the same height. The consequence is that this t h e r m o d y n a m i c system will cause evaporation from the u p p e r vessel and condensation in the lower one, until all the water will be transferred, as they would have been two vessels communicating by means of a tube. Another ideal experiment was suggested by Kelvin. If in a closed vessel a water reservoir and several vertical capillary tubes with different diameters, closed in the bottom, and partially filled of water were left for a sufficient long time to reach equilibrium, the following situation is expected. All the water columns in the capillaries will be found in equilibrium with the barometric distribution of vapour, i.e. the excess water were evaporated from the capillaries too much filled and were condensed into those too less filled, and the height of the water columns would be the same as all the capillaries were open at the two ends, and partially immersed and communicating in the same water basin.

136

/\

. . . . . . . .

_

. . . . -., ,'.'.'.'.-,-.

.

. . . . . . . . . ,.-,'.. 9 ,,-.-...-,..

~::: :!::'iii::iii!i!:::i:i:iiiii:i::::i':" . . . . . . . . . . . . . . . . . . . . . . . . . -..-. -...........-.-

. . 9 ..

9

.:.:...:.:.:....".'.','.'." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 ,.. 9 ,...,,..,....,.......,... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. :.:... ".:.:.:..".'.:.:.:.:. 9

.:.:.:.:

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

e(zl) > e(o

Fig.5.2 Ideal e x p e r i m e n t s u g g e s t e d b y Kelvin, b a s e d on the b a r o m e t r i c formula.

, ....,.,...,-~

e(r)

,.

< e(oo) .

.

.

.

.

.

.

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.

.

":::" "'::::.?i:i:i::: :::::::::::::::::::::::: .

.

.

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.

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-.

"'::i.i":'::i:':"'-::i: . . . . . . . . . . . . .

".:.:...

I e(oo)=

e(zl)

Fig.5.3 P a r a d o x that w o u l d arise if the external p r e s s u r e w e r e not d i s t r i b u t e d a c c o r d i n g to the b a r o m e t r i c formula, b u t w e r e constant w i t h height.

137 If the external pressure were not distributed in accordance with the barometric formula, but were constant with height, the following paradox would arise (Fig.5.3). Let us consider a closed vessel containing water in the bottom in equilibrium with its vapour; then a vertical capillary tube is partially immersed in the liquid, all at the same temperature. In the capillary a column of water goes up and stops at the height determined by equalising the Stevin's and Laplace's pressures. The pressure of the saturated vapour in contact with the liquid is not the same over the flat surface of the water in the bottom and over the meniscus, being lower over the meniscus where the surface is concave. In the vessel, if the vapour pressure were constant with height, the equilibrium pressure would be e(oo) and the vapour would gradually migrate towards the meniscus in the capillary, where the pressure is e(r ) < e(oo), establishing a gradient of concentration, and possibly of pressure, into the vessel. In the top of the capillary, the vapour would become supersaturated with respect to the meniscus curvature and would condense, adding new liquid into the water column. The molecules which condense into the meniscus would be replaced by other molecules which w o u l d evaporate from the free water surface at the bottom where the equilibrium tension is e(~). Thus, partiallly or totally neglecting the natural decrease of the vapour pressure with height, the above process would indefinitely continue with evaporation from the bottom, migration of v a p o u r into the capillary, condensation onto the capillary meniscus, displacement of the column to re-establish the original level and so on, in a perpetuum mobile mechanism similar to a reversed fountain. With the approximate Kelvin formula a p e r p e t u u m mobile is get; an equilibrium without perpetuum mobile is found with the rigorous formula (5.12).

5.2.2. Derivation of the Kelvin equation from the Gibbs potential Gibbs derived independently the Kelvin equation, on the basis of chemical potentials. Here the main guideline will be followed; details can be found elsewhere (Byers, 1959; 1965; Mason, 1971; Pruppacher and Klett, 1980, Young, 1993). Gibbs considered the conditions in an isothermal and isobaric system of more than one component, such as a solution, where there can be a change in the number of moles of a component. To this aim three main parameters should be defined: the Gibbs surface free energy G = U + Ps Vs-T . ~

(5.15)

the free enthalpy of the system

..~= U + Ps Vs

(5.16)

138 the Helmholtz free energy. . 7 = U - T .5r

(5.17)

where U is the free energy of the system at temperature T, Ps its pressure, Vs its volume, .~r

entropy.

W h e n the v a p o u r molar fraction Nn/M is transported from the plane surface of the liquid (or from the atmosphere) to the droplet, the increase in free energy is

~n AG = ~ - . ~

(e(r )

(5.~8)

T I n ~,e(oo)J"

After this v a p o u r has condensed, the increase AG is due to the increase of surface energy which is linked to the free surface S of the liquid under the action of surface tension c~, i.e. AG = cy ~ S. For a spherical droplet, the surface is S = 4~r 2 and the increase is dS = 8~r dr ; the volume V is V =(4/3)~r 3 and dV = 47r r 2 dr ; the mass which condenses is dm = p dV = 4re p r 2 dr ; hence dS = 2 d m / p r and AG = 2 cy @n p r. Substituting this finding in eq.(5.18) and considering that M / p = Vm, the Kelvin equation is obtained. This derivation is very general, and the Kelvin formula can be rewritten for any shape of meniscus, by using the ratio of the incremental values d S / d V of the meniscus surface and related volume (RH(r ) o Vm dS lnx 100 ) - . ~ / g T dV

(5.19)

e.g. d S / d V = 2 / r for a sphere; d S / d V = [(1/rl ) + (1/r2)] for ellipsoids with principal radii rl and r2; d S / d V

= [(1/rl ) - (1/r2)] for saddles with principal radii rl and r2;

d S / d V = 1 / r for a right circular cylinder (Fig.5.4) or a circular torus (where r is the radius of the cylinder or the generating circle, respectively; note that the formula is independent of the cylinder height or torous radius); and finally, for a cone of height h. one obtains d S / d V = 3(2r 2+h 2)/(r 2h ~ r 2+h

2).

5.3. THE FORMATION OF DROPLETS IN THE ATMOSPHERE: H O M O G E N E O U S A N D HETEROGENEOUS NUCLEATION The first problem in the formation of droplets is that r > 0 a n d this requires a supersaturation, i.e. RH>> 100%, or the intervention of other p h e n o m e n a which m a y counteract this physical effect. The Kelvin equation in the form (5.19) considers the

139 100

"

90 80

~9

70 6o

".~. ~

50 40 30

.......

0,001

0,01

0,1

1

Radius (~m) Fig.5.4 Relative Humidity (RH, %) in equilibrium with a concave meniscus of water with radius r (~tm), according to the Kelvin law. C: cylindrical meniscus; S: spherical meniscus.

;urface ..~ o

3

,-~ x

2

Energy

(U

0 rt-4 -1

Total

Energy

-2

Volume

Energy

-3 -4 -5 i 0,001

'

,

,

,

,

,

,I)

r*

, I

'

Radius

.

.

.

.

.

.

.

. 0,1

0,01

(~tm)

Fig.5.5 Free energy of a pure water droplet versus droplet radius and critical radius r*. Lines refer to the surface free energy, the volume free energy and the total energy (thick line).

140

energy balance derived from two counteracting factors: the positive work against the surface tension in the formation of the free surface of the meniscus (proportional to r 2) and the negative work deriving from the energy released by the vapour-liquid change of phase of some water molecules (proportional to r 3) which comes from the tendency of water molecules to aggregate in the liquid state. In the formation of a droplet by condensation, the surface area is 4Jrr 2 and the free surface energy is 47rr2c~; and considering in a similar way the contribution due to the increase of the volume, the elevation of the free energy due to the curvature of the surface is 4 (e(r)~. AG = 47r r 2 r~--~ ~ r3/9 .~/2~TIn ~,e(oo)J

(5.20)

The algebraic sum of these two contributions, characterised by different powers of r, determines a graph whose maximum AG* is a maximum of instability for the physical process, and the corresponding critical radius is r* (Fig.5.5). The critical radius can be determined under the condition d ( A G ) / d r = 0, and is 2

r* = /9 . ~

Gm

(e~r, ) ~ T ln~,e(oo)j

~

(5.21)

All the droplets with r < r*, called embryos, are unstable and tend to dissipate; after the critical radius is surpassed, the embryo droplet grows in microseconds to a 'mature' cloud or fog droplet. The growth may occur by accidental aggregation of other molecules, collision with other droplets, or coalescence. The formation of a pure water droplet, without the intervention of heterogeneous condensation nuclei, is called homogeneous nucleation. In this case, the system is composed of micro spheres of water floating in the air, and the radius of the droplets is positive and great supersaturation is required for equilibrium with the curved water surface, i.e. RH>>100%, T<
141 droplets on the m o n u m e n t surface, and in the presence of fog the m o n u m e n t is generally in temperature equilibrium with the air, so that condensation is not accelerated by supersaturation due to monument temperature below the dew point. Eventually, droplets formed on the vertical surface of monuments grow until the larger ones, due to their weight, run d o w n w a r d s colliding other droplets which supply further water and increase their mass. These rivulets form small deposits of water at the base or on other horizontal surfaces, this water reservoir is then adsorbed by capillarity, or furnishes the appropriate conditions for local weathering or biological deterioration. H o m o g e n e o u s nucleation can be generated in expansion cloud chambers, where very high supersaturation e.g. RH ~ 400 - 800% can be obtained for short times. Small droplets are formed on adiabatic cooling when the expansion ratio of the chamber exceeds 1.37 and R H ~ 500% (Mason, 1951) or also at the critical supersaturation RH ~ 400% (Madonna et al., 1961). In the early stage the droplets are aggregates of water molecules around existing ions. The water molecules have a large dipole moment, so that they can surround charged ions, and in this case the balance is made with three forms of energy: the surface energy 4~r2G, the energy due to the latent heat of condensation-(4/3)Trr3p Lv (where Lv is the latent heat of condensation or vaporisation) as discussed before, and the electric energy of the Coulomb field of the droplet q 2/(47rer), where q is the electric charge of the ion and e the dielectric constant. However, also in this case high supersaturation is needed, of the order of RH - 400%. If a droplet carries a charge q, the equilibrium relative humidity is

{RH(r )) In ~ 100

2 ~jym

q2

= r ~TT-8?rE r 4"

(5.22)

For this reason, in the free atmosphere droplets may only be formed by adsorption of water on some condensation nuclei. When water vapour condenses u p o n them, they form solutions onto which the equilibrium vapour pressure is relatively low (heterogeneous nucleation). In other words, the depression formed by the chemical solution compensates for the Kelvin overpressure generated by the convex meniscus of the droplet, so that condensation will occur and the droplet will grow. The most effective condensation nuclei reach the equilibrium at RH << 100%. A salt which becomes a solute by hygroscopic reaction with h u m i d air is called

'deliquescent' and many crystals with this property are found in the atmosphere; the most common is NaC1 generated by sea spray. The condensation nuclei begin to adsorb a n u m b e r of water molecules, and then grow in size becoming first

142 deliquescent, then a very concentrated hygroscopic solution, and later a dilute solution, but the last step occurs when their radius is greater than r *. However, the classical laws of the thermodynamics cannot be applied in the first steps of this process, because classical thermodynamics is only valid for infinitely diluted solutions. In particular, the V a n ' t H o f f factor i which for soluble salts represents the effective number of moles after dissociation of one mole of the original substance, e.g. i = 2 for NaC1 which transforms in Na + and CI-, varies as a function of the molality. Solution effects are not only important because of the h e t e r o g e n e o u s nucleation, but also because they cause condensation on surfaces or micropores at relatively low R H . Chemical contamination causes departures from the Kelvin law and may be taken into account with some small changes to the original formula. The vapour tension of a solution is lower than that of pure water. The osmotic effect due to the ionic dissociation of the hygroscopic salts which form the condensation nuclei, or which contaminate the surface of bodies, or which are included in micropores, may be very important. The solution effect is largely dominant in the presence of great concentrations of salts, as on the walls, or in the large pores with diameter D lying between I and 100 ~m, when the Kelvin effect becomes negligible. In the presence of hygroscopi~c salts, the Kelvin formula must be improved and two different approaches will be considered here. Mason (1971) considered the transfer of a small mass 6m of water from a contaminated droplet to a plane surface of pure water. The solution will undergo a decrease of free energy A G = rYs 6 S

- P

6n 6Vs = 2 rYs ~ Ps r

-P

6m

(5.23)

Ps

where rys and Ps are respectively the surface tension and the density of the solution, S and Vs the surface and volume of the droplet, P the osmotic pressure of the solution, variable with the molality. On the other hand, the decrease of the free energy is due to the work corresponding to the evaporation of the amount of water ~n with initial equilibrium pressure es(r ), expanding the vapour to the lower pressure of the free surface of pure water e(oo) and, finally, condensing it at this pressure with a process that is reversible and isothermal, so that 6m .J?~T In [es(r ) AG = M w ' e(~,) )

(5.24)

where M w is the molar weight of water. Equating these two expressions of AG and considering that the osmotic pressure P is

143

P=

.~Ir T Pw Mw

ins

In (1 + n w )

(5.25)

where the labels s and w refer respectively to the solute or the water, Pw is the water density, i the parameter closely associated with the Vant' Hoff coefficient for solution and depends upon the molality, and n is the molar fraction and ms the actual mass of the solute, the following formula is obtained:

[RH(r ) ln,

(2 as Mw

100 ) = ' p s r . ~ T - p s

__PwIn (1 + ins) cos0 nw

(5.26)

where RH(r ) = 100 es(r )/e(oo). The other formula, due to Wright (1936) is

(RH(r ,)

ln t 100 ) = (

2asMw i msMw .~/g ) cos0 ps r T Vw Pw Ms'

(5.27)

where ms is the mass of solute, Vw the volume of condensed water with dissolved salts, i.e. (4/3)~r

3

for droplets, and Mw/Pw is the molar volume Vm of water. The

result is a function of the type of a hygroscopic salt, its solubility, the degree of dissolution and amount of water which has already condensed; as a consequence, it is continually variable, although the dynamics are strictly determined by the initial conditions. Of course, both the Mason and Wright formulae hold whatever is the sign of r, and play an important role for the condensation in macropores which always contain hygroscopic salts. Both formulae show that the saturation pressure over a solution is lower than the saturation pressure over pure water. This happens because the saturation pressure is reached when the number of molecules of vapour that escape from the liquid equals the number of molecules that return into the liquid. In the case of a solution, the solute salt 'dilutes' the water reducing the number of H 2 0 molecules that escape; therefore, the equilibrium is displaced towards a lower value.

5.4. BUBBLES Water bubbles in air are well known: they are formed with a spherical layer of water with two air-water interfaces, and therefore two membranes: one external and one internal. For this reason the Laplace pressure exerted by them, and the energy

144 needed to increase their surface, is twice the above values found for a meniscus with only one interface. When the pressure inside a bubble increases by dp, also its radius increases by dr, and the external work 47rr2p dr accomplished against the surface tension (~ is transformed into free surface energy, i.e. 2 (~ d S = 2 c~ d(47rr2) = 167rr d r , the factor 2 arising because of the contribution of both the inner and outer surfaces of the bubble. The conservation of the energy requires that the external work equals the total increase of surface energy, and equating the two terms, a pressure twice the Laplace rI, given in eq. (5.8), is found. A bubble of air in water has only one interface and the pressure and the energy are as discussed in the previous sections. Although the surface tension tends to reduce the bubble size, as in the previous case but with only one surface, the pressure of the air entrapped inside counteracts it and the bubble can survive. A completely different situation occurs for ephimeral bubbles of vapour in water. At first sight, vapour bubbles in water might appear complementary to water droplets in air; but the change of sign of the radius of the meniscus makes ephemeral or impossible the life of vapour bubbles. The natural dynamics of the phenomenon, characterised by instability, leads the vapour bubbles (if any) to disappear in a very short time, and a comparison is more appropriate with embryos. A distinction must be made between bubbles determined by the presence of originally dissolved gases, e.g. CO2 in mineral water, and those composed of vapour only. In the former case, bubbles form when a rise of temperature makes the gas insoluble, and the pressure of the gas in the bubble opposes the contraction and vanishing of the bubble. In the latter, nothing can oppose the external pressure and the fact that the bubble is in condition of unstable supersaturation and the dynamics tends towards a smaller and smaller size of the bubble. The molecular forces acting in the surface layer of a liquid act as a membrane that does not allow the molecules to leave the volume of the liquid. Inside, the statistical distribution of the thermal motion shows that there are always some molecules having greater speed and being less bound to the bulk liquid. These can be considered in the vapour state, although inside the liquid, and their pressure equals the tension of saturation of the external vapour. The equilibrium shows dynamics with perfect symmetry of behaviour, where the number of molecules leaving the liquid equals those passing from the atmosphere to it. By definition, the boiling point

BP is the temperature at which the saturated vapour pressure (inside the liquid) becomes equal to the external atmospheric pressure. The physics of this process is not clear if one thinks about what may happen when the pressure of the external

145 16 14 12 .~ L.)

10

o

8

S

C 0 0,001

0,01

0,1

Radius (Bm) Fig.5.6 (a) Dew Point Spread (ADP, ~ in equilibrium with a concave meniscus of water with radius r (Bm), according to the Kelvin law. C: cylindrical meniscus; S: spherical meniscus. Linear scale. 100

10 k9 o

S

C

0,1 0,001

0,01

0,1

Radius (Bm) Fig.5.6 (b) Dew Point Spread (ADP, ~ in equilibrium with a concave meniscus of water with radius r (Bm), according to the Kelvin law. C: cylindrical meniscus; S: spherical meniscus. Logarithmic scale.

146 vapour equals that of the atmospheric pressure, but becomes clearer when thinking that the equilibrium is reached with the internal vapour pressure, and intense boiling starts as a consequence of the possibility of vaporisation in the whole mass of liquid water (Matveev, 1985). However, also in this case, only a heterogeneous formation of bubbles is possible, as we will see later. At temperatures below the boiling point (BP), i.e. T < BP, the incipient bubbles have very small negative radii and therefore, according to the Kelvin equation, they are in equilibrium with low RH; however, the bulk liquid all around constitutes a very supersaturated environment and vapour bubbles cannot form or, if formed, disappear immediately. Vapour bubbles can form only when T -~ B P and then they form on the surface of the vessel for two reasons: (i) the vessel temperature is higher there, possibly T >>BP; (ii) bubbles develop not as small spheres with very small radius, but starting flat, adhering to the plane surface of the vessel where the radius of curvature is practically infinite. When a bubble grows being filled with vapour, the displacement of water generates a more and more roundish shape, until the bubble dimension is so great that the bubble detaches from the vessel surface and comes up because of the buoyancy force. If a temperature fluctuation causes a t e m p o r a r y drop of temperature below the critical value, then the small unstable bubbles undergoing formation on the vessel are immediately destroyed, and the liquid water that replaces their volume impact violently against the vessel, forming the characteristic buzz which precedes boiling.

5.5. MICROPORE CONDENSATION AND STONE WEATHERING In the case of a pure, non contaminated, non reactive, non-porous surface, condensation occurs when the temperature of the surface Ts reaches, or drops below the dew point (DP) of the air, i.e. Ts < D P, irrespective of both the degree of saturation of vapour (RH) and temperature of the air at some distance from the surface. However, for simplicity, herewith it will be assumed that the air and material have the same temperature, at least in an air layer very close to the material, and the thermodynamic parameters will be referred to this layer in equilibrium with the surface. By remembering the results of Chapter 2 for the dew point spread, the same equation can be rewritten in terms of the Kelvin equation (Fig.5.6) RH

{237.7+t

ADP =-log10(1--~) ~, 7.5

) = -0.1158

(237.3+t~

r~

Vm ~,r.~/g T !

147 c~ [237.3 +t~ = 2.507 x 10-8 r ~ 273+t J"

(5.28)

Evaporation occurs when Ts > T w where Tw is the wet bulb temperature of the air. Observation of the value of Ts allows us to distinguish between the two processes and d e t e r m i n i n g for example w h e t h e r a surface is wet because it is cold (condensation) or it is evaporating as a consequence of capillary rise. However, contamination with soluble salts lowers the equilibrium R H (and raises the DP), or the presence of micropores causes departures from this simple scheme and condensed water may be found in micropores at usual conditions, and also in relatively dry environments. In the droplets, all the water is in liquid state. In porous bodies, or in general over a hydrophilic surface, the water molecules in contact with the material are absorbed and strongly bound with the internal surface due to the presence of dipoles or image forces; the bound is so strong that this water is considered to be in the solid state. Beyond this solid layer, others water molecules are in the liquid phase and free. In pores with radius rp < 0.1 ~tm the physical effect dominates; in pores with rp > 1 ~tm and c o n t a m i n a t e d by soluble salts, the physico-chemical effect which determines the equilibrium pressure for solutions may also cause condensation at lower RH, and this typically occurs in a marine environment due to contamination with sea salts. Water supplied by condensation causes dissolution of the material matrix, condensation-evaporation

cycles cause m i g r a t i o n

of d i s s o l v e d

salts and

recrystallisation in other parts, e.g. efflorescences and subflorescences, thus weakening the material a n d causing loss of the aesthetic value. This mechanism is clearly shown in thin sections of stones, where reprecipitated crystals are found in the pores (Fig.5.7). Wet materials, e.g. rocks or mortars, may have their mechanical resistance diminished. In other cases, the presence of a film of water may decrease the free surface energy of the material, weakening it (Winkler, 1986). In certain cases, as for e.g. argillaceous (containing clay minerals) limestone, water may alter the structure of the material, causing expansion, stress and fractures. In fact, the crystal structure is composed of a series of wafers and positive ions are frequently trapped between the wafers. Water is able to penetrate the crystal as it is attracted by the hydroxy groups causing the clay to swell. Of course, this happens only for clay minerals with expanding lattice, e.g. montmorillonite, vermiculite, but not for non-expanding ones, e.g. caolinite, illite, chlorite. When the RH decreases, the adsorbed water evaporates, but the structure between the wafers may have changed due to the formation of new crystals. The contraction leads to hysteresis, and in the

148 long run, adsorption-evaporation cycles cause irreversible damage (Torraca, 1981; 1994). The hygric dilatation may be of the order of 1 m m / m , and water repellent treatments cannot prevent hygric swells and shrinking, although they may be delayed (Wendler, 1997).

Fig.5.7 Thin section of oolitic limestone, where reprecipitated crystals are found in the pores. Authigenic dog toothed calcite crystals cover the oolites; gypsum is more frequent inside the pores. A large authigenic hexagonal calcite crystal is growing in the cavity. Material dampness and air humidity favour biological life and weathering; this negative phenomenon becomes greater and greater when the duration, or the frequency, of the time of wetness (TOW) increases. The TOW is an important descriptor for the growth conditions of microorganisms on materials. It reflects the correlation between material structure (e.g. porosity, inner surface, cation exchange capacity) and the biosusceptibility of the material, meaning the tendency to allow micrqbial contamination (Warsheid et al., 1993). Inside, the biological contamination is frequently restricted to certain physiological groups of microorganisms (e.g. fungi), whereas outside the microbial infections are mostly characterised by a complex network of algae, bacteria, fungi and lichens. During the time in which a metal or a stone is wet, chemical reactions occur between the pollutants deposited and the material (Laurenzi Tabasso and Marabelli, 1992); the damage is linked to the

TOW, although no general formula has been yet found to link the damage to the TOW. Condensation is also responsible for increasing the deposition rate of airborne pollutants. This fact is due to two different factors: (i) the particles and the hydrophilic gases that impact on a wet surface stick to it without bouncing, so that the capture efficiency of the surface is increased; (ii) when condensation occurs, near

149 the wet surface several microphysical processes occur, the ultimate result of which is the increased transport of gases and particles towards the surface as we will see in Chapter 8. The problem of surface moisture and condensation is very complex, and depends on the chemico-physical characteristics of both the atmosphere and the surface. The RH within a pore is a function of temperature, mixing ratio, pore geometry, presence and nature of soluble salts, and can be considerably different from pore to pore as well as from atmospheric RH. Total porosity, total pore surface, spatial association of pores (that may form pockets and necks), pore size, pore form, and pore radii distribution are important variables in monument weathering. Stones are characterised by a wide variety of pores and necks, with different shapes and sizes, which range from angstroms to millimetres and can be classified in several classes, depending upon their properties based on laboratory analysis (Fitzner, 1994) and mineralogical characteristics (Jeannette, 1997). The porosity may change with time, especially in the subsurface layer where migration of salts, leaching, dissolution, erosion, and other physical, chemical and biological attacks occur (Biscontin et al., 1993). However, although the situation is more complex, it is useful to introduce two basic types of pores: open and internal pores (Camuffo 1984; 1988). 'Open pores', with very large outlets compared to the pore volume are found especially on the surface of bodies. The typical shape is that of a hemisphere, or a portion of a hemisphere (Fig.5.8a). Open pores behave symmetrically with reference

Fig.5.8 (a): Condensation in an open pore. (b): Condensation in an internal pore. (After Camuffo, 1984, reprinted by permission of Kluwer Academic Publisher). to droplets suspended in the atmosphere: the smaller the pore, the lower the RH required for equilibrium with the water meniscus. For each open pore, condensation begins at a low critical RH(rp) determined by the effective radius of curvature of the

150 pore rp. This is the geometric radius of the curvature of the pore minus the thickness of the mono or bi-molecular layer of water molecules adsorbed and b o u n d in the solid state. When the RH increases, condensation occurs and the radius of curvature of the meniscus (rm) increases, i.e. the concavity of the meniscus flattens, following the equilibrium with the variations in RH according to the equation

/'m

2 r~Vm RH = ./r In (1--0-0)

(5.29)

An increase in RH corresponds to an increase in both condensed water and rm and vice versa. The hemisphere is completely filled at RH = 100%. All the steps occur in equilibrium with RH and the process is reversible.

'Internal pores', with ,~mall outlets, are typically found inside bodies (and connected to the atmosphere by a small hole facing the surface or entering other pores or capillaries, see Fig.5.8b) and these behave in a different manner. The condensation into the pore begins at the low critical R H = R H(rp), which is in equilibrium with the radius of curvature of the pore rp just wetted with a film of water. After a short time, when some condensation has occurred, the free space into the pore has been reduced and so the free surface area of the meniscus and the radius of curvature of the new meniscusrm. The smaller the new radius rm, the lower the equilibrium RH(m,). However, the actual RH inside the cavity, which initially was in equilibrium with the greater radius of curvature of the pore rp, now corresponds to supersaturation for the smaller rm,, i.e. RH(rp) >RH(m,) and the process is accelerated. Therefore, the initial level RH(rp), is no longer a neutral equilibrium value, but a critical value of unstable equilibrium which triggers off the complete filling of the pore. As a consequence, the process is now irreversible. Condensation in capillaries occurs similarly to internal pores, as condensed water makes smaller and smaller the radius of curvature of a cylindrical meniscus, ..

determining a condition of unstable equilibrium and accelerating the condensation. When a capillary is full of water, a spherical meniscus forms at the beginning of the capillary and the evaporation starts in a reversible way, as in open pores. Interesting is the case of the so-called 'ink-bottle' pores, i.e. cavities connected to other major cavities through smaller ducts, forming aggregates that can be compared to bottles having their neck in communication with the major cavity. According to the Kelvin law, in a porous material condensation occurs first in necks, which are the cavities with the smallest radius of curvature. When the necks are filled with water, air-pockets remain entrapped in the pores and further condensation is impossible in steady state conditions. Internal condensation may only continue when variations or

151 fluctuations in temperature or atmospheric pressure cause the displacement of the water inside the pore necks. Nocturnal cooling of the body may reduce the pressure inside the pores and cause the water condensed in the neck to be sucked into the pore. According to the Cantor's law, the required excess pressure is inversely proportional to the neck radius. When the excess pressure is sufficient, plugs of condensed water can be pushed out and trapped inside the pores, or can be forced to migrate into the material. Condensation may continue by means of these steps, so that the amount of adsorbed water is also a function of the pumping efficiency of these variations. Similarly, evaporation from an open pore starts at its outlet, removing water from the pore and increasing the radius of the free meniscus. Evaporation is triggered off when the ambient RH drops below a critical value which is calculated according to the Kelvin formula, using the radius of curvature of the pore outlet (ro), i.e. RH(ro). This critical value is lower than all the equilibrium values RH(rm) which can be calculated for all the increasing values rm, from ro to rp, which assumes the radius of the meniscus when the latter enlarges following the loss of liquid water. Inside the pore, after some evaporation, the relative humidity in equilibrium with the meniscus RH (rm) becomes relatively higher and higher in comparison with the external relative humidity which is R H < RH(ro) so that the external condition favours further evaporation. Consequently, the process is accelerated and is irreversible. Evaporation continues until all the liquid water (i.e. all the water inside the pore, except the first and second molecular layer in contact with the surface which is attached with a stronger ice-type bond) has evaporated. The condensation-evaporation cycles being thermodynamically irreversible present noticeable hysteresis as condensation occurs when triggered off by RH(rp) and evaporation by RH(ro). In practice RH(rp) and RH(ro) are not just two precise levels of RH, but two ranges, determined by the actual distribution of rp and ro in the porous material.

5.6. ADSORPTION ISOTHERMS The condensation-evaporation cycles can be represented by the so called BET (Brunauer, Emmett and Teller) adsorption isotherms (Brunauer, 1945; Gregg and Sing, 1967; Mikhail and Robens, 1983), in which the amount of adsorbed water (WA) is plotted against RH. In practice, this graph shows the change of weight due to the adsorption of water by an initially dry sample of material when the RH increases from 0 to 100% and then decreases again to 0%. The most common type (Fig.5.9) is

152 composed of branches forming a hysteresis loop. The first branch AB, characteristic of the very low RH, occurs w h e n all the material surface, both the external and internal (i.e. the visible surface and the surface in contact with the air, but inside the pores), is progressively covered with a layer of water in the solid state, with a final thickness of two or three molecular diameters. In this branch the graph of the adsorption is coincident with the desorption one. The condensation-evaporation process is characterised by a one-toone correspondence and is reversible depending linearly upon changes in RH.

E .~ o

D C rar~

~t

..q,.a

B

0

20

40

60

80

1O0

Relative Humidity (%) Fig.5.9 Adsorption isotherm for a condensation-evaporation cycle: water absorbed (WA) versus relative humidity (RH). In the intermediate RH range, after the total surface has been covered with this solid layer, a further increase in the RH leads to the formation of bulk, liquid water in the internal pores. This second branch (i.e. lower BC) becomes steeper and steeper as the pores are filled with water. In every pore with a radius rp the condensation occurs w h e n triggered by RH(rp) or by the chemical effect. If all the pores have the same size the condensation branch is very steep. In this branch the process is no longer reversible: if the RH decreases some minor hysteresis loops start. The third branch CD is characterised by very high RH, when all the internal pores are filled with water. In theory, this branch should be horizontal, as no further increase of W A is possible, also because w h e n RH = 100% the surface is in t h e r m o d y n a m i c equilibrium with the same number of molecules condensing and evaporating. In practice, this branch is tilted because the spectrum of the pores is wide and before reaching RH = 100% there are always some large pores which are

153 empty and which become progressively filled. In addition, the presence of contaminants or soluble salts causes the condensation to occur earlier, so that the vapour surrounding the sample is in a situation of supersaturation and condensation will occur, forming liquid films or droplets on the external surface (i.e. final rise DE). A similar condition of supersaturation occurs when the surface temperature drops below the DP, so that at the interface between the sample surface and the air the RH >100%. In any case, the amount of liquid water that can adhere to the external surface is modest, and the final branch is slightly tilted, with a sharper rise near the upper extreme due to the solution effect: If condensation stops before the droplets fall from the damp material, this branch is again characterised by a one-to-one correspondence and is reversible. On lowering the RH, the process first develops along the last condensationdesorption branch ED and then DC, until the external water has evaporated. Continuing to lower the equilibrium RH after all the pores have been filled with water, evaporation may proceed, emptying the pores and this may occur only when triggered by RH(ro). As RH(ro) <

RH(rp) a hysteresis loop is generated, the condensation branch being related to the size of the internal pores rp; the evaporation branch (upper CB) reflects the dimension of the outlet of the pores ro. If all the pores have the same outlet the evaporation branch is very steep. A laboratory method to determine the pore size consists in measuring the derivative of the amount of water WA which is adsorbed in the stone by varying RH. In fact, d W A / d R H , shows peaks corresponding to the dominant features of the pores, which are narrower or broader according to the distribution of the dimensions of the pores and their outlets. The Kelvin equation is the key to transform the values of RH which correspond to peaks into radii size. After all of the internal bulk water has evaporated, lowering the RH, layers of solid water (first branch BA) start to evaporate, but with a much greater latent heat (e.g. 2 or 3 times greater) than the evaporation heat in the liquid-vapour transition. Cycles involving the last branch DE mobilise the salts on the surface and subsurface layer; cycles involving the hysteresis loop dissolve and re-crystallise the soluble salts at a deeper layer and cause outward migration with the formation of new efflorescences. The mechanical stress that follows thermohygrometric changes in a structure weakened by long term dampness may have dramatic consequences. In addition to the chemical deterioration, the presence of water inside the pores favours biological epilithic and endolithic life, and biological weathering. Saturated environments should be carefully avoided. An experimental hysteresis loop similar to the above described one has been

154 reported in Fig.5.10. The laboratory test refers to a brick sample immersed at low temperature (i.e. a bath of liquid nitrogen) in a controlled atmosphere of nitrogen vapour, carried with a flow of helium. The partial pressures desired are obtained by varying the ratio between the nitrogen and the carrier gas, in order to obtain a controlled adsorption-desorption cycle. At that temperature the nitrogen is adsorbed into the brick, and the adsorption and desorption reflect in a change of the ratio of nitrogen to helium concentrations in the outflow. This ratio is determined by a thermal conductivity detector. The method is accurate and gives the pore size distribution of the sample. By expressing the data in volume (i.e. cm 3) of adsorbed nitrogen per unit mass of the sample, the same numerical values are obtained as for mass (i.e. g) of adsorbed water per unit mass of the sample, which are of more practical use. In the figure, the hysteresis loop occurs in the R H range from 50 to 85%, and the pores lie in the size range 18x10 -4 ~tm < r < 75x10 -4 ~tm. For R H above this hysteresis cycle, the isotherm continues to rise up to the last experimental value R H = 90%. This is due to the reversible filling of macropores which have an 'open' structure.

/ ,~

+

2

0

/

+

|

i

20

!

i

40

|

i

!

60

i

80

!

100

Relative Humidity (%) Fig.5.10 Adsorption isotherm for a brick sample, i.e. mass of water adsorbed ( W A ) per unit mass of brick, versus relative humidity (RH). The surface of metals is covered with layers of adsorbed water molecules whose number is a function of the R H and the type of metal or alloy. For all metals, the first monolayer starts to form at very low R H but it becomes completed only w h e n R H =

155 30%; for higher RH the specific metals differentiate e.g. the second layer is completed at 40% for Co and Au, and 55% for Ni and Fe; at increasing RH the deposition of water accelerates so that in the equilibrium with moist atmosphere ten or more monomolecular layers are deposited. The presence of heterogeneities (both structural or due to deposition of atmospheric pollutants) transforms the wet surface of the metal in an electrolyte for an electrochemicalcorrosion cell (Graedel, 1994). From the previous section it is evident that, when rp approaches ro, also the area of the hysteresis loop tends to vanish, When the pore population consists of aggregates of open pores, i.e. major spherical or irregular macro cavities including other smaller ones which have the appearance of hemispheres or micro-valleys, the hysteresis loop disappears and the desorption curve coincides with the adsorption one. In the case of materials characterised by ink-bottle pores, only the small cylindrical ducts (i.e. the necks) are filled of water and contribute to the hysteresis, as the condensation in a cylinder occurs with a cylindrical meniscus, and the evaporation with a hemispherical one. Given the small amount of water allowable in the necks of the ink bottles, the hysteresis loop is modest. Some very porous substances are used to buffer RH. This capacity derives from the fact that the moisture content of the substance varies greatly with the R H to which it is in equilibrium. The silica gel is widely used as it responds rapidly by absorbing or desorbing moisture when the ambient R H rises or falls. There are several types of silica gel with different buffering capacities. The greater the change of the equilibrium moisture for the unit change in RH, the greater the buffering capacity. The silica gel with regular density is more indicated for the intermediate and low RH; the silica gel with intermediate density is more appropriate for the high RH, and above 80% the buffering capacity becomes very effective. The silica gel can be conditioned to a specific level of RH by keeping it for a long time at the desired value of R H (e.g. in a closed environment conditioned by a saturated salt solution) until all the gel has absorbed the amount of moisture which is in equilibrium with the ambient RH. After this treatment, it can be used as a temporary buffer, as it will tend to absorb moisture if the RH will increase, or release moisture if the RH will fall. However, if it is put in a non previously conditioned case with objects in equilibrium with other values of RH, also the moisture content of the silica gel will vary, and the enforced buffering value will shift accordingly (Waller, 1992). Other porous or fibrous materials, e.g. wood, cork, wool, paper, have similar buffering properties. A most appropriate way to keep a constant level of RH in small closed volumes, is the use of saturated solutions, as discussed in Chapter 2 and Chapter 11.

156 It might be useful to outline that, when the adsorption is controlled by the Kelvin effect, loops in the adsorption isotherms are generated by the geometrical shape of pores and their communication outlets, but when another hydrophilic nature of the material is dominant, they may disappear. For instance, for the reasons previously discussed paper is characterised by an equilibrium moisture content without loops, which increases with RH, not exactly linearly, but with a higher rate at the lower and especially the higher humidity levels, similarly to a reversed 'S'. Of course, both the extremes of the natural humidity range (i.e. very elevated dryness and dampness) must be avoided in order to prevent the material from irreversible structural changes.

5.7. FREEZING-THAWING CYCLES When the temperature drops below zero, freezing-thawing cycles develop, and the pressure exerted by ice crystals in the pores of materials may have disruptive effects. At first sight, one would expect that the greater the size of the pore the greater the force, so that stones characterised by large pores and high total porosity will be more exposed to risk. However, things are different, and sandstones are quite immune from frost damage despite their low mechanical strength and their coarse pore structure. The maximum pressure expected in sandstone has been evaluated some ten times smaller than in a poor limestone. Poor stones non resistant to frost are characterised by a pore size distribution mainly peaked in the range 0.1 to 0.5 ~tm that are rare in good stone (Everett, 1961). Similarly, Torraca (1981) noted that the damage by frost is more likely to occur in materials which have a prevalence of small pores, i.e. with size between 0.1 and 1 ~tm, although the upper limit is not well defined as freezing damage has been found also in other stones with larger porosity. The problem of the damage caused by frost to porous materials is rather complex and d e p e n d s u p o n several factors: the pore size distribution, the geometrical combination of pores and capillaries, the Kelvin effect for water and ice. In a non humid climate the small pores have the highest probability of being filled with water at intermediate RH values, due to a combined action of the Kelvin law, and adsorption hysteresis but, on the other hand, in the pores with radius r << 0.1 ~tm, the Kelvin law causes a lowering of the freezing point for a curved meniscus. It is well known that freezing does not always occur at T = 0~

the smaller the

radius of the meniscus, the lower the freezing point. In nature supercooled droplets can be found in cloud as far as ATf = 40 K i.e.-40~

also supercooled water can be

found in pores and the theory of supercooling can be applied to determine the pore

157 size of porous bodies from the measurement of the release of latent heat at different temperatures (Fagerlund, 1973). When a porous material freezes, macroscopic ice crystals form in the larger pores and water is withdrawn from capillaries and finer pores where supercooled water remains longer. Thus, in principle, large crystals are expected to form in the larger cavities whereas capillaries and smaller pores behave as a reservoir of supercooled water that may be displaced (either in the liquid phase or due to the lower equilibrium tension of ice) and feed the ice crystals that have already formed. It is possible to calculate the change of the freezing point of water filling micropores with curved meniscus in the case of very simple pore geometry, and the sphere is the simplest one. In addition, there is some evidence that the liquid-solid interface in a capillary is spherical, at least when the capillary is not too small. The Laplace equation holds not only for liquids in equilibrium with their vapour, but also for solids in equilibrium with their liquid phase, i.e. 2 rYsl Hsl - - ~ cos 0

(5.30)

where the labels s, l refer to these two phases and rYsl = 17.2 erg cm -2. By proceeding as before with the derivation of the Kelvin equation, it is possible to compute the departure from the temperature of the change of state, as in eq.(5.28) but for melting ATf of ice spherules with radius r. It is known that a finely ground solid melts at a

lower temperature, and this physical law is largely used in foundries. Several equations exist with small empirical corrections (Fagerlund, 1973; Clifford, 1981; Iribarne and Godson, 1986); the chief equation for the Kelvin freezing point depression is ATf =

Tj

2 rYslM r Ps All

Ti 2 rYslVs r All

2 rYsl • r Ps Lf Tr

(5.31)

where M is the molar mass of the substance, Ps the solid density and AH the molar heat of fusion and Lf =AH/M the latent heat of fusion. For pure water AH = 18 (80 0.5 ATf) cal mo1-1 where 0.5ATf = f(Cw-Ci) d T where Cw and ci are the specific heats of water and ice at p = const. Laboratory experiments on freezing in micropores show that the observed data lie between two curves calculated with the above equation, the former computed with the surface tension rYslcharacteristic of the solid liquid interface, the latter with rYsv i.e. the solid-vapour interface (Fig.5.11). A possible interpretation for this is that,

at usual meteorological temperatures, the ice is always covered with a film of water,

158 so that in reality the solid-gas interface is the combined effect of two interfaces, i.e. solid-liquid plus liquid-gas, and the thickness of the liquid film between the two interfaces may change the observed values of the bulk surface tension.

U o%.

100

9~

1o

~

0,1

t,.i

0,01 0,001

0,01

0,1

1

10

Radius (~m)

Fig.5.11 Freezing point depression (ATf) calculated according the Kelvin equation for a spherical meniscus at the water-ice equilibrium (label sl, i.e. plot computed with the surface tension Ssl characteristic of the solid liquid interface), and the ice-vapour equilibrium (label sv, i.e. with Ssv for the solid-vapour interface). It can be observed that in the above equation the sign of ATf is linked to the sign of r and it might be expected to find symmetrically hot ice at +40~ in the same way supercooled water is found at-40~

However, ice crystals are convex and the water

in pores is characterised by a concave meniscus at the air-water interface, but the material-water interface is convex and is dominant in the case of icing, acting as a freezing nucleus; e.g. the method of determining the pore size of materials is based on supercooling. Probably, liquid microfoams might be similar to a structure with a dominance of negative radii of curvature to which these results might be applied; however, this phenomenon is theoretically possible, but has never been observed. Returning to the problem of the frost damage to monuments, Everett (1961) noted that the frost damage is not only associated with the existence of small pores in the already mentioned range, but with the simultaneous occurrence of pores of a critical size with larger pores. In his detailed study on the thermodynamics of frost damage, he found that the geometrical combination of cavities with different size plays a fundamental role, and that during freezing, the excess pressure Pa which is exerted in a large pore of radius rip connected to a supply of supercooled water at

159 the reference pressure by a capillary or fine pores of radius rfp is proportional to the difference of the inverse of the pore radii, i.e. , 1 1, Pa = k ~--f-- G--.)

(5.32)

where k is a proportionality coefficient. This difference may be small or large and is much more important than the individual value of each of the two terms. The contrast of large pores interconnected by fine pores gives the most dramatic results. Mechanical failure of the stone occurs if the excess of pressure determined by the above difference exceeds the mechanical strength of the porous material. In addition to the Kelvin effect, also the freezing point depression due to the solution of hygroscopic salts must be considered. Internal evaporation occurs first in the largest cavities and other water with dissolved salts is withdrawn from the finest adjacent pores. Considerable amounts of salts are transported and precipitated in the coarsest pores, and salt crystallisation takes place preferably in large pores because of the energetically favourable lower chemical potential (Ginell, 1994). The crystals are more abundant in the lower part and at the bottom of giant pores, where the solution concentrates during evaporation, becoming saturated and precipitating salt crystals. The larger the pore, the greater the possible amount of salt in the bottom. When the ambient relative humidity increases, the hygroscopic salts hydrate, then become deliquescent and a supersaturated solution forms and grows, until all the salt is dissolved; then the solution starts to dilute. Salts can be of atmospheric origin or leached from the soil, or due to constituents of the material, mobilised and transported by meteoric or ground water. In coastal regions NaC1 is a very important contaminant, which encourages condensation and lowers the freezing point. These salts lower the freezing point and prevent the mechanical stress due to the formation of ice crystals. The freezing point depression due to the presence of hygroscopic salts can be calculated with the simple formula valid for dilute solutions (for a derivation see Adamson, 1986):

ATf = Kfm

(5.33)

Kf is the freezing point depression constant and for water Kf =1.86 K mol-1; m is the molality of the solute. The formula shows that the value of ATf depends only

where

on properties of the solvent and the molality of the solute. By the way, the same formula holds for the boiling point elevation, but with the coefficient For water,

Kb = 0.514.

Kb instead of Kf

160

25 o v

I= 20 0

. !,,,~ ffl

. v.,,,i

o

10

N

5

~

1-I

L T

i

i

i

i

0

5

10

15

20

25

A n h y d r o u s S o lu t e W e i g h t (%)

Fig.5.12 Freezing point depression (ATf)due to the presence of dissolved NaC1 at different concentrations (anhydrous solute weight per cent, i.e. g solute/100g solution). The freezing point depression pores, as shown in Fig.5.12 where NaC1 weight in water (g s o l u t e / g 14% and

ATf = -5~

ATf is very important for large contaminated ATf is plotted versus the percent of anhydrous solution): ATf= -20~ per 23%; ATf = -10~ per

per 8% (Weast, 1985). This situation makes freezing in porous

materials at Venice, and other coastal sites, extremely difficult. Apparently, this factor seems an advantage; however, the longer permanence of a film of liquid water has m a n y other negative aspects (e.g. faster chemical kinetics, increased pollutant deposition, dissolved salt migration, biological life) that the positive ones are easily overcome. In addition, the contamination with soluble salts may lead to other important decay mechanisms, as we will see later.

161

CHAPTER 6

Atmospheric Water and Stone Weathering

6.1. ACID RAIN, RAINFALL AND CRUSTS Atmospheric water causes stone decay in several ways, which may be purely physical in nature, or a combination of physico-chemical processes (Camuffo, 1994; 1995). Chemical weathering is not directly related to the concentration of pollutants in the air, but to the joint action of meteoric water and pollutants which are deposited on the monument surface either in the dry or the wet phase. The wet deposition is the result of the atmospheric scavenging occurring in clouds, when the droplets are forming and growing (rainout), and during the fall of the droplets

(washout). Falling raindrops absorb hydrophilic gases and collect particles from the air that they transverse by means of complex deposition mechanisms that will be described in Chapter 8. As in dry deposition, the capture rate is less efficient for particle sizes ranging from 0.05 to 2 ~m and in this interval the main residence time of particles in the atmosphere reaches a maximum which is about I day. The amount of pollutants which is deposited in the dry phase is the result of: the concentration of airborne pollutants, the velocities of the different microphysical transport mechanisms near to and at the interface between the air and the artefact, and the capture efficiency of the surface itself. It denotes the net fraction of the atmospheric pollutants that are ultimately deposited on the monument and that may react with it. A measure of the pollutant concentration in the atmosphere without an estimate of the deposition velocities solves only a secondary part of the problem. Rainfall transports acid substances from the atmosphere to the surface of monuments. However, the purely meteorological nature of the precipitation is also of very great importance. In the Mediterranean climate it does not rain frequently in summer, and a great quantity of pollutants is deposited in the dry phase. The same occurs in winter in European regions which are under the influence of the ridge of high pressure that connects the Russian High with the Azorres Anticyclone. Under these conditions, the dry deposition that occurs in urban sites is much greater than

162 wet deposition. If precipitation occurs in the form of a heavy shower, the dry deposit is washed away quickly. Thus, knowing the intensity of the rainfall (i.e. amount per hour) may be more useful than the total monthly water precipitated. The frequency of rainfall may be even more useful in giving the first indication about the possible dominance of wet or dry deposition. In the last decades rainwater has reached alarming levels of acidity. This phenomenon has been considered one of the most important challenges of the modern society, affected by industrial, traffic and domestic pollution. In the past century several complaints were found in the industrialised England where rainfall was severely contaminated and smog obscured the day (Brimblecombe, 1987, 1992, 1995). However, the present-day activity is not the only responsible for the atmosphere acidification, as a number of interesting documents was found which describe acid rain and its effects since 1670, i.e. prior of the industrialised era (Camuffo, 1992), as well as caustic, foul smelling

'dry' fogs, which were reddish and

persistent, able to obscure the sun from one to several days, and caused damage to vegetation and illness to animals (Camuffo and Enzi, 1995). These 'dry' (i.e. nonwetting) fogs were so frequent during the Little Ice Age (i.e. from 1430 to 1850) and particularly in the past century, that the treatises of meteorology and agriculture distinguished between two kind of fogs: the 'wet' one which is favourable to the agriculture, and the 'dry' one which is dangerous to it. The cause of this natural acidification was the activity of the Mediterranean volcanoes. The 'dry' fogs were clouds of volcanic aerosols which were trapped in the planetary boundary layer in the warm season, when the atmosphere was particularly stable over the relatively cold sea waters and the Azores Anticyclone favoured calm or light winds. Explosive volcanic emissions may reach the stratosphere and be trapped there for two or three years, possibly affecting the earth's climate; but natural acidification of rainfall or fog, is typically generated by the less violent and continual emissions which remain trapped in the lower troposphere for days or weeks. In Southern Europe rainwater acidity is often buffered by the presence of alkaline particles, i.e. dust from the Sahara desert, that the Sirocco wind has first uplifted and then transported from North Africa to Europe (Prodi and Fea, 1979; Camuffo, 1990). The frequency of occurrence of this kind of precipitation varies with the geographic position, reaching 50% of the cases in certain regions of Italy. A great part of the Southern European territory is composed of liming soil, mainly of calcareous nature. However, also the soil of volcanic origin, or in any case non liming, is naturally protected by another phenomenon. When a precipitation with Sahara dust occurs, the droplets deposit on the ground a myriad of dust particles

163 that have not completely dissolved, thus forming a natural liming. When an acid rainfall follows, it will find the buffering deposit on the soil of the catchment basins, and the water that reaches rivers and lakes has lost part of its original acidity. For this reason the effect of acidification on the biological life of the water bodies of Italy is less dramatic than expected from the comparison with the Northern Europe. The situation is different for monuments, where the Sahara particles are easily removed by wind and rain, so that the surface is exposed to the aggression of the acid rain. However, another important difference exists with Northern Europe. In the North, the climate is rainy and the most part of the airborne pollutants are scavenged by rain and reach the soil transported by the droplets; in the South rainfall is less frequent and deposition occurs mainly in the dry phase. The contribution of rain acidity becomes less important and the key factor becomes that rain supplies water to the dry deposits that have accumulated on monuments. Although the acidity of the precipitated rainwater as well as the turbulent character of the run-off attacks the stone, rainfall is not as damaging as drizzle which wets the surface making the dry deposit chemically reactive, without removing it. Under these circumstances, the p H of the rain may be of little importance in comparison with the acidity of the dry deposit which generally contains elevated quantities of both acidic pollutants and catalysts, such as soot and oil-fired carbonaceous particles or carbonaceous fly ash due to the coal combustion (Del Monte et al., 1984a,b, Camuffo et al., 1984; Camuffo, 1986) which have been dominant in several European countries in the past and now are mainly limited to industrial areas of Eastern Europe. Acid water acts by dissolving both the stone surface and the binding between granules. In the latter case modest dissolution is sufficient to cause the loss of many granules, resulting in erosion. This rate of erosion may exceed the rate of dissolution by a factor of almost 2 for marble and 3 for limestone (Beadecker and Reddy, 1993). Many sulphation and dissolution processes occur especially in stones which have a calcareous matrix; metals are corroded; external frescoes and murals are lost. However, even in those cases where the particles deposited on frescoes or murals are not subjected to direct wetting by rain drops or run-off, an opaque layer is still formed, resulting in soiling and darkening. This, in turn means that the picture becomes less clear, so that each time a work of art is cleaned, it is subject to a stress brought about by the very nature of the intervention. The formation of crusts is related to the presence of water, but the necessary amount is generally supplied by rainwater, which is larger than that locally adsorbed by means of fog or condensation. These processes involve an amount of water which

164 is <
caused by the way meteoric water damps or washes the surface: where run-off dominates, dissolution and erosion occur and calcareous rocks form white areas; these areas are characterised by crystals of reprecipitated calcite and dolomite (Del Monte and Sabbioni, 1980) that form when the rainwater with contain the dissolved stone evaporates (Fig.6.1); where the stone is wetted but not washed out, black g y p s u m crusts originate (Fig.6.2a,b,c,d), with embedded carbonaceous particles which seem to play an important role in this process.

165

Fig.6.1 Whashing white area in a zone over which rainwater runs-off. The surface has been worn away by reprecipitated crystals of spatic calcite. The pitting is due to biocorrosion of microflora in the past (Trajan Column, Rome, after Camuffo, 1994, reprinted by permission of Butterworth-Heinemann). Field observations (Camuffo et al., 1982; 1987; Camuffo, 1984; 1986; 1990) have shown that, in the zones exposed to run-off, gypsum crystals were found only rarely, whereas a thin layer of spatic calcite and dolomite crystals due to reprecipitation was common. On the other hand, the maximum quantity of g y p s u m was found where run-off was prevented, i.e. in the black crusts. The acid rain hypothesis alone is not sufficient to explain the main phenomenon due to sulphation, i.e. the black crusts, which are one of the main problems affecting marble monuments. Sometimes they constitute an aesthetic problem only, sometimes they are d a n g e r o u s as they constitute a deposit of pollutants which interact with the underlying stone layer in the presence of water. By the way, the gypsum crusts due to simple sulphation by acid rainwater, should be whitish, and not black. In the case of marble and compact limestone, the visual features of the deterioration patterns could be related to the three main ways the water wetted the surface: (i) run-off is associated with washing white areas in the zones where the surface had been worn away; (ii) damping due to splashing droplets, or percolation

166

Fig.6.2 Examples of black crusts formed where rainwater wets (either splashing raindrops or percolation) but is unable to remove the dry deposit by means of run-off. (a): On marble, where the engraving of the letter A deflects the run-off (Aurelian Column, Rome; after Camuffo, 1984, reprinted by permission of Elsevier Science Ltd). (b): Below protruding decorations on limestone (Palazzo dei Priori, Padova); (c): In typical sheltered areas under the eyebrows and moustaches on marble (Constantine Arch, Rome). (d): Black deposits (mainly composed from gypsum and black soot) on a bronze statue, where windborne raindrops (and running water amount) are prevailing on the left side (Grand Place, Brussels).

167 near zones where run-off was present, is associated with black areas where black crusts dominate; (iii) absence of both run-off and percolation, but possible condensation is associated with grey areas where the stone was not chemically affected but covered instead with a layer of dust and particles. Although the specific mechanisms involved are still under discussion, fly ash, microsoot and single carbonaceous particles (formed during the combustion of oil) are active in forming black crusts when they are wetted by the percolation of rainwater. These combustion products contain sulphur compounds and catalysts and nucleate gypsum crystals when wetted, so that they become embedded in a gypsum crust. The gypsum partly results from the transformation of the underlying rock, and partly from particle nucleation. The black crusts have a dendritic appearance as a consequence of the mechanism whereby particles are deposited and bind together with gypsum crystals; the proportion between the gypsum and the particulate matter which has deposited determines the mechanical strength of the crusts. Where the underlying substrate is not marble or limestone or the calcareous rock cannot be sulphated, the gypsum is very scarce (i.e. only that originated by the particles) and the crust is very friable. All the black crusts examined, samples of which were taken from nearly all the European countries, contained carbonaceous particles and it has been possible to reproduce this mechanism in the laboratory (Sabbioni et al., 1993). Of course, these dendritic crusts cannot be confused with the black patinas of biological origin (e.g. fungal melanin, lichens, algae, cyanobacteria), with growth, combination and repetition of some elementary structures, possibly associated with biocorrosive pitting. In particular, the microflora also needs special microclimatic conditions to develop; chiefly a frequent supply of water. For this reason black biological patinas can be found in places where the formation of crusts composed of soot and gypsum is impossible due to the frequent presence of run-off (Fig.6.3a,b). Sometimes, the situation is more complex due to an interaction between anthropogenic deposits and biogenic black materials, e.g. soot entrapped in microbial films. As melanin is made up of mixtures of polysaccharides, proteins, lipids and aromatic compounds, biological patinas can be identified by means of pyrolysis/methylation of crust samples (Saiz-Jimenez, 1995). Green patinas typical of algae colonisation form on damp surfaces. In the windy and rainy climate of northern Europe, walls exposed to the dominant windborne raindrops .direction are favoured; in the less rainy Mediterranean climate, algae can be found in the most humid microclimates (e.g. Venice) and prefer the horizontal surfaces in the shadow, which are frequently reached by rainfall and where water remains longer (Fig.6.3c). It should be noted, however, that the mechanisms of biodeterioration are not simply

168

Fig.6.3 Comparison of crusts having different origin. (a): Black crusts originated by soot deposit, found in a capital: the parts where water runs are white, the parts wetted but not washed out are black. (Ducal Palace, Venice). (b): Black biological patches are found in places frequently wetted, where the formation of crusts composed of soot and gypsum is impossible due to the frequent presence of runoff, and white areas are found in dry, non washed areas where black deposits are expected in the case of heavy pollution. (Ravello, Italy). (c): Green patinas typical of algae colonisation form on damp surfaces. At Venice they prefer the horizontal surfaces on the shadow which remain damp longer (Piazza S.Marco, Venice).

169 restricted to clearly evident patinas, pitting or other corrosion damages. The absorption of corrosive and nutritional atmospheric pollutants is even increased by the presence of sticky biofilms (Wittenburg, 1994). This way, the stone colonising microflora accelerates passively the reaction rate of biochemical induced corrosion processes and influences in consequence the formation of crusts as their final result (Warscheid and Kuroczkin, 1997). This phenomenon was documented by nearly unaffected stone surfaces below biocidal acting brass settings which hinder the contamination of microbial biofilm (Becker et al., 1994). On stones exposed to low air pollution, biodeterioration might be more or less evident, e.g. for the presence of multicoloured photosynthetic algae, cyanobacteria or lichens. In highly polluted areas it might be possible that microbial infections are not easy to detect, although bacterial or fungal microfilms are present. Although the washing white areas are subject to dry deposition, the abundant run-off washes over the monument surface and in general removes most of the attached pollutants. Their action is continued by the falling rainwater. The result is the wearing of the surface which is only slightly or dramatically dissolved as a function of the total amount of rainwater and over which crystals of calcite and dolomite may reprecipitate. The effects found on monuments are the result of some factors: the physicochemical characteristics of the stone, the type of pollutants and their deposition rate, the local climate and the geometry of the monument. When one of these factors only slightly changes, the result will be very different. For instance, in heavy polluted areas of Central Europe, the deposition rate is so fast, that the blackening is largely dominant over the washout, so that the white areas generated by washout practically disappear. In these regions all the surfaces are covered with a thick black deposit, and chemical reactions occur especially in the parts of the monument which are wetted more often. The outer layer of the limestone is transformed in a black gypsum crust with a thickness that may reach one or few centimetres. In the long run, the different physico-chemical characteristics of the transformed layer cause the detachment and the fall of it. A new type of white area appears: the internal clean surface where the fracture has occurred, which is generally close to the interface between the uncontaminated rock and the crust (Fig.6.4). In zones where the atmospheric pollution has been drastically reduced, this breaking white area remains clear for a long time; in zones where the pollution is still high, these white areas are blackened again in a short time. When the stone is characterised by large pores and is absorbent, the visual features are quite similar. Vertical surfaces absorb falling droplets and run-off can

170

Fig.6.4 Breaking white area generated in a heavyly polluted zone: the white area is the internal surface where the fracture has occurred. Notre Dame en Vaux, Chalon sur Marne, France.

171 not develop, so that the dry deposit is not removed, and may be transported into the pores. Wash-out and dissolution may only occur where great amounts of water are collected, e.g. under windows. However, the running water is eventually absorbed by the porous stone; the running layer becomes thinner, the turbulence damps, the flow becomes laminar and then disappears (Fig.6.5). In a turbulent regime the surface is cleaned and eroded; in the laminar one the material removed from the upper surface is released onto the underlying rock. When the regime is laminar, the first layer in contact with the surface becomes saturated and is then chemically inactive. When it is turbulent, the chemically active solution continually changes on the stone surface which is subjected to heavy dissolution and erosion due to loss of granules.

Fig.6.5 Visual features of a porous calcarenite wetted by splashing raindrops (the gray wall), dissolution by run-off where rainwater may collect and run-off with turbulence (the white area below the window) and in laminar regime after adsorption, releasing the material previously removed (the darker gray area below the dissolution area). The Mayor's Palace, Brussels. A short note about a popular error that is well known to environmental chemists, i.e. about averaging the p H of rainfall. This parameter describes the hydrogen ion activity of rainwater, and is defined as-logl0[H+], where [H +] is the

172 h y d r o g e n ion concentration in moles per litre. Mixing two different volumes of different solutions with different

pHs, the pH of

the mixture is determined by the

final H + concentration, which can be computed after the proportions of the initial concentrations and volumes. The same is compute time averages of different

pH

values that have been found in successive samples of rainwater collected during one or more precipitation events. It is necessary to return to the original H + concentrations, average them (which is equivalent to mix together all the samples) and then compute the

pH of

the final mixture. Arithmetic averages of

pHs do

not

make sense.

6.2. MECHANISMS OF PENETRATION OF RAIN WATER AND EVAPORATION Penetration of rain water into the monuments while it is flowing over the surface also depends upon climatic factors, in addition to the nature of the material (Dullen, 1979). Penetration into capillaries and pores is possible only when the whole cavity surface (i.e. both the external and the internal one) is covered with a single or double layer of water molecules in the solid state, and this process is not possible when the surface is completely dry, i.e. not covered with monolayers of solid water (Camuffo, 1991a). When the surface of the material is still 'wet', i.e. covered with the monolayer of solid water, as generally occurs in the humid climates, liquid water penetrates (Fig.6.6a) by simply advancing towards the interior with a concave meniscus that does not experience any change in curvature (no external work due to surface tension); in addition, the concave meniscus forms a lower vapour pressure in front of it, which favours penetration into the capillary (positive work). In the case of a completely 'dry' surface, i.e. without the solid water monolayer, the meniscus of the water penetrating into the capillary is convex in the forward direction, and the meniscus must elongate gradually as the water penetrates into the capillary (Fig.6.6b). The work required against the surface tension and the higher vapour pressure over a convex meniscus is so great that water can not penetrate under such conditions and runs over the monument without dampening it. For dry materials a preliminary 'wetting' of the internal surface is a necessary condition for water to deeply penetrate and soak into it. In a hot, dry climate which is predominant during the summertime in southern Europe, m o n u m e n t s have the external surface and also, in the outer layer, the internal one (i.e. the internal surface of pores) completely dried out because of the strong warming associated with the intense solar radiation. This then means that

173 water, during a typical sudden shower in the afternoon, can not initially penetrate into the pores and capillaries of the stone, because these are not lined with a monolayer of water molecules in the solid state that would allow the liquid water to run over it.

Fig.6.6 Penetration of water into a wet capillary. (a): The meniscus is concave. (b): In a dry capillary the meniscus is convex and water cannot penetrate.

Even microbial biofilms regulate the penetration of rainwater: first they reduce the capillary water uptake preventing a rapid moistening of the uppermost material layer during showers, but later they conserve part of the water which has already penetrated into the material much longer than a non infected material will do, especially when surface-active compounds are formed due to the biomineralisation of hydrocarbons, frequently present on rock surfaces (Warscheid et al., 1991). The penetration of water is favoured by p u m p i n g mechanisms, and the wind is a very active generator of them. The first important m e c h a n i s m is due to the interaction between the m o n u m e n t and the wind field. An airflow with speed u will develop local pressures p over the m o n u m e n t in accordance with the Bernoulli's equation (which holds for an incompressible and inviscid, i..e. without viscosity, flow): 1 /9 U 2 +

p - const

(6.1)

where p is the air density and the kinetic term 0.5/9 u 2 has dimension of pressure and is called dynamic pressure. Each streamline is characterised by its own constant. The wind is unsteady in speed and direction and the m o n u m e n t causes continually local departures. In addition to the Bernoulli's changes of pressure far from the

174 monument, the effect is amplified close to the monument surface according to an aerodynamic coefficient, which varies point by point, and accounts for the interactions between monument shape and position, wind speed and angle of attack. Every change in the wind field is associated with a change in pressure. The wind exerts over the surface a net force along the flow direction

(drag) and across the flow

(lift) and a moment. In the frontal position, the drag drives the water into the monument, and the lift displaces it along the surface. All these components depend upon monument features and Reynolds number. The second mechanism is related to the formation of a boundary layer in proximity of the monument. The wind speed is affected by the presence of the monument and the aerodynamic disturbance forms a boundary layer where the air speed drops following a logarithmic profile with the distance from the surface until the air in contact with the surface adheres to it (no slip). This causes a retardation of the air motion and a pressure field which varies with the angle of attack. The third mechanism is intrinsic of the fluctuating character of the wind. Pressure fluctuations associated with wind gusts or lulls can amount to two or three hectopascals. They cause a fluctuating pressure difference between the interior and exterior of the monument, which may force the water in the layer running over the surface to penetrate into the cavities and be trapped in the pores. After many successive steps, water may penetrate deeply in the interior of the porous materials. External pollutants may also be trapped inside the material and continue the deterioration process each time microclimatic factors are suitable.

6.3. EVAPORATION FROM A DAMP MONUMENT The drying is also controlled by several factors, i.e. atmospheric, e.g. specific humidity gradient and air turbulence near the surface; intrinsic factors, e.g. pore and capillary size and distribution; another important factor is the type and concentration of dissolved salts. Gravity is also important for the downward transport of liquid water and determines a vertical gradient of dampness that is sometimes misinterpreted as capillary rise of ground water. When a wall or a stone is damp at its maximum capacity, the evaporation occurs first from the water film which covers the surface, and the water which is lost is continually replaced by other water transported by capillarity from deeper layers. The drying rate

3W/dt is controlled by

the exchange with the atmosphere, and mainly depends upon wind speed, ambient relative humidity and sunshine. In steady conditions, initially the flow of moisture is constant and laboratory experiments show that the weight W of a damp sample

175 decreases linearly and rapidly, so that 3W/dt is constant. When the capillary transport of liquid water becomes unable to supply water at the same rate as evaporation occurs, the whole of the surface is no longer covered with a water film, and the drying rate decreases until the mechanism is controlled by the diffusion of the moisture from the interior of the material. Laboratory experiments show a transition zone, in which 3W/dt lowers and lowers until it reaches a very small value. Consequently, the weight of the sample decreases slowly and slowly, and the plot of W versus t turns until it reaches another approximately linear trend, close to the horizontal, index of a very slow evaporation. In this step, the evaporation occurs inside pores and capillaries, and then the vapour migrates outside through the pore and capillary fringe, until it reaches the surface where is quickly dispersed into the atmosphere. In the transition zone, the evaporation occurs first in the pores which are closer to the surface and where the free meniscus allows the evaporation more easily; then in the deeper and smaller pores making slower the mechanism. After the time elapses, the vapour diffusion occurs through longer and longer paths and with smaller and smaller concentration gradients, so that also the exchange with the atmosphere and the drying rate decrease. In this last step, the loss of water occurs very slowly, reaching asymptotically the moisture content in equilibrium with the ambient. In practice, for a wall this step may last for a very long time, e.g. months, depending upon the thickness of the wall, the characteristics of bricks, mortar, plaster and colour coating, and the exchange with the atmosphere.

6.4. CAPILLARY SUCTION Capillary suction occurs in all the directions, but a precise mathematical formulation is given only for the vertical ascent, which is the most important problem. The rise of water by capillarity is a well known and important factor in monument weathering, especially in the case of historic brick buildings where the water front reaches considerable heights. The capillary rise can be simply calculated by means of the Laplace formula, isolating h from the geopotential height in the Stevin's formula 213

h = ~cos0

rpg

(6.2)

which states that the height h is inversely proportional to r and is affected by the wetting angle which changes with the physico-chemical characteristics of the surface

176 and the type and a m o u n t of dissolved salts. The formula is graphically reported in Fig.6.7 where h has been c o m p u t e d for cos0 = 1; the plot represents the u p p e r limit, as cos0 < 1. It can be observed that h reaches extremely high values for very thin capillaries (e.g. h = 1.47 km for capillary radius r = 0.01 ~tm at 20~

and decreases

rapidly w h e n the capillary size increases (e.g. h = 1.47 m m for r = 1 cm).

100000 10000 1000 r,j

100 ol-i

Q;

10

0,1 0,01

t

t

i

i

trill

0,1

t

t

t

tltttl

i

1

i

i

tlltll

t

t

t

iiiitt

10

t

100

t

t

tttlll

1000

t

t

t

ittl

10000

Radius (Bm)

Fig.6.7 Height h of the capillary rise versus the capillary radius r.

It is useful to c o m m e n t the above result, as for very thin capillaries it seems unbelievable. The volume occupied by one H 2 0 molecule in the liquid state can be obtained dividing the molar volume of water, i.e. 18 cm 3, by the Avogadro n u m b e r . / # - 6.02x1023, and the effective diameter is about 3 ~ (1,~ = 10 -4 ~tm). A capillary with radius r = 0.01 ~tm m a y contain 33 concentric layers having each one the thickness of a water molecule; the first 3 molecular layers near the capillary surface are b o u n d by molecular forces and cannot move, but the water molecules which are in the inner part of the capillary, beyond this critical distance, can move freely and liquid water can flow. H o w e v e r , the cross section of capillary is never constant, w i d e n i n g and thinning. In the case of these extremely thin capillaries, an irregular t h i n n i n g of the cross sections m a y be critical, hindering the free flow, and the probability of finding a capillary w i t h o u t any irregularity is extremely low. In practice, water suction is possible w h e n changes in the capillary section never attain

177 critical values, and laboratory tests show that capillaries smaller than 0.1 t,tm are practically unable to absorb water (Winkler, 1994). Capillary suction (in particular for g r o u n d w a t e r or collected rainfall) is therefore m u c h more efficient than condensation in causing dampness. This formula has been computed for the capillary rise (i.e. u p w a r d suction), equalising the component of force tangential to the capillary Ft, and the resulting Kelvin's effect, to the action of the gravitational force on the water column. It is obvious that capillary suction, governed by the presence of curved meniscus and Kelvin law, occurs in all directions. In particular, no theoretical limit can be found to the displacement of water along a horizontal or downward path. In comparison with capillary rise (i.e. along the vertical), capillary suction is more active on the horizontal direction, being not counteracted by gravitation, and is favoured by gravitation on the d o w n w a r d direction. This can be experimentally proved by supplying water into a small hole made on a wall plaster. The stain of d a m p masonry develops similarly to a growing vertical ellipse which has the upper focus on the injection hole. The m i n i m u m growing velocity is upwards, the m a x i m u m d o w n w a r d s and an intermediate value on the two opposite horizontal sides. In masonry, the vertical rise (where the suction force is opposed by the gravity) occurs at a rate which is half of the horizontal spread. The velocity at which water flows in a capillary is given by the Washburn equation dx 2 o cos0 -r p g x cosO dt - r 8 TIx

(6.3)

where x is the distance travelled by the water in the capillary, whatever is its direction, e.g. being inclined of angle q~ with reference to the vertical so that cosO equals 1 for u p w a r d displacements,-1 for d o w n w a r d and 0 for horizontal ones; 11 is the dynamic viscosity of water, e.g. 1307 ~tPa s at 10~ and 1002 ~tPa s at 20~

From

this equation it is possible to find the distance travelled by the water table after the time 1: is elapsed, i.e.

~/ x=

I:

r o cos0 211

which is often concisely expressed as

(6.4)

178 x=A ~

(6.5)

where the coefficient A includes the dependence upon the radius, the surface tension, the wettability and the viscosity. The penetration of water may continue for weeks or months. The velocity of penetration is faster at the beginning and is given by the above equations; later decreases. Similarly, the amount of adsorbed water WA varies linearly with the square root of the elapsed time x i.e. WA = B ~

(6.6)

where the coefficient B depends upon the characteristics of the material, although some exceptions have been noted (Gummerson et al., 1980). If there is divergence in the water flow with lateral spreading of the water front, the cumulative water absorption increases more rapidly than ~ (Hall, 1981). Capillary suction occurs with the progressive displacement of water, so that it cannot be stopped by pockets of air entrapped in the pore and capillary system, except for ducts without an outlet, in which the capillary pressure is counteracted by the entrapped air. Excesses of pressure which are generated by heating are important e.g. on porous tiles where the cavities are topped by the glaze of the decorative ceramic surface, especially when the thermal shocks are noticeable. A capillary closed at the upper extreme may be filled with water until the pressure of the air entrapped equals the Laplace pressure [I determined by the meniscus curvature, minus the Stevin contribution due to gravity, as it has been discussed in the previos Chapter. Solar radiation falling on the material with air pockets embedded causes an increase in the pressure inside the cavities due to the temperature rise AT according to the law of gases pV = (na +nv).~T

(6.7)

where na and nv the number of moles of dry air and water vapour, respectively. This excess of pressure causes the water meniscus to retreat and reach a new equilibrium due to the simultaneous presence of a gas and a saturated vapour, as follows: (i) na is constant and the partial pressure of dry air is inversely proportional to V; (ii) nv is not constant: in fact, AT causes a drop in RH and consequently new water molecules will evaporate to compensate the temperature effect until the original R H is reestablished, being the R H determined by the radius of the capillary (Camuffo, 1991b). The partial increase of pressure due to the vapour is shown in Fig.6.8.

179

I

0

|

.

,

,

i

|

5

,

,

,

i

10

,

|

,

|

I

|

|

,

15

|

I

20

,

,

|

|

i

25

|

,

,

.

30

Temperature (~ Fig.6.8 Increase in normalized partial pressure p(t)/p(O) of the water vapour following a temperature rise t (~ in a capillary due to both the vapour heating and the increase of the number of water molecules which had evaporated to re-establish the original RH in the cavity. Note that p(t) is not affected by retreat of water meniscus and increase in the volume of the cylindrical air pocket, the molecules being a saturated vapour and not a perfect gas.

The mean height reached by capillary rise is marked by a belt of efflorescing salts: where the water evaporates the salts end their migration and remain there, impregnating the masonry with thick surface and subsurface deposits. Of course, the damage is enhanced in the presence of soluble substances, osmotic effects and salt crystallisation. On plasters and frescoes, at high humidity, residual crystals of calcium oxide may hydrolyse becoming calcium hydroxide, causing pitting as a consequence of crystal growth. Crystallising salts have a disruptive effect as a consequence of pressure generated by the growing crystals, hydration a n d / o r thermal expansion. The osmotic effect causes an upward rise of the ions that displace the wet front upwards. In the region where water evaporates, the transported salts accumulate locally causing more and more damage (Arnold and Zehnder, 1990), as will be discussed later.

6.5. LOWERING OF THE EQUILIBRIUM VAPOUR TENSION OVER A SOLUTION In the previous section about heterogeneous nucleation it has been anticipated that salts dissolved in the water will lower the water vapour pressure because the

180 water molecules are effectively diluted by the presence of the salt. It is useful to discuss some basic results of applied physical chemistry (for further details see Kireev, 1977; Adamson, 1986) as this effect is often dominant and makes possible condensation in several circumstances. The Raoult's law for ideal solutions states that the saturated vapour pressure PA of the solvent A over a solution is always lower than over the pure solvent. The greater the concentration of the solute, the lower the equilibrium vapour pressure, i.e. the saturation vapour pressure PA of the component A over the solution is directly proportional to its mole fraction XA i.e. PA = Po XA where Po is the vapour pressure of the component A in the pure state, i.e. when

(6.8) XA

-

1. However, the concentrations of the solvent A and the solute B, XB, are linked by the simple relation XA + XB = 1, so that the previous equation can be rewritten as PA = Po (1-XB)

(6.9)

which can be rewritten in terms of the difference Ap = Po -PA. Applying the result to the water vapour, the lowering of the partial pressure Ae(X) of the water vapour in equilibrium with a diluted solution is directly proportional to the mole fraction X of the solute, Ae(X) = eoX

(6.10)

where, according to the c o m m o n notation, eo is the saturation pressure for pure water that has been indicated with e(~o) in the previous Kelvin's formulae, as the label 'o' is not anymore concerned with the curvature radius, but now indicates the pure sovent with 'zero' moles of dissolved solute. The Raoult's law is an ideal, limiting law for complete uniformity of intermolecular forces. A second ideal, limiting law, i.e. the Henry's law, for extremely diluted solutions, states that all the molecules of the solute B are completely surrounded by molecules of the solvent A and the partial pressure of the solute B becomes proportional to the mole fraction in the limit of zero concentration, i.e. when XB---~0 limpB = k XB

(6.11)

where k is a constant with the dimension of pressure and the behaviour of B is determined by the nature of the A-B interactions. In the case of deliquescent salts and concentrate solutions the situation is better described by the Raoult's law. The lowering of the vapour pressure can be related to the change in free energy

181

of the vapour by e

AG = .~/,~ T I n (~o)

(6.12)

where AG is the change in free energy of the vapour in going from the vapour pressure e to the saturation pressure for pure water eo. If the water in solution is in equilibrium with the vapour above it, AG also represents the change in free energy of the liquid water.

6.6. CLIMATE CYCLES, SEA SPRAY AND SALT DAMAGE Salts play an important role in decay because they can precipitate within an aqueous solution when the salt concentration becomes saturated for loss of water due to evaporation, or because some of them are deliquescent and crystallise when the ambient relative humidity drops below certain critical levels, or may change crystalline form or hydrate under some environmental conditions which may be changed by the presence of some contaminants, or may expand after heating. Environmental cycles of temperature or humidity, or periodic heating due to direct solar radiation may induce salt migration, precipitation, growth, hydration and expansion and may trigger disruptive cycles within the pores, causing fatigue or breaking the internal material structure. If a dilute salt solution within the pores is exposed to a low relative humidity, water will evaporate from the solution and the salt concentration will increase. The higher the concentration, the lower the vapour pressure in equilibrium with it, until a critical limit is reached, i.e. the lowest equilibrium R H at which the salt solution reaches saturation. If the ambient R H drops below this critical value, the water molecules will continue to evaporate and some salt crystals will begin to precipitate and grow. The mechanism is in some aspects similar to that has been described for freezing. Evaporation begins in medium or large pores which are in contact with the external environment and some precipitation begins. New water is withdrawn from the neighbouring small pores to replace the evaporated moisture. This transport leads empty the smallest pores, whereas the too large cavities remain empty. Arnold and Zehnder (1991) noted that salt crystals form mainly in pores from 1 to 10 ~tm diameter, and that they follow this sequence: crystallisation continues filling the pores where the crystallisation began, then crystals enter the neighbouring pores; successively small fissures are determined, and crystallisation continues in columnar growth able to lift spalls and detach crusts. They found also that the crystal

182 morphology is related to the substrate humidity: in the presence of liquid water large crystals grow completely immersed into the solution; on a damp substrate smaller and hygrometric crystals form a granular crust covered with a film of solution; in dryer environment, a humid substrate forms a fibrous crust; on less h u m i d substrates isolated columnar crystals grow; on nearly dry surfaces with localised supply of moisture the crystals are very thin and acicular, hair like, and are called

'whiskers'. New dampness may transform fresh whiskers in a more compact, differently crystallised crust. Every cycle of RH which crosses the critical equilibrium value causes a precipitation/redissolution cycle. In the general case several soluble salts are present inside walls or stones determining a very complex situation for their interactions. However, they precipitate in sequences according to their respective solubilities, whereas the most soluble remains in solution, determining time sequences of crystallisation or space patterns which reflect on vertical layering of the salt front when the source is groundwater capillary rise. In this case Arnold and Zehnder (1991) found that the salts are locally accumulated in a zone from 0.5 to 3 m above the ground level, with this typical sequence from the lower to the higher part: sulphates, nitrates, chlorides. This vertical fractionation was explained considering that, during evaporation, salts with low solubility become supersaturated and are the first to precipitate, while the more soluble salts can continue their rise and will precipitate at upper levels. The more soluble the salts, the more hygroscopic they tend to be (Arnold, 1983). For this reason, the upper layer is characterised by a high concentration of very soluble and hygroscopic salts, which tend to form a humid belt on the top of the rising damp. When a solution in equilibrium with its environment has reached saturation, every drop of relative h u m i d i t y causes evaporation, s u p e r s a t u r a t i o n and precipitation. Some solutions reach this critical condition at ordinary RH, and above the critical equilibrium levels of RH only the precipitated salts can be found. Several deliquescent salts can be found on monuments, e.g. NaC1 at RH = 75%, NaNO3 at

RH = 74%, Mg(NO3)a.6H20 at RH = 54%, Ca(NO3)2.4H20 at RH = 53%, when the temperature is 20~

but the equilibrium RH changes with temperature. Daily

microclimate cycles due e.g. to solar heating or room heating may induce crystallisation cycles in walls or monuments. For this reason, in the cold climate, weekly heating-cooling cycles in churches lead to important changes in the wall temperature, followed by severe damage due to crystallisation cycles. Some salts exist in two crystalline forms, i.e. anhydrous and hydrate, including

some'water of crystallisation' as part of their structure e.g. gypsum (CaSO4.2H20) and

183 anhydrite (i.e. CaSO4). In the transition from the anhydrous to the hydrated phase they expand and may damage the material in which they are embedded. Breaking waves and whitecaps gives a yearly production ranging from 109 to 101~ tons of sea salt aerosols which are transported inland and fall dissolved into raindrops. The production of whitecaps and the subsequent transport of sea spray depends upon the wind speed. The sea salt concentration increases exponentially with the wind speed. With winds below 5 ms q, a variable threshold of sea spray is found, either due to higher variability of the wind field over the sea or production of spray in the previous days. For wind speed <10 ms -1 the sea salt concentration increases with the first power of the wind speed; above this speed, the concentration increases again and reaches the third power at 20 ms -1 and more than the fourth power as the winds approach the hurricane speed (Blanchard and Woodcock, 1980). Certain sites are very unfavourable for stone conservation, due to adverse natural conditions determined by climatic cycles and sea spray contamination, worsened by the presence of anthropogenic pollution. Venice is one of them and will be presented here to elucidate the problem with reference to the daily and seasonal values of relative h u m i d i t y and air t e m p e r a t u r e

(Fig.6.9). The sea s p r a y

contamination increases not only the time of wetness, but also the solubility of some salts, causing many disruptive cycles. Initially the solubility of g y p s u m increases with the sea spray concentration until it increases by a factor of four when it reaches the maximum, and then decreases again. When a stone is contaminated with sea spray, the NaC1 may be either in the crystalline form or in solution with adsorbed water vapour. At ambient R H below 75% the NaC1 is in form of dry crystals, and at higher R H values it will adsorb water and dilute within it. The solubility of calcium sulphate in an aqueous solution of NaC1 will begin at R H = 75%, will increase to R H = 90% and then will fall again as the NaC1 concentration decreases, i.e. the R H increases. As the m a x i m u m solubility is reached at ambient R H = 90%, at each transition towards increasing or decreasing R H values, some g y p s u m crystal will form. This cycle studied by Price and Brimblecombe (1994) is extremely important in coastal areas. As every night the saturation is reached in Venice, every day this transition occurs twice. In addition, in the mid seasons and in summer, when the R H drops below 75% in the central part of the day, reprecipitation of the dissolved fraction of any soluble salt will occur every morning when the salt solution dries, and a partial dissolution will occur every evening when the ambient R H rises above 75% and the contaminated stones begin to wet. However, also in the absence of other soluble salts, the NaC1 alone is sufficient to cause severe damage. As not all the stones are in thermal equilibrium with the air, the number of cycles and the damage

184 will vary from exposure to exposure, from building to building, from stone to stone. The increase of gypsum solubility has another important effect. In the white areas, the gypsum crystals which reprecipitate over the original limestone surface are easily removed in a short time being redissolved by rainfall, leaving unprotected the limestone which is eventually dissolved by acid rainfall. 3o I 2520o

15 10 5"

~i

-5

1

2

3

4

5

6

7

8

9

10

11

12

Months 100 90 80 70 60 50 1

i

!

!

!

!

!

!

!

!

!

2

3

4

5

6

7

8

9

10

11

12

Months

Fig.6.9 Seasonal variation of the average daily range of air temperature and relative humidity at Venice.

Another interesting hydration/dehydration cycle determined in coastal sites by temperature changes was determined by Gordon and MacDonald (1953). They found (Fig.6.10) that at 40~ and ordinary pressure, gypsum, anhydrite and liquid water can coexist. Above 40~ anhydrite is the most stable form, below gypsum. However,

185 the presence of sea spray lowers the transition temperature: the latter decreases with increasing NaC1 concentration. When the solution contains 3 moles of NaC1, the transition temperature is 30~ at 4 moles 25~ at 5 moles 21~ at saturation (i.e. 6.15 moles) the transition occurs at 14~ This suggests that for most part of the year temperature and humidity cycles induce calcium sulphate crystals to undergo daily hydration/dehydration cycles with continuous expansion and contraction of their volume. 40

.:...., .......,..... :.:.:.:,:.:.:.:.:..... ............................ .:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:...,. .......,.......,...................,...... ...................................,...........

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~ iiiiiii~iiiiiiiiiiiiiiiiiiiiiii~iiiiiiiiiiiiiii~iiiiiiii~iiii....... ii;i~i~:~ o._. 25 iiii i.i!i!i!i!iiii ii!i!i!i i!i iiiiiii!iiiiiiiiiii!ii!iiiiiiiiii!i!i!!!!ii!i!iii!iiiiii i i!iiiii i!i iiii!!i! ii ~::::maxi!iiii .,,,,..._._,.,.,,...,.....,................,.......,

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iiii!i!iiii!ii!iiiiii!iiii!iiiiii!iiiiii i iiiiiiiiiiiiii i iii!iiiiiiiiiiiiiiiiii i iii!iiiiiiiiiiiiiii i iiiiiiii1 i iii i

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii o iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii i i ......

o 5 -5 ]!!i!i!i!i!i!i!!ii!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!!i!ii!i!i!i!i!i!i!i!i!i!!ii!i!i!!ii!ii!!i!i!i!i!i!i!!ii!i!i!!i!i!i!i!i!!i!!ii!!!i!i!i!!i!!i!!!i!i!!ii!i!i!!i!i!i!i!ii!iiiiil 0

1

2

3

4

5

6

7

8

Moles NaCl/1000g H20

Fig.6.10 Transition between gypsum and anhydrite induced by temperature and NaC1 contamination, in the presence of liquid water at ordinary pressure (after Gordon and MacDonald, 1953, reprinted by permission of the American Journal of Science) and average minimum and maximum temperatures at Venice, in January and July. Transition needs a lower NaC1 concentration in summer, and a higher one in winter. In the general case, a monument is non uniformly contaminated by this salt, or wetted by water, and on the surface the concentration of dissolved NaC1 is variable with height or orientation. Therefore, the parts which are most heavily affected by this mechanism change seasonally. The above examples have considered the presence of only one contaminant, but the real situation is much more complex. Other salts which are deliquescent at ordinary humidity levels, e.g. several minerals derived from nitrogen, extend the TOW and the range of ambient RH at which crystallisation and hydration take place; in addition, also the chemical reactions, and the minerals which are generated, may be influenced by the presence of sea spray. Thermal expansion too may intervene to continue the deterioration mechanism. The formed crystals will have mechanical characteristics different from the porous material. If its the expansion coefficient is greater, the new crystal will come in

186 contact with the internal pore surface and exert pressure when the temperature rises; if is smaller, when the temperature drops.

6.7. SOME COMMON ERRORS THAT SHOULD BE AVOIDED The risk of errors is particularly high in applications that are very complex and essentially of multidisciplinary character, especially when one expert (which is necessarily expert in only one or a few specific disciplines) gives a suggestion which may appear brilliant from his point of view, but which may have negative consequences in other fields. Although human errors probably are one of the main, but less documented, caus~ of decay, nevertheless their knowledge may help to avoid their repetition. This is specially true for the most frequent errors which are the consequence of wrong popular beliefs, or are the acritical repetition of remedies which have been proved useful in other apparently similar circumstances. As a practical application, a short list of useful examples is here enclosed.

6.7.1. Condensation or evaporation ? Several years ago I read the report of a panel composed of experts in conservation who suggested some remedies for the Chiesa dei Miracoli, Venice. The Church was built in 1489 on the edge of a canal and was severely damaged by dampness. The report was amazing for a loop of contradictory statements which arrived at a wrong suggestion that, unfortunately, was applied. The incoherent loop of self-generating causes and effects was more or less as follows. The wall is damp, then evaporates. The evaporation forces the wall temperature to drop. When the wall temperature is dropped, condensation begins to occur. The suggestion is to warm the air in proximity of the wall. By warming the air, the relative humidity lowers. When the air is dry, the condensation stops. The problem is solved. The wall was damp, very probably due to capillary rise increased by the presence of sea salt, and evaporated. Evaporation does not indefinitely lower the temperature of the interface between the air and the stone, but tends to approach the wet-bulb temperature. The t e m p e r a t u r e of evaporation (i.e. the wet-bulb temperature), is well defined thermodynamically, and is higher than the temperature of condensation (i.e. the dew point). As evaporation and condensation occur at two different temperatures, none of them can be the cause of the other one. Never evaporation may cause condensation, and when the two temperatures approachr the net flux of moisture stops and there is no practical exchange between the wet surface and the atmosphere.

187 The suggestion of warming the air in order to lower the relative humidity and stop condensation on a cold surface is scientifically unsound. Condensation occurs on a cold surface, whose temperature is below the dew point irrespective of the air

relative humidity. In the Chapter 2 we have seen that the DP is a function of the specific humidity only and the latter is lowered only if moisture is removed from the air, not if the air is heated. However, another mechanism may intervene, which eventually may stop the condensation. In the case of actual condensation on a cold wall, by heating the air, in the long run also the wall is heated. When its temperature becomes higher than the dew point, condensation stops. For this reason it is much more convenient to warm directly the wall, not the air (Camuffo and Valcher, 1986). In addition, by heating the air another negative mechanism was generated: the wall was damp for capillary rise and the water evaporated in the atmosphere; by lowering the relative humidity the evaporation rate was increased as well as the migration of the soluble salts and the formation of efflorescences. Theoretically, this process will stop only when all the water in the channel will evaporate passing through the church walls. Evidently, the distinction between the elementary concept of condensation and evaporation is a basic one i n meteorology, but not always familiar to people working in other disciplines. A similar error was recently repeated for the Basilica of Santa Maria Assunta in Torcello, Venice (built 639). The diagnosis was again that the capillary rise caused evaporation and cooling and, consequently, the airborne pollutants were claimed to deposit on the mosaics by means of the Stefan flow (see Chapter 8). As it has been explained, evaporation cooling cannot generate condensation, and the Stefan flow which is associated with capillary rise and evaporation works against deposition of airborne pollutants. In this case the problem is capillary rise, mobilisation and transport of internal salts, and deterioration of walls, plasters, mosaics and so on. Another error, that is commonly found in conservation textbooks, is the analysis of the so called interstitial condensation inside a wall. This problem is very important and some typical situations are discussed in Fig.6.11 which shows some profiles of T and DP in a cross section of a wall, the left hand side being in contact with the exterior atmosphere and the right hand side with the interior microclimate. (a) The first figure (Fig.6.11a) shows the unrealistic situation prospected in some authoritative textbooks without further specifications to illustrate the so called interstitial condensation., This situation is claimed typical of wintertime, i.e. inside the temperature is high (domestic heating), outside is very cold, and the air temperature is shown to be below the dew point. Looking at the drawing, the following assumptions have been assumed: (i) the temperature and the dew point profiles are

188

(a)

(b) T. In

DP

OU

T.

DP.

T

In

Tout

out

DP

(c

in

DEI n

0

(d) Tin

Tin DPin

DP.i n

in

DI

T

oul

E

DP O1

Fig.6.11 Winter temperature (T) and dew point (DP) profiles across the external wall of a heated building. The label "out" is for outside and "in" for inside. (a): Situation prospected in some textbooks under the following unrealistic assumptions: T and DP are stationary outdoor and indoor; the temperature outdoor is much lower than indoor and is also lower than the DP. In the left side part of the wall (shaded) where T < DP the interstitial condensation would occur. (b): Under the same assumptions, but T > DP, no intersection is possible between the two profiles and there is not a slab of wall where condensation occurs. (c): In manned buildings the vapour released by people rises the DP indoor. When the temperature inside and outside are different and constant, the stationary profiles are as indicated and no intersection is possible. (d): Under non stationary conditions the temperature and dew point distributions inside the wall vary continually with time and depth, with curved, non linear profiles. (e): When the outdoor temperature raises rapidly and the wall remains cold inside. The moisture can reach by diffusivity a cold slab (i.e. T < DP, shaded area) and saturation will occur inside the wall.

189 linear within the wall, which means that both T and DP were stationary outdoor and indoor for a very long time, e.g. several days; (ii) the specific humidity and the dew point are same outdoor and indoor; (iii) the temperature outdoor is much lower than indoor and is also lower than the DP. The illustrative sketch shows that the dew point is reached somewhere at mid wall thickness: the slab of wall on the left, colder than the D P is wet, the slab on the right, warmer than the D P is dry. The main comment is that the third hypothesis of this illustrative example, i.e. T < DP, is a meteorological absurd: never in the nature the air temperature drops below the DP. A similar condition can be obtained only in laboratory experiments for a very short fraction of second, operating with expansion chambers. (b) The second figure (Fig.6.11b) is under the same boundary assumptions, but being realistically corrected T >_DP. It is evident that no intersection is possible between the two profiles and there is not a slab of wall where condensation occurs (i.e. interstitial condensation), except for a possible contribution of the Kelvin and Raoult laws which are not considered in this example. (c) In manned buildings the vapour released by people rises the DP indoor. When the temperature inside and outside are different and constant, the stationary profiles are as indicated in Fig.6.11c and no intersection is possible. (d) Under the effect of daily external and internal forcing, i.e. daily cycles of temperature and specific humidity outside a n d / o r inside, the temperature and dew point distributions inside the wall vary continually with time and depth, with curved, non linear profiles (Fig.6.11.d). (e) Due to the different velocities of heat conduction and moisture diffusion, it cannot be excluded that in some specific cases the two curves intersect (Fig.6.11e) determining an internal damp slab. This especially occurs w h e n new w a r m and humid air arrives and envelops a cold monument. Without considering the Kelvin's and Raoult's laws, the two chief possibilities that condensation occurs in a wall are the following. (i) The air temperature inside is higher than the air outside and often also the specific humidity inside is much greater than that outside (e.g. indoors humidifying systems, concentration of people), so that the dew point of the air inside is much higher than the dew point of the air outside. Some moist room air migrates from inside to outside through the pore and capillary fringe of the wall. When this air meets a wall slab whose temperature is lower than the dew point of the air crossing the wall, it begins to condense. In some particular cases, walls have been protected against this problem by inserting a barrier against airflow through the wall, e.g. a polyethylene foil; in practice, however, failures were unavoidable and the results very bad (Padfield,

190 1995-97. By the way, in that publication some other nice examples are reported). (ii) According to the weather vicissitudes, the air outside changes very frequently, and in a short time, both its temperature and specific humidity. On the other hand buildings respond to the climatic forcing with a much greater delay determined by their heat capacity, heat conductivity, hygroscopicity, moisture diffusivity and so on. When after a cold period to which the building walls have adapted, new air is transported by a changing wind, warmer and moister, the wall temperature may be found below the dew point and in this case condensation occurs immediately. The most effective situation is when the outdoor temperature raises rapidly and the wall remains cold inside, and T has a U shaped distribution inside the wall. The moisture which progresses by diffusivity more rapidly than the heat by conductivity can reach a cold slab (i.e. T < DP, shaded area) and saturation inside the wall (Fig.6.11e). This situation is very typical when the warm and humid Sirocco wind blows from North Africa and in the transition season between winter to summer, when the seasonal temperature wave in the walls follows with lag the seasonal change of the air, whose content of moisture increases with the growing season. For this reason wall condensation in Autumn is much less frequent than in Spring. The Kelvin's and Raoult's laws state that the vapour pressure lowers over concave menisci or when the rain or dew water is contaminated by soluble salts. The immediate effect is that also the equilibrium RH for saturation drops and the DP rises. This means that devices aimed at heating the works of art to prevent condensation, should be triggered by the appropriate values of RH or DP, otherwise spurious wetting-drying cycles are forced with the effect of worsening the situation. This negative experience has unfortunately occurred too many times to important decorations exposed outdoors, e.g. marble bas relieves or bronze panels nailed down on wood doors, that undergone ageing cycles, instead of receiving the expected protection.

6.7.2. Not only rising dampness Dampness in the lower part of buildings is popularly attributed to capillary rise of ground water and the remedy is inevitably the same: to interrupt the supply of new water by cutting the walls and inserting an impermeable layer (e.g. lead, plastic) or impregnating brick and stones with polymers or other water-repellent substances. This intervention is absolutely correct when the actual cause is capillary rise, but exceptions to this rule are very frequent, and the apparent analogy is that adsorbed (or percolated) rainwater, under the influence of the gravity force, tends to descend d o w n w a r d s and is ultimately found to affect, for long periods, the basement of

191 buildings. An interesting example is given by the Romanesque Baptistery of the Cathedral of Padova, whose interior was painted in 1375-78 by the Florentine Giusto dei Menabuoi. At present the exterior is in brickwork, but probably it was originally protected by frescoed plaster, as some remains of sinopite are still visible. The bare bricks, the mortar joints and the presence of scaffold support holes facilitate the penetration of water during rainfall. Once penetrated the thick walls, the water migrates in all the directions, but the downward one is favoured by gravity, so that an accumulation in the lower part becomes evident. The drying rate is extremely low, depending upon the hygroscopic nature of the walls and the exchanges with the ground (i.e. percolation, moisture migration) and the atmosphere (evaporation). The lower rows of frescoes (i.e. the first two metres) were deteriorated by the dampness and the efflorescences which formed during the wall drying. The cause was erroneously attributed to capillary rise and near the floor a lead layer was inserted into the walls. This old intervention prevented rainwater from descending through the foundations and reach the ground; it was stopped at the led layer level, and the only possibility was to evaporate into the atmosphere, increasing dramatically the formation of efflorescences. Suspecting this alternative possibility, it was easy to compare the moisture content in several points above and below the lead layer, and the portion of wall between the ground and the lead was found dryer. The remedy was to remove the lead, to open some ventilation holes in the wall and keep it ventilated for a few years, and remove the efflorescences once the wall was dried. As the exterior was traditionally remembered in brickwork, it was not shielded with new plaster, but made water-repellent (but perspiring) in order to avoid new penetration of rainwater. This happened more than ten years ago and the restored frescoes are in very good conditions. Another interesting case was offered by the Saint Rocco Oratory (built 1542), Padova, which holds very fine cycles of frescoes of the 16th century. The first two metres were severely damaged by dampness and the owner, on the ground of the opinion of some experts based on some thermograph images which confirmed the lower temperature of the basement, decided the cut of external walls. I was contrary to this decision, for two reasons: (i) the front of the salts deposited by the water table was not horizontal but showed maxima in correspondence of down spots which were included into the walls; (ii) a small window in the lower part of the wall obliged the water to migrate all around: in the case of uprising flow the part just above the lintel was expected to be dryer than just below the window sill, and viceversa. A field survey that measured the specific humidity gradient close to the wall

192 surface demonstrated that below the window the wall was dryer and in addition shown that the evaporation was greater in correspondence of spouts. This lead to conclude that rain water was released by the spouts and migrated along the walls making wet the lower part. This advice was ignored and the wall cut was decided. However, the excavation shown that the foundations were absolutely dry and confirmed the latter analysis. After new spots have been installed out of the walls, the walls began to dry and the problem was solved. A similar problem was found in the Urbino Ducal Palace, built by Laurana in 1468, and the Cavalli Palace (XVI century), now M u s e u m of Geology of the University of Padova. In both buildings marked damage was observed on the lower part of the walls and on the floor. Accurate field surveys demonstrated that rain water was penetrated through disconnections at the edges of window sills, entered the wall, descended along the building structures, reached the floor and spread horizontally. Water percolated from window stills at the upper floor of the Ducal Palace had the possibility of following more complex paths and reach unexpected zones where the carved stones shown severe weathering. Several hypotheses were suggested, but a microclimatic and petrographical study (Bernardi et al., 1985) identified that the dissolution and recrystallisation of the calcium carbonate, and the transformation and crystallisation of gypsum inside the stone, occurred only in the areas where the rainwater arrived by internal percolation.

6.7.3. Drying damp murals W h e n a wall with murals has been incidentally soaked due to rainwater infiltration or other causes, it is exposed to high risk of damage for biological attack, chemical reactions or decreased resistance to physical injuries. In addition, two immediate problems arise: (i) the mobilisation of soluble salts with formation of efflorescences and (ii) the soiling due to the increased deposition rate of airborne particulate matter, as all the particles that impact on a wet surface remain trapped there for the adhesive force exerted by the film of water. The longer the time of wetness, the heavier the soiling and the more severe the risk of biological and chemical deterioration. In addition, any restoration is possible when the wall is dry. For all these reasons it is desirable to dry the monument as soon as possible, and in effects it is not rare to hear conservators which order to ventilate and heat the room to increase the drying rate. Unfortunately, this practice has the negative consequence of increasing the damage due to the efflorescences and in several cases I had to counteract the opinion of experts willing to ventilate rooms with walls and frescoes soaked by rainwater percolated through the walls. Possible suggestions are: (i) Searching to favour the evaporation from the opposite side of the wall in order to

193 diminish the flux of moisture across the mural and, consequently, the total amount of dissolved salts which deposit on the painted surface. In the case of the Padova Baptistry some external briks were removed from the wall, in order to favour back ventilation and internal drying. In Bulgaria, a Thracian h y p o g e a n tomb near Kazalunk has been excavated all around and in the free space obtained digging between the tomb and the earth tumulus a drying system was installed, to dry at a very low rate the tomb from the exterior, with migration of water from the wet interior to the dry exterior, thus avoiding the formation of efflorescences and other damage on the frescoes inside the tomb. (ii) Covering the painting with sheets of Japanese paper, so that the water with the dissolved salt will cross the sheet of paper and evaporate forming the efflorescences which will encrust the paper and not the mural. Once the evaporation with the salt migration is terminated, it is possible to remove the paper with the mineral encrustation from the dry wall.

195

CHAPTER 7

Atmospheric Stability and Pollutant Dispersion

7.1. INTRODUCTION Physical p h e n o m e n a such as: the w a y in which the solar radiation is absorbed by a surface and the energy is partitioned between the solid medium and the atmosphere; the interactions between the m e d i u m and the atmosphere, or the b e h a v i o u r of the a t m o s p h e r e and its ability to t r a n s p o r t or disperse pollutants,

are problems common to several disciplines. Also the same findings

can be applied to different scales: from the large scale of physical geography and long range transport of pollutants, to the local scale of u r b a n climate and pollution, to the microscale of the m o n u m e n t surface and the internal b o u n d a r y layers which develop in the air close to it. The general results can be adapted to m a n y specific cases and, probably, the application to the microscale and, in particular, to indoor environments attains the highest level of complexity. In fact, on the m e d i u m scale there is only one source of heat: the sun; only one surface: the soil; only one medium: the ground. In a room there are several sources or sinks of heat: lamps, heaters or air conditioning devices, solar radiation through windows; the surfaces are six, with different orientation with reference to the gravity force (air mixing is generated in the same way either by a w a r m floor or a cold ceiling); in addition the surfaces are not h o m o g e n e o u s , having doors, w i n d o w s and other peculiarities; the material of which the floor, the ceiling and the walls are made is not the same. For a given m o n u m e n t the same findings can be applied at least two times: on the medium scale to know the ambient in which the m o n u m e n t lives (or dies), and on the microscale to interpret the interactions with the environment and the deterioration mechanisms. As the local scale is particularly important in m a n y cases, this chapter will mainly refer to it, with some specific applications to the microscale. All the findings will be precious in the applications of the next chapter, which will be especially focused on the

196 microscale. The practical need to calculate or forecast the path and concentration of gaseous pollutants has resulted in many studies which have tried to evaluate how the dispersion of the effluents is determined by the dynamics to which the planetary b o u n d a r y layer is subjected (PBL). The PBL consists of the first atmospheric layer that is the most affected by the direct influence of the earth's surface and extends vertically to an altitude of 1000- 1500 m. The dispersion of pollutants is, essentially, linked with the transport and mixing of air masses which are conditioned by the dynamic behaviour of the PBL with perturbations and asymmetric forcing. The geophysical parameters involved are many. None of them, singly, can simply and completely account for the various phases of this process; for this reason attempts have been made to relate these parameters in various ways to obtain new, more abstract and global parameters that are more useful in specific applications. Air turbulence is originated in two key ways. Thermally generated turbulence, caused by convective movements resulting from the heating of the earth's surface, is particularly important and is responsible for phenomena such as fumigation and looping which will be briefly described later. Mechanically induced turbulence, which is due to fluctuations of wind directions and intensity or caused by friction and presence of obstacles, is also of considerable importance. From a physical point of view, the most important factors are: 9 9 9

atmospheric stability generated by the vertical temperature gradient as a result of heating or cooling of the earth's surface (thermal factor), the wind and the turbulence characterised by meteorological phenomena or induced by the roughness of the earth's surface (mechanical factor), the combination of mechanical and thermal factors and the spatial distribution of topographic (or architectural) discontinuities or temperature changes. It is clear that the wind intensity u is related to the dilution of the effluents;

the direction ~ from which the wind blows indicates the successive path, and the variations in wind intensity and direction affect the dispersion. However, it is not an easy matter to quantify this mechanism. The distance to which the pollutant has been transported can be calculated in a simple manner only in the case that the wind were stationary, with no significant changes in direction or speed. In the case of non stationariety, the path is not straight and the value of the average

197 wind speed and the integral Iu dt only represent the quantity of air passed through the measuring sensor during the sampling interval. The transport is in first a p p r o x i m a t i o n r e p r e s e n t e d by the average wind speed along the p r e d o m i n a n t direction, and is correctly determined as the vector sum of the instantaneous

wind vector u i observed at regular intervals, i.e. as 2ui. In

particular, the wind vane always indicates a wind direction, also in the absence of wind. In the case of calm, or in the intervals between intermittent wind, i.e. when the speed is zero, the directions recorded by the wind vane are meaningless and their monitoring is misleading. However, the majority of meteorological records is based on time averages, where it is often impossible to distinguish between real wind direction and permanence of the vane in the previous position after the wind has dropped. In a Cartesian system of reference, the instantaneous wind vector u(t) can be expressed by means of the components u(t)sina(t)and u(t)cosa(t) and the displacement of a puff released by a point source is represented by fu(t) sina(t) dt and yu(t) cosa(t) dt, and it is easily recognised that ~ <sina> • sin,

(7.1)

and similarly for the cosine so that the popular practice of measuring a n d < a ~ separately may be useful for several meteorological purposes, but is not appropriate for the accurate determination of the transport of airborne pollutants. Similarly, directional fluctuations indicate the horizontal fan within which dispersion occurs. The vertical dispersion is determined not only by vertical fluctuations but also by the soil roughness and atmospheric stability. A simple treatment of the problem presupposes that the atmospheric properties, during the diffusion process, are constant in time and homogeneous in space and also, there is no alteration in the effluent as a result of decomposition, deposition, chemical or photochemical reactions. The effect of the scale of the turbulence can easily be summarised. If the size of the eddies (i.e. all the elements of the fluid which characterise the turbulent motion, each one with an identity and a life history of its own, e.g. rotors, vortexes) is much greater with respect to the size of a puff of smoke, this latter is moved (translated and rotated) by the large eddies, without bringing about any variation in the dilution or form. If the size of the eddies is much less than the size of the puff, all the gaseous particles within the puff are subject to translation

198 and rotation, but neither the shape nor the position of the puff itself changes. If, finally, the size of the eddies and the puff are of the same order of magnitude, the dispersion is much more effective.

7.2. THE VERTICAL TEMPERATURE GRADIENT AND PLUME BEHAVIOUR The study of the stability of the atmosphere in relation to the vertical temperature gradient has led to many useful developments. In terms of vertical t e m p e r a t u r e gradients, the following definitions are used: superadiabatic gradient, adiabatic or neutral gradient, subadiabadc, isothermy, inversion gradient. These gradients are associated with some typical behaviours of the plumes (Fig.7.1). The temperature profile of the atmosphere (as measured by a radiosonde, and indicated by the continuous line in the diagram on the right of the figure) is always compared with the adiabatic one, conventionally indicated F, which is defined as the particular value AT/Az =-1~

m (represented in

Fig.7.1 with a dotted line). It is to be noted that it is also customary to speak in terms of lapse rate =-gradient in order to deal with positive figures instead of negative ones. A t e m p e r a t u r e gradient is defined as being superadiabatic

when it

corresponds to the vertical cooling defined by the temperature gradient AT/Az <1~

m, or AO/Az < 0~

m, so that an air parcel raised adiabatically

becomes warmer than the air surrounding it, gains buoyancy and is accelerated u p w a r d s , while if it is lowered it becomes colder and denser than the s u r r o u n d i n g air so that it is accelerated d o w n w a r d s (unstable equilibrium, Fig.7.2a). This instability leads to rising hot flows (named thermals) and descending colder ones which operate a continuous mixing of the air masses in the PBL, when the soil surface is considerably heated by solar radiation. The development of the superadiabatic layer is somewhat delayed with respect to the intensity of the solar radiation and in northern Italy it reaches a m a x i m u m altitude of about 250 m in the winter and about 400 m in the summer. With respect to the dispersion of pollutants, the rising and descending currents of the convective cellar movements cause a characteristic continuous up and down movement of a plume (Fig.7.1a), called looping. In this condition, a source at the surface level is in a better situation to disperse emissions while an elevated source, on the other hand, more easily pollutes the ground level, and is,

199

Fig.7.1 Behaviour of plumes under different atmospheric stability

200

T(z) ~

"... F

dT/dz < - l ~

"'""",.

batic profile

.4..a

~xo

~

a

.,

Temperature

T(z)

dT/dz = - l ~ adiabatic profile

,4..a ~

b Temperature

F

.4..a

+,

\\

)

dT/dz > - l ~ subadiabatic profile

~3

.,..~

C Temperature Fig.7.2 Vertical temperature profile T(z) and stability of the air masses. (a) An air parcel, displaced upwards from its initial position, follows the adiabatic profile G and becomes warmer than the air at the same level and is accelerated upwards. A similar situation occurs for a downward displacement, but in this case the parcel becomes colder and is accelerated downwards. The equilibrium is unstable. (b) An air parcel, which is vertically displaced, always remains at the same temperature of the adjacent air, and is in neutral equilibrium. (c) An air parcel displaced upwards becomes colder than the adjacent air and is forced to return to the original position. The same for downward displacements. The equilibrium is stable.

201 therefore, worse for health. The adiabatic gradient is equal to AT/Az = -1~

m, or z~O/Az = 0~

m, so that each vertical adiabatic motion changes the temperature of an air parcel exactly as the vertical actual distribution of temperature of the environmental air, thus leaving the parcel in neutral equilibrium with the surrounding air. For this reason the atmosphere is said to be neutral (Fig.7.2b). This type of gradient forms with overcast sky or w h e n there is a strong wind. The overcast sky tends to reduce the radiative balance (i.e. solar income and infrared cooling) and keeps the soil surface and the atmosphere in neutral equilibrium; the turbulence induced by the strong wind leads to homogeneous mixing of the air masses and there is no stratification. Under neutral

atmospheric

conditions,

a pollutant

is s y m m e t r i c a l l y

dispersed according to the Gaussian law with respect to the axis of the plume (or with respect to the trajectory, in the case of a punctual release, i.e. a puff). If the trajectory determined by the wind transport is a straight-line, the dispersion gives rise to a cone of pollutant which is denser at the apex (beginning of dispersion) and then along the axis (or in the more general case along the trajectory, which is defined as the centre of each cross section) and its concentration decreases moving radially away from the axis. The conventional name of this dispersion is

coning (Fig.7.1b). A subadiabatic gradient is AT/Az > -1~

m, or AO/Az > 0~

m. In

this case an u p w a r d adiabatic movement makes the air parcel colder than the air at the level it reaches, so that the parcel is forced downwards, towards its original position. The opposite occurs when the parcel is displaced downwards. Thus, the stable equilibrium tends to keep each air parcel at its original level, and the atmosphere is said to be stable (Fig.7.2c). Two i m p o r t a n t subclasses can be mentioned: the isothermy, i.e. AT/Az = 0~

m, with the temperature T being

constant along the vertical (moderate stability) and the inversion, i.e. AT/Az > 0~

m, a positive gradient, with the temperature T increasing with the

altitude (strong stability). Under these conditions the emissions tend to stay at the same level a n d frequently they are found with moderate ventilation and weak sunlight. The inversion subclass is typical of clear windless nights, that is, with infrared radiative loss (i.e. net soil heat loss) and no turbulent mixing. Isothermy may occur under weak radiative exchange (haze or thin stratus cover), especially in the transition between neutral atmosphere and inversion or vice-versa. The greater the atmospheric stability, the greater the suppression of the

202 turbulence and the smaller the mixing and the exchanges between atmospheric layers at different levels. A pollutant emitted at a certain height is, thus, trapped at that level, and can therefore only be transported and dispersed along that horizontal plane. The plumes emitted from tall chimneys remain aloft, while those emitted at ground level can not rise into the atmosphere. As far human health or monuments are concerned, this is the most favourable situation for elevated sources, but the less favourable for low level sources. If there is a variation in the wind direction along the vertical (directional wind shear) then a plume during its initial rise will become fan-shaped, the top being continuously dragged in a different direction from the lower part. This configuration is called

fanning (Fig.7.1c). When a neutral layer is found above the stable one, as typically happens above the nocturnal inversion layer, the pollutants released from tall chimneys can not be dispersed downwards crossing the inversion, but they can be dispersed u p w a r d s once they have entered the neutral layer. The process of rising pollutants in this situation is called "lofting " (Fig.7.1d). An important phenomenon (opposite to the previous one) typically occurs each morning after a calm night. After sunrise, when the solar radiation starts to warm the soil, a thin ground based mixed layer develops, generated by the growing solar radiation. The nocturnal inversion layer begins to erode from below, the base of the inversion being the top of the ground based superadiabatic layer under development. When the top of the superadiabatic layer reaches the altitude where the pollutants have been entrapped during the night, the pollutants are immediately transported up and down (looping) through the lower layer due to the violent mixing, which results in a sudden rise in the concentrations at ground level, and this process is known as "fumigation" (Fig.7.1e). In the PBL various sublayers may sometimes overlap one above the other, each with a different gradient. In the middle of the day, for example, because of the strong solar irradiation, a ground based superadiabatic layer, can be found. This is characterised by intense convective activity that mixes particles, gases and vapours dispersed within the layer. Above this, an adiabatic layer or a subadiabatic one can be generally found. At night, on the other hand, because of the radiant cooling of the ground, the first layer is frequently an inversion with a subadiabatic layer above it. In this case the vertical mixing is suppressed and smoke stratification and fanning are formed in the inversion layer and even

203 coniform dispersion in the upper neutral or slightly stable layer. From thermodynamic surveys (e.g. radiosondes) the vertical distribution of t e m p e r a t u r e is shown. The successive runs, made launching r a d i o s o n d e s at regular time intervals, measure how the temperature distribution aloft evolves d u r i n g the course

of the day. This is s h o w n

with

a two

dimensional

representation with the altitudes in ordinate and the time in abscissa. There, the isotherms (as well as the isolines of any other t h e r m o d y n a m i c parameter), by their reciprocal distance and position, indicate the intensity of the vertical gradients, the overlap and the dynamic evolution of the atmospheric layers. Each vertical intersection corresponds to a vertical profile. All of the isolines which correspond to each degree and half degree are drawn. If in this plot the distance d is measured, along the vertical, between one isoline and the next one, the layer is adiabatic when two isotherms, which differ 1~ each other, are found at the exact distance d = 100 m; if d < 100 m the layer is superadiabatic, while if d >100 m it is subadiabatic. The isolines are vertical and widely spaced when the gradients are of the isotherm type, or vertical and close w h e n there is a s u d d e n change of air masses, e.g. the change of a breeze. Where there is an inversion, at the upper levels the isolines are characterised by higher T values. When passing from stable to neutral or superadiabatic zones, the isolines are subject to a sharp turn, and the joining of all these bends indicates the base or the top of these layers. The base and top of these layers begin and end at ground level or aloft at the point where they meet each other. Fig.7.3 is an example which illustrates this, and corresponds to the terminal

part of the erosion of the n o c t u r n a l

inversion

and

the

development of the mixed layer. In order to forecast the course and dispersion of gaseous effluents, it is necessary to know the exact height at which the effluents have been emitted into the atmosphere, as well as the stability of the various layers at which the PBL is divided and also the horizontal discontinuities that are found. It follows, therefore, that the path and dispersion of the emissions s u s p e n d e d in each stratification may be different in the various substrata, so that sometimes, urban and industrial pollutants, emitted at different heights, have different destinies, the former affecting certain areas and the latter, others. It may be useful to note that when T and z are represented diagramatically, the neutral atmosphere is defined by the slope of F = 1~

m, while a steeper

slope indicates instability and a flatter one, stability. Very often, the eye can not immediately evaluate the exact numeric value of the slope and thus recognise

204 800

15-

16

600

17 J=

400

18 17 j

19

,.,,..,~.....~.:::...~......-~...:~.:.~....~ . .,~

/

200

0 ' ",~........;~':'~;";'~'?"'...................., 20 2'2

6

'

~

'

~i

'

t,

'

~

'

~o

time (h)

800

]23/22

,.~

600

- -

400

2 0

0 20

22

0

2

4

6

8

10

time (h)

Fig.7.3 (a) Vertical versus time representation of the air temperature T; (b) vertical versus time representation of the potential temperature O. Padova, night from 8 to 9 July 1978. In figure (a) the stable layer (i.e. inversion and isothermy) is shown with shading. Note that the inversion began to form at 7 p.m. (i.e. one hour before sunset) and grew until 11 p.m. when the nocturnal breeze arrived. The dynamic effect lowered by some 50% the top of the inversion and the colder air masses caused a sudden drop of temperature. After the sunrise (4.30 a.m.) the soil began to warm, form a ground-based mixed layer and erode the inversion from below. All the soundings have been made with the same radiosonde attached to a fishing nylon wire; one sounding every hour.

205 the degree of stability from a diagram of this type. When, instead, this is represented in terms of potential temperature O in a vertical vs. time cross section, the effect is m u c h more immediate in that instability, neutrality or stability are represented, respectively, by AO/Az < 0~

AO/Az > 0~

m, AO/Az = 0~

m,

m, whereby F corresponds to the intersection with the abscissa

axis at an obtuse, right and acute angle, respectively, and this differentiation can be immediately seen by the naked eye. However, near the ground level and in the small scale T = O.

7.3. EFFECTS DUE TO TOPOGRAPHIC HORIZONTAL INHOMOGENEITY Sometimes

the

PBL is not characterised by only one of the above

characteristic layers, but special effects may derive for the simultaneous presence of different layers, either in the vertical (multiple layering) or in neighbouring regions, e.g. mainland and sea, with a frontal area where the two layers are in contact and overlap. In the event of topographic inhomogeneities, such as, for example in a coastal region, the different temperatures of the sea and the mainland determine b o u n d a r y layers with different stability. When these layers are pushed by the general circulation in the other region, an internal b o u n d a r y layer (IBL) develops along the frontal area. Variations in the temperature gradients are found especially w h e n the geophysical dissimilarities are extensive, such as, for example, along the sea coast. When the soil warms up or cools down, superadiabatic or inversion gradients are generated, but the temperature of the water, and the temperature gradient above it, tends to remain the same. A plume of smoke which, during the night is moved by a land breeze, travels from the stable layer above the land to the unstable one at the marine surface that is relatively warmer (Fig.7.1f). From then on, the local convection causes looping. This is a characteristic type of fumigation and often occurs in Venice, not only during night-time, but also d u r i n g the whole winter. In fact, the Venetian hinterland during winter is very cold and characterised by stability for most of the day, whereas the Adriatic sea and the lagoon are relatively w a r m and generate a continuous mixing of the overlying air masses. The industrial area is located in the hinterland and the pollutants are e n t r a p p e d at a certain altitude in the stable layer. When the air masses are transported over the lagoon, a very high concentrations of pollutants can reach

206 the sea level, and especially the city centre, where the urban heat island increases the convective movements and turbulence. Another IBL develops near the coastline. For example, during the daytime of the mid and hot seasons, the relatively unstable mass of marine air transported by the sea breeze becomes completely unstable as it moves inland, so that a mixed layer develops. The height h of this IBL increases parabolically, as it moves inland, and for Italy it is computed with the equation (Anfossi et al, 1976):

x h = a co ~ /

(7.2)

which has been adapted from the original van der Hoven (1967) formula, where a = 0.05 ms -3/2, x is the distance from the coast, u is the wind speed and co represents the Brunt-Wiisfilfi frequency (considered a frequency in that it has the unit of time -1) defined as

r = g 30 6) ~z - g

31nO

(7.3)

Oz

where g represents gravitational acceleration, z the height with respect to the soil, O the potential temperature (in K). The Brunt-V~iis~il~i frequency characterises the atmospheric stability on the basis of the vertical temperature gradient 30/-3z. Another IBL develops d o w n w i n d of the coast, in the wind profile, because of the change in the surface roughness as the wind moves from the marine surface to the hinterland or vice-versa. This layer develops at an altitude that is proportional to the distance from the coast with a h/x ratio that lies between 1/10 and 1/20 (Elliott, 1958, Panofsky and Townsend, 1964), and which varies according to wind intensity (Schlieting, 1955, Echols and Wagner, 1972). The so called 'urban meteorology' studies similar p h e n o m e n a , as well as those due to the formation of haze linked with vapour emissions and to the condensation on the airborne pollutants. These act as condensation nuclei and, in turn, are heated aloft by the solar radiation and lead to the characteristic vertical inversions.

207 7.4.

THE

URBAN

CLIMATE:

HEAT

ISLAND

AND

AERODYNAMIC

DISTURBANCE The urban climate (Landsberg, 1981) is of the uppermost importance as most of the population lives in cities, and in the same place also the majority of the cultural heritage is concentrated. The very fact that a town exists, the architecture of its buildings, the town use and the people activity, alters, locally, the regional climate, leading to characteristic interactions with the atmosphere that may be more, or less, violent. Such interactions have led to a new definition of local climate: the urban climate, the main characteristics of which can be synthesised as follows. In a town, the absorption of solar irradiation is elevated as a consequence of several factors: the presence of many vertical surfaces close between them (buildings and streets) which entrap the solar radiation after a multiple reflection and behave as a black body, the storage of heat in materials such as terracotta tiles, bricks and asphalt, the different albedo of the roofs and black streets; in addition, heat released by h u m a n activity, mainly domestic heating and traffic. All these factors determine a temperature m a x i m u m in contrast with the s u r r o u n d i n g countryside. This is the so-called 'heat island' effect which is particularly evident in the evening and the first hours of the night. The urban island has also contradictory aspects: e.g. the local rise of temperature tends to reduce relative humidity, time of wetness and the intensity and frequency of fogs with respect to the s u r r o u n d i n g rural area; on the other hand, the local a u g m e n t a t i o n of pollutant

concentration

and

condensation

nuclei,

tends

to

increase

photochemical smog, haze, fog and t h u n d e r s t o r m frequency. For instance, London was a foggy town and the period of high pressure in 1952 caused a thick, persistent fog and m a n y people died (Brimblecombe, 1987). After a severe regulation abated the emission of particulate matter which acts as condensation nuclei, the fog frequency was drastically reduced. The heat released by the town generates buoyancy, thus originating the convective rise of the air masses. Under moderate stability conditions, the rural area is covered with low stratiform clouds or (high) fogs, particularly frequent in the winter and mid-seasons, and the air which is convectively raised perforates the lower stable layer and a blue sky can be seen just above the town. This convection is even stronger in the summer when the altitude attained by the

208 ascending column of w a r m air reaches the cloud condensation levels, forming small cumulus clouds, typical of the fine weather. If the cumulus clouds grow sufficiently, rain storms may occur over the town or the area d o w n w i n d of it. Showers are more frequent in large towns, and the urban pollution contributes to increase the frequency of summer precipitation, because it supplies condensation nuclei. During the night, when the nocturnal inversion has been formed in the surrounding rural area, the ground, which is covered with colder and denser air, lies in a layer with still air while a fresh wind slips rapidly above the stable ground based inversion layer; the inversion is attenuated or destroyed in the case of intense, turbulent wind aloft. It is well known that buildings tend to establish ground level areas shielded from strong wind. However, distortions in the wind field are not homogeneous and there are areas where the speed is, effectively, attenuated while in other it is accentuated, because of induced turbulence or channelling. A passer-by walking across these areas may mistake them for gusts of wind, but a local observer knows exactly the limits of the area where, for example, umbrellas are blown inside-out. Interesting studies of wind field perturbation within a built environment and wind tunnel experiments on urban models have been described by Plate (1982) and Simiu and Scanlan (1986). The taller buildings may emerge from the stable layer and protrude into the mixed layer of more intense wind. In this case, the turbulence induced in the cavity region and the wake d o w n w i n d exchanges momentum, so that the upper layers are slowed down and the lower ones are accelerated. Urban ventilation can, therefore, be greater than the rural one during the night. Tall buildings may exert important local departures to the wind field and form critical frontal situations, typically shielding, accelerating, deflecting, creating building channelling, corner streams, or inducing turbulent wakes or vortex flows. These effects cause well known

discomfort in the p e d e s t r i a n

areas and several consequences

on

monuments, especially those associated with the transport of falling raindrops, surface washout and deposited pollution removal.

7.5. DISPERSION AND TRANSPORTATION OF POLLUTANTS IN A CITY With respect to the dispersion and transportation of airborne pollutants,

209 various m e c h a n i s m s

are involved. The activity of convective rising and

divergence of the air masses above a town means that in the s u r r o u n d i n g areas other air d e s c e n d s

and converges, forming a large convective cell. This

m o v e m e n t tends to lower the plumes emitted from chimneys near the outskirts of the town, fumigating into the town. The turbulence induced locally by the buildings, can also lead to an increase in the concentration of pollutants at ground level if the pollutants were originally released or transported at stack level. Pollutants emitted at ground level are, instead, more widely dispersed for the same reason, so that their impact on people who live on the ground floor is reduced, but is increased at upper levels. The overall geometry of the town may lead to the so called canyon effect. First of all, the wind nearly parallel to the main streets is channelled and the air flow remains e n t r a p p e d in these urban valleys or canyons, increasing the concentration of the pollutants continually emitted by traffic. If the wind aloft crosses the street, a stationary horizontal vortex is formed in the urban canyon, partially entrapped between the two rows of buildings facing each other. The aerial flow at roof level, instead of crossing aloft the street, descends into the street and then rises again along the opposite side distributing to the windows the pollutants emitted at roof level (e.g. domestic heating, plumes from tall stacks) and on the street. If the angle of attack is intermediate, a helicoidal motion is generated into the street with similar effects (Munn et Rodhe, 1985). A n o t h e r d r a w b a c k is generated by the urban convective m o t i o n and pollution, which ultimately increase the local precipitation. The falling rain drops are very effective in removing particles suspended in the atmosphere as well as a good part of the gaseous substances, so that these are carried d o w n into the town in the form of the so called acid rains. While not undervaluing the acid rain p h e n o m e n a , it should be remembered that in an urban environment, the wet deposition of pollutants (i.e. acid rain) is only a very modest fraction when compared with the deposition during the dry phase and that this latter causes much greater damage. One question that should be asked is, what is the difference between the urban climate and an undisturbed one (Cayan et Douglas., 1984; Jones et al., 1986; Lee, 1992). There is no easy answer, in that there is no undisturbed climatic area, given that the regionalclimate is characterised by many microclimatic areas, the average of which could be considered, with extreme caution, the approximate average. There are m a n y studies which attempt to establish, in a general sense,

210 the d e p a r t u r e between the climate in an urban area and the s u r r o u n d i n g countryside. This a p p r o a c h is based, obviously, on the c o m p a r i s o n of environmental data, measured simultaneously at various sites, in order to show the local disturbance that emerges at the urban site. This problem has a clear implication when interpreting the long series of meteorological observations. In fact, the early instrumental observations began two or three centuries ago in the outskirt of small, green towns, which have

grown changing their climate.

However, the study of these long series is of uppermost importance for knowing the climatic changes. This is especially true because these observations are well documented and continued, without interruption, for centuries. An example is given by the instrumental series of Padova which began in 1725 and is composed of atmospheric pressure, air temperature, frequency and amount of precipitation, wind direction and other observations, and only at present is under investigation (Camuffo, 1984; 1990; Camuffo and Zardini, 1996). These very important series, however, have a serious inconvenience in that towns have grown considerably over the last years and it is not easy to evaluate the urban disturbance in the recent times. In fact, not only town have grown as a consequence of the number of inhabitants, but have undergone dramatic changes when gardens have been substituted with new buildings, when the streets have been asphalted, when the building technology were changed. Also the rural climate all around is variable, its documentation is not as old as the urban one which, at one time was only moderately affected by the presence of humans. Even the rural territory has, in m a n y cases, been altered by land clearing, reclamation and transformation, therefore affecting the type of natural or agricultural vegetation which grew there, so that the whole energy balance at ground level has been altered and, consequently, the exchange with the atmosphere.

7.6. WIND FRICTION NEAR A SURFACE Shearing stress and friction velocity are two fundamental parameters for the mathematical treatment of several processes in the PBL, especially those linked with the vertical transport of momentum, or turbulence generation. The friction strength of wind blowing at a tangent to a surface, per surface unit area is called

shearing stress or surface shearing stress, and is indicated by the symbol ~: and is of the order of 1-10 dyne cm -2. This shearing stress is due to the sum of a turbulent

211 c o m p o n e n t and a viscous one. Near the g r o u n d the viscous effect dominates and the N e w t o n ' s law on viscous friction applies, so that 7: is p r o p o r t i o n a l to the vertical gradient of the horizontal w i n d 3u/3z, called wind shear or, simply shear, i.e.

~U

r = t.t 3z

(7.4)

w h e r e /.t is the coefficient of molecular viscosity, also called dynamic viscosity or, more simply, viscosity. For air # is slightly d e p e n d e n t u p o n temperature, e.g. ~ --1.7x10 -4 poise (i.e. g cm -1 s -1) at T = 0~ and /1 = 1.81x10 -4 poise at T = 20~

and is

i n d e p e n d e n t of pressure except for very low pressures. The so called height of the surface b o u n d a r y layer h is defined as that height above the g r o u n d below which the stress m a g n i t u d e varies less than 20%. As ~: is the m a g n i t u d e of the surface stress in dyne cm -2 and is typically of the order 1-10 dyne cm -2, h ~ 2000 ~: and ranges between 20 and 200 m (Lumley and Panofsky, 1964) Moreover, the d y n a m i c viscosity can be expressed in terms of the kinetic theory of perfect gases: 1

/.t = ~ 19 c ~

(7.5)

w h e r e p is the gas density, c the average speed of the thermal motion of the gas particles and ~, the m e a n free path. For air at T = 0~

and under standard

condition ~, ~ 5.5x10 -6 cm. The viscous d r a g w i t h i n the a t m o s p h e r i c viscous sub layer w h i c h is i m m e d i a t e l y adjacent to each surface can be d e t e r m i n e d w i t h r as above; h o w e v e r , b e y o n d the viscous sub layer, at a considerable distance from the g r o u n d (or from any surface), the turbulent effect dominates and the drag can be expressed in terms of Reynolds stress, or the rate at which horizontal m o m e n t u m of the air is being transferred vertically to the surface by m e a n s o f t u r b u l e n t transfer r =-p

(7.6)

w h e r e u' and w' are the fluctuations of the w i n d (eddy velocities) along the m e a n w i n d direction and the vertical;

physically, r e p r e s e n t s the vertical

212 transfer of m o m e n t u m associated with the vertical component of the wind speed, i.e. the eddies present in the wind field or originated by the soil roughness. Both eq.(7.4) and eq.(7.6) show that the vertical transfer of the m o m e n t u m

is

proportional to the vertical gradient of the wind speed, as will be discussed later. In the case of h o m o g e n e o u s wind field and isotropic turbulence the w i n d fluctuations are r a n d o m l y distributed along the axes x, y, z so that < u ' w ' > = 0, and r =0. As the dimension of ~: can also be interpreted as energy density, by analogy with the dissipation of the kinetic energy of the wind which is dispersed by the e d d y turbulence per unit of volume of air, it is possible to introduce a fictitious speed u, that is homogeneous along the vertical, and is called

friction velocity as

it is linked with the friction, defined as

Given that u , has the dimension of a speed, it derives from t u r n i n g a complex p h e n o m e n o n into a useful p a r a m e t e r which does not i m m e d i a t e l y correspond to any definite physical entity. In the turbulent layer, on the basis of the

Reynolds

stress, the friction velocity is defined by m e a n s of the eddies

contribution as

u , = ~

(7.8)

and in the viscous layer by the continuous, laminar increase of the wind speed as

u, =

~/ I~ 3u

(7.9)

~ Oz"

From these expressions it can be seen that u, is physically linked with the transport of m o m e n t u m from one level to a different one. In a general way, u, can be expressed as a fraction of the average wind speed , i.e.

213

u,--

N

(7.10)

where the index of roughness N varies from 3 for perfectly smooth surfaces such as snow or a calm lake surface, to 13 for grassy land.

7.7. THE VERTICAL FLUXES OF HEAT, MOISTURE AND MOMENTUM In the atmosphere, a vertical profile of air t e m p e r a t u r e also implies a vertical transport of heat, as well as a wind shear implies a vertical transport of m o m e n t u m . The vertical fluxes of heat H, moisture L~E and m o m e n t u m r are defined respectively:

H = p Cp = p Cp f o ' ( t ) x w'(t) dt = - p Cp KH

LyE - p Lv <m vW'> = p Lv

r = -p

=

3<0> 3z

/ m, v(t) x w'(t) dt - - p L~KE

-pfu'(t)

xw'(t)dt

= p KM

3 <3z mv>

3 3z

(7.11)

(7.12)

(7.13)

where p is the density of the air, Cp the specific heat at constant pressure, w is the vertical

wind

component,

the latent heat of vaporisation and E the

Lv

evaporation (or condensation) rate. As the vertical displacements involved are generally modest, the air temperature T can be used instead of the potential temperature O. As usual, the brackets <> indicate the average value and the label ' indicates the fluctuating value, e.g. u (t) = + u ' ( t ) . The integrals of the correlation p r o d u c t s b e t w e e n the fluctuating values of the vertical w i n d component w' and the corresponding fluctuations of the (potential) temperature p

O', moisture m v ( t ) o r

speed u

p

represent the net transport of the related

properties along the vertical. The sign minus has been introduced because in the surface boundary layer the fluxes are counted positive upwards. The coefficients K H , Ka, and KM, represent diffusivities, and several rough assumptions are often made in the surface PBL to make easier the mathematical

214 treatment of this complex mechanism. The first assumption is that the vertical fluxes are constant with height (i.e. no accumulation or horizontal divergence); the second, often used quite successfully in engineering applications, is that all the coefficients are equal, although this has been verified only in near adiabatic conditions. This assumption allows to predict the distribution of a particular flow from measurements of another one. However, during strong inversions the radiative heat exchange and the pressure fluctuations may cause important departures for the heat and m o m e n t u m transfer. For a discussion on this implication on diffusion models see Lumley and Panofsky (1964). The coefficient of heat exchange, KH, also known as the eddy diffusivity of

heat, refers to the heat flow due to the vertical transport of heat, either because of the convective motion o r / a n d the vertical component of the wind fluctuations. It is defined as the coefficient of proportionality between the turbulent heat transfer and the vertical gradient of the air temperature,

KH = - ~

3O 3z

(7.14)

This formulation represents the physical process that typically occurs near the soil surface in superadiabatic conditions. When the soil is hot, the air in the viscous sublayer near the surface which is in contact with the soil is heated by conduction, gains in buoyancy and eventually escapes out of the viscous sublayer. This hot air mixes with the environmental air above, i.e. in the superadiabatic layer, and forms bubbles of warm air that tend to rise for their buoyancy (thermals). At this point the lower atmosphere is characterised by a positive temperature gradient and a convective motion develops. This motion is formed by many individual cell motions, with the hot cores formed by uprising thermals, associated with lateral descent of colder air which closes the cells. A net upward transport of heat is originated when the vertical uprising movements of the air w' are associated with the transport of warmer air (O') as well as d o w n w a r d movements with colder air, i.e. >0, for both the upward and the downward transport, as both 6)' and w' change sign. The same result can be found also in another particular case, although in the absence of convective cell motion. This happens in the central part of windy days when the atmosphere is neutral, but the soil is hot. In this case the wind eddies coming from below are warmer than those

215 coming downwards, leading to the same result. When the soil is colder than the air, in the presence of fresh wind, the eddy turbulence transports heat d o w n w a r d and <0. If the soil is cold and there is no wind, the air stratifies, and tends to suppress turbulence, i.e. w' ~ 0 a n d also the product ~ 0; in the case of stable atmosphere, the heat is not transported by eddies, but flows downward very slowly by means of conduction. This is another mechanism, characterised by a small efficiency and is no any more represented by O' or . Similarly, the coefficient of eddy diffusivity of moisture is defined as

KE = -

<m' v w'> 3<mv> 3z

(7.15)

The coefficient of mechanical exchange, KM, also called eddy diffusivity of

momentum or kinematic coefficient of eddy viscosity, represents the capacity of the atmosphere to exchange vertically the momentum as a consequence of the eddies induced by wind, and is defined as the coefficient of proportionality between the vertical momentum transfer and the gradient of the wind speed:

KM = 3

(7.16)

3z If the wind speed increases with height, the turbulence which exists between two levels brings up some parcels of air with slower velocity, and brings down some faster ones, exchanging m o m e n t u m . The greater the turbulence (and the coefficient KM ), the greater the tendency for the distribution of the wind speed to become uniform.

7.8. HEAT BALANCE AT THE SOIL OR THE MONUMENT SURFACE The atmospheric stability, the dynamics of the PBL and many interactions between the soil (or a monument) and the atmosphere are governed by the heat balance at the soil. This balance considers how the net flux of radiant energy q~ is partitioned. The net flux q~ is the global solar income I$ minus the shortwave

216 radiation Sq" reflected from the soil and the longwave component LI" reflected and emitted as black body infrared thermal emission, i.e. cI) = 1,1,-(S'r+L'~).

(7.17)

Therefore, q~ is the radiant energy adsorbed or emitted by the soil. During the day the solar income dominates and q~ > 0; during the night the radiative loss dominates and q~ <0; in practice, 05 is positive when the flow of energy proceeds from the atmosphere to the soil, i.e. 4~$ > 0, and vice-versa q~l" < 0. Every day, the integral value jq~ (t) dt = 0; from winter to summer these 24 hr integrals are generally small and positive showing the seasonal daily gain of heat, from summer to winter negative. At the soil (or m o n u m e n t ) surface, the radiant flux of energy q~ is transformed into three heat fluxes: i.e. heat conduction G into the ground (or the material), sensible heat H into the atmosphere and latent heat L~E into the atmosphere. This can be expressed by means of the equation of partitioning of the energy per unit surface and unit time, called also heat balance equation: = G + H + LyE.

(7.18)

Given the convention adopted for the sign of q~, the other fluxes are positive when the heat flow proceed in the direction shown by the arrows: i.e. G$ from the soil surface to the deeper layers, HI" and LvE'~ from the soil surface to the atmosphere; the opposite sign indicates respectively: -G, the conduction of heat from the deeper layers to the soil surface, -H, the soil is cooling the air, -LYE, the surface condensation. The rate at which heat flows through a building wall or a soil level at a depth z below the surface is directly proportional to the temperature gradient that is found at that depth, i.e.

G -

- ct

3T 3Z

(7.19)

where ct, called thermal conductivity, is a coefficient of proportionality which is constant only for a homogeneous medium. In the ground this is not strictly valid, as the moisture content in the soil, affected by rainfall, dew, evaportation and fringe diffusivity, changes with time and depth. For an infinitely thin layer,

217 the heat transfer is regulated by the equations 3G 3z--C

3T 3t

(7.20)

3T 32T 3t - K 3z 2

(7.21)

w h e r e C is the heat capacity of the m e d i u m and K = c t / C is called t h e r m a l diffusivity. The latter coefficient physically expresses the speed of propagation of a

t h e r m a l w a v e into a m e d i u m , w h i c h is p r o p o r t i o n a l to the capability of t r a n s m i t t i n g heat in the presence of the unit t e m p e r a t u r e g r a d i e n t (thermal conductivity) and inversely proportional to the capability of storing heat (heat capacity). W h e n all the fluxes are positive, the heat balance equation shows how the radiant energy adsorbed by the soil surface is partitioned among the heating of the deeper layers of the ground, the heating of the atmosphere and the evaporation; w h e n one or more of these fluxes change their direction and become negative, the equation shows the w a y in which each flux is transformed, supplies to or receives energy from the other fluxes (Fig.7.4). One or more components of this balance m a y be also zero, e.g. 9

= 0 w h e n the sky is completely overcast or

slightly after the sunrise or before sunset; G = 0 twice a day w h e n the heat flux into the ground inverts direction, or in the case of non conductive surfaces; H = 0 w h e n air and soil surface have the same temperature and there is no evaporation or condensation; LvE = 0 w h e n the soil is dry and there is neither condensation nor evaporation. Marble and bronze m o n u m e n t s have a very little porosity in comparison with the soil, so that the a m o u n t of water adsorbed in the pores is extremely modest. For them LvE -- 0 and the energy balance is practically reduced to 9 = G + H. The white Carrara marble of the Trajan Column, Rome, becomes some 10~ hotter than the air and dark surfaces become m u c h more hotter (Camuffo, 1993; Camuffo and Bernardi, 1993). Dark stones become some 20~

hotter. Bronze

m o n u m e n t s are hollow, and the thickness of the bronze layer is of few m m , so that the term G might appear negligible at first sight. However, this is not true: the very great thermal capacity of the m o n u m e n t absorbs a huge a m o u n t of heat, which reflects in a rise of temperature. Dangerous fluctuations of m o n u m e n t temperature occur with the oscillations of the wind speed or w h e n passing clouds

218 temporarily s h a d o w the monument. For example, in clear s u m m e r days the temperature of the St. Mark horses, Venice, fluctuate within a 6 min period due to the turbulence induced by the city on the sea breeze, and every day the t e m p e r a t u r e d r o p p e d some 15~

in 15 min when the horses entered in the

shadow of the bell tower; afterwards they experienced a nearly symmetric rise of temperature which accelerated fatigue failure, especially on the tree legs which are b o u n d on the Istrian stone basement, less sensible to expansions (Camuffo, 1981a; Camuffo and Vincenzi, 1985). -~

50-

4030 rO 2o

~

=" ~

lO o

-lo 6

8

10

12 Time

14

16

18

20

(h)

Fig.7.4 Energy balance 9 = G + H + LyE during the daytime, at Padova, Italy (46~ lat N), in August. Legend: q~, thick line; G, thin line; H, dotted line; LyE, dashed line.

The daily cycles of q~ change slowly with the season, are affected by the cloudiness or abrupt changes of soil albedo, e.g. after showers, and vary with the seasonal change of the solar radiation and the vegetation. The moisture content of the soil, and the vertical gradient of it affect the amplitude of G, H, LyE and cause some asymmetry or delay. In fact, after a drizzle or an abundant dew, the u p p e r layers are moister, so that the evaporation rate is greater in the morning than in the evening, when the soil is dryer. The curve of LvE is skew with the m a x i m u m i n the morning, and H has a similar skewed trend, but with the m a x i m u m in the afternoon, when the evaporation is reduced and more energy is employed to w a r m the air. After some clear days, the upper layer of the soil will dry, so that the evaporation rate will increase in the afternoon, w h e n the heat wave reaches the deeper, moister layers. In this case the curve of LvE is skew

219 showing a greater evaporation rate in the afternoon and, consequently, the maximum of H occurs in the morning. By plotting in a Cartesian reference frame the instantaneous values at the time t of the fluxes G(t), H(t), or LvE(t) versus ~(t) for a whole day, an ellipse is obtained, which is clockwise or counterclockwise, with the major axis more or less tilted, and the minor axis more or less wide, the entire ellipse being slightly displaced upwards or downwards (Fig.7.5). Therefore, the daily cycles of G, H, LvE can be calculated by means of the equations:

3q~(t)

G(t) - al q-~(t) + a2 3t

3q~(t)

H(t) = bl qXt) + b2 3t

+ a3

(7.22)

+ b3

(7.23)

3q~(t) LvE (t) = cl q~(t) + C2 3t

+ C3

(7.24)

where the coefficients al, bl, c1 indicate the first order proportionality between each flux and the radiative income, i.e. the inclination of the major axis of the ellipse; a2, b2, c2 indicate the influence of the gradient of moisture into the ground which causes positive or negative departures from linearity, i.e. the width of the ellipse, and the sign shows whether the ellipse is described clockwise or counterclockwise; a3, b3, c3 indicate the background flux, independent of qL and the experimental problem of the divergence of the fluxes a n d / o r the storage of energy, as the four fluxes that appear in the balance equation cannot be measured exactly at the same level as three fluxes are in the atmosphere and one is underground.

7.9. MAIN PARAMETERS USED IN MEASURING ATMOSPHERIC STABILITY AND TURBULENCE 'A precise definition of turbulence is difficult, if not impossible,

to give'

(Plate, 1982). For this reason several parameters have been introduced, each of them may be, time by time, very useful or inappropriate. However, turbulence, and the opposite physical regime, characterised by still air, are fundamental in governing the mechanisms

of pollutants

deposition

and heat and mass

220 30

.J J J

25 ,_r r

20 r,,J b,O

u.a

15

=

10 .

-

j

J

Y

-5

|

i

0

,

i

20

,

i

40

|

60

80

( m w / c m 2)

@

50

J J J J J J

40 c4 r,J

30 bO

20 ~4

10

J J 9

J

J J |

0

I

10

.

i

20

,

i

,

30

i

40

.

i

50

.

60

(mw / cm 2 )

Fig.7.5 Plot of the evaporation rate LvE (mg cm -2 h -I) versus the net radiative flux q~ (mw cm -2) at Padova: (a) at the end of August, a few days after a shower, (b) in September, several days after a late August shower .

221 exchanges. Monitoring atmospheric turbulence or stability in field surveys is very important and often extremely difficult. For this reason it is fundamental: first, to become familiar with the most important definitions and their physical meaning, and then to balance theory with the specific problem under consideration, as well as w i t h the i n s t r u m e n t a l facilities and the experimental limits. W i t h o u t this effort,

the

environmental

monitoring

risks

to be

a mere

collection

of

meaningless data. A t m o s p h e r i c stability can be defined as the t e n d e n c y to mitigate (or accentuate) vertical m o v e m e n t s or existing turbulence. M a n y p a r a m e t e r s have been i n t r o d u c e d to w h o l l y and quantitatively describe certain a t m o s p h e r i c conditions, each of which illustrates a particular characteristic. These are not just limited to providing mathematical models, but have also resulted in furnishing new criteria for classification which have been particularly useful. It w o u l d be here advisable to r e m e m b e r some of the better known ones, those that have led to successive d e v e l o p m e n t s in the interpretation of this p h e n o m e n o n . These parameters are all somewhat abstract in nature, in that they have been introduced to give greater flexibility in forming the mathematical formulation of turbulence, and their importance lies within this context. However, it is always possible to give a physical explanation - even though this m a y not always be i m m e d i a t e l y clear- and shall be underlined wherever possible.

Kinematic

viscosity ( v )

The kinematic viscosity is an atmospheric variable which is useful to define the next parameter of stability. It is the ratio between the dynamic viscosity ~ and the density p. of the fluid, i.e.

v =P

(7.25)

and depends upon both air temperature and pressure. For air at sea level pressure and 20~

p = 1.205x10 -3 g cm -3 and v = 0.15 cm 2 s -1. It is the factor of

proportionality in the equation relating the accelerating (retarding) effects on the air motion, i.e. 3u ~ a t , generated by fluid friction in a given wind speed profile:

3U

32U

3t - v 3z----~ 9

(7.26)

222 Equating eq.(7.7) to eq.(7.9), and operating with the help of eq.(7.6) and eq.(7.13), the kinematic viscosity v results equal to the kinematic coefficient of e d d y viscosity KM. This is only a logical similarity as the e d d y visciosity was i n t r o d u c e d in 1877 by Bussinesq in analogy with the laminar flow relation existing between the stress and the velocity shear. Physically, for reasons of continuity, this equalisation applies only to the transition zone between the viscous layer and the external turbulent regime to which the above equations respectively refer. In fact, although KM is analogous to v, it is expected to be much larger than I~/p to account for the greatly increased flux capabilities of the turbulent flow in comparison with the molecular transport (Brown, 1991).

Reynolds number (Re) Re is the non-dimensional ratio between inertial and viscous forces of a moving fluid: Lu

Re = ~

(7.27)

where L and u are, respectively, the characteristic length and speed of the system, while v is the kinematic viscosity of the fluid. The physical significance of Re can be deduced from the fact that the inertial forces tend to separate parcels of fluid that had, initially, distinct speeds. On the other hand, the viscous forces tend to lead to a certain uniformity in the speeds at points close together and attenuate the dissimilarities. At low Re values, when the viscous forces predominate over the inertial ones, the flow is laminar. A critical Rec value is reached w h e n the inertial forces become so great with respect to the viscous ones, that turbulence is set up. The Re number is often used in the field of hydrodynamic stability and in the onset of turbulence. For example, in the case of a fluid that flows at a certain speed u over a surface, a internal boundary layer near the surface develops, that is initially laminar and becomes turbulent after the fluid has covered a distance L so that Re reaches the critical value Reo which generally lies between 105 and 3x106. In the atmosphere, Re is generally greater than Rec, so that the air is most frequently in a turbulent regime. Outdoor Rec is greater than in other closed systems; in pipes for example, it is 2500 < Rec < 5000.

223

Richardson (gradient) number (Ri) Ri is expressed in the form of a gradient (Richardson, 1920) and is the nondimensional ratio between the buoyancy forces (Archimedes) and the inertial ones due to the wind: g 3p g 30 ~2 p 3z 0 3z Ri - [3u~2 -- ~U 2 -- ~,~U ,~2 ,

(7.28)

,

where co represents the Brunt-V~iis~il~i frequency. The temperature gradient (and the related heat flow) which appears at the numerator, is normally negative during the day; during the clear, windless nights is positive, but may be negative during the windy or rainy nights. The sign of this number is determined by the temperature gradient, while the denominator is always positive, the negative values being an index of instability and the positive of stability. The numerator of Ri measures the density stratification or static atmospheric stability due to the temperature gradient. The denominator is of dynamic nature and measures the destabilising effect, linked with the wind profile. In practice, the Ri represents the ratio of the work done against the gravitational stability and the energy transferred from the ensemble motion to the eddy turbulence. When this, and the following parameters, are measured in the air close to the ground, there is no difference between the actual temperature T and the potential temperature @. In practice, considering equal the two parameters at the soil level, at the height 10 m the difference @- T equals 0.1~ which falls within the limits of experimental accuracy. For this reason, in microclimate studies, these two parameters are used without distinction and often T is preferred.

McVehil ratio (KM/KH) This parameter is the ratio of two coefficients which define the vertical transport of m o m e n t u m (KM) and heat (KH) between two adjacent layers of the atmosphere (McVehil, 1964). When (KM/KH) > 1, the mechanical turbulence generated by the wind dominates over the thermal convection. When, however, (KM/KH)< 1, the convective mixing dominates over the eddy turbulence. Often, for reasons of simplicity and in the lack of observations, modelists assume (KM/KH)= 1;

224 however, this a s s u m p t i o n is valid in near-neutral and unstable conditions (Lumley and Panofsky, 1964).

Richardson flux number (Rf) Rf is linked with Ri and to the previous ratio:

KH

Rf - Ri KM

(7.29)

which quantifies the role of the turbulence in the vertical transport of heat and m o m e n t u m , by means of the vertical flows of these properties. Rf can be written as a non-dimensional ratio of two fluxes: the nominator is linked with the production (or destruction) of turbulent kinetic energy by means of the vertical heat flux H of the thermal convective motions, the denominator with the shear p r o d u c t i o n (or destruction) due to the dynamic action of the wind, which involves the vertical transport of m o m e n t u m and the gradient of the wind speed, i.e. the wind shear. The Rf number can be rewritten in the following way:

g 0

Rf--

~u

(7.30)

3z This p a r a m e t e r has the sign minus as it was introduced to obtain positive n u m b e r s in the original studies on the onset of turbulence in a thermally stratified atmosphere. At Rf ~ 0.2 a balance is reached between the generation and destruction of turbulence, and for this reason this value is called the critical

Richardson

number.

Monin-Obukov length (L) L is a dimensional ratio (it has the unit of a length) which characterises a diabatic wind speed profile (i.e. with an exchange of heat) that involves both the sensible heat flow H, and the friction velocity u, (Monin and Obukov, 1953). The Monin-Obukov is defined as:

225

3 L=-u,

cpp 3 cpp 6) H =-u* k g H kg 0

(7.31)

3

where k ~ 0.4 is the von Karman's constant. The term u, p at the n u m e r a t o r represents a dynamic factor; the denominator involves the heat flow in entropic terms i.e. H/O. As u, represents the shearing stress, L is determined from the boundary conditions of drag and gain of entropy at the surface. When the heat flux vanishes, this length is infinite. It is negative during superadiabatic conditions and positive during inversions. In clear night conditions, a transition height is found, where the eddies generated by the wind shear begins to be counteracted by buoyancy and Rf-- 1. This transition height can be individuated as the Monin-Obukov length.

H6gstr6m ratio (S) S compares the thermal stability given by the vertical gradient d O/dz, with 1

the wind destabilization pressure ~p 2

due to the wind kinetic energy

(H6gstr6m, 1964) as follows

30 3z S - 2.

(7.32)

All of the above parameters require measurements that are either very difficult to realise or not particularly reliable. For this reason, the H6gstr6m parameter has been introduced, as it involves the static and dynamic coefficients in a simpler form.

Sutton turbulence index (n) and the logarithmic wind profile This and the following parameters do only consider the wind profile. It is much simpler to measure the wind profile alone (or only the temperature profile), rather than complex measurements of the above parameters. However, when only a single profile, representing approximately either the thermal or dynamic aspects, is taken into account, the degree of approximation should be considered case by case, depending on the aims and the degree of accuracy

226 required. The Sutton turbulence index has been defined for the theoretical study of wind turbulence (Sutton, 1947) and is based on the analysis of the vertical profile of the wind speed measured at two levels, z I and z 2: U(Zl) U(Z2 ) --

(~22)n/(2-n)

(7.33)

The Sutton turbulence index n generally lies between 0 and 1 in cases of maximum and minimum turbulence, respectively, and is generally in accordance with other results, but not always unequivocally. This index only considers the bulk effects of eddy turbulence and convective mixing on the wind profile and gives the degree of erosion on the basis of the logarithmic profiles, as suggested by the theory of similarity. This theory requires that, expressing the atmospheric variables in an appropriate dimensionless form, the profiles of these new variables must have a unique form when stated in terms of the basic independent parameters, also expressed in dimensionless form. Under this circumstance,

the mathematical

formulation is the same, w h a t e v e r

the

atmospheric parameter involved. The similarity theory is very practical, not always rigorous. The logarithmic wind profile was derived from the observation (in wind tunnel experiments) that in the turbulent regime the mean wind speed varies with the distance from the surface following the law O

3z

U.

--

-kz

(7.34)

where k is the von Karman's constant, and the shearing stress has been found constant throughout an air layer close to the ground, called surface layer or constant stress layer. By integrating the above equation, the logarithmic wind profile is obtained, i.e.

1 z - k lnz--~o

(7.35)

U,

where the constant of integration Zo is called roughness length and physically represents the height at which the average wind speed vanishes, i.e. = O.

227

Deacon number (~) Defined as ~U

3 In 3z (7.36)

/~= 3 1 n z

is only related to the vertical profile of the wind speed, as the Sutton's index, without discriminating the effects due to the transfer of heat and m o m e n t u m (Deacon, 1949).

R parameter The R parameter only takes into account the wind profile or, more precisely, the wind attenuation at the ground due to friction and the exchange of momentum and is represented by: Us

R - Ug

(7.37)

where Us represents the wind at ground level and Ug the gradient wind (i.e. the wind determined by the pressure pattern, undisturbed by the soil roughness).

Wind standard deviation (ry) The standard deviation ry of the wind, is the wind turbulence statistically defined in terms of amplitude and frequency of the departures from the average value. Both the fluctuations in the wind direction 0, i.e. c0, and speed u , i.e. ryu are considered; the normalised value ryu/ is used directly in the equation to determine the concentration distribution in the Gaussian diffusion models, as we will see later this Chapter, as well as in Chapter 12.

7.10. PLUME DISPERSION Several models

have been developed

to predict

the concentrations

downwind of a single source. The Gaussian model has been widely used for its simple mathematical representation and the agreement with the observed data

228 for long term averages. This model assumes that the dispersion is due to the random effect of the eddies in the atmosphere which broaden out the plume when it progresses in the d o w n w i n d direction. In the case of a neutral atmosphere and steady wind direction, the maximum concentration is found along the plume centreline and lateral diffusion is due to atmospheric turbulence; in the case of a wind direction continually variable around a prevalent direction, the plume meanders and the maximum concentration is again statistically found along the mean wind direction, d o w n w i n d from the source. The crosswind distribution of concentrations is represented by a bell shaped curve very narrow near the source and gradually broadening with increasing distance from it, i.e. as time elapses after the smoke release. If a Cartesian reference is assumed, with the x axis along the wind direction, the y perpendicular to it, but in the horizontal plane, showing the lateral displacement, and the z on the vertical, the atmospheric stability will differentiate the standard deviations of the wind fluctuations in these three directions, respectively ~x, ryy, ~z (also called diffusion coefficients) and the plume dispersion will be affected accordingly. When the atmosphere is unstable, vertical motions are favoured by convection, and ~z dominates; when the atmosphere is neutral the diffusion coefficients are similar; when the atmosphere is stable, vertical turbulence is suppressed, i.e. ryz---~0, and O'y describes the fanning or the meandering of the plume in the horizontal plane. For an effective height h of an elevated point source, e.g. a stack, the solution for the plume concentration at ground level ~,(x,y,z=O,h) takes the Gaussian form Q e x p - (2Gryy + ~,(x,y,O,h) ~ ryx ryy

(7.38)

where Q is the source strength and the average wind speed at the height of the plume. Of course, the ground level concentration directly d o w n w i n d of the source is found by putting y = 0 in the previous equation, which reduces to

K(x,0,0,h)-

~ryxryyQexp-( h~2z2).

(7.39)

The maximum ground level concentration Xmax is obtained by equalling to

229 zero the time derivative of the previous equation, i.e. 2 Q ryz Xmax = e rr < u> h 20"y

(7.40)

(where e is the Neper number) and occurs at the distance x where ryz- h~ ~/7.2. The effective

height of the source h is the height at which the plume

stabilises after an initial rise. h is therefore given by the geometrical stack height

hst plus the plume rise Ah which is due to the momentum effect (determined by the vertical speed of the smoke into the chimney and the interaction between the vertical stack jet and the horizontal wind flow) and the b u o y a n c y effect (determined by the emission temperature, i.e. the low density of the smoke, which is w a r m e r than the surrounding air). Several formulae exist, which depend

upon

the jet speed

and

emission

temperature

as well

as the

environmental air speed, temperature and stability.

7.11. STABILITY CATEGORIES TO EVALUATE THE ATMOSPHERIC STABILITY From a practical point of view, the routinely use of complex parameters which describe the atmospheric stability, is limited, substantially, to very few cases where detailed m e a s u r e m e n t s can be carried out. Even u n d e r ideal conditions without any discontinuity at ground level and in stationary regimes, where it could be assumed that Gaussian diffusion prevails, forecasting the wind turbulence or simply deducing it from other meteorological parameters without calculating it from wind fluctuations and the vertical temperature gradient is still a problem. Many scientists have dedicated much of their time in search of a reliable method which supplies reasonable values of wind variance and plume dispersion from other simple observations. Practically, the method consists in determining classes of stability and linking them to typical values of ry. The stability classes are determined on the basis of observations and very simple considerations that are, however, valid only in a general sense. These criteria tend to focus on the link between the dynamic evolution of the PBL and bulk classes of turbulence which summarise the situation. This practical point of view leads to the definition of classes of stability, as follows.

230 7.11.1.

Brookhaven

The first f u n d a m e n t a l contribution is due to the Brookhaven National L a b o r a t o r y (Singer and Smith, 1953), which defined five classes of w i n d turbulence and tried to correlate each with temperature gradients, wind intensity, seasonal and d i u r n a l cycles, solar radiation, cloud cover and the Sutton t u r b u l e n c e index. The Brookhaven turbulence categories, referring to w i n d records taken over a period of one hour, are defined as follows: TABLE 7.1 Brookhaven turbulence categories A B2 B1

C D

fluctuations in the wind direction of more than 90~ fluctuations of between 90~ and 45~ fluctuations of between 45~ and 15~ the anemographic trace, because of the continuous and regular fluctuations, seems to be a wide, uniform band the trace can be compared to a continuous line and any eventual fluctuations do not exceed 15~

The categories are closely linked with the temperature gradient and more precisely, in order of decreasing instability: A, B2, B1, C and D. The D class is characterised by dispersion in a stratified atmosphere, and the stability is m u c h greater with respect to the other classes and is often associated with m a r k e d inversions, but sometimes with unstable conditions too. The correlation with the wind intensity is less strict. The A and B2 classes are generally associated with weak winds while the C one with strong winds. The B1 and D classes a p p e a r u n d e r considerably variable conditions. The w i n d s associated with D under stable conditions, in particular, are weaker at ground level and more intense higher up. By combining these results, the class, depending upon the type of turbulence is obtained: convective or mechanical. The A and B2 types, characterised by weak w i n d s u n d e r unstable conditions, are, essentially, of a convective nature. The C type is mainly of a mechanical nature, being associated with strong winds and neutral gradients. The B1 is of a mixed nature, while the D type is characterised by very modest turbulence. The seasonal character is visible but not very m a r k e d .

The h o u r l y

distribution is, on the other hand, evident. The A and B2 types make very little contribution and only occur in the m i d d l e of the day. Similarly B1 varies seasonally from 10 - 20% to 85%, while D is almost complementary to B1, the sum

231 of these two represents approximately 85% of the total cases. The C type, in qualitative terms, has the same trend as B1 but is much less marked. The correlation with direct solar radiation confirms what has already been said about A and B2 but the C class is mostly associated with weak sunlight or cloud cover, while D is linked with clear night-time sky or weak daylight sunshine, or extensive cloud cover and isothermy or transitory phenomena late in the afternoon. Singer and Smith also underlined that their results, when supported by a clear correlation, could be extended to other sites in open countryside at any latitude and climate similar to Brookhaven, as long as an anemometer with similar characteristics was used at an altitude of about 100 m. Their study, in practice, shows which parameters are most closely connected with certain classes of turbulence at a given site, confirming some precise dynamic relationships. At the same time, the study showed that any correspondence is of a statistic nature, the

values

often

varying

greatly

and

are

not,

therefore,

one-to-one

correspondences, and should thus only be used for broad considerations.

7.11.2. Pasquill A further contribution to this problem was made by Pasquill (1961, 1962, 1974) who tried to combine, in a more flexible way, the theoretical and experimental results obtained by the various research groups. The basic hypotheses were: stationary wind conditions with both vertical and horizontal Gaussian distribution of the concentration; wind constant with height and airsoil interactions which allow the representation of the dispersion coming from an actual source, or from a virtual source. Pasquill stated that even under these conditions the effective height reached by a plume and the lateral spread must be calculated by measuring the variance of the wind fluctuations. However, in the absence of any direct measurement, in the case of brief emissions (lasting a few minutes) and fairly close to the ground in open, flat countryside, Pasquill proposed using approximate evaluations of the plume spread and height for the six stability categories that can be characterised in terms of wind intensity, sunshine (in England) and cloud cover. The advantage is that the categories can be attributed on the ground of the knowledge of prevalent local climatological characteristic. Under conditions of great stability, he suggested that no values be proposed, because the results could be somewhat erroneous. It should be quite clear that such values can not be used in urban or industrialised

232 areas because of the additional dynamic turbulence generated by buildings. The six categories determined by Pasquill mirror the results obtained by the Brookhaven climatic correlations, and are defined in Tables 7.2 and 7.3, where the sunshine intensities defined "strong" or "weak" relate to the values m e a s u r e d at m i d - d a y in the s u m m e r or winter, respectively, in England. Night is defined as the period that runs from one hour before sunset to one hour after sunrise, w h e n the balance of the radiant exchange between the earth and the sky is annulled (in England) passing from a positive flux during the day to a negative one at night. It was suggested that the D category be used for the first and last hour of the day, as defined above, and for the periods, night or day, characterised by completely overcast sky. The conditions of great stability were introduced successively.

TABLE 7.2 Pasquill Stability Categories A: extremely unstable conditions B: moderate instability C: slight instability

D: neutrality

E: slight stability F: moderate stability G: great stability

TABLE 7.3 Key to Pasquill Stability Categories Surface wind speed (at 10m) (m/s)

daytime: strong insolation

daytime: moderate insolation

daytime: slight insolation

nighttime: thiny overcast >_4/8 low cloud

<2 2-3 3-5 5-6 >6

A A-B B C C

A-B B B-C C- D D

B C C D D

E D D D

nighttime: clear sky or cover <3/8 low cloud F E D D

These categories became very popular when the dispersion coefficients Cry, ryz have been plotted versus d o w n w i n d distance after the f u n d a m e n t a l works of Gifford (1961, 1976). These plots, known as Pasquill-Gifford diagrams (Fig.7.6),

233 10000

~

o

1000

A B C

r~ ol,-i ,-c:l

D E

F

100

o N

9 v,..i

10

100

1000

10000

100000

D i s t a n c e from the source (m)

1000

A

o

9 i,.-i r~

o!-i

C

D

100

10

~J

p,

100

1000

10000

100000

D i s t a n c e f r o m the source (m)

Fig.7.6 The Pasquill-Gifford dispersion coefficients o-v, O'z showing the horizontal and vertical standard deviations of the plume concentration distribution, for the different stability classes A to F. (a) The lateral dispersion coefficient ~y, and (b) the vertical dispersion coefficient ryz are plotted versus the downwind distance from the source.

234 were obtained from experimental values of the plume standard deviations derived from wind data and pollutant concentration levels under different atmospheric stability. The plots of dispersion versus downwind distance form, on a double logarithmic paper, a set of parallel lines, one per each stability category, when Cry, is represented, and a set of divergent lines for ryz. The simplicity of using this method for estimating the dispersion coefficients, in a time when computer and suitable data recorders were not yet invented, made soon very popular this classification. 7.11.3. Successive extensions

Turner (1964) extended the classification to urban areas while Smith (1972) developed a scheme which took into account the roughness of the ground, the development of the mixing layer, theoretical and experimental data resulting from a further 10 years of field research. Pasquill's work however, because its application was extremely simple, was, in practice, the most popularly known and utilised by those who did not have any on site experimental data or when it was more convenient to use crude approximations than do measurements of the required values. Consequently, the terminology: 'equivalent to a certain Pasquill class' (McElroy, 1969) was introduced to get over the limits regarding the

application of these categories. In reality, it is necessary to be very careful when applying criteria of stability to different sites, especially if these have topographic anomalies such as, for example, mountain or coastal sites (Dobbins, 1979; Camuffo, 1981b; Berlyland, 1991). The fundamental consideration is that each site must be defined in terms of local climate by looking for the various dynamic phases that the PBL is subject to. In the most favourable case, whereby the operator is sufficiently familiar with the criteria, it would be possible to correlate, in a first instance, and then deduce the local turbulence from the type of parameters that proved to be the most efficient.

235

CHAPTER

8

Dry Deposition of Airborne Particulate Matter: Mechanisms and Effects

8.1. INTRODUCTION The dry deposition of pollutants involves all the particles suspended in the air, from the finest ones with a molecular size, to the largest ones, coarse as grains of sand. Naturally, the size of the particle is of fundamental importance, in that the air acts as a discontinuous medium of suspension with r a n d o m bombing for the smallest ones, and a continuous hydrostatic or h y d r o d y n a m i c m e d i u m for the largest ones. It is therefore necessary to make a first sub-division, based on a comparison between the diameter D of the particle and the mean free path ~ of the molecules of the carrier gas. For air, at standard conditions, ~ = 0.065 ~tm. However, it is not simple to define a diameter for non spherical surfaces. Martin defined it as the distance between opposite sides of a particle, measured crosswise of the particle and on a line bisecting the projected area. Feet p r o p o s e d the measure of the length of the distance between two tangents on opposite sides of the particle profile. Another popular definition is the diameter of a circle whose effective area equals the projected area of the surface. Another definition of effective diameter is the diameter of a sphere having the same properties (e.g. aerodynamic, optical) of the particle. The list of definitions might continue, but in this context it is sufficient to know that the "diameter" of non spherical particles may have a definition which is not unique and must be adapted to the problem under consideration; in the following this term will be used in a very general sense. The parameter u s e d f o r determining the discontinuum or the continuum character of the medium is the so-called Kundsen n u m b e r K n , defined as 2~ Kn = D

(8.1)

236 i.e. the ratio between the mean free path of the gas )~ and the particle radius D / 2 . The molecular regime, is determined by the condition that Kn >> 1, i.e. D is much smaller than ~, and molecular impacts occur individually and punctually, each with their own singularity after random time intervals. In the continuum regime Kn << 1, the size of the particle is much greater than the average mean free path

of the molecules in the air; there are so m a n y impacts together that their individual contribution is averaged out. The single impacts of air molecules loose their identity and the air can be considered a continuum medium. Between these two extreme approximations, a transition regime whereby Kn ~ 1 (D ~ ~) is considered. Here, the resulting net effect of the impacts of the air molecules decreases rapidly as the volume of the particle increases. The mobility of the particle also decreases with decreasing Kn, i.e. increasing D, in that, during its movement, a large particle necessarily impacts on an ever greater number of air molecules, so that the viscosity of the air becomes more and more important. Deposition occurs as a result of various causes w h e r e b y microphysical p h e n o m e n a and the local microclimate can reduce or increase the deposition rate, with a different efficiency depending upon the particle diameter. Some deposition mechanisms vary their efficiency according to the size of the particles and also act simultaneously for the same type of particle (exercising reinforcing or opposing forces), resulting in a rather complex process. For each mechanism, and diameter size, the quantity of particles which deposit on a surface depends upon their concentration in the atmosphere, i.e. if all the particles have the same probability of sticking on a surface, the higher the concentration, the greater the number of particles which deposit. However, the probability of depositing varies with the particle size and the microphysical state of the air near the surface. In fact, a huge number of fine to m e d i u m particles are found suspended in the atmosphere because they have a long residence time, and a small number of coarse particles are found, because they deposit in a very short time. It is possible to describe this problem in terms of speed instead of time. In fact, the statement that the n u m b e r of particles N ( D ) with a specific size (i.e. expressed with the diameter D ), which will reach the unit surface per unit time, is proportional to their concentration C(D) in the ambient air, is formulated as N(D) - Vdep • C(D)

(8.2)

237 the coefficient of proportionality Vdep has the dimension of space x time -1 and is called deposition velocity

or deposition

rate. It is important to remind that the

coefficient Vaep is not a constant value, but a complex function of the particle diameter, the air temperature, the gradients of temperature and moisture, the relative humidity, the electric field, the air turbulence, the surface characteristics and other factors that will be discussed later. For this reason, to equal values of concentration C may correspond very different numbers N of particles which deposit. In practice, N can be reduced either reducing Vdep or C; the former method requires appropriate microphysical conditions obtained on the ground of an accurate knowledge of the theory of deposition; the latter needs a simple filter. All the commercial devices are based on_air filtering, but they do not consider that the air motions they generate wi,ll increase v&p; this negative consequence, and the non-linearity of this p h e n o m e n o n , m a y vanish the benefit, or also increase the deposition. This apparent paradox is justified by the consideration that N is proportional to C, whereas Vdep has a higher order dependence u p o n some variables, e.g. air turbulence. For instance, if the air in a room is naturally still, thermally stratified, as usually, and if one wants to purify it by forcing the air to pass through a filter, the ventilation and the turbulence that will be induced might cause a deposition much more severe than the dirtier, but more stable air, would have done. It is possible to decide the measures to adopt in order to reduce N by lowering Vaep on the g r o u n d

of the theory and the e x p e r i m e n t a l

observation, based on special field surveys carried out to know the deposition mechanisms that are active in the room. However, not all the particles that impact on a surface adhere to it, so that it is necessary to consider the complete balance of all the forces acting on the surface and its capture efficiency. The forces in play are the molecular forces of contact and adhesion, those of an electrical nature or due to the presence of a film of water, the anelastic deformation of the impacting particles and the surface. In the following the main deposition processes will be described; further details can be found in more general studies (Friedlander, 1977; Pruppacher and Klett, 1980; Sehmel, 1980; Hinds, 1982; Hidy, 1984; Seinfeld, 1986; Buffle and van Leeuwen, 1992) or other specific papers mentioned in the following.

8.2. R A N D O M WALK AND BROWNIAN DIFFUSIVITY The Brownian motion, also called random walk or the drunk's walk, is the

238 irregular m o t i o n of particles due to the thermal b o m b a r d m e n t

with air

molecules, which are in a state of violent agitation corresponding to the thermal level. This motion was discovered in 1828 by the botanist Robert Brown, but the formula for the process was calculated by Einstein (1905, 1956) and widely discussed by other scientists (Chadrasekhar, 1943i Ming Chen W a n g and Uhlenbeck, 1945; Wax, 1954). A particle is defined as being a Brownian one when its size is small (Kn >> 1), or not too large compared with those of the molecules of the fluid, and is sensitive to changes in m o m e n t u m at each impact. In the molecular regime, as a result of every single casual impact with the molecules of the fluid, the kinetic energy tends to level out around their average value, while the motion of every single particle can be described in terms of casualty. If the motion of a single Brownian particle is observed, its trajectory is a zigzag path, where the end of each rectilinear tract was determined by an impact. C o n s i d e r the individual displacement vector si which represents the rectilinear displacement of the particle from the i-th collision to the next; then the position vector rn = ]Lsi which joins the initial position of the particle to the final one, after n collisions. The bold, here and in the following, is used for vector notation. It is possible to calculate the mean square displacement from the initial position undergone by the particle after a certain time t, i.e. = <~ij si sj > = <~i si 2> + <~iCj si" sj > where <]~i Si 2

>

(8.3)

represents the mean square displacement after each impact, and

the algebraic sum of the scalar products of the casual displacements is = 0, as the contribution of r a n d o m positive factors equals the contribution of negative ones. The previous expression reduces to t = n a 2 = a2~--i = ot t

(8.4)

w h e r e a represents the mean displacement after each collision, At the mean interval between two consecutive impacts and 0t = a2/At. The motion of a particle in a viscous fluid is described by the Langevin equation" d2x dx m dt 2 = - f ~ + Fx

(8.5)

where m is the particle mass; f the friction coefficient; Fx the casual force acting on the particle, and the random character of the impacts gives - 0.

239 The friction coefficient f for large particles is based on Stokes law f=-3~/zD in laminar regime, where/~ is the dynamic viscosity of the fluid. For very small particles, i.e. Kn >>1, f is proportional to the second power of D, according to the

Epstein equation (1924) 2 rc(z D2 ~ / 2 r c k T f = ~ (I+ --~--) p m

(8.6)

where 0~-- 0.9 is an empirical correction coefficient, p the air density and m the mass of the air molecules. The Brownian motion is governed by two acting forces which are of different nature: the first one is the viscous drag, proportional to the velocity in accordance with the Stokes law in the continuum regime (Kn << 1); the second is r a n d o m , typical of the d i s c o n t i n u u m regime (Kn >> 1), and is due to the molecular bombing. Dividing both terms of eq.(8.5) by the mass m, the same equation can be re-written in the classical form

dv dt-

- 13 v + a ( t )

(8.7)

where the unit of the coefficient 13 is a time -1 and can be interpreted as the inverse of the viscous relaxation time of the particle and a(t) is the random acceleration. By multiplying both sides of eq.(8.5) by x and transforming according to the identities

d2x Xdt 2 -

X2 dx d ~ X d t - dt

d2 x2 2 [dx~2 dt 2 -~dtJ ;

(8.8)

and considering that the displacements made along the axes x, y, z are equally probable, i.e. <x2> = = = /3, one obtains

<X2> =

t

d<x2>

Ot ~-;

dt

o~ - 3'

d2<x2> dt 2

dx\2 = 0;

_~

<m (-d--/) > =

"

(8.9)

The principle of the equipartition of energy <m (dx/dt)2> = k T, where k is the Boltzmann constant, i.e. k = 1.38

1 0 -16

erg ~

allows the calculation of the

value ot = 6 k T / f , and the mean square displacement can be expressed:

2 6kTt 9 = f

(8.10)

240 This equation, first derived by Einstein (1905), constitutes a probabilistic representation of the displacement expected. The mean square displacement of the diffusing particles increases linearly with elapsed time and fluid temperature T; it decreases inversely to the (dynamic) fluid viscosity/1. The dispersion of particles which were originally close, is the most probable result due to the natural re-organisation of the internal distribution of a system as a consequence of individual and casual molecular impacts. This happens without the intervention of collective organised motions which characterise the hydrodynamics, which holds in the continuum regime and is governed by fields of force or pressure gradients. The diffusion coefficient can be derived in terms of random walk (Seinfeld, 1986) by integrating the equation which governs the concentration C of Brownian particles 3C 3t - ~ V 2 C which gives 3<x 2 >/3t = 2 ~ a n d

(8.11) <x 2 > = 2 ~ t . Equating the value of <x2> =

(1/3) given by eq.(8.10) with the result obtained integrating eq.(8.11), the Brownian diffusivity ~ i s obtained (Fig.8.1): kTCc = 3 n ~t D

(8.12)

This is the fundamental Stokes-Einstein relation which has been improved with the addition of the empirical Cunningham slip correction factor Cc (Fig.8.2). In the continuum regime, C c--~ 1, and ~ varies as D - l ; however, in the discontinuum regime, when the aerodynamic mobility of the particle increases, Cc is given by the equation 2~ Cc ~ 1+ 1.657D

(8.13)

and ~ varies as D -2. In practice, Cc increases the efficacy of the Brownian process for the smaller particles, when the number of simultaneous molecular impacts becomes smaller and smaller, and the net resultant is less and less attenuated. The Stokes-Einstein formula shows that the diffusivity is proportional to the air temperature which determines the molecular excitation, but is inversely proportional to the fluid viscosity and particle diameter; in the case of large

241 particles a very great number of random impacts is averaged and the net resultant tends to zero, as well as the diffusivity. The diffusivity is i n d e p e n d e n t of the particle density, unlike the velocity arising from the thermal excitation. 0,11

]

0,01 0,001 0,0001 (/]

0,00001 0,000001 0,0000001 0,00000001 0,000000001 0,001

0,01

0,1

I

D

I0

I O0

(l.tm)

Fig.8.1 Brownian diffusivity ~ (cm2/s) of particles in the size range from 0.001 <_D <_100 ~m. 1000

1 100

Cc 10

I

0,001

,

i

!

,

i

,

iii

0,01

i

,

,

i

,

i

iii

,

,

,

i

,

i

,,i

0,1

,

,

,

,

I

D

,

,

,,i

I0

i

i

,

!

,

,

,

I00

(~tm)

Fig.8.2 Cunningham slip factor Cc versus particle diameter D (l~m).

Einstein (1905) derived t:he diffusion coefficient considering a solute, with non homogeneous concentration C, dispersed into a fluid, contained in a cylinder

242 with unit cross section. $1 $2 are two parallel cross sections normal to the cylinder axis, and spaced between them 2Ax, where Ax represents the mean displacement u n d e r g o n e by the solute molecule due to the impacts which have occurred during the time interval At. S is the cross section just in the middle between $1 and $2. C1 and C2 are the concentrations in proximity of two sections $1 $2. Only half of the solute particles initially enclosed in the portions of cylinder between the sections $1 S and S $2 will move in the direction of the other section, passing t h r o u g h S, i.e. (1/2) C1 Ax and (1/2) C2 Ax. The net amount of solute which diffuses across S in the interval at, i.e. ~at, is given by the differenceof the two above quantities, i.e. (]SAt = (1/2) (C1-C2)Ax. Comparing the differential and finite terms, i.e. C1 -C2 dC (8.14) Ax - - d n where n is the direction of the cylinder, axis, and substituting in the previous expression, 1 dC (/)At = -2 zix2 dn "

(8.15)

The net flux per unit time is (/bAt

AX2 d C

=At - - 2 A t

(8.16)

dn

and the diffusion coefficient results the coefficient of proportionality between and the concentration gradient -dC/dn: AX2

~

(8.17)

= 2At

However, although the final displacement Ax is the result of many r a n d o m steps, Ax can be substituted with the Brownian mean free path KB, so that At = ~,B/,

where is the mean speed of the Brownian particle, i.e. -- 0.5 XB .

(8.18)

243 8.3. BROWNIAN DEPOSITION A new parameter is useful: the

Schmidt number Sc defined

as

v

Sc- ~

(8.19)

i.e. the ratio between the kinematic air viscosity v and the diffusivity ~ o f

the

particles. In practice Sc represents the ratio between the momentum diffusivity (linked to v) and the mass diffusivity (linked to ~ . In the case of a low Sc the particles have a great diffusivity, are very small and scarcely conditioned by the viscosity of the medium, so that they will easily cross the laminar layer which envelops smooth surfaces when the turbulence is moderate, and impact on the surface. For high Sc the particles are giant, with small diffusivity, and this kind of deposition becomes less and less relevant. In practice, the Brownian deposition is very important for particles with D ranging between 0.001 and 0.01 ~tm, is still important for D of the order of 0.1 ~m, but is negligible for micronic particles. Following the gas theory, the average thermal speed Vth (or root mean square velocity) of airborne particles in equilibrium with air can be calculated from the translation kinetic energy Ec = (3/2) k T,

~3kT Vth

=

m

~ / 18kT -

lr, p p

(8.20)

D 3

where m is the mass and

pp the

density of the particle. The

mean velocity of

the

flying particles VMB (Fig.8.3) can be calculated by integrating the product obtained multiplying each individual velocity (given by the Maxwell-Boltzmann distribution) by its probability, i.e.

~8~8kT~48kT VMB =

3-~ V t h -

lr, m

-

lr2pp D3

(8.21)

It can be assumed that the Brownian deposition velocity VB is equal to the mean velocity of the flying particles at the beginning of the process but, after some time, the interfacial layer will be progressively depleted of the particles which stick on the surface and new particles will arrive from the atmosphere. After the time At, the number N of particles that will have deposited on the surface is

N(At ) 2 ~ ~~ . At

(8.22)

244 A new concentration layer originates near the surface, and the flux of particles which impact on the surface is now conditioned by the development of the concentration layer. In this layer, C varies in the course of the time and with the distance z from the surface. In stagnant air the concentration layer evolves regularly and C at the interface and beyond a certain distance is homogeneous and constant. 10000

_--

1000 100 10 L~

.

1,

;> 0,1 .

0,01 0,001

o,oo~

.......................................

o,o~

o,~

D

Fig.8.3 Maxwell-Boltzmann velocity diameter D (lam).

,~,,,,

~

VMB

~o

~oo

(ILtm)

distribution of suspended particles vs. particle

The deposition velocity is conditioned by the particle diffusivity ~ and by the factors which determine the development of a very thin diffusive layer based on the surface, having thickness a(t), in which it can be assumed that C(z) varies linearly with z. Under this assumption, the Brownian deposition velocity vB(t) is vB(t)- ~(t)

(8.23)

and numerically coincides with the values of ~ (Fig.8.1), but expressed in cm s -I, for the case of a layer having thickness 6 = 1 (Fig.8.3). The value of 6(t)is characterised by the dynamic regime of the fluid, the thickness of the air layer in the region near the surface, the particle size and the time t elapsed after the formation of the concentration layer.

245 8.4. THERMOPHORESIS Thermophoresis (literally: transport due to temperature) is due to the fact that in the presence of a temperature gradient in the atmosphere, a particle is pushed towards the lower temperature because of the asymmetry of molecular impacts. The p h e n o m e n o n was already known in the last century in that scientists had recognised that no particles were found near very hot bodies. However, it was Einstein (1905, 1956) who gave the first mathematical explanation for the phenomenon. In the molecular regime, the particle is hit by air molecules with individual m o m e n t u m (pi)h on the part of the hotter air, and minor (Pi)c in the colder part, so that the statistical effect is that the particle experiences a net m o m e n t u m

Y,i(pi)h- ~,i(Pi)c

which delivers a net impulse; the result is that the particle moves towards the colder part. This explanation is true for the small particles in the molecular regime, but not for the large ones, in the continuum regime. In fact, suppose a cubic particle with side Alx, oriented with the temperature gradient. As the size of the particle increases the impacting surface (Alx) 2 also increases, as too the temperature variation at the two faces of the particle normal to the gradient. As the thermophoretic force is proportional to the temperature gradient, a further increase of AT proportional to Alx is expected, so that the total gain should be proportional to (Alx) 3. However, in practice this is not true, as the increase of the particle size leads to a reduction in particle mobility. The problem cannot be looked at anymore from the point of view of the statistical thermodynamics but is of hydrodynamic nature in the continuum regime. The mechanism depends upon the temperature jump at the gas-particle boundary which is determined by the thermal conductivity of the gas and the particle, and depends also upon the regime of flow past the particle; the resistance of the fluid is proportional to the velocity in laminar conditions and varies with quadratic law in non laminar conditions. Epstein (1924) made a careful mathematical treatment of the exchange of momentum between the gas and a sphere in order to determine the resistance experienced in their motion through gases, critically reviewing all the previous theoretical and experimental results by Langevin, Cunningham, Lenard and Millikan. He considered the two cases of spherical particles (droplets) very small and large compared with the mean free path of the gas. Introducing the ratio of the heat transported through the particle interior to the heat received in unit time from the molecular impacts, i.e. the ratio of the internal conduction of the particle to the external of the gas, he found a complete agreement between theory

246 and experiment. In the case of comparatively large spheres he started with the consideration that the particle exercises an important influence on the whole character of motion of the gas molecules, so that the conditions of motion of the gas are perturbed by the appearance of a system of h y d r o d y n a m i c stress, dependent upon the velocities. The physical meaning of the stress components is the transportation of a given component of momentum in a given direction. He then applied the principle of conservation of mass and that of conservation of energy, i.e. the number of molecules impinging on a surface element of the particle is equal to the number reflected by it, and the energy brought by the i m p i n g i n g molecules is equal to that of the reflected ones. Under these hypotheses, the force of resistance experienced by a large particle (i.e. when Kn 2 --> 0) in the presence of a surface slip is the momentum conferred on the sphere by the molecules of the fluid in which the sphere is immersed, which can be found in all the text books of hydrodynamics. Similarly, Talbot et al. (1980) considered the case of molecules colliding obliquely on the surface of the particle: the normal component of the m o m e n t u m is compensated, but not the tangential one, especially in the case of skin friction. On average, air molecules coming from the hotter gas region deliver more tangential momentum than those coming from the colder region, and the net result is a tangential momentum transfer. Different formulae have been proposed to calculate of the thermophoretic velocity VT. In the molecular regime (Kn >> 1): v dT VT = - 8~:T dn

VT .

dT 3Vdn . . . 4(1+8)T

(8.24)

v dT 0.55 T dn

dT VT =-0.33 T dn

(8.25)

(8.26)

where r represents a correction factor, generally r = 0.9. Eq.(8.24) represents the first approach due to Epstein (1924) and eq.(8.25) to Waldmann a n d Schmitt (1966). Equations (8.24) and (8.25) are independent of particle size; eq.(8.26) is inversely proportional to D for the presence of (~ and it describes better the experimental results. In the continuum regime (Kn << 1):

247 o-k 2a dT VT = - 2 P (kp+ 2ka) dn

(8.27)

dT 0.15 ~ dn

(8.28)

V T

"-"

-

where v is the kinematic viscosity of the air, n the distance from the surface, cr an aerodynamic slip factor, generally cr = 0.2, kp, ka the thermal conductivities of the particle and the air. The (8.27) is the Epstein equation as reported by Friedlander (1977). Two formulae where proposed for the entire Kundsen range. The formula by Pruppacher and Klett (1980)

ka dT V w = - B P dn

(8.29)

where the particle size, expressed in terms of Kn, and ka and kp are included in the coefficient 0.4 (1+o~ Kn) (ka + 2.5kp Kn) B = - (1+ 3Kn) (kp + 2ka + 5kp Kn)

(8.30)

where 0~ = 1.257 + 0.400 exp(-1.10Kn). The formula by Talbot and al. (1980) is v K dT VT=- T dn

(8.31)

where the parameter K

K=

2 C (R+C'Kn){I+Kn [1.2+0.41 exp(-0.22Kn)]} (I+3C'Kn) (1+2R + 2C' Kn)

(8.32)

is expressed in terms of the ratio R = ka/kp, Kn and the constants C = 1.147; C' = 2.20 and C ' = 1.146. In general 0.1 < K < 0.6. The graphs of eq. (8.29) and (8.30) are reported in Fig.8.4 which has been c o m p u t e d for R = ka/kp = 0.2. The two equations are substantially coincident for fine particles; beyond D = 0.01 ~tm the departure increases and increases, and the equation by Talbot et al. overestimates excessively the velocity of large and giant particles. Other theoretical studies and comparisons with experimental data are reported by Hidy and Brock (1970; 1972); Slinn and Hales (1970) and Prodi and Tampieri (1982). In general, the t h e r m o p h o r e t i c velocity of fine or large particles is

248 p r o p o r t i o n a l to the intensity of the temperature gradient in front of the surface w h e r e deposition occurs (the surface is colder than air). If however, the surface is w a r m e r than the s u r r o u n d i n g air, the t e m p e r a t u r e gradient is inverted so that the thermophoretic force tends to protect the surface against deposition. It should be r e m e m b e r e d that in front of the surface, the gradient of the air t e m p e r a t u r e diminishes exponentially as the distance n from the surface increases. Thus, at the interface w h e r e thermophoretic deposition occurs, the g r a d T is m u c h more intense

t h a n the a v e r a g e m e a s u r a b l e

value AT~An even at the m i n i m u m

distance An allowed by the instruments. 0,001

.= -

r.t3

0,0001

Talbot et al.

--

r,j

0,00001

0,000001

........................................., 0,001

0,01

0,1

D

,

,

1

10

100

(ILtm)

Fig.8.4 Comparison of the thermophoretic velocity V T computed by means of the formulae suggested by Pruppacher and Klett (1980) and Talbot et al. (1980) for a the unit temperature gradient dT/dn=l~ The former is more close to the experimental data; the latter departes at the medium size and the error increases with the larger particles.

8.5. DIFFUSIOPHORESIS The diffusion process involves the d i s p e r s i o n of molecules w h i c h are, initially, close to each other as in a random walk, a walk which moves from an o r d e r l y one to a d i s o r d e r l y one or rather, m o v i n g from a n o n h o m o g e n e o u s situation to a h o m o g e n e o u s one. Pure diffusion occurs w h e n some molecules of a species "A" are immersed in fluid "B" and because of molecular agitation, the "A" molecules gradually move a w a y from their original p o s i t i o n , so that after a

249 sufficient long time, there will be an equal distance between the "A" molecules that are thus uniformly distributed t h r o u g h o u t the "B" fluid. This is the p u r e diffusion of "A" in "B", and "B" remains apparently unaffected, except for having participated in the dispersion of "A". If the concentration of "A" is so high that the concentration of "B" is also initially affected, showing a m i n i m u m where "A" is m a x i m u m , then "A" diffuses diverging in "B" and "B" diffuses converging in "A" by m u t u a l diffusion. If the concentration of "A" is so great that the partial pressures are also involved, the problem cannot be treated any longer in terms of statistics of r a n d o m motions and diffusion, but in terms of partial pressures and mass convection, using the laws of the hydrodynamics. A transition regime can also be c o n s i d e r e d ,

in w h i c h

both

these

approaches,

i.e. statistics

and

h y d r o d y n a m i c s , are simultaneously involved. W h e n dealing with atmospheric pollution, the concentrations are usually so low that the first case is appropriate; the condensation on a surface and the evaporation in the free air are examples of the second case. Forced e v a p o r a t i o n m a y be an example w h e r e the partial pressures are affected. There are various processes in the a t m o s p h e r e that can give rise to non h o m o g e n e o u s

concentrations

of v a r i o u s

gases. We will

concentrate here on the w a t e r v a p o u r because of the high or low levels of concentration that m a y be locally reached and the effects that m a y follow on the deposition of pollutants. There are m a n y sources or sinks of water vapour, such as natural or h u m a n combustion, transpiration and respiration by living beings, condensation, evaporation, sublimation. Gradients in the concentrations of both water vapour Cw and dry air Ca give rise to two diffusive flows, but in opposite directions and the n u m b e r of these molecules Nw

Na

which cross the unit surface in the unit time interval is given

by the Fick equation

Nw

=

dCw ~2/wa dn

dCa Na = CJaw dn

(8.33)

that has already been seen deriving the Einstein formula, and ~wa = ~aw is the coefficient of m u t u a l diffusion between dry air and water vapour; experimental observations give Taw = 0.239 cm 2 s -1 at T = 8~

This equation was derived in the

heat transfer theory and is based on the assumption that diffusivity is constant in space. Of course, d C w _ dCa dn - dn

(8.34)

250 Any particle that is s u s p e n d e d in a region where dry air and v a p o u r molecules are m u t u a l l y diffusing, is subject to two opposing phoretic (i.e. transport) forces and is drawn by the resultant, in the direction of the flow which exerts the preponderant action, i.e. the dry air flow given that the mass of the air molecules (ma -~ 29) is greater than that of vapour (mw = 18). The resulting diffusiophoretic velocity Vd is given by the equation: Vd = - Craw ~-(faw dya dn

(8.35)

where Gaw is the diffusion slip factor (~aw

m w - m a

=

_

_,

(8.36)

(yama+ywmw) - (ya+Yw)~/m w m a

calculated on the basis of the molar fractions of dry air Ya and v a p o u r Yw, respectively Ca "~a = (Ca + Cw)

Cw ~w = 1 - y a = (Ca + Cw)

(8.37)

A v a p o u r concentration gradient thus leads the particle to follow the m o v e m e n t of the air molecule, going in the opposite direction to that of the vapour. In the event of a wall that releases vapour for surface or subsurface evaporation (e.g. in the micropores or the capillary fringe), if only the effect of pure diffusiophoresis is considered, all the particles tend to approach the wall and deposit there; on the other hand, if a surface absorbs water vapour, the opposite occurs. However, the diffusiophoresis will generate transport another phenomenon: the Stefan flow, that will radically change this situation.

8.6. STEFAN FLOW In t h e case of an initial non h o m o g e n e o u s distribution of dry air and v a p o u r , the process that leads to reach a uniform distribution of both the constituents leads to pure diffusiophoresis as discussed above. If however, the q u a n t i t y of dispersed v a p o u r does not remain constant (as in the case of condensation on a surface, or evaporation), then an additional p h e n o m e n o n is generated, that is, the Stefan flow (Goldsmith et al, 1963; Slinn and Hales, 1970; Pruppacher and Klett, 1980; Prodi and Tampieri, 1982; Vittori, 1984). This is the

251 result of some microphysical processes that all take place at the same time and therefore, are rather complex. None of these steps can be taken individually and a partial look at the p h e n o m e n o n easily leads to misunderstanding, and for this reason it is often misinterpreted. To describe this p h e n o m e n o n , it is useful to consider a cold surface on which condensation occurs, at t e m p e r a t u r e T which is only slightly below the dew point DP i.e. T = D P - ST. In a cloud droplet 8 T is really an infinitesimal value, but in the case of a m o n u m e n t measurable values AT can be reached. At the interface between the air and the surface where the water molecules deposit, the v a p o u r pressure diminishes by a quantity 8pw and assumes the v a p o u r saturation value esat(T), which is given by the Magnus formula. This determines a local m i n i m u m , even t h o u g h very modest, with respect to the u n d i s t u r b e d value Pw, so that Pw - 8pw = esat(T). It might be useful to remember that in practice the value of Pw is a small fraction (i.e. 0 to 3%) of the total air pressure and 8pw is a small fraction of Pw, so that 8pw is a very small fraction of the total pressure and d e p e n d s u p o n the t e m p e r a t u r e difference between the condensing surface and the free air. In the case of a cloud droplet which is always in a close or strict equilibrium with the surrounding air, 8pw is zero or nearly zero; in the case of a relatively cold m o n u m e n t and w a r m , h u m i d air, 8pw m a y reach substantial values, to one or a few hPa. Therefore, in the air (i.e. dry air and water vapour) close to a condensing surface, a weak convective hydrodynamic transport of the whole air mass is generated in order to compensate for the drop of pressure 8pw. As at the interface a n u m b e r of vapour molecules are continuously subtracted from the atmosphere by condensation and, moreover, the convective flow that is incoming has fewer vapour molecules due to the concentration gradient of the v a p o u r established near the condensing surface, the concentration of dry air molecules increases near the surface. Therefore, the partial pressure Pa increases by Spa = -Spw so that the total a t m o s p h e r i c p r e s s u r e p = pa+Pw

remains

homogeneous, in that this is an open system in equilibrium. Briefly, the system at the interface reaches a dynamic equilibrium with a lower concentration of w a t e r v a p o u r and a higher one of dry air, which d e t e r m i n e two opposite diffusive flows, one of vapour towards the surface, and one retrograde of dry air, with the consequences discussed in the previous section. The key of the problem is now to see how this equilibrium can be kept for a long time, because the higher concentration of dry air molecules which has formed near the surface, generates a retrograde diffusive transport of the dry air molecules, and the surface is a sink of vapour, but not a source of dry air.

252 Therefore, the departure of the molecules of dry air leads to a local reduction of the total pressure and, as a consequence, a convective mass transport of a

hydrodynamic nature develops, which exactly compensates the system keeping it in dynamic equilibrium, i.e. with stationary p as well as the localised m a x i m u m

Pa + ~)Pa. It should be noted that, in order to describe as clearly as possible this p h e n o m e n o n in all its details, it has been divided into logical subsequent steps, that are not separated in the nature. The reality is summarised saying that the surface condensation leads to establish two opposite gradients of water vapour and dry air, with a diffusiophoresis; this situation generates a compensating hydrodynamic flow, which is known as the Stefan flow. A more detailed definition for the Stefan flow is based on the balance of one component, as follows. The condition that the net transport of dry air at the interface of the condensing surface has a null balance (neither an accumulation nor a deficit of dry air) means that the diffusive transport of dry air is exactly

compensated for, at each point, by the hydrodynamic transport surrounding air, this latter being called the Stefan flow.

of the

From the above definition, the speed vs of the Stefan flow can be calculated from the balance of the n u m b e r of the dry air molecules at the interface, i.e. equating

vsCa which represents the h y d r o d y n a m i c flow due to the convective

transport of dry air described in eq.(8.2), with the Fick diffusive flow of dry air due to the concentration gradient described in eq.(8.33), and taking into account of the opposite sign of these two flows, i.e.:

vsCa-

~2~;aw

dCa dn

(8.38) "

Isolating vs, using the definition of Ya in eq.(8.37) and remembering that the sum of the concentrations Ca + Cw remains constant, one obtains

Yaw dya vs = 7a dn

(8.39)

A particle in the proximity of a condensing surface is subjected to two counteracting mechanisms: the Stefan flow and the diffusiophoresis. However, the diffusiophoresis is much weaker, and the net result in vector terms is

(~aw d ya

V R = V S + V d -" -

(1+Craw T w ) -Yw dn - 0.8 vs

(8.40)

253 as (~aw7w

=

0.21; this means that the Stefan velocity is largely dominant over the

diffusiophoretic one, and the net result is the Stefan velocity reduced by 20%. It can be noted that vs is, moreover, the only one responsible for the transport of large particles. Like thermophoresis, in fact, diffusiophoresis tends to vanish for the larger particles (i.e. for Kn ~ 0, VR --~ Vs) while the active transport due to the h y d r o d y n a m i c Stefan flow has the same efficiency for every type of particle, even those of some micrometers in diameter. This

very

efficient

phoretic

mechanism

develops

either

during

condensation or evaporation, and it transports, indiscriminately, all the particles near the surface d u r i n g condensation, or opposes all the other deposition processes during evaporation. Vittori (1973) measured the dust free space around an evaporating droplet, i.e. the distance over which the Stefan flow is dominant and pushes away all the suspended particles, and in his experimental work this dust free layer was found to be some 360 Bm thick. At first sight it w o u l d seem that the condensation (that is, a surface temperature equal or inferior to the dew point of air) is reached in an internal environment only in exceptional cases. It should be remembered, however, that this p h e n o m e n o n occurs in the micropores very frequently, as can be seen from the Kelvin equation. From experimental data, Goldsmith et al. (1963) related the deposition velocity VR to weak pressure gradients dp/dn VR = 1.9x10 -4 dn dp

(8.41)

with VR in cm s -I and d p / d n in hPa cm -1. Unfortunately, there are no direct measurements for the case of monuments, and laboratory experiments are very difficult to do. Applying this formula to the typical value for heavy condensation on m o n u m e n t s reported above, i.e. 8pw = 1 hPa, and the dust free space found by Vittori for dn, the order of m a g n i t u d e of the deposition onto the m o n u m e n t surface is found, i.e. VR = 5x10 -3 cm s -1. This is very slow, but the effect can not be ignored as at this speed the equivalent of an air layer of some 18 m m is swept in a hour, and in a clear night condensation may continue for several hours. Another empirical formula derives from the observation that the Stefan flow is a consequence of the average displacement of the gas which substitutes the water molecules which condense on the surface, or vice-versa in the case of evaporation. Dimensional considerations lead to relate the molecular masses of

254 dry air, water vapour, condensation (or evaporation) rate ~ ( g cm -2 s-I) 9

ma~ mwp

VR = ~ - - =

1.6 ~

(8.42)

The n u m b e r of particles captured d e p e n d s u p o n the a m o u n t of c o n d e n s e d v a p o u r and the concentration of particles in the atmosphere. The VR is about 0.005 cm s -~ for every 100 W m -2 of latent heat transferred by condensation, which is e q u i v a l e n t to the deposition of 0.15 m m h -1 of a layer of water. On a m o n u m e n t , the condensation occurs at a lower rate than on a herbaceous surface, which can reach 45 W m -2 so that VR < 3x10 -3 cm s -1. This indicative value is very similar to the above found with the Goldsmith formula. The opposite occurs with evaporation, keeping in mind however that, while c o n d e n s a t i o n is a slow but continuous process, evaporation can occur very quickly under certain circumstances if a great deal of energy (e.g. direct sunshine) is s u p p l i e d and there is sufficient ventilation. Therefore, in the e v a p o r a t i o n phase, this h y d r o d y n a m i c flow, even for relatively brief periods, can efficiently protect a surface against the deposition of pollutants, in that the VR in the e v a p o r a t i o n phase can reach values that are 10 times greater than in the condensation phase. To avoid confusion, it is necessary to specify that this complex effect that enables the calculation of resulting deposition velocity VR is called in several ways. Some people have called VR with the name 'Stefan' only, as in a first-order approximation, because the h y d r o d y n a m i c Stefan flow is largely d o m i n a n t with respect to m u t u a l diffusion. From others, instead, the resulting effect is only called diffusiophoresis, placing the accent on the initial phase that starts the whole process.

8.7. GRAVITATIONAL SETTLING In the general case of particles immersed in a viscous fluid, forces do not cause acceleration, but lead to a final velocity v so that the intensity of the force F is balanced by the resistance R exerted by the fluid on the particle and v = F/f, where f is the friction coefficient which characterises R. The gravitation generates the net Archimedes hydrostatic balance Fg Jr D3 Fg = -~ (Pp- Pa) g

(8.43)

255

where pp and Pa are the densities of the particle and the air respectively, and g the acceleration of gravity. The viscous drag of the air R is derived from the Stoke law (for spherical particles) and corrected for aerodynamic departures linked to Kn :

R =

3~/~Dv (l+o~Kn)

(8.44)

where 0~ is the same coefficient defined for eq.(8.30). In laminar conditions the terminal settling velocity vg is: PP gg Vg = D2 PPg18/lCc (1- Pa)pp-- D 2 Cc 18

(8.45)

where Pa/Pp which is of the order of 10-3 can be neglected in comparison to 1. The formula clearly shows that in still air the sedimentation velocity is proportional to the density of the particle and to the square of its diameter D and becomes proportional to D for fine particles, when Kn >>1 and the Cunningham Cc varies as D -1. The particle density usually ranges between pp = 1 g cm -3, e.g. water droplets and pp = 2.65 g cm -3, e.g. quartz granules. In the case of non-spherical particles the aerodynamic effect due to the shape, expressed in terms of equivalent aerodynamic diameter, can'be calculated. Note that dust and desert sand granules acquire a spherical shape because of constant rolling. Sedimentation deposits the larger particles on horizontal surfaces and is particularly efficient in calm air, especially for particles having a diameter greater than 2 gm. The settling velocity Vg is shown in Fig.8.5. When convective motions occur, the descending and uprising airflows apparently compensate and the average effect of d o w n w a r d s and u p w a r d s motions leaves unaffected the average values. However, the presence of convection generates mixing and turbulence, so that the Stokes law cannot be applied. The turbulent drag is much greater and particles remain much longer in suspension following the microscale air movements. Therefore, during the daytime, when HVAC systems and people movements generate turbulence and resuspension, the concentration of coarse particles is higher than during the night, when they sediment more quickly in still air (Fig.8.6).

256 100

10

0,1 0,01 0,001 0,0001 0,00001

0,000001 [ 0,001

i

i

i

iiiii

i

0,01

i

i

i

i iiii

|

i

i

i

i iiiii

i

0,1

1

D

(~tm)

i

i

i iiiii

10

i

i

i

i iii

100

Fig.8.5 Gravitational settling velocity Vg of the suspended particles vs. particle diameter D (~tm). 100000 10000

,9,

1000

r,J

100 ,.~

10

12

0,1

24

0,01 0

1

10

Particle Diameter (~tm) Fig.8.6 Changes in spectral distribution of the concentration of suspended particles during the day. During the visiting time, the sources, resuspension and turbulence determine a given concentration distribution (thick line) which in the following hours, when the air is still, is impoverished of coarse particles, which sediment more quickly. Museum Correr, Venice, measurements at 12.00, 24.00, and 6.00 of the next day, the 12 and 13 February 1996

257 8.8. ELECTROPHORESIS Deposition due to electrostatic forces does not differ very much from gravitational sedimentation, in that both cases involve movement generated by a force field. There are, however, some differences that should be pointed out. The first- and the most obvious - is that electrostatic Coulomb forces are positive or negative, are inversely proportional to the square of the distance and integer multiples of the elementary charge e of an electron, corresponding to the degree of ionisation of the particle or the surface on which the particles is attracted. This may be caused, for example, by ultraviolet radiation or violent impacts of gas molecules or particles (colliding with each other or foreign bodies). Atmospheric dusts are highly charged. The principal mechanism of charging is the so called

diffusion charging i.e. airborne

ions

and

the development of charge through random collisions of particles.

Particles

formed

by condensation

at room

temperatures are initially uncharged, but they rapidly become charged by gaseous ions which diffuse to them. Splashing raindrops form a myriad of charged fine droplets which are attracted by and stick on nearby surfaces. Smokes resulting from combustion are highly charged when first formed, e.g. 74% of particles in smoke tobacco where found charged (Cadle, 1965). Smoking cigarettes in closed environments is extremely dangerous as the electrostatic charges lead particles to stick on surfaces in a short time. The electrostatic forces, however, do not only arise when both the particle and the surface are charged, but also a charged particle can generate an equal and opposite charge (image charge) on the approaching an uncharged surface, or a charged surface may generate a dipole on a conducting particle, such as for example, on water droplets. Furthermore, electrical charges may be generated even when neither of the two bodies was initially charged

(contact charging).

Electrical forces may arise because of the difference of potential that is generated when two different bodies meet because of the local interaction of the permanent charges on the surface of the two bodies. Contact charging occurs during the separation of non-metallic (semi-conductor) particles from solid surfaces. Dust and paint, for example, are both semi-conductors and the electrical interaction depends upon the relative donor-acceptor properties of the surfaces that come into contact with each other. Electrostatic deposition becomes important only in the presence of low relative humidity, while in damp environments the conductivity of the air increases and the surface is covered with a film of water molecules so that the

258 p h e n o m e n o n is greatly reduced; on the other hand, h u m i d i t y increases the adhesion of particles on moist surfaces, enhancing the capture efficiency of the surface (Phenix and Burnstock, 1990; Buffle and van Leeuwen, 1992). It should be noted that the 'particle' is not only an agglomerate of inorganic a n d / o r organic molecules, or a fragment of a mineral, but also implies biological structures such as fungal and bacterial spores, 'dwarf cells' or even vegetative cells. Due to their specific surface charge, depending on their nutritional status and related growth pattern, as well as on the composition of the s u r r o u n d i n g a t m o s p h e r e and surface solution, they are even attracted or repelled by the material surface (Marshall, 1984).

8.9. PHOTOPHORESIS When a suspension of particles is subjected to an intense beam of light, a motion is generated, called

photophoresis. This

phenomenon is measurable only

with black particles containing elemental carbon, e.g. candle smoke, soot or fly ash g e n e r a t e d by the combustion of wood, charcoal, oil. There is not an universally accepted theory to explain this mechanism. The first idea is to think that photons possess a m o m e n t u m q hv h q = --~ = ~

(8.46)

(where h is the Planks constant, v the frequency and )~ the wavelength associated with the photon and c is the light speed) and therefore a light beam may exert a force on the particles which absorb or reflect photons. The pressure p exerted by a light beam is E P = c (I+R)

(8.47)

w h e r e E is the energy incident on the unit surface per unit time and R is the reflection coefficient, i.e. R = 0 for a totally absorbing black body, and R = 1 for a totally reflecting mirror. A mirror undergoes a pressure which is twice the pressure exerted on a black surface. However, this simple explanation based on the so called radiation pressure is not realistic, as suspended particles do not straightforwardly advance as they were p u s h e d by a pressure, but they proceed either linearly, or in the form of

259 spirals, loops and so on. This behaviour is more commonly interpreted in terms of radiometer effect, i.e. the absorbed photons generate temperature unbalances on the particles and the surrounding gas, so that the resulting effect is similar to that for particles in a temperature gradient. Spiralling motion is therefore generated by the particle rotation which changes the orientation of the temperature gradient and the associated thermophoretic effect. In fact, laboratory experiences ,on the radiometer effect in a gas (Landsberg, 1979) have shown that the effect of light pressure is largely overwhelmed by the effect of the convective motions in the gas, generated by the temperature unbalances due to the light absorption. The radiometer theory (Cadle, 1965) predicts that the m a x i m u m pressure pmax is exerted when the gas mean free path equals the effective dimensions of the particle, i.e. Kn = 1, and is given by the equation

848,

Pmax - 2 D

(where/~ is the dynamic viscosity and M the molecular weight of the gas) so that the photophoretic force Fph is described by equations which change with the gas pressure p, i.e. it varies as the cube of the particle diameter at low pressure, as the square at intermediate pressure, and linearly at high pressure, as follows:

Fph =

a p D3

24 T

Gp

for Kn >> 1

(8.49)

which is the formula derived by Rubinowitz in 1920 for the low pressure, where a is an accommodation coefficient and G p is the thermal gradient within the particle; in the transition region where the particle size is about equal to the gas mean free path, Hettner derived in 1926 this formula

Fph = 0.25 ~ /a D 2 Gp

~

a .~

- P - + Pmax

MT Pmax P

for Kn = 1

(8.50)

and the following one for the high pressure region

FPh=

3 ~ ].12D .~Gp 2pM

for Kn << 1.

(8.51)

This mechanism suggests once more that works of art should not be lighted with intense radiation, and smoke or soot particles not only produce the worst

260 blackening, but also are the most respondent to this effect.

8.10.

AERODYNAMIC

DEPOSITION:

INERTIAL

IMPACTION

AND

INTERCEPTION When a fluid motion undergoes a sudden change, all the airborne particles are subjected to two forces: the drag of the fluid and their inertia. The latter tends to maintain the initial m o m e n t u m so that individual trajectories depart from the air stream and a number of particles may impact on a collecting surface, where they can adhere or (more rarely) bounce. The larger and heavier the particles, the greater the conservation of m o m e n t u m and the departures; for this reason this deposition mechanism is very efficient for micronic particles and is most efficient w h e n the particles measure about 4 - 5 gm and the air velocity is high. This first kind of aerodynamic deposition, called inertial

impaction, occurs w h e n the inertia force acting on a particle is greater than the viscous force of the fluid so that the particle cannot exactly follow the path of the airstream and impact on a collecting surface. On the other hand, smaller and lighter particles are dragged a r o u n d the obstacle by the deflected airstream before contact can be made. However, some of

them m a y have their trajectory approaching the surface and they come into grazing contact with the surface just because the flow brings them within touching distance. This second mechanism, called inertial interception, is less efficient, especially because the trajectory progresses in the viscous layer near the surface and the particle is slowed down, and becomes important only in the presence of surface roughness. These two forms of aerodynamic deposition occur w h e n e v e r there is an airflow near a surface as the friction generates turbulence; the air stream may be part of a more general circulation, or may be generated by pressure differences (e.g. open w i n d o w s a n d / o r doors) or may be due to thermal imbalances which generate convective motions over or along surfaces. Also in the case of laminar m o t i o n , u n e v e n areas m a y cause local particle trajectory d e p a r t u r e s

and

interception on a surface which is close to the trajectory. As the Reynolds number (7.27) can be used as a measure of the ratio of the inertial forces to the viscous forces, and is also an index linked to the onset of turbulence, it is evident that the efficiency of this deposition can be related to this parameter as well as to the the Schmidt number (8.19) which is the ratio between

261 the m o m e n t u m and the mass diffusivities. Wind tunnel experiments over an even, flat surface have s h o w n (Hicks, 1982) that the velocity of aerodynamic deposition Va for small particles can be expressed in terms Sc of and the friction velocity of the air stream u, Va = A u , Sc -2/3

(8.52)

where the coefficient A is 0.06
0,001

0,0001

0,00001 0,001

|

|

|

|

|

J

|

|

!

|

0,01

D

|

|

|

|

|

|

|

0,1

(~m)

Fig.8.7 Aerodynamic deposition velocity v a of small particles, i.e. with D < 0.1~tm.

However, w h e n the air speed becomes too fast, the airborne particles do not stick a n y m o r e and the particles which were deposited are r e s u s p e n d e d in the atmosphere. However, there is no a well stated correlation between turbulence

262 and speed, so that it would be more correct to associate the deposition rate w i t h the particle mass and the degree of turbulence rather than the average flow velocity of the fluid. The inertial contribution is greater w h e n the particles are larger and the surface is rough, but it is difficult to express as a mathematical formula because it is greatly influenced by the micro distortions in the fluid and local coarseness. Inertial deposition is typical when there are air currents, or w h e n walls are not in thermal equilibrium with the air. Colder walls cause the air in contact to b e c o m e colder, denser and to sink, forming a descending stream along the surface; vice-versa, w a r m e r walls form uprising currents. When a free convective motion develops along a vertical wall, an internal boundary layer (IBL) is formed near the surface (Schlichting, 1979). The beginning of the m o v e m e n t is at very low speed and in laminar regime; when the air progresses, the speed increases as well as the thickness of the IBL. After a critical distance Lcrit when the speed has reached the critical value

Ucrit , a

sharp transition occurs to the turbulent regime.

In the case of a wall w a r m e r than the surrounding air, i.e. uprising flow, the critical condition can be expressed in terms of the Reynolds n u m b e r Re, measuring the distance L from the base of the wall and the air speed U near to the surface at the level L; in the case of colder walls and descending currents, the process is the same, but starting from the top of the wall. In a room, the onset of the t u r b u l e n c e is g o v e r n e d by the atmospheric stability, the difference of temperature AT between air and surface, and the surface roughness. The dynamic system m a y reach stationary conditions or may oscillate between some limiting configurations which are d e t e r m i n e d by b o u n d a r y conditions or forced by external perturbations. In a turbulent regime, the inertial deposition is greatly increased, with the effect of blackening the surfaces in a short time. In the case of smooth surfaces, the transition between laminar and turbulent regime occurs when the Rayleigh number Ra is Ra ~ 109. This number is given by the product of other two numbers, i.e. the Prandtl (Pr) and Grashof (Gr) number. The former is defined v

Pr = -

(8.53)

K

i.e. by the ratio of the kinematic viscosity and thermal diffusivity K of the fluid and for air is Pr = 0.71; it is a balance between the efficacy of two m e c h a n i s m s which transport energy, namely advection (the m o m e n t u m is linked to v) and

263 conduction. The Grashof number is defined

Gr = g ~ AT z 3 v3

(8.54)

w h e r e / 3 is the air expansion coefficient, AT the temperature difference, and z the length of the path followed by the air stream generated by AT. Gr is a measure of the relative importance of the effects of the buoyancy (linked to ]3 and AT ) and inertial effects (as the airspeed increases with the path length z as shown later) compared with the viscosity, and the onset of the turbulent regime occurs w h e n

Gr > 109. For example, when a smooth wall surrounded by stagnant air is only AT = 0.1~

w a r m e r than the air, the transition in the uprising flow occurs at z - 4 m

from the floor, where the edge of the IBL is located; for AT -1~

at z - 2 m.

H o w e v e r , the surface r o u g h n e s s of real walls or u n a v o i d a b l e a t m o s p h e r i c perturbations anticipate the transition to turbulence. The thickness 3 of the free convection IBL and the m a x i m u m speed w* of the air stream can be calculated with the formulae (Isachenko et al., 1977; Camuffo, 1991) 423

p ka z

2 ) ( ~ Pa Cpg AT

w * - 3.95

-1/4

~2/~ - ~ A T

(8.55)

(8.56)

w h e r e Cp is the isobaric specific heat of the air (see Fig.8.8 and Fig.8.9). The m a x i m u m speed w* is found at the distance 3" = 0.385 from the surface. In order to give an example of the airspeed for AT = 0.1~ = 1~

w* = 4.8 cm s -1 at z = 1 m; for AT

w* = 15 cm s -1 at the same distance from the floor. The average speed <w>

of the convective air stream can be found integrating w over the whole thickness of the IBL, and is <w> = 0.633 w*. In the turbulent regime, each point of the fluid (and therefore also the particles transported by it) can be represented by a vector velocity that has a high fluctuating component perpendicular to the surface. As a result, m a n y particles are t h r o w n against the surface with a great m o m e n t u m even though, before colliding with it, they must first cross, inertially, the very thin laminar and viscous layer that, in theory, should lie near the surface. When the regime becomes turbulent, the profile of the average air speed in front of the surface

264 10

AT = 1~

rj v

AT = 0.5 ~

AT = 0.1~

1

0,1

1

z

10

(m)

Fig.8.8 Thickness of the free convection layer 8 (cm) vs. the distance z (m) covered by the airstream from the edge of the layer.

100

rd3

10

AT

1

0,1

1

10

z (m)

Fig.8.9 Maximum speed w* of the airstream in the free convection layer at the distance z (m) from the edge of the layer.

265 changes: the maximum speed is reduced but the speed close to the surface grows rapidly. The deposition rate, in the event of turbulence, increases greatly: the functional dependence is, again, due to the mass of the particles; the average speed of the air running in front of the surface is not important; the degree of turbulence is very important, as it determines the intensity and frequency of the fluctuating components perpendicular to the surface. In the case the air flows over a rough surface with a laminar movement, the coarseness of the surface causes the fluid to deviate continuously from a rectilinear motion so that the vector velocity acquires a small fluctuating component which is perpendicular to the direction of the average movement, and this alternately points towards the surface and away from it. During these sharp changes of direction, the particles with the largest mass tend to continue their inertial motion, s o m e of them colliding with the surface. At low impact velocities (modest AT values) the particles don't have sufficient kinetic energy to bounce and overcome the attracting forces of the wall, so that almost all the particles that touch the surface remain attached to it. This means that heavy turbulence is less effective in deposing particles. Ideally plotting deposition versus turbulence, it starts as an increasing function of turbulence, reaches a m a x i m u m and then decreases again. Unfortunately, this plot has not yet experimentally determined. The deposition rate depends not only upon the particle mass, but also upon how fast the fluid runs over the surface and its roughness. This mechanism is not, however, particularly efficient in a laminar regime, especially if compared with deposition in a turbulent regime. It should be noted, however, that in the absence of external perturbations, at any given atmospheric stability and on any given rough surface, the air velocity does, nevertheless, play a part in the development of turbulence and, for example, the Reynolds number Re sets it at a certain value, even though partial and conventional.

8.11. ADHESION OF PARTICLES TO PAINTINGS OR OTHER SURFACES Once the particle hits a surface, it can bounce or stick on it. The fraction of particles that remains on the surface depends upon various factors: the main ones are the nature of the adhesion forces and the physico-chemical properties of the particle and the surface. Surface roughness and particle size and shape are also important. Macroscopic roughness can hold fine particles in the surface cavities,

266 and large particles better adhere on very smooth surfaces. On this respect, wax or painting varnish have a negative influence, although they ultimately separate the underlying surface from the particles deposit (Zimon, 1982; Phenix and Burnstock, 1990). Van der Waal forces, of molecular nature, are very effective adhesive forces. A particle which approaches a surface, experiences an attractive force which is proportional to the particle diameter but inversely proportional to the distance between the separation distance between the particle and the surface. Large particles close to the surface are more easily captured. Once the particle sticks on the surface, the larger the contact area, the stronger the adhesive force. Deformation at the contact zone (e.g. elastic particles or presence of wax or varnish), increases the contact area and the adhesion force. Small or flat particles have in general a greater ratio between contact area and total volume. In the range from fine to micronic particles (i.e. D <2 ~tm) the particle size is of the same order of magnitude of the submicronic surface roughness and the adhesion force is inversely proportional to the particle size, being largest with the finest particles. The smaller the diameter, the closer to the surface, the particle will be immersed in the viscous layer and shielded by surface roughness, and the less easily it can be removed by atmospheric turbulence. In addition, adhesive forces are much more larger than the weight of small and fine particles. In the large particles range 2 < D < 200 ~tm, the situation is very variable depending upon the roughness scale. Giant particles (dust), i.e. D > 200 ~tm, are mainly found on the horizontal or very rough surfaces, as their weight exceeds ordinary adhesive forces on dry surfaces. Electrostatic charges can be found either on suspended particles or on surfaces, and particularly on paint surfaces. Electrical forces exerts when two bodies have opposite charges or when the particle or the surface is electrically charged and the charged body (e.g. the particle) induces the image charge on the other body (e.g. the surface). Coulomb attraction between a charged body and the induced image charge is the most common mechanism, as only one charged body is sufficient to exert forces with all the neighbouring bodies. This attraction governs the transport of particles in the electric field which has been established between the actual charge and the image charge, and the adhesion of the particles to the surface. This adhesive force continues until the actual charge is dissipated; however, after the charge has disappeared, the particles stick again on the surface for the continuous action of the molecular and possibly other forces. In particular, when a surface is damp, charges are rapidly dispersed and electrical forces disappear. Electrical forces are also generated when fly ash, soot, dust and other

267 particles are charged by contact charging, as donor-acceptor forces for semi conductors, as already discussed.

Liquid film adhesion (also called capillary force) is due to the presence of a liquid film which covers the solid surface of m o n u m e n t s or buildings. Sand castles built by children on the sea shore are the most popular example of the great strength of this force. When a particle touches the wet surface, the liquid film adheres to it, and the surface tension tends to (partially) envelop and possibly englobe the particle forming a meniscus all around the contact area. This p h e n o m e n o n is called also 'capillarity' and is common in all the wet materials and ice, which is always covered with one monolayer or a few molecular layers of liquid water. The force exerted by liquid film adhesion is so large that a wet surface captures every particle that collides with it, and for this reason a wet surface is called a 'black surface'. Surfaces contaminated with deliquescent salts have a longer time of wetness and a more severe soiling. In principle, in humid environments wax and some varnishes make idrophobic the surface (i.e. the wetting angle tends to 180 ~ and the surface is water repellent) but the advantage against wettability is lost in dry environments for the action of two negative factors: the greater deformation of the surface in the contact zone and the smooth surface which favours adhesion of large particles, especially by action of electrostatic forces. Also biofilms exert adhesive properties, which increase the dry deposit of aerosols and particles, and the formation of non-biological crusts over biological precursors (Koestler et al., 1996).

8.12. VERTICAL DISTRIBUTION OF PARTICLES IN STILL AIR AND THEIR RESUSPENSION BY TURBULENCE In equilibrium with air, airborne particles which do not coagulate behave as a gas and it is possible to apply the kinetic theory of gases. An example has been the computation of the thermal velocity and the Maxwell-Boltzmann velocity (eq.(8.20) and eq.(8.21)). The same can be applied to the barometric formula for an isothermal atmosphere, with no vertical air mixing. The Dalton law for gas mixtures, according to w h i c h each gas is distributed in space with a partial pressure which is independent of the partial pressures of other gases, leads to the consequence that each gas can be considered independently, and the vertical pressure distribution for the i-th gas or type of particles can be written:

268 ,zMig, z pi(z) - Pio exp(,-./?~ T ) - Pio exp(-~7i )

(8.57)

w h e r e Pio is the pressure at the level z = 0; M i is the molar mass of the gas or particle and H i - . : ~ T / M i g the scale height, i.e. the height z where the pressure reduces by a factor l / e ; e.g. for molecular h y d r o g e n (M = 2) H(H2) - 425 km; for molecular nitrogen (M = 28) H(N2) - 30 km; for molecular oxygen (M = 32) H(O2) = 27 km. This differentiation b e t w e e n the molecular species is not found in the free a t m o s p h e r e , for all the vertical motions and large scale t u r b u l e n c e that favour homogenisation. In the case of particles, which are m u c h m o r e heavier than gases, the scale height is accordingly reduced, and a gravitational separation of different sizes is possible in a stagnant atmosphere inside a room. The above equation can be rewritten in terms of concentration , zMig, Ci(z) - Cio exp(,-,~ T )

-- C i o

exp(-~//)

(8.58)

10000 1000 100 10

10%

r,.;

N

-

90%

o,1,_= Z

o,oi

!

0,001 0,0001 0,001

0,01

0,1

D

1

(~m)

Fig.8.10 Barometric distribution of particles in equilibrium in a isotherm, stagnant atmosphere. For each particle diameter three levels z90, z50 and Zl0 have been computed which represent the heights where the concentrations become 90%, 50% and 10% of the value at soil level. Fig.8.10 has been calculated for the particle density p = 1 g cm-3; in this figure per each particle diameter three levels z90, z50 and ZlO have been c o m p u t e d which

269 represent the heights where the concentrations become 90%, 50% and 10% of the soil level value. From the graph it appears that in a room the distribution of particles with D = 0.001 ~tm is practically unaffected; at D = 0.01 ~tm, z90 = 8.27 cm, z50 = 54,6 cm and zl0 = 181 cm; at D = 0.1 ~m these heights are exactly reduced by three orders of magnitude and so again at D = 1 ~tm; i.e. the near totality of the particles with D = 0.01 ~tm is contained in the first 2m, with D = 0.1 ~tm in the first 2 m m and with D = 1 ~tm in the first 2 ~tm. When the air is still, the gravity and the kinetic theory oblige the m e d i u m and large particles to follow the barometric distribution and for each diameter size a floor based concentration b o u n d a r y layer is formed, which contains the near totality of these particles still suspended in the air. This means that every source of turbulence which causes a mixing near the floor, e.g. walking, using vacuum cleaners, is responsible for the resuspension of the particles with D >> 0.01 ~tm, whereas the particles with D << 0.01 ~tm do not stratify but are continually mixed by Brownian diffusion. As in stagnant air large

and giant particles accumulate in very thin air layers near the soil, it would be possible to activate in museums and historical buildings a nocturnal drainage with floor suction which removes most of the pollutants which are present in lowermost layer of a stable atmosphere, after the barometric equilibrium has been reached. This theoretical finding has never been applied, but seems a cheap and effective way of removing suspended particulate matter without the use of filters and the negative consequences they produce. Direct observation of the concentration profiles is difficult, as the presen t day particle analysers usually work in the range 0.1< D _< 10 ~tm and the experimental apparatus requil~es a very detailed vertical resolution near the floor, which is impossible for the mixing caused by the suction. Better results will be achieved when

reliable m e a s u r e m e n t s

experimental

evidence

will be possible at D = 0.01 ~m. The only

is limited

to o b s e r v a t i o n

of the

increase

of the

concentration of large a n d giant particles after having generated turbulence near the floor. Turbulence is too weak for taking off the particles that have been deposited on the smooth floor and stick there, and only raises the particles by mixing the floor based concentration layer with the upper air. A short c o m m e n t about v a c u u m cleaners: they tend to drain a w a y very coarse granules, which are then broken, g r o u n d , pulverised, m u l t i p l i e d in number, and b r o u g h t back to the ambient in form of a cloud of fine particles which will deposit again after some time. Only a fraction of the material sucked in remains e n t r a p p e d in the filter. Some products n o w are supplied with a

270 microfilter suitable to detain a consistent fraction of the pulverised matter. Solely centralised vacuum cleaning systems with airtight piping or with external breather pipe, installed with the outlet outdoors, permit the suction of the dust inside and the breather emission outside.

8.13. HOW SOILING DEVELOPS Soiling is caused by the deposition of natural or anthropogenic particles. These particles induce different optical effects because of their various sizes, shape and nature. Their range varies from just a few hundredths of ~tm to some tens of ~tm. The shape can be spherical as in silicate particles emitted by carbon combustion, or they may be articulated as in pollens, or irregular like grains of sand, or fibrous and prismatic as in wood combustion or in the case of vegetable or animal fibres, or bunches like the soot in diesel combustion. There are semitransparent particles such as alumosilicate or quartz granules, or completely opaque such as the carbonaceous ones generated by combustion of candle, oil or coal. Once deposited, the various particles have different effects, which may be physical and optical, linked to the physiological response of the eye (Bouma, 1947; Thomson, 1986; Eastaugh, 1990). The physical effects, even though complex, can be objectively defined. In the case of completely opaque particles, the paintings gradually become darker and darker as the particles are deposited and as the "free" clean space is reduced, which diminishes exponentially. In the case of s e m i ' t r a n s p a r e n t particles, the dimming of the colours depends upon the thickness of the layer formed over the painting, but again the loss of visibility of the image is exponential. Phenix and Brustock (1990) found that most of deposit in paintings consisted of a monolayer of adhered particles. Only the fine, submicronic particles were found as multiple layers in aggregates. These particles were grey and mostly rounded, clumped or dispersed on the painting surface. In the case of soiling resulting from opaque particles, the blackness progresses as the cumulative section Y~(ni Xi), where ni is the number of particles having diameter Di and Xi is the cross section of each individual particle which has deposited, i.e. Xi = ~Di2/4 for spherical particles. In this case the cumulative section varies with the second power of the radius, exactly as the total surface ~(ni Si) where Si = ~ D i 2 is the individual surface. As the total surface of the suspended particles frequently reaches a maximum in the range of the small-average sized

271 ones (a peak a r o u n d a tenth of a ~tm) e.g. soot from diesel motors, which in addition is difficult to filter, and m e d i u m sized ones, e.g. candle smoke, these particles should be regarded with the highest attention. However, in reality, this peak is not constant and the distribution may also be bimodal. In the case of soiling due to semi-transparent particles, the thickness of the deposited translucent layer varies with the cumulative v o l u m e which has deposited ~(ni Vi). The volume Vi varies with the third power of the radius of the particle and the spectral distribution ni Viincreases greatly as the diameter increases, especially at the micronic and supermicronic size (Seinfeld, 1986). However, the distribution of the particles in the atmosphere d e p e n d s u p o n various factors, so that there are many deviations with respect to the above rule. In the case of closed environments, not visited by the public, the large particles sediment more quickly while the fine particles are s u s p e n d e d in the air for longer; in this case the very small n u m b e r of large particles that remain in suspension may cause a decrease of the total surface and total volume for the great diameters or also bimodal distributions (Fig.8.11). In this case, the most critical ones are the large particles, e.g. quartz granules and other alumosilicates.

10000

1000 > 100 ,-.-.i

10

r,./b

2;

0,1

0,01

.

0,1

.

,

.

!

1

10

D (~tm) Fig.8.11 Spectral distribution of the number N of suspended particles, total surface S and volume V expressed in terms of dN/dlnD (cm-3, squares), dS/dlnD (~tm2 cm -3, diamonds), d V / d l n D (Itm 3 cm -3, circles), where D is the particle diameter (~tm). Kunsthistorishes Museum, Vienna, 26 August 1992, 3 p.m.

272 The deposited layer is not homogeneous and internal diffraction and refraction form, which tend to cause the underlying colours to be put out of focus and lighten. The scattering depends upon the dimension and shape of the particles. Moreover, the particles themselves are coloured so that the original colours tend to take on false shades which add to other foreign colouring due to the reflection of the colours in the surrounding environment. As a result, the painting gradually darkens, blackens and the colours are toned down or change. In the case of paintings, uniquely based on colours, the dry deposit covers the surface reducing the chromatic yield and legibility, diminishing the artistic value of the work of art and violating its interpretation, as, for example, happened with the Michelangel paintings in the Sistine Chapel. This means that the soiling must be removed using the necessary methods, even though these are, basically, undesirable, because they always subject the work of art to various risks and stress due to its manipulation. In the case of sculptures or architectural works the shapes are spoiled even though legible, but, however, the aesthetic beauty and their exploitation may be severely compromised, as, for example, the magnificent buildings in Venice which were originally white with decorations and then became black because of deposits of carbonaceous particles. However, while the deposited pollutants are dry, the damage is only aesthetic (even though this may be considerable), but it does not affect the physical integrity of the material that the monument is made of. The biggest problem is when the deposit becomes wet, because then there are chemical reactions which can attack the material and irreversibly damage the work of art. A direct correlation between the degradation of works of art and the concentration of pollutants suspended in the atmosphere (and remaining there) is meaningless, but rather it can be searched between degradation and the pollutants which are deposited on the monument surface. The flux of particles which deposit on a surface is proportional to the concentration of particles having the same diameter, but the deposition velocity is not the same for all the particle diameters, and not all the particles are equally dangerous. We have seen that the deposition mechanisms vary with the particle diameter, surface characteristics, microclimate and air-surface interactions. The degradation of monuments depends, therefore, upon the quality and quantity of the pollutants deposited, whether or not there are catalysts, and the way in which the surface is wetted (e.g. pouring rain that washes over the dirty surfaces or fine rain that activates the pollutants without removing them), the frequency and duration of

273 the wetting, in addition to the intrinsic factors (e.g. nature and strength of the material, surface roughness, porosity). The knowledge about the chemico-physical characteristics of the individual particles, their relative a b u n d a n c e in the a t m o s p h e r e and the d e p o s i t i o n mechanisms that favour the transport and the adhesion of some types of particles to the surface rather than other, should lead to a p r o f o u n d review of the dynamics of chemical aggression and should also clarify ideas about what can or can not be done to reduce the negative effects of this dramatic chain of events on the cultural

heritage.

It helps also to interpret

the traditional

chemical

monitoring. For example, a traditional chemical investigation of s u s p e n d e d particles which have been collected on a filter would show which elements dominate and that there may be only traces of others. The spontaneous reaction w o u l d be to concentrate attention on the prevalent chemical c o m p o u n d s , neglecting those present in only m i n i m u m quantities. However, keeping in mind that the mass is proportional to the volume, it can easily be seen that sometimes there are a few coarse particles that characterise the total mass but which are located in few points and have a small or no influence on the whole surface. On the other hand, however, there may be many h u n d r e d s of thousands of tiny aggressive particles which are spread all over the surface, but which were, traditionally, considered negligible because of their small total volume. Several case studies have shown that the microclimate plays a fundamental role in the deposition processes (Camuffo, 1990; 1991; Camuffo and Bernardi, 1986; 1991; 1993; 1994; 1995). It would be possible resolve the problem by going to the root and completely removing the particles suspended in the air by means of accurately filtering the air and leaving the microclimate free to meet its destiny. H o w e v e r , filtering is very costly and the complete absence of particles is practically impossible in environments which are visited by the public who transport them. It is, therefore, necessary to find a balance: halving the number of particles also seems halving the rate at which blackening occurs, under the same conditions. Unfortunately, the same conditions are difficult to find in that either there

is a loss of the

delicate

thermal

equilibrium

with

the wall

and

environmental atmospheric stability or should the ventilation near the walls be increased which could mean a net increase in the bulk deposition rate. In a similarly negative case, a filter system w o u l d reduce the concentration of s u s p e n d e d particles but could make the deposition mechanisms m u c h more active, giving rise to an unfavourable balance. The best results are reached only when the appropriate microclimate is fully established.

274 8.14.

WHAT

IS

THE

MOST

HEATING

APPROPRIATE

AND

AIR

CONDITIONING SYSTEM TO AVOID SOILING? The bulk deposition is the result of the combination of several deposition mechanisms,

some

of them

reinforcing

and

some

opposing.

Brownian

deposition is always active whatever the orientation of the surface, and the same holds for aerodynamic impaction and electrophoresis. Gravitational settling acts on the horizontal surfaces facing upwards. Thermophoresis, diffusiophoresis and the Stefan flow may be either directed towards the surface (whatever its orientation)

or

in the

opposite

direction.

We have

already

seen

that

diffusiophoresis and Stefan flow always combine slightly reducing the efficiency of the Stefan flow.

Zo = 10 cm 0,1

5

rjr3

0,01 (J

p,

0,001 0,0001 0,00001 0,001

J

|

|

J

|

|1!

|

J

i

|

J

0,01

|

|,!

|

0,1 D

t

|

J

|

|

|s!

|

|

|

i

~

|

1

i's'

10

(~m)

Fig.8.12 Upper and lower limit of particle and gas deposition velocity V versus particle diameter D calculated by Sehmel (1980) for stable atmosphere, u, = 30 cm s-1, p = 1 g cm -3 and different roughness heights, i.e. from Zo = I cm (thick line) to Zo = 10 cm (thin line). The deposition velocity increases with roughness.

A possible thermophoretic

idea

is to counteract

deposition

with

an

appropriate

effect (Nazaroff and Cass, 1987). H o w e v e r , it s h o u l d be

remembered that each mechanism has a different efficiency which depends upon the size of the airborne particles (Fig.8.12), so that it is impossible to find a general solution for the whole size spectrum,

i.e. c o m p e n s a t i n g

exactly all the

275 mechanisms in a part of the spectrum generates unbalances in other parts of the spectrum. Brownian deposition is particularly active on the finest particles; thermophoresis acts prevalently on the submicronic particles, while impaction dominates on the micronic range. Creating a positive thermophoresis means having the surface warmer than the surrounding air, thus generating an upward convective flow and aerodynamic deposition. Positive thermophoresis can partially oppose Brownian deposition in the middle of the spectrum, but it can not prevent deposition of large and giant particles by impaction, and anyway, a w a r m surface will blacken. In the case of a cold surface, thermophoresis acts negatively against the surface itself, giving rise to thermophoretic deposition of the smaller particles, adding to the effects of the inertial deposition of the larger ones. The m i n i m u m damage is, therefore, obtained when the temperatures of the wall and the air facing it are exactly the same. The efficiency of inertial impaction compared with thermophoresis can be deduced by looking at the blackness found above radiators. The blackness is not uniform as expected if only a drop of temperature between the wall and the air were involved. There are some well marked "V" zones, above the brackets which attach the radiators to the wall (Fig.8.13) which can be explained by the turbulent wakes generated by the brackets on the uprising flow (Camuffo, 1991). The uniform blackening above the radiator is due to the combined effects of thermophoresis,

aerodynamic

impaction

and Brownian

deposition.

It is,

however, possible to observe the thermophoretic effect combined with the Brownian one, but separately from aerodynamic deposition, looking at some micro cracks that form in the paint on the wall. These micro cracks locally deviate the stream of uprising air current by a few millimetres so that they are sided by a cleaner micro band not licked by the uprising flow, and therefore protected against inertial impaction. These considerations lead to the conclusion that ideal microclimatic conditions are those where the indoor air is thermally stratified in order to suppress turbulence and reduce convective motions. Atmospheric stability is reached w h e n temperature increases with the height and there are no hot surfaces that can induce convective motions. This means that the floor temperature cannot be more elevated than the temperature of the air in contact with it. In fact, the lower the floor temperature the greater the stability of the air above. Similarly, the ceiling temperature should not be lower than the air that touches it. In addition, at each height the wall temperature should be always equal to the air in front of it in order to avoid air currents along the walls.

Fig.8.13 (a)" "V" shaped blackening which is typically found above the brackets which attach the radiators to the wall, due to the turbulent wakes generated by the brackets on the uprising flow. (b)" The same effect, i.e. hydrodynamic turbulence generated in a laminar flow by a perturbing obstacle, is evident in the water layer overflowing from a dam.

277 Heating and air-conditioning systems, as well as humidifiers, are installed with the only purpose of controlling room temperature and relative humidity, but they do not care if they increase the deposition. In fact, although they introduce clean air, the indoor turbulence and mixing they cause increase the overall deposition rate and the soiling of works of art. The installation of these devices must care in a global way the control of the thermodynamic state of the air and of the efficiency of the actual deposition velocity which is a consequence of the microphysical processes which have been established at the interface between the air and the objects. Both the inflow of new air and the extraction of room air must be considered from this global point of view. Heating systems are unable to ensure a temperature constant in time and homogeneous in space. The distribution of heat generates preferential paths for the hot air masses, with or without forced ventilation; in the latter case steep gradients, turbulence and inertial deposition are generated in the rooms. In addition, a step rise, or a drop of temperature, occurs every time the system is switched on/off. The problem is not in designing new powerful or sophisticated machines, but rather in being able to distribute the new air in a room both steadily and homogeneously. The problem of the time variability can be solved using a modest but uninterrupted emission of heat which remains active for the whole season, continual day and night, only gently modulated with the season needs, just to balance the heat loss with the exterior. The popular practice of short time powerful heat emissions followed by cooling should be definitely abandoned. The space distribution should be made with many, extended and well distributed sources, avoiding the use of forced ventilation, as fan-coils do. However, the heating system and heat distribution are often conditioned, especially in historic buildings, by several aesthetic reasons or architectonic needs, and in many cases the priority is absurdly given to the container instead of to the content. Another problem is due to the cultural principle which gather together exhibits in a room with a major interest in associating objects on the ground of history of art and aesthetics, to which conservation problems are sacrificed. In the most fortunate case, gathering in the same room materials with c o m m o n conservation problems is allowed only in stocks deposits. In most cases exhibition needs and history of the art are the only actual arbitrator which determines the expectation of life of the exhibits, and HVAC are installed following these directives by technicians inexpert of conservation science. A further problem is that not always the climate desired by guardians and visitors is the best for the works of art. Differentiated solutions can be found, e.g.

278 in this case it would be advisable to separate persons from objects with a glass pane and create two independent micro climates. However, very often this is not possible and one of the two, people or objects, must adapt: more generally this means that objects are given up because they cannot protest as people do. No regulation exists on heating historical buildings, and no any heating system has been especially devised for heating churches, although the potential d e m a n d is enormous as well as the business. For instance, frequented urban churches need a c o n t i n u o u s heating, and a seasonal u n i n t e r r u p t e d

very

moderate floor heating may be an acceptable solution. The problem is different for the one day per week use: the sudden heating of the whole church is very dangerous, uncomfortable, expensive and often requires anaesthetic solutions. In this case it is better to abandon the idea of a general heating and the pews might be gently heated in order to form a warmer and more comfortable island for people. The very first problem is that there is not always awareness of the real needs, and inappropriate, traditional machines continue to be p r o d u c e d and installed. If priority were really given to conservation, some minor cultural or practical sacrifices would be accepted by owners, conservators and visitors; after that more appropriate heating systems will appear with the opening of new market capacity. The heating systems are sometimes made with hot air inlets from the floor, that generate strong convective m o v e m e n t s which continually mix the air masses in the whole room and raise all the suspended particulate matter which lie in the concentration b o u n d a r y layer near the floor. Sometimes the hot air inlets are at a middle height on the wall, and a forced flow of air crosses diagonally the room, forming two main vortexes which increase deposition of particles on the surfaces and may favour evaporation and wood shrinking. Other times the hot inlets are in the ceiling and a stable stratification forms in the room, which is the best condition for conservation. Also the position of the outlets for the extraction of the air is important. When they are installed close to the inlets, the air goes immediately into the outlets with little benefit for the room. When they are on the opposite side of the inlets, and there is no atmospheric stability, the hot air flows directly from the inlets to the outlets forming a dangerous path of hot air which crosses the room. If the room atmosphere is stratified, the hot inlets are on the top and the suction is on the bottom, all the room air is progressively substituted, layer by layer, before the new air goes out. In addition, when

the a t m o s p h e r e

is stable,

the floor-based

outlets

suck

away

the

concentration layer which contains the most part of the suspended particulate

279 matter having large or giant size. The existence and drainage of the concentration layer near the floor have never been considered up to now. A similar situation can be discussed for the air conditioning. Cold air inlets from the ceiling form falling rivulets of cold air which is eventually mixed with the local air; this method is very effective but generates small eddies with all the negative effects generated by turbulence. When they are allocated near the floor, the cold air which is introduced in the room expands in the bottom forming a cold layer, and then rises filling .the room with m a n y air layers whose temperature increases with height. It is important that the cold inlets are in the lower part of the rooms, but above the concentration layer. In this case the formation of the concentration layer is not perturbed, and with a moderate suction from other outlets at floor level, it is possible to drain out the main part of the large and coarse particles. The Stefan flow is often originated when the wall paintings cool during the daily temperature cycles adsorbing moisture into the micropores. In order to avoid this drawback, the room temperature should be as stationary as possible and much higher than the dew point. The best preservative methods are permanent, passive ones (such as, thermal insulators, screens against direct radiation, the use of materials with an elevated thermal or hygrometric capacity). These are not exposed to sudden malfunctions

or

break-downs

which

may

occur

in

active,

although

technologically advanced equipments. Usual temperature regulation systems, air conditioning, humidifiers and other active devices have two negative features: the risk of dramatic thermohygrometric shock as a result of break-down, and the practical impossibility of distributing heat and moisture in each room without creating gradients in proximity of the points where heat or moisture are emitted or adsorbed.

8.15. INAPPROPRIATE POSITIONING OF PAINTINGS Not every portion of wall is appropriate for hanging paintings. The problem is not only avoiding the disturbing glare of the opposed windows or lamps, and the most frequent errors are the following. (i) The painting is over a heater (Fig.8.14). Every time the heater starts to operate, the painting is immersed in a hot, dry air current, which alters the temperature and the equilibrium moisture content of the painting, shrinking and

Fig.8.14 Incorrect position of paintings in museums. (a): The painting was over a heater and has been removed. The contrast between the clean wall on its back and the soiling all around is evident. (b): The painting is exactly over a fan-coil heater.

281 generating internal tensions in the panel, or the frame, the canvas and the colour coating. New tensions with the opposite shrinking occur when the heating is off. As the heating system is turned on/off very often, this position generates every day m a n y cycles and fatigue which damage paintings and cause fading. In addition to the mechanical deterioration, also blackening occurs because the hot airflow generates inertial deposition of airborne particles, thermophoresis, electrophoresis and increased Brownian deposition rate. A corbel put over the heater attenuates only a bit the dramatic effects. However, in the case of heating with forced airflow, e.g. fan-coil, all the zone affected by the air movement should be avoided. This means that often also the wall in front of the blowing heater is not appropriate.

The painting is near humidifiers or dehumidifiers. Often these devices are placed at strategic points in order to counteract the relative humidity variations caused by thermal changes. Humidifiers form clouds of humid, and often also cold air, which envelope all the paintings nearby and then move through the room, transported by the air movements. The paintings are alternatively (ii)

immersed in and out of these clouds, with the cycles of internal stress that have been described above. As these devices are mainly placed in zones protected in corners of rooms or near walls, the clouds which form are even more concentrated and very dangerous. All the outlets for the emission of vapour, dry, hot or cold air should be as far as possible from the works of art and distributed in a capillary way in order to avoid the formation of humidity or temperature gradients. A better alternative is to place these devices at the centre of the rooms, far from the objects, and where the visitor can benefit of the air conditioned. (iii) Direct light beams from windows or lamps. Light may favour chemical reactions (mainly oxidation), discolouring and heating, with all the negative effects that have already been discussed. Also the position of lamps is important, especially if lamps are of incandescence type. The heat dissipated by incandescent lamps forms a convective cell which develops growing vertically, over the lamp, as the downward development is in general impeded by the air stability which is very often present in the indoor environments. The air movement associated with the convective motion ~is responsible for heavy soiling of the surfaces. This means that lights should be placed as high as possible to limit the extension of the convective cells, and soiling, into spaces over the exhibits (Camuffo and Schenal, 1982; Camuffo, 1987). For this reason it is advisable, whenever possible, to light paintings with light beams coming downwards. (iv) Doors and windows, when they are simultaneously open for the morning

282 cleaning, generate very dangerous air currents. All the objects affected by the current experience more intense exchanges of heat end especially moisture, with very negative effects. (v) Another common error is to hang wood panels or frames with two or more brackets rigidly sealed to both the wall and the wood. When the wood expands or contracts for temperature or humidity changes, the sealed brackets oppose these m o v e m e n t s and generate tensions which may overcome the resistance of the material, especially if junctions are present. It is also to be remembered that ambient monitoring is useful only if m a d e in the correct way. Thermohygrographs are generally placed in a corner of rooms, and very often on the floor. Some examples in Chapter 1 have shown that in the horizontal plane it is usual to find a difference of several tenths of degree between one part of a room and another; however, the natural air layering inside close e n v i r o n m e n t s

makes the vertical gradient

m u c h more

remarkable,

reaching often a few degrees difference between ceiling and floor. In the case that the heating (or the air conditioning) is made by means of emission of hot (or cold) air, the stratification is much more conspicuous, reaching several degrees. Although the air stability plays a positive role in suppressing indoor turbulence, measurements taken in only one or few points, and especially near the floor, are not representative of the actual ambient conditions in which works of art, h u n g at higher levels, are immersed. Attention should be paid that tall objects, e.g. wood statues, paintings, preserved in an excessively stratified air, have their base and their top immersed in air layers with very different t e m p e r a t u r e and humidity. In the long run this generates internal tensions to the material as well as migration of moisture and heat with dramatic effects.

8.16. UPLIFTING OF GIANT PARTICLES AND WIND EROSION In addition to the gentle deposition, the violent impact of giant particles and the wind erosion must also be considered. This is often confused with other phenomena. Alveolarization of stones may be due to several causes, and is often incorrectly interpreted as 'wind erosion'. Apparently, the action of the wind is very often involved: e.g. formation of severe pitting and interconnected, deep holes with loss of granular material with a honeycomb like structure, is very c o m m o n in carbonatic rocks with biochemical or detritic origin, having an internal non h o m o g e n e o u s texture like biocalcarenites (Fig.8.15a) or marine

283

Fig.8.15 (a) Biocalcarenite weathering with honeycombe like structure which is improperly attributed to wind erosion. Sevilla, Spain. (b) Similar weathering in a marine sandstone. Rhodes, Greece.

284 sandstones (Fig.8.15b). Rainwater dissolves the bonds between granules; w e t t i n g / d r y i n g cycles enhanced by wind or solar radiation cause solution, mobilisation and recrystallisation of internal salts; thermal cycles may add internal stress. The consequence is the breaking down of the weaker parts. This weathering is intrinsic to the nature of this rock (Zezza, 1976; 1994). For example, biocalcarenites have a texture of organic origin produced by burrowing organisms during the sedimentation in the Miocene. The bioturbations, of rounded and elongated form, constitute the denser and more resistant part of the calcarenitic deposit, with granules cemented better than in the rest of the sediment in which they are contained. When the less resistant part is weathered, any mechanical factor may be responsible for the ultimate fall of the loose granules. In particular, moisture is one of the factors involved in the adhesive forces (interparticle surface forces and electrochemical forces) acting on the independent granules (Fletcher, 1976). For this reason the loss of material is more visible on windy days when the wind reduces the adsorbed moisture as well as the cohesion forces, and the turbulence favours the fall of the disaggregated granules in an unstable equilibrium. Although the wind action is partly involved in this form of weathering, we cannot speak of 'wind erosion'. Wind erosion (also called 'corrasion') occurs when abrasive particles impact with great energy and for long time, causing extensive micro mechanical damage which eventually results in macroscopic effects of two kinds: fringing of the softer part of stones (Fig.8.16a) or making round holes (Fig.8.16b) in stones which initially had some small cavities: with fresh wind the hard sand granules are obliged to whirl, eventually smoothing, eroding and enlarging the host cavity. The process starts on existing cavities, e.g. micropitting, or the so called tafoni, i.e. natural cavities more frequent in coastal areas or desert regions, due to salt weathering, that may grow and reach the dimension of small caverns (Smith and McAlister, 1986). The erosion rate increases with the hole diameter and the centrifugal force of sand granules. The dust entertainment occurs in the presence of wind and turbulence. The problem is not yet clear in all details, as the smaller grains are inside the laminar b o u n d a r y layer or shielded by coarser grains. A mechanism (Bagnold, 1941; Gillette, 1980) is that some grains are dragged by wind, start rolling and creeping on the coarse soil, bounce on the existing granules and during leaps and bounces may be uplifted by wind. When a flying granule impacts on the soil, the collision can raise other granules that are then uplifted by wind. Another even more efficient mechanism is the presence of turbulence especially in the form of dust

285

Fig.8.16 Two examples of corrasion: (a) fringing of the softer part of stones; (b) making round holes in stones which originally had some small cavities where sand granules in presence of wind are forced to whirl eventually smoothing, eroding and enlarging the host cavity. Giza desert, Egypt.

286 devils or windwirls, originated by the uneven topography or in the contact zone between two air masses with different speed or density. Devils and windwirls are non stationary free vortexes and the core is represented by a vortex line around which the air rotates forming hyperboloids of rotation with the p r e s s u r e decreasing from the exterior to the interior. The soil is composed of granules and the free spaces between them are filled with air at external barometric pressure. When the windwirl, with its drop of pressure in the core, moves licking the soil, a jump of pressure is determined across the surface layer. This jump causes the 'explosion' of the air pockets below the surface and the surface granules are ejected into the core depressure where they are entrained at upper levels by the spiralling airstreams. There is a threshold velocity for wind to impress motions to granules and uplift them. The greater the granule and its weight, the greater the threshold velocity, which varies with the square of the diameter of the particles, i.e. proportional to the aerodynamic cross section of the granule to which the wind drag applies, not to the weight which varies with D 3. However, for very small granules the mechanism is different. Decreasing the size of the particles, other factors arise: small granules are better shielded between the coarse ones; they are protected by the viscous layer in which are immersed; the adhesive forces (especially van der Walls forces) which bind the grains to the soil are stronger. The finer the granule, the more intense the threshold wind speed Vt. In practice, the relation between the granule diameter and threshold velocity shows a dependence similar to a parabola (with a logarithmic distribution of D), with the m i n i m u m at Vt = 4 m s -1 and D = 100 gm. These are the first granules to be raised; then, w h e n the wind speed increases, a symmetric uplift of both the smaller and the greater granules occurs. Once uplifted, the energy of a flying granule is linearly proportional to its density, the second power of the wind speed and the third power of its diameter. The finest dust particles, i.e. D

< 1 gm, are airborne and follow the wind

stream flying around obstacles without impacting on them. Small dust particles which have inertial force greater than the viscosity of the air, undergo inertial interception, or even also impaction, on the surface and deposit there; the main effect is to make the surface dusty, not abraded. Broadly speaking, all the dust particles with a diameter D < 100 gm are airborne, may or may not deposit, but they are not dangerous for abrasion. In the medium size range, i.e. 100 < D < 600 gm, granules are sufficiently large to be dangerous, but too heavy to fly for a long time. Granules in this intermediate size interval are temporarily lifted and soon

287 fall and are transported by means of successive leaps and bounds, so that they proceed 'saltating'. The height of the leaps depends upon the roughness of the soil, but on average this phenomenon only affects the first meter above the soil. Granules larger than 600 ~tm cannot erode as they cannot be lifted by the wind and move only by creeping and rolling. Grains that are coarser than 6 mm cannot be moved by the wind. (Bagnold, 1941; Pye, 1987; Barndorff-Nielsen and Willets, 1991). In conclusion, at ordinary wind speed, only grains in the leaping range 100 < D < 600 ~tm are effective in terms of erosion, but only near the base of the monuments. This weathering is important only in sandy, windy regions and has been extensively discussed in the case of the Great Sphinx (Camuffo, 1993) which is situated near the border of the Giza desert, Egypt. In this case, signs of severe corrasion actually appear at elevated levels of the monument, i.e. between the mid-body and the neck. However, other parts of the monument do not suffer erosion at all. The lower part which is actually covered with a stone masonry, shows exfoliation caused by the combined action of soluble salts and groundwater. The damaged stone is flaky, with so thin and weak scales (Fig.8.17) that sand blasting is excluded there. Again, the face is still covered with a soft red coating made of animal blood (Fig.8.18) which was attributed to the New Kingdom (1555-1075 B.C.) (Getty Conservation Institute, 1990). The presence of this coating after some millennia is a clear demonstration that the face has never suffered corrasion. In order to explain this apparent paradox it is necessary to consider the local aerodynamic features and the monument history. The head of the Sphinx was made working a block of rock protruding from the soil and the body, which is below the original ground level, was obtained by digging all around an excavation which is some 12 m deep and 10 in width; only the back of the Sphinx is at the original soil level (Fig.8.19). In the past millennia the excavation was filled of desert sand and the Sphinx was submerged, except the head. The dunes and the wind removal of sand changed continually the level of the soil and the eroding level of the saltating sand varied between the mid-body and the neck following the changing height of the dunes (Fig.8.20). Actually, with the excavation cleared out, the gravitational settling is sufficient to determine a parabolic trajectory to the initially horizontal inertial motion of saltating granules which arrive at the upper edge of the excavation and fall in the bottom without impacting on the monument, or hitting only the edge of the basement. However, in the presence of cross-wind, the aerodynamic field into the excavation is far from the inertial

288

Fig.8.17 Exfoliation of the masonry which covers the lower part of the Sphinx.

Fig.8.18 Fragments of red coating on the face of the Great Sphinx which are remains of ancient colouring made with animal blood.

289

Fig.8.19 The body of the Sphinx was obtained by digging all around an excavation. When the wind blows, two stationary vortexes form in this excavation, and they change the trajectory of the coarse granules which are driven by the wind drag, the gravity and the inertia forces. The practical result is that all the abrasive granules fall into the excavation without reaching the monument.

Fig.8.20 The Great Sphinx when was submersed in the dune sand. The aeolian erosion of the Sphinx was due to the coarse grains in the range between 200 and 600 ~tm which arrived in the saltating mode. Dragged by the wind, these grains proceed by leaps and bounds and reach I m above the sand level. In the past millennia, when the monument was partially submersed in the sand, the rising and lowering level of the dunes continually varied the height of the erosion, which lies from mid body to the neck. (Photo Vercelli, 1920).

290

motion: the canyon effect generates a circulating region within the square cavity (Tritton, 1988), similar to a vortex with horizontal axis (as shown in Fig.8.19) which deflects the granule trajectories, moving them away from the monument. The excavation is a sink for all the abrasive particles which arrive in the saltating mode and these cannot reach the monument. Keeping clear the excavation is the best preservation method. Pure corrasion is extremely rare in urban areas, although wind erosion is improperly attributed to many other forms of degradation, which possibly depend u p o n wind speed in addition to other variables. Normal weathering of biocalcarenites (mainly due to dissolution of the binding cement and salt crystallisation) is a common example, as fall of disaggregrate granules is visible in windy conditions, as already mentioned. In general, urban environments haven't many grains of a dangerous size and buildings reduce the wind speed near the ground, except for some narrow places where wind channelling occurs; in addition, m o n u m e n t s are situated on a base which is usually above the dangerous height. The weathering that affects the base of urban monuments is mainly due to frequent mechanical collisions, capillary rise of rainwater, dissolved pollutants and animal urine a n d / o r other biological attacks; in cold regions freezing-thawing cycles are also important near ground level.

8.17. KINETIC ENERGY AND SAND BLASTING Besides pressurised spray water, also sand blasting is commonly used to clean monuments. This method utilises compressed air to impress kinetic energy to abrasive granules and remove surface crusts and dirt. It can be applied in dry conditions, or adding also some small jets of water in order to attenuate the impact of the granules and (partially) wash the surface. More detailed information on the method and the opportunity of using it can be found elsewhere (Lazzarini and Laurenzi-Tabasso, 1986; Ashurst and Ashurst, 1989); here the attention is only focused on the physical principle. The formula for the kinetic energy Ec of spherical granules having density p, radius r and speed v is 2

Ec = ~ ~ p r 3 v 2

(8.59)

In this formula, the granules of the abrasive are characterised by p and r, and the

291 speed of the stream of compressed air is determined by the air pressure in the compressor, nozzle size and type, distance progressed after the nozzle and lateral distance from the axis of the stream. In addition to the energy of the impacting granules, also their hardness and shape are important; e.g. glass spherules are less harmful than rough sand granules. However, air pressure, nozzle and abrasive characteristics are not sufficient to determine what h a p p e n s at the m o n u m e n t surface, as the airflow speed varies with the distance from the nozzle. In addition, the same Ec can be obtained with different combinations of r and v, as it is shown in Fig.8.21. In this figure, the Ec has been computed for quartz, i.e. p = 2.7 g cm -3, different granule radii and for some selected airstream velocities, i.e. 1, 5, 10, 15 and 20 m s -1. The formula has three degrees of freedom, i.e. p, r and v, and v is not fully defined with the compressor pressure and nozzle characteristics, so that among the variables instead of finding the distance of the nozzle from the surface it is possible to find included the 'skill of the operator', and the 'supervision of the work', which are not objective parameters, but very important factors. 1012 1011 10 ~o ~,

109

~

10 a

9 ~,,,i

~

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10 7 106 105

I 1

.i.

,

,

,

,

|

10

|

,

,

,

,

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,

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Radius (~m)

Fig.8.21 Kinetic energy (Ec, dyne) of the grains used for sand blasting as a function of the grain radius r and for some selected airstream velocities, i.e. v = 1, 5, 10, 15, 20 m / s for the density of quartz (p = 2.65 g/cm3).

292 This example has been chosen in order to show that not always all the variables can be controlled in a scientific way, and that personal experience is also an important factor, that becomes even much more useful if it can be transmitted in strictly objective terms. Science operates to abandon personal variability and transform empiricism in general laws.

295

CHAPTER 9

Introduction to Field Measurements

9.1. WEATHER

STATIONS

AND

OBSERVATIONS

FOR

MONUMENT

CONSERVATION Meteorological measurements are routinely taken to describe the atmospheric conditions for weather forecasting, airport assistance, agriculture, climate analysis and so on. Every station is considered as part of a global network which covers the whole earth. As all the measurements must be comparable, the type and class of instruments, their exposure, the site, the times of observations, the methodology and procedure, the presentation of the data are regulated by a precise normative. This has been published by the World Meteorological Organisation (WMO) as "The Guide to Instrument and Methods of Observation" (1983) and "Compendium of Lecture Notes on Meteorological Instruments" (1986). Other useful details or suggestions are given by National Meteorological Services (e.g. UK Meteorological Office, 1981). In the case of specific microclimate studies, every measurement is finalised to monitor one or more microclimate variables in view of increasing knowledge about a specific problem. The purpose of the investigation is the key factor in determining the choice of instruments and operational procedures. Only after making clear the survey objectives, the funds available and the accuracy needed for the data, it is possible to decide the type of sensors, the number and location of sampling points, the sampling frequency and duration, the appropriate period for measurements and all the other details. Differently from technical assistance or technological service, research cannot be bound by a standard normative; it however can give useful indications to facilitate the work of people who prefer to take advantage from previous studies and apply or compare methods and technologies that have proven to be of wide interest. The transmission of researchers' experience is useful in doing routine measurements as technicians can benefit of methods supported by scientific background, and in addition avoid

296 waste of time and money. With this aim and under these limits, the application of specialists experience cannot be observed as a normative or a standard, but as an indicative guideline which summarises some useful examples. Taking reliable measurements is not simple: the operator's capability is not less important than the instrument class. In fact, the most common errors are due partly to the instrument (i.e. insufficient quality of the sensor, instrument calibration, scale graduation, signal conversion, data processing and recording), and partly to the operator (i.e. influencing the variable with the operator's presence; using inappropriate operative methodology, exposing the instrument in an inappropriate way, incomplete shielding against external disturbances; choosing measuring points scarcely representative of the site under study; choosing sampling times inappropriate to describe the natural evolution of the variable; choosing inappropriate periods for surveys). It is evident that, when a good class instrument has been purchased, all the errors should be referred to the operator. Not always observations needed for conservation can be found in standard weather stations or aerodrome observatories, because the topography near the station may be completely different from the monument site; not all the required variables are measured; the sampling intervals, the accuracy, the data analysis and representation may be inappropriate for this aim. The most frequent microclimate observations required for conservation purposes are:

Surface and air temperatures, their space gradients (both on the horizontal plane and on the vertical) and time rates. Particularly important are gradients close to the artefact surface. Frequency distributions or average values, daily and seasonal spans, short term variability.

Dew point and dew point spread; relative humidity, andspecific humidity: as discussed for air temperature.

Time of wetness: distribution on the m o n u m e n t surface; daily and seasonal values for some points with different exposure.

Atmospheric stability: vertical gradient of the air temperature and measurement of air turbulence.

Direct (and possibly diffuse)solar radiation falling on the m o n u m e n t surface at different exposures and during the yearly cycle. Computer simulation is precious to improve the knowledge of the problem.

297

(Micro) ventilation in several points near the artefact surface. Average values and fluctuations for turbulence analysis. Direct observations on the site are extremely important, as the wind flow pattern is strongly perturbed in the presence of obstacles, and in the wake behind them the return flow has the opposite direction, so that records taken with standard weather stations may be completely different. However, weather data of wind speed and wind direction (dominant direction and variability) are also useful for a better interpretation of the field observations in a wider meteorological context. Another important characteristics of a fluctuating wind is the gustiness, i.e. the rapid changes of intensity about a mean level, called gusts (peaks) and negative gusts or lulls (valleys). Frequency and strength of gusts should be noted, when available. They constitute a basic indication of the eddy turbulence.

Precipitation frequency, duration, intensity and amount, length of dry intervals, from local measurements or standard weather stations. Note that tall buildings may substantially affect the precipitation in the area nearby for two reasons: the aerodynamic perturbation to the wind field and the electric field that may generate. The time interval between one precipitation and the next is another important variable, in order to know whether the m o n u m e n t has been dried forming a wetting-drying cycle, as well as the time available for dry deposition.

Hydrometeors

roses, i.e. direction and frequency of windborne droplets or ice,

either generated by precipitation or suspended in the air. The roses are obtained reporting on the compass, per each direction, how many times each type of hydrometeor was associated with wind blowing from that specific direction. These roses are very useful not only to clarify the climatic features of a region, but also to put into evidence which side of a monument is exposed to frequent wetting, washout and so on. The concerned hydrometeors are: drizzle (very light liquid precipitation composed of small droplets, with diameter between 0.2 and 0.5 mm, which fall slowly to the ground), rainfall (falling drops greater than 0.5 m m in diameter), shower

(a s u d d e n

and short duration,

violent liquid

precipitation from convection clouds; drops are usually very large, up the limit value of 6 mm in diameter), hail (solid precipitation in the form of balls or pieces of ice, called hailstones, with diameter ranging from 5 to 50 mm, falling from

snow (solid precipitation which occurs in large snowflakes at temperatures near 0~ or in a variety of minute ice crystals, when the temperature is well below 0~ or fog (which is not a precipitation, but is

cumulonimbus

clouds),

composed of fine droplets more or less suspended in the air, which reduce the

298 visibility to less than 1 km). Also the energy supplied by hail or raindrops, when they impact on the monument, is important. The Rome case study (Fig.9.1) shows that drizzle, rain and hail are prevalently associated with the Sirocco wind, blowing from south-east, i.e. along the sea coast; showers are generated by the same wind as well as the sea breeze which blows perpendicular to the coast (i.e. from south-west); snow arrives from every inland side and never from the side facing the Thyrrenian Sea; fog has mainly a continental origin, and descends to Rome following the valley of the River Tiber (north-north-east). With the aim of illustrating the theory presented in the previous Chapters, the experience of m a n y field surveys will be herewith s u m m a r i s e d .

The

conservation scientist needs to know which parameters are available from WMO or National Meteorological Services, as well as purposes, characteristics and limits of those observations (for this reason some essential notes have been here reported) before deciding to make new punctual observations, with different aims. The purpose is not to summarise a treatise on microclimatological methods (e.g. Munn, 1970) or experimental techniques (these can be found in several textbooks, i.e. the above mentioned reference reports, and in addition: Wexler, 1956; Moses, 1968; Doebelin, 1990; Linacre 1992), but to show the differences between standard meteorological methods and research needs, to discuss the main problems and give a number of useful suggestions to the operators working in the field of conservation. For this purpose, only the measurements of temperature, humidity, air motions and precipitation, which are the observations most frequently needed for conservation, will be illustrated.

9.2. STATISTICAL REPRESENTATION OF THE DATA Statistical representations in terms of averages are very popular, but in recent times the frequency of occurrence of specific p h e n o m e n a has been preferred in climatology, as the climate of a site is better characterised by the repetition of some meteorological events.

The occurrence of a rare, extreme

event does not change the local climate, but affects the average values. The consideration that local weather characteristics are more soundly based on the frequency of occurrence of some typical phenomena suggests to disregard anomalies and concentrate on the frequency distribution of the events. The well known wind roses, a n d the less familiar hydrometeors roses, are two examples of a frequency oriented representation of only one, or two

299

Fig.9.1 Hydrometeors Roses (i.e. direction of the windbome drizzle, rainfall, shower, hail, snow and fog) at Rome.

300 60 50 o ~ 40 (/3

~ 30 0 ,x= t~ 20

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3

6

9

12

15

18

21

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T i m e G M T (h)

Fig.9.2 a,b: Presentation of air temperature (in June, at Venice) in percentile and histogram form. Period: 1961-1994. In this example, the air temperature approaches a Gaussian distribution in a first approximation, but not the relative humidity. In the case of a Gaussian distribution, the 15, 50 and 85 percentiles (thick lines) correspond respectively to - o, and + o.

301 100 ,~, 0

~ I-i

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Relative Humidity (%)

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Fig.9.2 c,d: As for Fig.9.2 a,b, but for relative humidity. In the distribution of RH, the dotted lines at 58.66%; 70.08%; 80.79%; 89.88%; 96.51% show the critical levels at which condensation occurs in the micropores with radius r=0.002 ~m; 0.003 lum; 0.005 ~m; 0.01 ~m; 0.03 ~m, respectively. The intercepts with the percentiles give the frequency of the condensation-evaporation cycles in the above mentioned micropores.

302 combined variables. This presentation has the further advantage of avoiding the problem of computing averages of non linear parameters, e.g. RH or pH, or of non unimodal distributions, e.g. wind direction. In terms of frequency, the presentation of data is usefully made by means of the percentiles (Fig.9.2), and particular interest have the 15, 50 and 85 percentiles, which in the case of a Gaussian distribution of the data Yi correspond respectively to - o , and + o. Also the mode, which is the value which occurs most frequently and is representative of the so called 'typical' climatic situation, is preferred to the mean, which is a mathematical abstraction, based on the actual values of the whole set of observations. Of course, in the case of u n i m o d a l s y m m e t r i c a l distributions, the 50 percentile, the m o d e and the m e a n are coincident. In the case of a bimodal distribution (e.g. spring and a u t u m n precipitation, sea and land breeze), the 50 percentile and the mean are still coincident, but represent anomalous events, whereas the two modes show the two typical situations. For the above reasons, the most appropriate representation should be decided according to the specific aims of the research: e.g. in the case of the RH at Venice, it is more useful to know the monthly values of the 50 percentile which vary with the season, instead of the mode, which is 100% for nearly the whole year.

9.3. FREQUENCY OF OBSERVATION The frequency of observation is important not only to arrive at a sound statistical description of the local microclimate, but also to reconstruct from a limited set of data the trend and departures of a given parameter. The interval between two observations is chosen with the aim of recording the time history of the p a r a m e t e r

with the m i n i m u m n u m b e r of observations.

It is strictly

d e p e n d e n t u p o n the type of the problem as well as the frequency of the oscillations of the variable and the level of smoothing that is required. If an atmospheric variable has periodic oscillations and one observation is made at sampling intervals slightly shorter or longer than the oscillation period, each sampling monitors a point of the next oscillation but in a slightly different phase lag, and the plot of the observations apparently shows a new wave with a period and wavelength close to a multiple of the original oscillations (Fig.9.3). This wave is generated by the many observations which have been necessary

303

before reaching the same phase (or a value close to it) in the short term oscillations. This p h e n o m e n o n is n a m e d aliasing and, in order to elude it, M u n n (1970) s u g g e s t e d to avoid m e a s u r e m e n t s of i n s t a n t a n e o u s values at fixed intervals of time in the case of periodic oscillations in turbulence analysis.

w-,, t~ o~,,t t~

Time

Fig.9.3 When a periodic variable (thin line) is observed at fixed intervals of time (circles) which are close to the cycle period, the data analysis generates a new wave (thick line), with greater period and wavelength. This phenomenon is called aliasing.

As atmospheric variables continually fluctuate in a few seconds, it is fundamental to have clear ideas about what kind of information is needed, e.g. main trends or variability. From the former point of view fluctuations constitute

noise, from the latter, signal. The choice may result very different according to the aim: (i) if only the daily cycle of one or few p a r a m e t e r s (e.g. the air t e m p e r a t u r e or w i n d speed and direction) is needed, all the short period fluctuations are smoothed out using sensors with a sufficiently long time of response, or making several sampling and numerically filtering the data before recording; in this case a few tens of observations per day can be sufficient; (ii) if the m e a s u r e m e n t is concerned with the study of the air turbulence, a high frequency sampling and very fast sensors are necessary to monitor the short period fluctuations; in this case the number of observations is so large that high capacity recorders are required. In meteorology, for synoptic purposes, all the variables are measured for 10 minutes only every 6 hr, i.e. at 6, 12, 18, 24 hr (principal synoptic hours) or every 3 hr, i.e. 3, 6, 9, 12... (secondary synoptic hours); for flight assistance 10 minutes every hour. The practice of measuring only during the last 10 minutes of each hour leads to a high probability (i.e. 50/60 = 83%) of missing important short lived phenomena, such as passage of fronts, windwirls and so on. For instance, in 1994 the gale wind of a windwirl severely damaged roofs in the famous Piazza dei

304

Miracoli in Pisa, which is in the UNESCO List of the World Cultural Heritage. The w i n d w i r l passed between two sampling times of the two meteorological stations placed in the same site and in the nearby airport. Both stations missed the event and the record of the day showed an absolutely ordinary situation. For this reason it should be necessary to measure 'continually', without gaps or with an elevated frequency. In order to reduce the excessive amount of data, it is possible to compute and memorise the average values of outside temperature, humidity, sunshine or rainfall every 10 min; in the case of parameters with high variability, e.g. wind, or indoor temperature and humidity changes near HVAC systems, also the extremes and possibly the variance should be r e c o r d e d continually or with very high frequency. The choice of the length of the sampling interval At is determined by the Nyquist frequency 7r/At, which is the highest frequency that can be used in Fourier transform and, consequently, gives the longest period which is detectable from a sampling with finite length (Wei, 1990). However, as problems and applications are so many and so different, it is not convenient to state thumb rules except for the general statement t h a t the

sampling frequency, the interval for averaging and the length of the observation period should be decided together with the characteristics of the experimental apparatus as a function of the specific problem and the specific variable.

9.4. LENGTH OF OBSERVATION PERIOD M e a s u r e m e n t s should be taken for a period sufficiently long to give a complete description of the ambient variability (i.e. if there are cycles, they should be completely monitored, and the most important cycles are the daily and the yearly ones) and field surveys should cover a certain n u m b e r of cycles to be statistically representative. If a fraction of cycle is monitored, it shows an apparent trend and the data are misleading or of difficult interpretation. If turbulence is investigated, or special transient phenomena, e.g. the perturbation caused by the turning o n / o f f of the HVAC or lighting systems, the monitoring can be m a d e only for the relatively short period which is necessary and, if possible, it should be repeated a n u m b e r of times in order to increase the confidence in the data representivity. Very often the problem is to do interventions as soon as possible, so that it is unbelievable to collect data for years. Therefore, it becomes customary to follow the seasonal cycle with surveys of one or a few weeks m a d e at the most

305 important parts of the seasonal cycle, mainly in the heart of the winter (January or February) w h e n the climatic wave reaches the extreme values, in the early spring (April) w h e n the thick walls are still cold preserving a m e m o r y of the cold season and the air becomes w a r m and h u m i d , so that surface condensation is favoured, and in the heart of s u m m e r (July or August) w h e n extreme values of the hot season are reached. In winter and s u m m e r the HVAC systems work at their m a x i m u m , and it is important t o know how they control or perturb the microclimate in order to reach a more homogeneous and steady distribution. When a short survey is made, it is advisable to gather the synoptic weather analysis

and

the regional

meteorological

data,

in o r d e r

to connect

the

m e a s u r e m e n t s taken with a wider climatic context and get a clear idea of the representatity of the survey.

9.5. RESPONSE TIME OF A SENSOR When average values or trends are needed, slow sensors are preferred, as a long time constant tends to smooth out the rapid fluctuations and noise is filtered without needing an elevated n u m b e r of observations. On the other hand, fast response sensors are necessary in other cases, especially w h e n monitoring the impact of rapid or transient phenomena. Therefore, it is important to k n o w the time response of each transducer and then select the appropriate one in every opportunity. When the m e d i u m surrounding a sensor undergoes a step change of the p a r a m e t e r under examination, e.g. a drop in temperature AT, the sensor approaches the new temperature gradually, and the time required to change by a stated proportion of the step change is called response time. The equation which describes the rate at which the sensor approaches the m e d i u m temperature Tm is dT dt

- -

T - Tm =

-

-

-

(9.1)

where T is the temperature of the sensor, and 9 a characteristic p a r a m e t e r with the dimension of a time, called time constant. The time constant is i n d e p e n d e n t from AT but varies with the rate at which the sensor exchanges heat with the surounding m e d i u m . The exchange rate is determined by several factors, i.e. heat capacity of the sensor, type of m e d i u m , specific heat, conductivity and possibly convective motions which increase the capability of exchanging heat, especially in the case of turbulence. If the m e d i u m is the air, and ventilation increases, the

306 time constant decreases, being roughly inversely proportional to the square root of the ventilation speed (Fig.9.4). Especially in the case of air m e a s u r e m e n t s , it is useful to r e m e m b e r that the specific heat of the sensor is m u c h more greater than that of the air, and the sensor t e m p e r a t u r e follows the air t e m p e r a t u r e w i t h a delay; for very fast sensors this is one or few seconds, for slow ones several m i n u t e s or m u c h more. The response of a wet bulb t h e r m o m e t e r is conditioned by both the sensible and the latent heats, and in general is not longer than the dry bulb. In water, "c is one order of m a g n i t u d e shorter than in air, and it slightly decreases w h e n the fluid from still becomes stirred. This finding is useful not only for t e m p e r a t u r e , b u t also for relative h u m i d i t y as well as the o t h e r parameters,

and

the a b o v e e x a m p l e

merits

a more precise mathematical

treatment. 1

____

Y _

.. --2j._e-__,_

0,1

12,"

0,01 0

5

10

15

20

25

Time (s)

Fig.9.4 In a linear-logarithmic paper, the plot of 1-[To-T(t)]/AT to obtain the time constant is a tilted straight line which begins at 1 when t = 0 (i.e. instant of the step change) and continues until the measured value of the normalised heating/cooling becomes smaller than instrument repeatability or ambient fluctuations e.g. 0.01. In this graph, the three straight lines show the responses of same fast thermistor in three different conditions, i.e. immersed into water (w); in air at 3 m / s ventilation rate (as) and at 12 m / s (a12). The ordinates of the intercepts with thehorizontal straight line y = 1-exp(-1/2) give the time constants "Cw,"c3, and "1~1,2 respectively. W h e n the m e d i u m u n d e r g o e s a step t e m p e r a t u r e c h a n g e AT = T o - T i n , w h e r e To is the value at the instant t = 0 w h e n the t e m p e r a t u r e has changed, and if after the change Tm remains constant, eq.(9.1) can be integrated and gives

To-T

= ( T o - T m ) exp(-~)

(9.2)

307 After the time t = I: is elapsed, the o u t p u t has reached l / e , i.e. 63.2% of any step change and this is the definition of the time constant. This value is easily obtained plotting the normalised heating or cooling [1 - (To- T(t))]/AT (ordinate, logarithmic scale) versus t (abscissa, linear scale). The plot (Fig.9.4) is a tilted straight line which begins at 1 w h e n t = 0 (i.e. instant of the abrupt change) and c o n t i n u e s as far as the m e a s u r e d value of the n o r m a l i s e d h e a t i n g / c o o l i n g becomes smaller than one of these two limiting factors: instrument repeatability or a m b i e n t fluctuations. At this point the straight line stops and the graphic r e p r e s e n t a t i o n is i n t e r r u p t e d . If it were continued, it w o u l d s h o w r a n d o m fluctuations f o r m e d a r o u n d the asymptotic final value. Of course, only the straight line is useful to d e t e r m i n e the time constant or other characteristics response times, i.e. the times to respond to l / e , 90%, 95% or 99% of AT. These are the abscissas corresponding to the ordinates y ~ = 1 - 0.632 = 0.368; Y90 = 1 - 0.90 = 0.10; Y95 = 1- 0.95 = 0.05 or Y99 = 1 - 0.99 = 0.01 which are, respectively, t~ = lz; t90 = 2.31:; t95 - 3z; t99 = 4.61:. This also means that is useless to carry out a m e a s u r e m e n t for a time longer than 51: in that the sensor has already reached equilibrium and every change is due to the arrival of other air masses, representative of another situation u n d e r development. Waiting too m u c h is an error, not a s y n o n y m of more precision. The air t e m p e r a t u r e continually fluctuates up to a degree or two in a few seconds. W h e n it is i m p o r t a n t to monitor this variability, fast sensors are used w i t h c o n t i n u o u s or high frequency sampling. This especially occurs w h e n m o n i t o r i n g a b r u p t changes of t e m p e r a t u r e generated by turning o n / o f f HVAC systems,

when

temperature

fluctuations

are

generated

by

atmospheric

turbulence, or w h e n quick m e a s u r e m e n t s are required. Slow sensors are used to define

the a v e r a g e

meteorological conditions,

as e.g. r o u t i n e

aerodrome

measurements. H o w e v e r , fast sensors are more flexible, as they can be used for either instantaneous or average values. An average can be obtained from them in different ways: (i) taking several close observations and c o m p u t i n g the 50 percentile or the arithmetic mean; (ii) integrating a continuous m e a s u r e m e n t (e.g. a variable frequency, a voltage) with electronic devices; (iii) d a m p i n g the o u t p u t applying a low-pass filter; (iv) increasing the time constant of the sensor, e.g. in the case of a t h e r m o m e t e r by covering the bulb with some substances (e.g. a droplet of bee wax) which increase the heat capacity and act as a thermodynamic low-pass filter.

308 The first m e t h o d requires a large m e m o r y capacity in the data logger or an electronic device that computes the 50 percentile or the average before recording it; the second and third need an integrating or d a m p i n g filter before monitoring the data; the fourth system is the simplest and cheapest one, and in addition the wax protects the sensor against water and shocks. If more than one sensor is used, attention should be paid that the mass of wax which covers each sensor is always t h e same; and this can be done with a precision balance. It is i m p o r t a n t to r e m e m b e r that well calibrated sensors with different time constants give exactly

the same output in a calibration bath or in steady state conditions, but a different response in dynamic conditions, as they have a different memory of the past values. This is a very general statement which suggests that m e a s u r e m e n t s should

a l w a y s be taken w i t h the same i n s t r u m e n t and that it m i g h t be

m i s l e a d i n g to c o m p a r e m e a s u r e m e n t s of the same p a r a m e t e r taken w i t h instruments of different kind. The displacement of a sensor before it has reached thermal equilibrium m a y d e t e r m i n e i m p o r t a n t distortions to the measurement. An example is given in Fig.9.5 which shows a vertical time cross section of the air temperature, and the final part of the erosion of a nocturnal inversion, measured rising up and pulling d o w n a high resolution radiosonde for the low troposphere. The ascent and the descent speed were prudentially kept at 1 m s -1, while the factory suggested the excessive speed 3 m s -1. However, also 1 m s -1 was excessively fast. In fact, the graphs show: (a) the zigzagging path of the isotherms, reflecting the alternation of the provenance of the sensor, i.e. a profile from w a r m to cold and the next from cold to warm; (b) the apparent isotherm distribution which is obtained by using only the rising runs; (c) the same but for the descending runs; (d) the temperature distribution obtained averaging the data transmitted during both the ascent and the descent in order to combine the opposite effects. The situation is even more complex in d y n a m i c conditions w h e n

a

p a r a m e t e r d e p e n d s u p o n m o r e than one variable, and these interfere in a different w a y with their time constant. A nice example is given by compact systems constituted of a battery and an electronic apparatus, e.g. a data-logger or a transmitter, housed in a miniature plastic case together with a temperature and a humidity

sensor,

which

communicate

with

the

exterior

through

some

ventilation slits. The sensors are relatively fast and data are sampled at short or p r o g r a m m a b l e time intervals, but nothing is specified about the heat capacity of the whole encased device and the delay introduced by the case. For example, a commercially available instrument, sized 7 x 4 x 2.5 cm, had fast sensors but its

309 600

-qP,-

g ,= t~ o,,~

.."qP"

q

13.5 14

500

V

14

.qp. '15 r

,1 $

400

15

15

3(10

.-:".:.:i

1(

I;

200 ~8 100

18 13,

0 5

6

7

8

Time

9

10

mll

2 5

7

8

9

10

11

11

12

Time (hr)

4001

6

6

(hr)

',i

7

8

9

Time

10

(hr)

11

12

13

6

7

8

9

10

Time (hr)

Fig.9.5 Vertical time cross section of the air temperature, and the final part of the erosion of a nocturnal inversion (dashed area), measured rising up and pulling down a high resolution radiosonde. The time and space coordinates of the radiosonde during the ascent and descent are indicated with a thin line and evidenced with an arrow. The graphs show: (a) the zigzagging path of the isotherms, reflecting the alternation of the provenance of the sensor, i.e. a profile from warm to cold and the next from cold to warm; (b) the apparent isotherm distribution which is obtained by using only the rising runs; (c) the same but for the descending runs; (d) the temperature distribution obtained averaging the data transmitted during the ascent and the descent in order to combine the opposed effects.

310 mass and the very low ventilation through miniature slits required more than one hour to reach equilibrium. An important improvement was obtained cutting the plastic case all around the sensors in order to facilitate the exchanges with the ambient air; after having opened this new window, the time constant was nearly halved dropping to 7 min, i.e. 21 min for reaching 95% of the change. An illustrative experiment is shown in Fig.9.6, where the data logger was subjected to a square wave temperature and humidity change, displacing it at the time to from an initial ambient at Ti = 12.2~

and RHi = 31% to another well

ventilated ambient, warmer and dryer, at Tf = 22.2 and RHf = 25.8%. The plot shows that after to the temperature rose from Ti to the final higher value Tf approaching it asymptotically, as expected. On the other hand, the fast RH sensor gave an unexpected result: the output immediately rose with a m a r k e d overshoot (peak value greater than 41%); afterward, the RH decreased following the gradual heating of the case, and reached equilibrium only when the case t e m p e r a t u r e had reached equilibrium. This apparently anomalous result is explained as follows. The fast humidity sensor (a thin film capacity sensor) passed nearly immediately from the initial value of specific humidity 2.7 g / k g to the final value 4.3 g / k g and the SH values calculated from T and RH shown that this parameter was always correctly measured (graph not reported in the figure). However, being programmed in terms of RH, the transducer was conditioned by the case temperature. The new air, which was moister in terms of S H, at the beginning was cooled by the cold case and this caused the initial rise of RH, i.e. the overshoot; the progressive warming of the case determined the decrease of the RH, which stopped when the case had reached the new equilibrium. From this example it is evident that, after a fast environmental

change, the

t e m p e r a t u r e passes gradually from the initial to the final value, but the temperature delay forces the RH to initially depart with a peaked overshoot (or an undershoot), which may go outside the span characterised by the initial and final values. Only after this critical period, the RH gradually reaches the final value. If the change in temperature is gradual, the over- or undershoots are avoided, and the RH approaches gradually, with a certain delay, the new value. This was tested with a sinusoidal temperature oscillation forced in a climatic chamber where the specific humidity was kept constant, as follows. Three capacitive relative humidity sensors were introduced in the chamber, i.e.: (i) the same fast sensor described above, but housed in a compact case as commercially available, with relatively high thermal capacity and low ventilation; (ii) another

311 45

24 22o

40

"~"

35

","

Tf

2018RH i 16-

[-

30

RHf

14-

25

Ti

1210

0

. 10

.

. 20

. 30

. 40

.

.

. 60

50

. 70

r ,1-1

~

20 80

90

100

T i m e (min)

Fig.9.6 A miniature data logger has been displaced at the time to = 20 min from an initial ambient at Ti = 12.2~ and RHi = 31% to another ambient at T / = 22.2 and RHf = 25.8%. The plot shows that at to the temperature (thin line) rises from Ti to the final higher value Tf approaching it asymptotically; on the other hand, the fast RH sensor, is conditioned by the temperature of the case: the RH output (thick line) immediately rises and then decreases following the gradual heating of the case, and reaches equilibrium only when the case temperature has reached its equilibrium.

100

! -F,,4

60

f,,! .

.

.

.

//

20 i 0

100

,

,

,

j

,

,

,

,

200

3O0

400

T i m e (min) Fig.9.7 Response of different relative humidity (capacity) transducers to a sinusoidal temperature oscillation forced in a climatic chamber, at constant specific humidity. The tested transducers are: (i) a fast sensor housed in a compact case as commercially available, with relatively high thermal capacity and low ventilation (thick line); (ii) another identical transducer, i.e. housed in the same case but with the ventilation hole opened by us (gray line); (iii) the same fast sensor but externally connected to the case in order to avoid the effect of the thermal inertia (thin line). The heating and cooling cycles repeated periodically, reaching every time the dew point.

312 identical transducer, i.e. housed in the same case but with the ventilation hole opened by us, i.e. the same used in the previous test, (iii) a third identical fast sensor but externally connected with the case in order to avoid the effect of the thermal inertia (Fig.9.7). In the chamber the heating and cooling cycles repeated periodically, approaching every time the dew point, so that the RH followed a continuous cycling. The fast sensor was able to follow the cycle; the sensor in the case with the additional open window showed a cycle topped at a lower RH; the sensor in the original unaffected case had a cycle topped with a much lower R H . The outputs were the same in the dry region but different in the wet, showing an asymmetrical response. These examples show that the response in dynamic conditions is not easily predictable, and that large errors might be originated by humidity transducers with different thermal capacity.

9.6. ESSENTIAL GLOSSARY

Accuracy: the extent to which the measurement approaches the true m e a s u r a n d value, often expressed as the ratio of the error to the full scale output, indicated as + percent of the range. Ambient conditions: the microclimate and other environmental conditions (e.g. rainfall, dew, f r e e z i n g / t h a w i n g cycles, humidity, temperature) of the m e d i u m surrounding the sensor. Bimodal distribution: a distribution with two distinct modes (see mode). Damping: When an instrument is subjected to a forcing step function, the output m a y reach a s y m p t o t i c a l l y the final value (first-order m e a s u r i n g instruments), or oscillate a r o u n d it with overshoots and u n d e r s h o o t (second-order measuring instruments). The attenuation of the signal which smoothes the response of second-order instruments is called damping. This may be obtained with an electronic filter or mechanically with a friction. Mechanical damping is especially important for wind vanes. Distance constant: the length of the path travelled by the wind in the time interval required for a output of a wind sensor to reach 1/e = 63.2 % of a step change of wind speed. Drift: gradual deviation from the original characteristics. The deviation increases with time and severity of ambient conditions (e.g. temperature, pressure, humidity).

313

Hysteresis: the m a x i m u m difference in output, when the same m e a s u r a n d value of the parameter is reached first with increasing values, then with decreasing ones. It is generally expressed as percent of the full scale output.

Linearity: the closeness of a calibration curve to a straight line. Mean: the arithmetic average <x> of a set of N values of the variable x: 1

<X> = ~ - ~X i

Median: the middle value in a set of values. Mode: the value which occurs most frequently. Percentile: a value in the range of set of data which separates the range into two groups, so that a given percentage of data lies below this value.

Precision: the closeness of the output to the true measurand value. Range: the interval of values that are intended to measure, or that are potentially measurable, or that have been measured, specified by their upper and lower limits.

Reliability: the probability that a t r a n s d u c e r will satisfactorily p e r f o r m its function. It can be measured by the variance of repeated measurements of the same value of the m e a s u r a n d p a r a m e t e r , taken u n d e r the same conditions.

Repeatability: the ability to reproduce the same output when measuring the same value of the measurand variable, taken under the same conditions. It can be expressed as the m a x i m u m difference of the output readings or in + percent of the range.

Representativity Also w h e n the measure is not affected by instrumental errors, not always the o u t p u t characterises the actual value of the m e a s u r a n d parameter in the site and the time instant under investigation. This happens typically w h e n the value of the parameter is not homogeneously distributed or the measurement is taken in a point where the measurand has a singular value. Measurements are done to define the parametric values of a surface or a site, and observations are limited to one or few points which should characterise a wider space. A measurement that characterises the value of the variable in its context, as expected, is called representative.

Resolution: the ratio of the output step change to the full scale output, generally expressed in percent. It represent the smallest detectable change of the measurand parameter. If the output varies with continuity, the resolution is infinite.

Response time: the length of time required for the output to rise to a percentage of its final value, w h e n the m e a s u r a n d parameter has u n d e r g o n e a step

314 change. When the percentage is 63.2 %, it is called time constant. About 95% of the step change is reached after 3 time constants. Of course, the response time (and the time constant) are i n d e p e n d e n t of the span of the o u t p u t change.

Sensor: the functional part of the instrument, which couples it to the m e a s u r a n d variable (i.e. the input) generating a mechanical or electrical signal which is the output of the sensor.

Sensitivity: the ratio of the change in the transducer output to a change in the value of the measurand parameter.

Specificity to the response: the capability of an instrument to respond only to the changes of the variable that it is designed to measure and be insensitive to all the other ones.

Threshold: the m i n i m u m value of the m e a s u r a n d variable that can be detected by the transducer. If the variable does not start from zero, the threshold is the smallest change of the variable which results in a measurable change of the output, but in this case it is better to speak in terms of resolution.

Time constant: the time required to detect and indicate 1/e = 63.2 % of a step change. See also response time.

315

C H A P T E R 10

Measuring Temperature

10.1. MEASURING AIR TEMPERATURE

10.1.1 Choice of the sensor Several kinds of good sensors are commercially available, not all equally suitable

for microclimate

study. The principal

types are: liquid-in-glass

thermometers (i.e. mercury or spirit thermometers); bimetallic thermometers; electrical resistance thermometers (metal resistance sensors and thermistors); thermocouples. The choice is determined by several factors, i.e. compatibility with the ambient conditions, measuring range, resolution, accuracy, response time, drift, compatibility with the recording instrument and cost. The outdoor measurements generally require a much greater temperature range than the indoor ones. If the sensor has a sufficiently elevated resolution, by limiting the range and expressing data as a percentage of the range, more accurate measurements can be obtained. In this sense, indoor measurements can be more precise than outdoor ones.

10.1.2. Response to the air temperature and infrared radiation It is i m p o r t a n t to avoid the s i m u l t a n e o u s use of different kinds of thermometric transducers. Any thermometer furnishes the temperature of the sensor, which is not exactly the same of the air, as each sensor responds in a different way to the infrared radiometric forcing as well as to conductivity and convection. When different kinds of well calibrated sensors are immersed in a water or oil bath, they give the same o u t p u t because their t e m p e r a t u r e is conditioned only by the bath temperature. In fact, the external IR radiation is shielded by the bath vessel or is completely adsorbed after the radiation is penetrated a few micrometers into the liquid. The specific heat of water is 3 order of magnitude greater than that of air. Sensors which respond in the same way to the air temperature but not to the radiometric forcing may give different readings

316 and generate confusion. Screens may attenuate this problem, but not solve it. The rise of temperature of a thermometer exposed to environmental I R radiation is the principle on which globe thermometers are based. These consist in a temperature sensor placed at the centre of a hollow 'black' sphere which absorbs IR from surrounding surfaces. Frequently, these globes are made of metal (e.g. copper, aluminium) and the sphere is painted with black colour. There is no doubt that the sphere absorbs the visible radiation and appears black to the eye, but the metal below the coating may reflect the IR, as it often occurs. For this reason the coating should be very thick and made of pigments absorbing in the IR region, which do not necessarily appear black to the eye. After the sphere has reached equilibrium, the temperature measured at the centre of the sphere gives an approximate measure of the effective temperature experienced by people or objects in that room. The overheating, i.e. the globe thermometer temperature minus the air temperature, gives the contribution of the radiant heat. This method is used in health physics to study the heat stress in workshops. This principle which furnishes the above useful application, is also a drawback in that IR radiation affects any thermometric measurement, and is negligible only for very thin metallic sensors which are reflecting the I R radiation, e.g. thermocouples, platinum resistance transducers. An abundant literature exists on this subject, and special reference has been made to UK Meteorological Office (1981); WMO (1983; 1986); Benedict (1984); Schooley (1986); Michalski et al. (1991); Nicholas and White (1994). 10.1.3. Thermometers A short description is here reported of the most c o m m o n l y used instruments, discussing their advantages and limits, especially in view of their

application in the field of microclimate analysis and diagnostics. Mercury-in-glass

thermometers The mercury-in-glass thermometers is, or at least was, commonly used for

routine measurements and as a secondary laboratory standard to which compare other kinds of sensors which undergo rapid ageing or drift. Meteorological station mercury thermometers are some 40 cm long and cover the range -30 to 60~

with scale division 0.2~

The advantages of the mercury as thermometric

liquid are: small thermal capacity, high thermal conductivity, small deviation from linearity, high boiling point and freezing point at-38~ This is a problem only for mountain sites or polar regions, b u t with the addition of thallium the

317 freezing point is lowered to -58~ The change of output, expressed as change of the mercury column length `4h due to the change of temperature AT, is given by the equation:

,4h = AT

Wo (~1- ~2) A

(10.1)

where Vo is the volume of mercury inside the bulb at standard temperature, ~1 and ~2 are the cubic coefficients of thermal expansion of m e r c u r y and thermometric glass, i.e. ~1 = 1.8 lx10-4 ~

]32 = 2.53x10-5 ~

respectively, and A

the cross-sectional area of the capillary. The sensitivity of the m e r c u r y thermometer is given by the ratio ,4h/,4T and the larger the reservoir Vo and the smaller the section A of the capillary, the higher the sensitivity. This can be represented by the equation ,4 h ,4 W Wo (]~1- f12) AT Wo (~1- f12) AT -re r2 AT = re r 2 AT = /1; r2

(10.2)

where r is the capillary radius. This equation shows that the sensitivity increases proportionally to the bulb volume and with the inverse of the square of the capillary radius. However, the larger the volume Vo the greater the heat capacity and the longer the time constant of the thermometer, so that sensitivity a n d time of response have opposite requirements. The main errors of this kind of thermometer are: (i) Thermometer heating, when the observer goes too close to the thermometer for reading the scale, and remains for a too long time, influencing its temperature, or when the thermometer is not adequately shielded against infrared radiation. (ii) Parallax, when the reading is made with the eye placed not at the same height of the top of the mercury column. (iii) Emergent stem, when the temperature of the bulb is not the same of the surrounding

medium,

i.e. w h e n

the t h e r m o m e t e r

is not completely

surrounded by only one medium having the same temperature. This error may be important for measurements of solid bodies. (iv) Drift, when the characteristics of the thermometer change slowly with time, e.g. the bulb of the thermometer tends to contract slowly over a period of years, rising the temperatures. (v) Departure from linearity and inequality in the expansion of the liquid and

318 glass. (vi) Capillarity, which may influence the height of the mercury in the capillary tube. (vii) Elastic errors, due to exposure to a large range of temperature in a short time, or to large changes in external pressure. (viii) Scale division and calibration. Also spirit or other thermometric liquids are used, for their greater sensibility (thanks to a much larger expansion coefficient) but they have some problems: adhesion to the glass, stronger deviation from linearity, drift due to polymerisation and slow changes of the liquid properties, breaking of the liquid column. Their use is not recommended. Liquid-in-metal

thermometers

Liquid-in-metal or pressure thermometers consist of a sensitive bulb, an interconnected capillary tube and a pressure measuring device such as a Bourdon tube. They follow an equation similar to the eq.(10.1) which has been discussed for liquid in glass thermometers, i.e. (10.3)

A V = Vo (~1 - 3a) AT

but with the appropriate coefficients, and ,62 has been substituted with 3a, where a is the coefficient of linear thermal expansion of the bulb material. In meteorology, this sensor is used to drive the arm of the recording pen of thermographs, and in the US this is accomplished according to the Weather Bureau specification No. 450.1201. The time constant is some minutes, so that all the short period temperature fluctuations are smoothed out. This kind of transducer is used in industry and sometimes in meteorology, but is not relevant in microclimate studies. Bimetallic

thermographs The bimetallic t h e r m o g r a p h

is c o m m o n l y

used

both

in

standard

meteorological stations and museums. It is mainly associated with a hair hygrometer and the resulting instrument is the well known thermo-hygrograph. The bimetallic sensor is composed of two thin metal strips having different coefficients of thermal expansion, roll-welded together along one of its flat sides. It provides a mechanical output, i.e. the displacement of the free end of the strip. This end is usually connected with a pen, whose movement is amplified and

319 used to trace the temperature records in clock thermographs. It is useful to remark the two main characteristics of this instrument. (i) The thermograph is a linear transducer, as the displacement of the free end of the strip is a linear function of the temperature change. (ii) The sensitivity of the sensor is directly proportional to the square of the length of the strip and p r o p o r t i o n a l to the difference in the thermal coefficients of expansion of the two metals, but is inversely proportional to the thickness of the strip. (iii) The time constant is few minutes, so that this instrument smooths out all the short period temperature fluctuations. (iv) The resolution in the strip chart recorder is generally from 1 to 1.5 m m per ~ and the time scale division is 15 min for daily clocks and 2 hours for weekly clocks. The resolution in reading the strip chart is some 1~ (v) The accuracy is no better than +1% of the range which generally varies between 45 ~ and 90~ (vi) The friction between pen and chart is excessive compared with the force supplied by the bimetallic strip, so that the graph is smoothed out, with underestimate of the maxima and overestimate of the minima. These instruments are not accurate, but are very popularly used in museums. The most common sources of error are: (i)

Lack of maintenance and periodic calibration.

(ii) Exposure in a position non representative of the parts of the room where works of art are placed, e.g. near the room corners where the air is stagnant and on the floor, at a height different from that of the exhibits. (iii) Dirt, dust and pollution which increase the friction of the instrument. (iv) Excessive friction between pen and strip chart. (v) Corrosion or mechanical damage to the bimetallic strip. All the above causes of error show that this instrument needs a frequent cleaning, and particularly of the bimetallic strip and the pen. The latter should be carefully cleaned with alcohol. After cleaning, the instrument calibration should be controlled as well as the fine regulation of the three adjusting screws (i.e. bimetallic

element,

magnification,

pen

pressure).

Monthly

control

and

maintenance is recommended, but in practice this necessary operation is usually neglected. Platinum resistance sensors A l t h o u g h iron, copper, nickel and other metals have a t e m p e r a t u r e

320 coefficient of electrical resistance greater than platinum, p l a t i n u m resistance sensors are preferred for their stability in time and non corrodibility, which are i m p o r t a n t characteristics especially in h u m i d or polluted environments. The platinum resistance sensor is an electrical resistance, made of very pure platinum wire, 0.1 m m in diameter or less, used sometimes as a wire and more usually w o u n d on a glass or ceramic rod. However, thin deposited p l a t i n u m films are also common, as well as several type of probes with special windings for different purposes. For a metal, the electrical resistance R ( T )

is described by a MacLaurin

expansion of the successive powers of the increase of temperature, R ( T ) = R(To) (1 + a A T + b A T 2 + ..... )

(10.4)

where R ( T o ) is the resistance of the sensor at the reference temperature To = 0~ AT is the temperature change and a, b .... are constants, characteristics of the metal used. The p l a t i n u m resistance is characterised by the following values a = 3.968x10 -3 ~

b = -5.847x10 -7 ~

c = -4.22x10 -12 ~

but within the interval of

meteorological observations is in a very good approximation described by the first two linear terms of the series and is linear within +0.3% of the whole range. As it presents an excellent stability, the measurements are reproducible within 0.01~ A n o t h e r a d v a n t a g e of these sensors is that they are cheap. Metal resistance thermometers should be compared with. a standard every year. Thermistors

Thermistors are essentially semiconductors which behave as resistors with a high t e m p e r a t u r e coefficient of resistance. The electrical resistivity varies with the t e m p e r a t u r e

and

is u s u a l l y negative,

i.e. decreases

with

increasing

t e m p e r a t u r e unlike metals. The response function is an exponential one of the type:

R(T)-Ro

exp(A)

(10.5)

w h e r e all the coefficients are constant and depend on the material used. By differentiating the above equation, the temperature coefficient B is obtained

B =

dlnR A dT - - T 2

(10.6)

321 which has a negative, parabolic dependence upon temperature. The sensitivity of thermistors varies with temperature, but at ordinary values it is one order of m a g n i t u d e higher than that of platinum resistance sensors. It is important to note that thermistors are heated by the current load, and that the supply should be very well calibrated in view of the limited natural heat dissipation. Thermistor t h e r m o m e t e r s should be c o m p a r e d with a s t a n d a r d thermometer every year, if they are of good quality, or every month if they are of low quality, and re-calibrated because the characteristics of the sensors are not very stable and suffer ageing. The main disadvantage of thermistors is the functional dependence which is characterised by a non-linear resistance versus temperature. Linearisation is mainly obtained using analogue circuit techniques, but also sensor linearisation is possible and has been accomplished p r o d u c i n g linear o u t p u t t h e r m i s t o r assemblies. These consist of two or three thermistors assembled as a single thermistor and of an additional resistor. With an a p p r o p r i a t e choice of the elements, these packages are interchangeable within a stated tolerance. Although standard

thermistors

are

generally

inexpensive,

the

cost

of

linear,

interchangeable, low drift thermistors is elevated. Linear response transducers have the advantage of a simpler electronic circuit or data processing, and have a h o m o g e n e o u s accuracy on the whole range. Linear thermistors in a selected range of t e m p e r a t u r e s are obtained with a suitable combination of two subcomponents:

a thermistor

composite

and

a resistor

set c o m p o s e d

of a

c o m p e n s a t i n g n e t w o r k of two or three precision metal film resistors. Further details on these and other temperature transducers can be found in Schooley (1986), Doebelin (1990), Michalski et al. (1991), Nicholas and White (1994). A c o m m o n method to obtain linearisation of standard thermistors is to use a Wheatstone bridge circuit (Fig.10.1) with the resistance sensor RT(T) which constitutes one arm of the bridge, and measuring in the deflection m o d e (i.e. with the bridge out of balance) the output voltage. This is, in general, a linear function of the b r i d g e excitation E (i.e. the bridge b a t t e r y voltage after stabilisation), but a non linear function of the resistance of the elements R1, R2, R3 and R T(T) of the four arms. W h e n the sensor calibration curve R T(T) is known and expressed with a polynomial regression, the appropriate resistance of

R1, R2 and R3 of the other three arms can be properly calculated and adjusted, so that the exponential curvature of the sensor is compensated by means of the non linearity of the bridge circuit which has been appropriately unbalanced.

322

R1

IMI Fig.10.1 The basic Wheatstone bridge in deflection mode for the case of a thermistor T. The two resistors R2 and R3 are adjustable to set up the bridge to linearise the response ofT, as seen by the meter M. E is the stablised excitation voltage. The m e t e r M,

which measures

the o u t p u t

voltage across the t e r m i n a l s ,

instantaneously follows the variations of the sensor, and with an appropriate choice of R1, R2 and R3, the o u t p u t voltage directly equals the value of the thermistor temperature. O u t p u t accuracy and departure from linearity can be better than 0.1~

Main sources of errors are: instability of the bridge excitation;

c o n d e n s a t i o n or rainfall which forms a shunt of liquid w a t e r b e t w e e n the thermistor leads if these are not well insulated; drift of the thermistor or other resistors of the bridge. For psychrometric measurements, the assembly of two basic Wheatstone bridges for two thermometric sensors T1 and T2, are necessary. It is possible to change from the reading of T1 to T2 or vice versa operating on a commutator. Two adjustable resistors are used to set up the bridge for the thermistor, during the calibration of the device. If the meter has an elevated impedance (as the main part of the electronic meters have), the current across it vanishes and the meter measures the output voltage R1

R(T1)

e(T) = ( R1 + R2- R(T1) + R3

) E.

(10.7)

Both p l a t i n u m resistance sensors and linear thermistor transducers are very small (Fig.10.2), accurate (better than 0.1~

repeatable and reliable, linear or

323 linearisable, interchangeable within 0.1~

and with fast response, e.g. time

constants < 1 s can be found. However, it is advisable to buy one or some tens of sensors and calibrate all together in a calorimetric bath. It is so possible to individuate whose of them give a closer response, so that it is then possible to operate substitutions or match two or more of them with a very similar response. In practice, the precision of 0.1~ is satisfactory in most cases, and matching of the order of +0.01~

can be done without difficulty. Linearised thermistors are much

more sensitive than p l a t i n u m resistance transducers, but also m u c h more expensive.

Fig.10.2 Small thermistors used for fast response in psychrometers: one is free and one is inserted into a hypodermic needle, forming a fast response probe.

Thermocouples Thermocouples are based on the Seebeck effect, i.e. a small thermoelectric current is generated w h e n two different metal wires are put into contact at both ends with their junctions having a different temperature. If one junction is open, a contact electromotive force is generated. The current, or the electromotive force, is in a first approximation proportional to the temperature difference AT between the two junctions. A better approximation is obtained with a MacLaurin expansion with the second power of AT. The electromotive force of some of the most c o m m o n junctions is: iron-constantan: 52 pV/~ pV/~

copper-manganin: 41 pV/~

alumel: 41 p V / ~ pV/~

copper-constantan: 43

manganin-constantan: 41 pV/~

p l a t i n u m - c o n s t a n t a n : 34 p V / ~

chromel-

p l a t i n u m - r h o d i u m : 6.4

The strongest electromotive forces are obtained with the less expensive

324 junctions, and not with the rare metals which are generally used to resist to high temperatures. The materials used for thermocouples should be carefully aged by electrical annealing because the electromotive force is influenced by mechanical deformations. A problem is that the wire it conductive and can transport heat, changing the temperature at the point under investigation. The main advantages they offer is that they have a very low sensitivity to IR radiation and a small time constant, of the order of 1 s. If more than one set of thermocouple junctions is used in series, the electromotive force is increased proportionally to the number of junctions. Another important advantage is that they are very cheap. As thermocouples respond directly to differences of temperature, they are convenient to measure temperature gradients. For this reason they are in principle suitable for measuring the wet bulb depression in psychrometers, as this instrument requires an accuracy better in detecting the temperature difference between two sensors than in knowing the exact value of the dry bulb thermometer. However, the electromotive force generated by the wet bulb depression is very weak. The sensistivity of a thermocouple to temperature changes is much lower than that of a platinum resistance sensor and especially of a thermistor. Thermocouples need a cold reference junction that is usually immersed in melting ice. This fact limits the practical use of these sensors. Another alternative is to compensate the cold junction temperature by using a resistance bridge compensation circuit (WMO No.622, 1986). The change of resistance of the thermocouple with changing ambient temperature creates an out-of-balance bridge potential, compensating for the missing cold junction. A further possibility is to measure with an independent thermometer the reference temperature at one juction of the thermocuple, and then measure with the other juncion the differences in temperature.

Quartz thermometer The sensor is a quartz piezoelectric resonator which is connected to an electronic solid state oscillator. The latter supplies a small amount of power to the resonator which acts as a highly selective filter that holds the oscillation frequency very close to the natural frequency of the resonator. The resonant frequency of the quartz crystal sensor undergoes a change in frequency which depends upon the change in temperature, following a third-order polynomial equation of T. By a proper choice of the cutting planes of the crystal, the

325 coefficients of the second and third order powers of T can be made zero, and in this case the resonant frequency becomes a linear function of the temperature (Michalski et al., 1991). Once the probe has reached the equilibrium with the surrounding fluid, the quartz t h e r m o m e t e r readings are very accurate and may constitute a good reference s t a n d a r d for calibrating other t h e r m o m e t e r s or m a y be used in precision calorimetry. The probe response time is a few seconds in stirred water, and is quite long in still air. However, by counting all the oscillation pulses, it is possible to integrate with a great precision over a time interval: the longer the sampling time, the higher the resolution. For this reason commercially available instruments have options for different sampling intervals and c o r r e s p o n d i n g resolutions, e.g. increasing by 10 the sampling period, the last digit represents a resolution 10 times greater, so that incredibly high resolutions, as far as 10-5~ or 10-6~ can be attained. It should be remembered however, that these readings are accurate only in the case the probe has really reached equilibrium with the fluid, and the temperature is stationary, otherwise the precision is merely illusory and misleading, being only a precise average of the sensor temperature during the sampling time interval. 10.1.4. Screen

The result of a temperature m e a s u r e m e n t is a signal p r o v i d e d by the transducer as a function of the sensor temperature. However, the temperature of the sensor does not necessarily coincide with that of the air or the surface. The thermal equilibrium of the sensor includes not only the conductive heat exchange with the air which comes into contact with the sensor, but also the energy arrived with visible or infrared radiation from remote bodies. In fact, the air is transparent to the visible and to the main part of the infrared spectrum. The incoming radiation is an important source of error, and may cause departures from some tenths to several degrees. Under extreme conditions the difference may reach 25~

A screen is necessary to reflect this income. However, it is never

possible to reflect completely the energy income, or avoid the nocturnal radiative loss. The double louvered screen of standard weather stations may introduce an error of +2.5~

during strong sunshine and calm of wind, and -0.5 on clear, calm

nights (WMO, 1983). Another source of error is rainfall, when the wet screen evaporates and approaches the wet bulb temperature. For outdoor measurements of temperature and humidity, the instruments should be installed inside a shelter to minimise the effects of sunshine, rainfall,

326 and other adverse w e a t h e r situations. In the case of standard meteorological observations, the Stevenson screen is popularly used, i.e. a box m a d e of a low c o n d u c t i v i t y material (generally wood or plastic), painted white inside and outside to reflect radiation, having double louvered walls which enable good ventilation while minimising the effects of radiant heat. The roof is m a d e of two layers of w o o d with an air layer between them and the floor is slatted to permit free air circulation. The door is on the northern side and enables the personnel to observe or do the maintenance of the instruments. These are placed between 1.25 and 2 m above the ground. Meteorological shelters need to be cleaned frequently and repainted every year but this recommendation is often neglected. Several kinds of screen have been designed to house electrical type t e m p e r a t u r e sensors. They are characterised by a single or double, highly reflective shield (mirror or white paint) with natural or forced ventilation. The shield m a y consist of one or two concentric tubes, a single or double d o m e or multiple plates, made of metal, plastic or mirrored glass. The multiple plate non v e n t i l a t e d version is an extension of a m o d e l with acrylic plastic dishes developed by Hadlock et al (1972). In windy, rainy regions, the radiation error is negligible, ventilation is not necessary and the shield m u s t protect the sensor against rainfall arriving from any angle. In sunny, low wind regions, a motor blower which induces a forced ventilation (e.g. 3 m s -s) in the area of the sensor is applied to reduce stagnant air and overheating. For non ventilated shields the overheating error varies with the wind speed, e.g. in a sunny day the overheating of a white thermoplastic multiplate radiation shield is +1.5~

at 1.5 m s -1 wind

speed, +0.7~ at 2 m s -I and +0.4 at 3 m s -l. The best results are obtained with a double wall glass tube, silvered on all interior surfaces, then evacuated and sealed, like a heavy d u t y v a c u u m bottle with open bottom. The cylinder is kept vertical, with the open bottom facing d o w n w a r d s and with a blower located at the upper top which continually forces the ventilation inside. In this case the error is limited within +0.05~ Also indoor measurements need a screen, but in the case that the sensor is n e v e r hit by direct solar b e a m s or spot lamps light, the screen m a y be less sophisticated. Good results are obtained with two methods c o m m o n l y used for radiosondes: (i) a tube is made of white polystyrene foam which is reflective, bad conductor and has a very low thermal capacity; (ii) a tube is built with a very thin foil of a l u m i n i u m , perfectly reflecting on the outer side and blackened on the internal one. In the case of metal shield a lower disturbance is obtained with a double concentric shield and this caution c a n b e used in the absence of forced

327 ventilation. A c o m m o n size is a cylinder with some 10 cm diameter and 20 cm height. The sensor is placed in the middle of the tube and radiosonde ascent provides ventilation; for use in a fixed location a fan can be included on the bottom. When the sensor is located in sites where all the surfaces have a nearly h o m o g e n e o u s t e m p e r a t u r e and there are no important sources of radiative perturbation, there is no need for shields. 10.1.5. Instrument location

The site of a s t a n d a r d

weather

station should be m e t e o r o l o g i c a l l y

representative of the area in which it is located and free from local perturbations generated by trees, buildings, water bodies, air pollution. A plot of level ground, sized 6 by 9 m and covered with short grass is generally used for the installation of meteorological instruments. Meteorological phenomena take place on time and space scales completely different

from

those

of m o n u m e n t s ,

which

are g o v e r n e d

by the

local

microclimate. Differently from standard meteorological or airport observations, it is not possible to state a similar guideline for conservation. In the case of microclimate m e a s u r e m e n t s for the cultural heritage, observations m u s t be made when and where necessary, according to the aim of the survey. However, it might be useful to remember that the air temperature is not the same at all the heights, and that the choice of the height is very important. O u t d o o r the air temperature is essentially governed by the soil temperature: during the night time the soil is coldest and the temperature increases with height; during day the soil is hottest and the temperature decreases with the height. In summertime, in the central part of the day the bare sand may reach 70~

and the air temperature rapidly decreases by 30-40~

in the first 2 meters of

atmosphere. This show h o w the 'air temperature' m a y a p p a r e n t l y change locating the sensor a bit up or down. The essential point is that there does not exist a generic 'air temperature' T, but T is a punctual and instantaneous value of a function which is variable in the space and time coordinates. Also in closed rooms the temperature is not the same at all the heights, but tends to stratify in horizontal layers, the hotter air being trapped below the ceiling and the colder and denser air being closer to the floor, with a difference of the order of 1 or 2~ in usual conditions, but that may reach 20~

or more. Measurements made to

test the horizontal homogeneity of the temperature in one room or in one floor must be all exactly made at the same horizontal level; in the case of alpine churches with hot air heating, where a vertical gradient of some 7 ~

was

328 found (Chapter 1, Fig.1.11), a vertical displacement of 10 cm of the sensor will introduce an apparent change of temperature of 0.7~ When an ambient monitoring can be performed using only one instrument (e.g. a thermohygrograph), it is extremely important to know the representativity of the instrument location, with reference to the whole room or the site. In fact, temperature and humidity vary either temporally and with space, e.g. responding to the solar radiation through glass panes, the opening of doors and windows, the switching on/off of light, or other HVAC systems. Measurements made in points particularly shielded or too much exposed to air currents, or in the proximity of HVAC, or perturbed for the presence of h o t / c o l d water pipes are non representative of the real situation and their interpretation may induce to a wrong management of the ambient conditions. A micro-mapping survey should be made to know the temperature distribution inside a room in order to choose the most representative point for the location of the instrument and especially of the sensors for the control of the room temperature and humidity.

10.1.6. Measuring vertical profiles of air temperature and room atmospheric stability Vertical profiles of air temperature are very important as they constitute a measurement of the atmospheric stability responsible for the dispersion of airborne pollutants and their deposition via inertial impaction. Outside, profiles are measured with tall towers, or mini radio-sondes raised by small spherical balloons (in urban areas a small cluster of balloons is preferred for safety reasons, Fig.10.3) or heavier radio-sondes raised by large tethered balloons, e.g. kytoons (Fig.10.4), shaped as a dirigible with small wings at the back which are inflated by the,wind and stabilise the kytoon by damping the oscillations forced by wind gusts. The gas used in meteorology to blow up balloons is hydrogen, but this gas should be managed by well trained personnel only, because it is very dangerous and risks to explode especially in the presence of electrically charged bodies. helium is safe, but much more expensive and determines a slightly less buoyancy (the mass of helium is twice the mass of a hydrogen molecule). The suggested practice is to fill balloons with a hydrogen and helium mixture popularly used for toys balloons which is cheap, light and non explosive. In urban areas, for the onset of wind, the balloon may reach ground far from the operator and it constitutes a strong attractive for children.

329

Fig.10.3 In urban areas, mini radio-sondes raised by a cluster of small lattice balloons are preferred for safety reasons.

Fig.10.4 Heavier radio-sondes raised by large tethered kytoons, shaped as a dirigible with small wings at the back which are enflated by the wind and stabilize the kytoon.

330

Balloon Wind

Radiosonde Fwt Motor Whinch

/

\

Fig. 10.5 Forces acting on a tethered balloon: Fwd horizontal, very strong, due to the wind drag; Fwt along the wire due to the tension which becomes dominant during the recovering operation and is now tilted, forming an obtuse angle with Fwd; finally, the weak vertical force due to the buoyancy Fb. Meteorological radiosondes and low troposphere radiosondes (resolution 0.1~

1% R H and 0.5 hPa atmospheric pressure) with lattice or neoprene balloons

are made to be launched only once and be lost. However, if the study is limited to the lower part of the planetary boundary layer (PBL), e.g. the nocturnal inversion layer and first kilometre of the diurnal mixed layer, it is also possible to use several times the same radiosonde. The method consists in tethering the balloon, which can be launched and recovered with a nylon fishing wire, 0.7 m m diameter (Camuffo, 1980; 1982). During the ascent the buoyancy force of the balloon turns freely the wire roll; the descent is made winding the fishing wire on the roll by means of an electric motor. This operation is possible only in case of calm or low wind speed. In the case of no wind the forces are only two, opposed along the vertical: Fb, the upward buoyancy and Fwt, the d o w n w a r d traction of the wire. The operation is easily made controlling the d o w n w a r d force. In the presence of wind the balloon is subjected to three forces (Fig.10.5): Fwd horizontal, moderate to strong, due to the wind drag; Fwt along the wire due to the tension which becomes dominant during the recovering operation, and forms an obtuse angle with Fwd; finally, the weak vertical force due to the buoyancy Fb. The resultant of these three forces obliges the balloon to descend

331

slantwise and the wire curvature risks to approach too much, or touch the ground. In u r b a n e n v i r o n m e n t s miniaturised systems are often preferred, but small balloons risk to break for the lattice tension when they are recovered. If two or t h r e e b a l l o o n s are used to diminish the risk of catastrophic b r e a k d o w n and fall, the turbulence generated by the balloons cluster forces violent vibrations and increases the risk of bursting. An effective remedy has found by enveloping the cluster, or the only one balloon, with a light hunting or fishing net, and attach the wire to the net. The surface stress of the lattice is therefore better distributed and the b r e a k d o w n risk reduced. The minisonde attached to a balloon (size: 1 m 3) or a balloon cluster makes possible vertical runs also in city centres, operating in very small gardens and small roof terraces, as we did e.g. in Venice, and the cost is m u c h cheaper than the use of 80 m 3 tethered balloons which need a m u c h larger operating space so that they can be used only in rural environments. Using the same radiosonde several times, the data of each run are taken with the same instrument,

and

are a b s o l u t e l y c o m p a r a b l e , w i t h o u t

the p r o b l e m

of the

intercalibration errors. By reporting the results of each run in a d i a g r a m and drawing

the isolines, vertical time cross sections of the t h e r m o d y n a m i c

properties of the PBL are easily obtained. Fixed towers or portable masts can be used for profiles on a smaller vertical extent. Some 10 m folding masts with a tripod b a s e m e n t are commercially available, but even more easy to use are extensible masts, with the antenna composed of an assemblage of 5 concentric sections with clamp collars to which instrument can be hung. This mast can be extended by p u m p i n g air with a hand pump. Opening the valve and loosening the clamp collars, the mast retracts. Inside buildings, u n d e r non perturbed conditions, the air is near always stratified in horizontal layers, whose density decreases with height. The layers are not horizontal, or the stratification m a y even disappear, w h e n there are sources of m o m e n t u m (air currents) or heat (formation of convective cells). In addition, in m u s e u m s vertical profiles show the difference of t e m p e r a t u r e of the air masses which come into contact with the lower part and the top of a painting or a statue. In m u s e u m s , small portable masts with sensors placed at floor level, 1, 2 and 3 m are in general sufficient, as this height is representative of the air layer where exhibits are exposed. W h e n rooms or churches with i m p o r t a n t d o m e s are too tall for being controlled with a portable mast, and an opening exist on the ceiling, it is possible to let d o w n a rope with sensors and record the temperature and h u m i d i t y profile on that vertical. This method was used several times, e.g. for the Giotto's Chapel,

332 P a d o v a (Camuffo and Schenal, 1982), with thermistors or high resolution radiosondes for the lower troposphere. An easier system, not conditioned by the presence of openings, is to fill with the hydrogen and helium mixture a black tethered meteorological balloon and slowly rise it into the room. As it reaches quickly equilibrium with the surrounding air, by training it with a radiometer, it is possible to know the temperature of the air at various heights, which are determined by means of the tethering wire length. The balloon should be inflated not too much in order to preserve elasticity and reduce vulnerability if a rough surface is touched, and the black colour is preferable to avoid reflected radiation. In order to furnish a well visible target also in tall rooms the size of the balloon might be 2 m in diameter, and for this size 300 g balloons are needed. For non exceptionally tall rooms 100 g balloons are sufficient. This m e t h o d is more attractive than easy. A common sampling time for indoor temperature and humidity is one data acquisition every 10 minutes or less, in order to monitor transient p h e n o m e n a such as room cleaning, w i n d o w s and doors opening for ventilating and so on. Longer intervals (e.g. one acquisition every hour) might not monitor important perturbations, e.g. room cleaning with open windows. In Chapter 7 several criteria have been presented for the measurement of the atmospheric stability. The majority of them take into account that the atmospheric turbulence is determined by two main factors: (i) a vertical temperature gradient generated by the contrast of temperature between air and soil, which in the case of hot soil originates convective mixing and instability; in the opposite case of colder soil, thermal layering (ii)

and stability; the eddies generated by the wind and expressed in terms of wind gustiness,

shear, speed. It is evident that outside the wind plays an important role, but inside it is practically absent, or is substituted by a very modest ventilation or local convective motions. For this reason, inside the thermal factor becomes largely dominant and in general it is sufficient to measure the vertical profile of the air t e m p e r a t u r e with a chain of sensors, or to measure the floor and ceiling temperatures with two fixed radiometers, as it has been previously discussed. However, dealing with a closed environment, several causes of stability and instability must be considered in addition to the floor and ceiling temperatures. Stable conditions are generated when HVAC systems introduce in the room new air with density very different from the ambient air. In the case of hot air, it rises

333

for its buoyancy up to is trapped by the ceiling and diverges, and part of it mixes with the ambient air. The hot air cushion aloft, the cold ambient air in the bottom, and the mixed air at the intermediate levels, determine a thermal layering and atmospheric stability. Similarly, when cold air is introduced, it sinks generating again a thermal layering. In the absence of HVAC, thermal stability is generated only when the floor is colder and the ceiling is warmer and the walls have intermediate temperatures. A cold ceiling generates instability like a warm floor for the symmetric reason; hot walls induce uprising air currents and cold walls descending ones; in general this perturbation is appreciable only close to the walls, but these are often painted, or there are paintings or tapestries. As floor, ceiling and wall temperature anomalies cannot be excluded, the indoor stability is better monitored by an integrated system composed of a vertical chain of air temperature sensors and some fixed radiometers pointing at the floor, the ceiling and the walls. If some ventilation (either natural or forced) exist, a measurement of the air speed should be included. If only one air speed sensor is used, e.g. a hot wire anemometer, the stability can be expressed in terms of the H6gstr6m ratio which considers the ratio between the vertical gradient of t e m p e r a t u r e and the destabilisation effect of the wind kinetic energy, measured in only one point, intermediate between the two points in which the temperature sensors are placed. Vertical temperature gradients might be measured with thermocouples. This kind of sensor simplifies the problem of the perfect intercalibration of sensors, and is theoretically convenient when differential measurements are needed, because the electromotive force which is generated is a function of the t e m p e r a t u r e difference between the two junctions. However, in order to overcome the problem of a weak signal generated by a small t e m p e r a t u r e difference, well calibrated and matched thermistors are generally preferred.

platinum

resistance

sensors

or

10.2. MEASURING SURFACE TEMPERATURE Surface thermometers and radiometers are commonly used to monitor surface temperatures. Thermometers should reach thermodynamic equilibrium with the surface without perturbing it or suffering for other external influences; radiometers do not need time to reach thermal equilibrium, but are sensitive to

334 reflected IR radiation. Both present advantages and problems, as follows. 10.2.1. Contact sensors

Contact sensors have a flat surface which is put into contact with the object to investigate. The equilibrium is reached when, at the interface b e t w e e n the sensor and the m e a s u r a n d surface, the exchange of heat stops; however, also a bad contact m a y led to the same result, leaving sensor and surface at different temperatures. This particularly happens when the surface is rough so that only a few points of the artifact are in contact with the sensor, and the small air pocket w h i c h remains b e t w e e n the artifact surface and the sensor acts as a good insulator. In order to improve the thermal contact, a grease or a gelatine can be smeared on the flat side of the sensor. A commonly used material in industry is silicone grease with included metal p o w d e r to improve the heat transmission. This m e d i u m , however, can not be applied in conservation, as it stains the work of art, and other clean substances should be preferred. Another problem is that the outer side of a contact sensor is exposed to the a t m o s p h e r i c agents, e.g. different air t e m p e r a t u r e and solar radiation. To minimise these perturbing factors this side is isolated but, if it is exposed to direct solar radiation, it needs an extra shield. A further problem is that the presence of the sensor perturbs the surface temperature, especially in the case of a surface which is w a r m e d by the solar radiation. In fact, the skin of the surface that is hit by solar beams becomes hot, but the small area to which the sensor is attached remains shielded and colder. The sensor exchanges heat with the deeper layers below it, in the colder area, and mainly becomes in equilibrium with them, although it receives some heat which converges laterally from the hot lighted surface. Consequently, the surface sensor instead of measuring the skin temperature measures the temperature of a colder, sub-surface layer. This is a problem of representativity of the measurement, not an instrumental error. The opposite occurs during the night time, w h e n the m o n u m e n t looses heat by infrared radiation, except the small area which is in contact with the sensor. Similarly~ ~w h e n the m o n u m e n t is wet and its surface temperature drops to the wet bulb temperature, the area in contact with the sensor is not affected by forced evaporation and a different temperature is found. As always, the variable that is monitored is the sensor temperature and the actual surface t e m p e r a t u r e remains unknown, except for the contact sensor approximation. In steady-state conditions it is assumed that a body is in equilibrium with its

335

s u r r o u n d i n g atmosphere. When a sensor is put into contact with the surface, it alters the radiative balance and the conductive and convective exchanges, so that the t h e r m a l distribution of the b o d y surface is locally altered. The sensor generates a new heat flow from (or to) the surface, and where the thermal contact is not ideal, a thermal contact resistance is introduced. Therefore, it can be concluded that a sensor will always interact with the surface under investigation, so that measurements will be in any case perturbed. W h e n p a s s i n g from the s t e a d y - s t a t e to the d y n a m i c conditions,

the

departure between the actual temperature and the measured value will increase. This is apparently expected w h e n the thermal response of the sensor is slower than the response of the body surface, but in practice this always happens because the presence of the sensor perturbs the heat exchange between the surface and the environment. Only w h e n the radiative balance does not affect too m u c h the surface temperature and the ambient conditions remain stationary for a sufficiently long time, the m e a s u r e m e n t becomes representative of the surface t e m p e r a t u r e . When the radiative gain or loss makes the skin temperature of the body different from the subsurface layer, a possible w a y to monitor the real t e m p e r a t u r e is to leave free the surface and then touch it with the sensor for a very short time. H o w e v e r , the heat capacity of the sensor affects the t e m p e r a t u r e of the few protruding points of the surface in contact w i t h the sensor. For this reason it is necessary to proceed with further steps. The m e t h o d consists in touching the monument

surface w i t h

the sensor in points

different

from that u n d e r

observation in order to bring the sensor to a closer and closer temperature so that the observed point will not be affected by the sensor influence, as follows. When the sensor touches a surface, in a short time it reaches a new equilibrium and its temperature goes closer to the u n k n o w n value under examination. Repeating a n u m b e r of times this operation, a better and better approximation is obtained, with the sensor approaching more and more the undisturbed skin temperature. After some of these m a n u a l operations, w h e n the o u t p u t readings r e m a i n u n c h a n g e d , the asymptotic value is reached, and it is possible to read the t e m p e r a t u r e of the point u n d e r observation m i n i m i s i n g the influence of the sensor. This m e t h o d has been successfully applied several times, e.g. the Aurelian and Trajan columns, Rome (Camuffo and Bernardi, 1993) or Pisa Tower; the drawback is that it needs an operator.

336

10.2.2. Radiometers and remote sensing

Radiometers provide indirect measurements of area temperatures, based on the principle of measuring the IR emission of bodies. In order to reduce the effects of atmospheric absorption of some IR bands due to the presence of water vapour, CO2, 03 and other green-house gases, the 8-14 ~tm window is generally adopted. Radiometers are essentially of two types: those which reproduce the thermal image of the objects and the non-imaging transducers which measure the total power of the IR radiation which reaches the sensor. These measurements have the advantage that they do not physically perturb the surface under investigation and do not cause damage to the works of art to which contact sensor cannot be stuck. They constitute a non-destructive method which is particularly appreciated in the field of works of art. Another important aspect is that they are remote sensing devices, and make possible measurements on ceiling or other surfaces reachable with difficulty, or on moving surfaces. Finally, their output is representative of a more or less large area, being less conditioned by local departures or fluctuations. On the other hand, the measure is affected by: (i) the presence of extraneous reflected IR radiation which constitutes a serious problem for outside measurements during the daytime, (ii) the emissivity of the surface and its Lambertian nature, (iii) suspended aerosol or moisture which adsorb the IR signal. For further details see Wolfe and Zissis (1989), Kondratyev et al. (1992). Imaging instruments (e.g. thermovision based on television sensing systems using electron-beam scanning) are expensive but a thermal image is of immediate understanding for specific problems, showing hot spots, energy loss, cold zones that might possibly be generated by water percolation or other u n k n o w n reasons. They are useful in the building diagnostics, especially when rapid temperature changes and uneven heat transmission put into evidence surface temperature anomalies due to subsurface inhomogeneity. The analysis of the IR image is made with the help of false colours and advanced computer techniques. Non-imaging

instruments

(infrared

thermometers)

are

commonly

employed in field surveys for measuring the temperature of non accessible surfaces. They measure the heating of a sensor placed in the point of convergence of the cone of the flux of IR radiation, whose optical angle is controlled by a diaphragm. The diaphragm is fixed or adjustable; adjustable diaphragms allow the use of the instrument for close or remote monitoring, or for averaging the temperature over a small or wide area. Close position a n d / o r small angles give

337 high resolution and point measurements; long range a n d / o r wide angles give the temperature averaged over a wide area. A cause of error is the diffraction of the collecting radiation at the limiting aperture, which d e p e n d s u p o n I R wavelength and therefore object temperature. A real surface both emits and reflects radiation with a relative intensity which varies from one material to another; the m e a s u r e m e n t is based on the emitted component, but the radiometer (as well as the operator) is unable to distinguish it from the reflected one. The mechanism is also complicated because the reflected radiation from liquid or solid bodies consists of two components: the well k n o w n surface

reflection and the bulk reflection, i.e. the portion of the

radiation which was transmitted into the material, and was reflected by internal backscatter; the latter is independent of the surface condition. The problem in taking reliable m e a s u r e m e n t s especially arises w h e n there are other i m p o r t a n t sources of IR radiation, or the surface under investigation has a low emissivity and a high reflectivity. In this case the measurement is not representative of the body temperature. When a metal or another reflecting surface is investigated, particular care should be placed in order to avoid the IR radiation emitted by the operator, or other bodies, in particular the sun and clouds. If the surface is Lambertian (this approximation is particularly good for a rough surface), the operator influence can be avoided by observing the surface with slant angles. However, for most surfaces the emissivity is dependent upon the angle o~f view and drops near grazing incidence. In this case a nearly n o r m a l incidence is preferred. Radiometric m e a s u r e m e n t s are based on the k n o w l e d g e of the surface emissivity r and the spectral radiance in the band used by the instrument. The simplest case (blackbody) is r = 1 and a known, continuous spectrum; in general, however, the uncertainty about these two characteristics is a source of error. Bodies with the same t e m p e r a t u r e but different emissivity generate different radiometer outputs. An adjustable emissivity control in the instrument permits to correct the output, adapting the transducer to the characteristics of each surface, in order to obtain accurate temperature measurements. However, the emissivity of the object is u n k n o w n . A used method is to cover the surface target with a coating (e.g. soot) or a film with known emissivity in the IR band used for the radiometric

measurement.

H o w e v e r , this m a y alter the b o d y - a t m o s p h e r e

interactions and the surface temperature. The actual value of r can be found empirically,

adjusting

r on the r a d i o m e t e r setting until the true surface

temperature (known by means of a surface thermometer) is indicated.

338 It is necessary to pay attention that the emissivity of a surface may change with time from a value typical of the dry material to a value close to 1 (i.e. surface wet by rainfall or covered w i t h a film of water when the surface temperature is below the dew point), and this happens frequently with outdoor monuments. The emissivity changes during the day with the water content of the surface layer, in the presence of drying-wetting cycles, and with the surface temperature or w i n d s p e e d .

H o w e v e r , surface soiling, particle deposits, efflorescences,

hygroscopicity of surface salts, biopatinas and other factors may substantially alter the b o d y emissivity. The same occurs for the surface reflectivity, and this also changes with the angle of incidence. For instance, the reflectance R from a water surface varies from 2.5% at normal incidence, and becomes R = 8% at 60 ~ 35% at 80 ~ and 97.5% at 90 ~ incidence. As the emissivity is r = 1-R , this factor is very important, as a wet surface observed at small incidence (grazing) angles becomes a pure reflector and the emissivity of the water film which envelops the b o d y vanishes. In such a condition, the only IR radiation which reaches the observer is originated by other extraneous bodies. Another important factor is that the emissivity is a function of the spectral wavelength ~, i.e. r = ~(~), and materials have a more or less deep valley in the spectral emissivity which can fall in the instrument bandwidth, thus changing the a p p a r e n t radiometric temperature. Most organic materials, e.g. w o o d , parchment, have a low emissivity in the visible part of the spectrum, and high in the IR. On the other hand, metals covered with a thin layer of oxide seems very dark, but the oxide becomes transparent at longer wavelength, so that in the IR range the surface becomes reflecting and with low emissivity, typical of a pure metal (Nicholas and White, 1994). Of course, it is convenient to compare radiometric observations with other horhogeneous (i.e. radiometric) measurements, and for this reason a complete set of measurements (e.g. ceiling, floor, walls and murals) should be made with the same type of transducer. The instrument calibration should be verified before and after the use, by pointing the radiometer at a reference surface, which behaves as a perfect black body. A used reference is the free surface of a bucket of water, as in the normal direction r = 0,96 i.e. close to 1. However, care must be taken that the water tends to stratify in layers with different density, and the surface layer is affected by evaporation so that its temperature tends to drop to the wet bulb temperature. As the IR radiation is absorbed in a few micrometers of water, the radiation emitted is originated in the very surface layer which has a temperature

different from the bulk water, where the bulb of the truth

339 thermometer is immersed. The best reference is a blackbody cavity, which has an emissivity which approaches the unity. This can be obtained with a can blackened inside, with the internal size very large and the aperture very small, so that the internal reflections are so many that there is equilibrium inside and an external radiation that penetrates is practically extinguished. If the internal surface of the cavity has gradients in temperature, the blackbody emission is a combination of spectra, and introduces an error in the calibration. In order to be isothermal, the can should be immersed in a mixed liquid with known temperature. Mixing should be made generating turbulence with up and d o w n movements, not with rotation that does not destroy density layering. When the reflectivity of an external radiation is zero, also the emissivity equals the unity. A practical formula which determines the effective value of the emissivity IBeffo f a cylindrical cavity with a small opening is 2

ra s

=

1- (1-ec)

(10.8)

2 ~'c

where ec is the emissivity of the internal surface of the cavity, r a and r c the radius of the aperture and the cavity, respectively (Nicholas and White, 1994). It is useful to know the emissivity of some materials, some of which are reported in Table 10.1, which suggests that e.g. stones or heavily oxidised metals can be measured with a radiometer, but this practice is not r e c o m m e n d e d for polished or slightly oxidised metals or other IR reflecting surfaces. As an example of the characteristics of commercially available instruments, the main technical specification of the IR transducers most widely used for microclimate measurements are: spectral band-pass 8 to 14 pm, field of view from 4 ~ to 20 ~ scale r a n g e - 3 0 ~ to 100~ resolution +0.1~

accuracy +0.5~

repeatability +0.1~

noise effective temperature less than 0.05~

than 1 s, operating e n v i r o n m e n t - 1 0 to 50~

response time less

and R H < 90%. More sophisticated

i n s t r u m e n t s are also available, with accuracy, repeatability and resolution improved by an order of magnitude. They are particularly useful in detecting anomalous

areas

during

transient

conditions.

However,

the

better

the

i n s t r u m e n t characteristics, the more elevated the cost, and the thinner the surface layer that takes advantage of the finer investigation as very small, and short period, temperature changes (i.e. AT ~ +0.01~

are smoothed out in a very

short depth so that only skin, or just sub-skin disturbances can be detected.

340 TABLE 10.1 Emissivity of some materials Material

Emissivity

Material

Emissivity

Water Grass Snow (old-fresh) Clay (dry-wet) Sand (dry-wet) Soil (dry-wet) Lacquer (white-dark) Oil paint Paper (white) Wood (oak) Glass Porcelain, glazed Brick (glazed -red)

0.96 0.90-0.98 0.82-0.99 0.95-0.97 0.84-0.96 0.90-0.98 0.92-0.97 0.87-0.98 0.93 0.90 0.91-0.94 0.92 0.75-0.93

Concrete Plaster (rough coat) Soot on a solid surface

0.92 0.91 0.91-0.94

Asphalt Basalt Dolomite Dunite Feldspar Gypsum Granite Quartz (agate) Silicon sandstone Brass (polished-oxidised) Bronze (polished) Copper (polished-oxidised) Iron (polished-oxidised) Iron rust Lead (polished-oxidised) Steel (polished-oxidised)

0.96 0.90-0.92 0.96 0.89 0.87 0.93 0.81-0.93 0.71 0.91 0.03-0.61 0.1 0.05-0.78 0.21-0.78 0.75 0.05-0.63 0.07-0.79

(Source: Platridge and Platt, 1976; Oke, 1978; Green and Maloney, 1984; Wolfe and Zissis, 1989; Lide, 1990) Comparing

a

radiometer

having

accuracy

+0.5~

with

a

contact

t h e r m o m e t e r h a v i n g the same class, observations with the m a x i m u m d e p a r t u r e of +1~

are expected. However, this is not always true, also excluding errors due

to IR reflection. The reason is that a r a d i o m e t e r and a t h e r m o m e t e r m e a s u r e t e m p e r a t u r e s at different depths below the surface. The radiometer observes the

effective radiation temperature w h i c h is representative of a t e m p e r a t u r e b e l o w the surface at a depth 1/A()~), where A(X) is the spectral absorption coefficient of the material. In absorbing materials, this layer is the skin. On the other hand, to reach e q u i l i b r i u m , a contact t h e r m o m e t e r exchanges heat for a d e e p e r layer, w h o s e extent d e p e n d s on the heat capacity of the sensor and the initial difference of t e m p e r a t u r e , so that the m e a s u r e m e n t is more p r o p e r l y r e p r e s e n t a t i v e of a deeper subsurface layer. This problem arises w h e n there are subsurface gradients, as it always occurs in dynamic conditions, or w h e n the body is irradiated by direct or diffuse solar radiation, or is cooling via IR emission, or is utilising latent heats of e v a p o r a t i o n or condensation. Historic buildings or stone m o n u m e n t s m a y sustain very large t e m p e r a t u r e gradients, as their heat transfer to the a t m o s p h e r e is v e r y low. This m a k e s difficult a c o m p a r i s o n b e t w e e n r a d i o m e t r i c t h e r m o m e t r i c observations.

and

341

C H A P T E R 11

Measuring Humidity

11.1. MEASURING AIR HUMIDITY

11.1.1. Measuring principles Several kinds of instruments, based on different principles, have been devised to measure the a m o u n t of v a p o u r in air. The h y g r o m e t e r s can be grouped in several categories, some of them more, and some less known. (i) H y g r o m e t e r s d e p e n d i n g on the addition or removal of water vapour, e.g. p s y c h r o m e t e r , diffusion h y g r o m e t e r , gravimetric, volumetric and p r e s s u r e methods. The p s y c h r o m e t e r may be considered as a s t a n d a r d for accurate observations; the other methods are of minor interest. (ii) Hygrometers based on sorption methods, e.g. mechanical hygrometers with h u m a n hair or p a r c h m e n t sensors; electric h y g r o m e t e r s with thin film capacitance sensor, or with resistance polymer sensor, or with aluminium oxide, polyelectrolyte, carbon, piezoelectric sensors. The measuring principle may be a mechanical displacement, a change of the electric resistance, capacity or inductance, or a change of vibration frequency. These sensors, and in particular thin film capacitors or resistors are largely used in commercial instruments because of their low cost, high resolution and fast response. The negative aspect is drift, especially after contamination. (iii) H y g r o m e t e r s b a s e d on condensation, e.g. dew point or frost point h y g r o m e t e r s , water equilibrium h y g r o m e t e r s for particular s a t u r a t e d salt solutions. None of them is reliable at low or very low RH and only a few at very e l e v a t e d R H values. All p r e s e n t i m p o r t a n t drift or d e p a r t u r e s after contamination or ageing, or both. For this. reason careful maintenance and frequent calibration are essential. An analysis of all these transducers would be too long, and of limited interest as only few types are recommendable in this field. In the following only

342 the most important types will be commented. For information about other kinds of hygrometric sensors please see Wexler (1965), Meteorological Office (1981), WMO (1983; 1986), Doebelin (1990), Harriman (1990).

11.1.2. Hygrometers Hair hygrometer There is no doubt that the most widespread instrument is the well known hair hygrometer which, since a long time, has served a huge variety of users and is especiallyappreciated for its easy use. It is desirable that the user of this kind of transducer be aware of its errors (typically between 3 and 30%), advantages and limitations (see Davey, 1965, and the above reference books). The response of the sensor is only very little affected by temperature; the hair responds to relative humidity but is also dependent upon mechanical load and surface contamination. The length of the human hair, when the grease has been thoroughly removed, increases by a value ranging from 1.7 to 2.5% when the RH rises from 0 to 100%, and the elongation AL/Lo, where Lo is the dry air length, is approximately proportional to the logarithm of RH, at least for not too dry environments, i.e. for RH>20%, and is usually calculated by means of the equation

AL L--ff= k ln(RH )

(11.1)

where k is a coefficient of proportionality. However, better approximations on the whole range 0 < RH < 100 % for increasing values of RH and hydrated hair are given by the functions:

AL Lo

kl ~/ RH

(11.2)

AL Lo = k2 ln2(1 +RH)

(11.3)

AL Go

=

k 3 ln2(1 +~[RH )

(11.4)

=

k4 ln(1 +RH) ln(1 +qRH )

(11.5)

AL no

343 AL Lo = k5 R H 2 + k6 R H + k7

(11.6)

which give similar results, and the constants depend u p o n the final elongation at saturation; in general 17x10 -4 < kl < 25x10-4; 8x10 -4 --- k2 --- 12x10-4; 30x10 -4 _
ln(1 +RH)

(11.7)

where 37x10 -5 ___k8 < 54x10 -5. All these formulae are s h o w n in Fig.11.1. 0,02 0,018 0,016 0,014 0,012 <1

0,01 r

0,008 0,006 0,004 0,002 0 0

i

i

i

i

20

40

60

80

100

Relative Humidity (%) Fig.11.1 Elongation of a hydrated hair (thick line) for increasing RH and elongation computed with the formulae in equations (11.1) to (11.6) (thin lines). The best approximation, i.e. (AL/Lo) = 9.3x10 -4 ln2(1 +RH) is shown with an intermediate thickness line. Tensile load: 1 g. The gray line shows the eq.(11.7) for not well hydrated hair or hysteresis for decreasing RH. From the graphs it is evident that, increasing saturation, the hair looses sensibility and becomes insensible to supersaturation: it has the same elongation at R H = 100% and w h e n is immersed into water. For this reason i m m e r s i o n in

344 distilled water is an easy method to calibrate the transducer at the upper limit of its range. The response time of the hair is not constant: it depends upon temperature, stress on the hair, RH value and direction of RH change. It increases when the air temperature decreases; at room temperature the time-constant varies from 0.5 to 3 minutes. Measurements below freezing temperature need more and more minutes to reach equilibrium, and at -40~

the hair becomes insensitive. The

response is faster for high h u m i d i t y levels as well as for the direction of increasing humidity, following the natural hygroscopicity of hairs. It is also faster for hair under stress when charged with external load (e.g. the tension due to the series of linkage to the recording pen arm), but tension generates long term drift. The sensor is affected by hysteresis, so that the same output can be observed for different values of RH depending on the past environmental values to which the sensor has adapted. The largest errors occur especially in dry conditions, and the permanence in dry environments decreases the hair sensibility. The hair is composed of different layers that respond in a different way. When the sensor is well h y d r a t e d , it presents a so-called 'wet' calibration curve to which all instruments refer; however, after some days in dry condition, it reduces the hydration level of the outer layers and follows another 'dry' curve. To minimise the uncertainty due to hysteresis, both the calibration curves (i.e. for the 'wet' and

'dry' hair) are always referred to increasing humidity. The transition 'wet' to 'dry' occurs only after continue permanence at low relative humidity, and this is the case of most heated rooms and m u s e u m s in winter. For this reason hairs should be regenerated very frequently, immersing them into distilled water. The frequency of this operation is determined by the ambient R H and the span of daily cycles; the dryer the ambient, the more frequent should be the regeneration repeated; e.g. in an ordinary room the regeneration should be made at least every week by keeping for a whole night the hairs immersed into water. In very dry environments this operation should be made more frequently, at least daily. This imposes an unacceptable limitation. Hairs are very sensitive to chemical contamination and cleaning with ether is necessary every time hairs have been exposed to air pollution, or contaminated with soot deposits or grease, being touched with bare fingers. Each week, the transducer should be calibrated at both low R H and saturation two times: i.e. before the use, after being cleaned and regenerated, and at the end of the use in order to evaluate the drift. Without all these operations, it is not clear which ambient R H corresponds to the instrument output. A clear indication that the instrument is being used out of calibration is

345 given when the sensor reaches saturation, and the pen remains for several hours very stable in the same position of maximum at elevated values of RH, different from 100%. Such maxima may be found at any value between 75% and 120% and show how much the upper limit of the span has changed. The response time can be reduced by flattening the hair. Hair rolled flat is much more faster than ordinary hair: at room temperature it is 3 to 5 times faster; below zero one order of magnitude or even more. The speed may also be further increased applying a greater rolling pressure. The faster response involves also negative aspects: for rolled hairs the 'wet' to 'dry' transition occurs after a few hours of dry environment. Another drawback is that rolled hairs have their strength decreased and, consequently, their drift increased.

Thin film capacitor hygrometer H u m i d i t y sensors made of thin film capacitor elements are often used for i n d o o r s / o u t d o o r s measurements, as they constitute the best method w h e n the temperature drops below zero, or measurements should continue unattended for a relatively long time (e.g. one week or more). A dielectric film (e.g. acetal polymer,

cellulose acetate butyrate)

absorbs water v a p o u r

from the air

establishing a state of humidity in equilibrium with it. The capacitance changes proportionally to the equilibrium moisture content of the film which is in turn proportional to the relative humidity of the air, so that the output is linear and independent of the actual value of the air temperature at which the RH has been attained. The change in dielectric constant is measured with a capacitance bridge. This kind of sensor is very fast, i.e. response time which varies from 1 or a few seconds to a few minutes; has a low hysteresis, i.e. +1% (or less) from 5 to 95%

RH; is relatively accurate, i.e. accuracy +1 or +2%, and has high resolution, which may vary from 0.1 to 1%. The main problem is the drift, especially in polluted environments. For this reason the probe is often inserted into a filter which protects the sensor against air pollution, dirt or splashing droplets; also oil and grease vapours may form a film which prevents the absorption of water molecules. However, the presence of a filter slows d o w n the free exchange with the atmosphere and increases the actual time of response. This is not a problem for several applications (e.g. long term ambient monitoring) but is an i m p o r t a n t limit w h e n fast response measurements are needed. They need calibration every few months, or every year in the most optimistic case. In the best instruments, in order to avoid the problem of drift, the calibration runs automatically after set-up, activating two calibration points, at

346 low and high RH, obtained by means of reference saturated salt solutions. Electrolyte hygrometer

This s e n s o r m e a s u r e s the i m p e d a n c e of a h y g r o s c o p i c s u b s t a n c e ,

an

electrolyte, which absorbs water molecules to produce a solution. The hygroscopic electrolyte tends to establish e q u i l i b r i u m w i t h the s u r r o u n d i n g a t m o s p h e r e , w i t h o u t drift and has a very fast response. Commercially available sensors are declared h a v i n g a time constant less than 10 s, a repeatability of 0.1% RH, and a r a n g e u n u s u a l l y e x t e n d e d t o w a r d s d r y n e s s , i.e. from 0 to 95%. H o w e v e r , although this sensor has a good performance, it is fast only after it has established t h e r m a l equilibrium with ambient air, and this stabilisation requires 2 to 3 min. This time is the limiting factor and should be considered as a more realistic time constant in the field, w h e n both t e m p e r a t u r e and h u m i d i t y are variable. The m a n u f a c t u r e r suggests calibration with a d j u s t m e n t every 6 to 12 m o n t h s , and more care is suggested in the case of operation in a polluted environment. Psychrometer

The

psychrometer

is an

instrument

based

on the

readings

of t w o

t h e r m o m e t e r s , exposed side by side: one being bare and dry, and one with the bulb covered with a wet muslin. At the equilibrium, i.e. w h e n the heat Qv lost by e v a p o r a t i o n from the wet bulb equals the sensible heat Qs transferred from the a m b i e n t air to the colder w e t bulb, the p s y c h r o m e t r i c f o r m u l a is o b t a i n e d as discussed in Chapter 1, i.e. (11.8)

e = ew - A p (T - Tw)

where

A

is the p s y c h r o m e t r i c

coefficient, w h i c h

is i n d e p e n d e n t

of the

e v a p o r a t i n g surface area, i.e. the size of the wet-bulb wick covering, but is slightly d e p e n d e n t on ventilation rate and, to an even minor degree, on p s y c h r o m e t e r design, size and d i m e n s i o n of the dry and wet bulb, ambient t e m p e r a t u r e and relative h u m i d i t y . H o w e v e r , w h e n ventilation is in excess of 2.5 ms -1 (and p a r t i c u l a r l y in the r a n g e b e t w e e n 3 and 5 ms-l), A is n e a r l y c o n s t a n t a n d s u g g e s t e d values for the classic A s s m a n p s y c h r o m e t e r with m e r c u r y in glass t h e r m o m e t e r s are A = 6.2x10 -4 K -1 (WMO No.8, 1983) and A = 6.667x10 -4 K -1 (UK Meteorological Office, 1981). Some values of A versus ventilation rate v are: A = 13.0x10 -4 K -1 at v = 0.12 ms-l; A = 9.0x10 -4 K -1 at v - 0.50 ms-l; A - 7.8x10 -4 K -1 at v = 1.0 ms-l; A = 7.1x10 -4 K -1 at v = 2 ms-l; A = 6.7x10 -4 K -1 at v = 4.0 ms -1 ( W M O No.622, 1986). In order to get an idea about the error derived by an incorrect value

347 of A, at t = 20~

a 10% change of A causes a relative h u m i d i t y error ARH = 0% at

R H = 100%; A R H = 0.7% at R H = 80%; A R H = 1.4% at R H = 60%; A R H = 2.2% at R H = 40%; A R H = 3.0% at R H = 20%; A R H = 4% at R H = 0% (UK Meteorological

Office, 1981), w h e r e it a p p e a r s that at o r d i n a r y t e m p e r a t u r e and h u m i d i t y in m u s e u m s the error is small; it decreases at higher t e m p e r a t u r e and increases at lower t e m p e r a t u r e . Both dry and w e t bulb t h e r m o m e t e r s are ventilated w i t h a forced air flow with speed generally ranging from 3 to 5 m s -1, w h e r e the above p r o p o r t i o n a l i t y coefficients become more constant and less d e p e n d e n t u p o n the ventilation rate. Please note that the W M O No.8 (1983) suggests the w i d e r interval from 2.5 to 10 m s -1, but 2.5 m s -1 is close to the limit of error (2 m s -1) and every slow d o w n of the fan, e.g. for a not well charged battery, m a y cause a super evaluation of the wet bulb t e m p e r a t u r e and, consequently, of the m e a s u r e d RH. On the other hand, a too fast v e n t i l a t i o n rate causes an u n n e c e s s a r y p o w e r c o n s u m p t i o n .

For

e l e v a t e d R H values, slower ventilation rates are sufficient, b u t w h e n the R H drops, fast ventilation is necessary to cool the wet bulb to its full depression. The fan speed is a limiting factor in dry environments. M e a s u r e m e n t s accurately taken with a p s y c h r o m e t e r can be considered as a home

standard,

i.e.

a useful

reference

to c o m p a r e

and

calibrate

other

i n s t r u m e n t s . In particular, the p s y c h r o m e t e r is the m o s t accurate i n s t r u m e n t n e a r 100% R H

a n d is s u p e r i o r in this region to all the other sensor types

(Wiederhold, 1975). H o w e v e r , it has two i m p o r t a n t limits. First, it c a n n o t be c o n v e n i e n t l y u s e d w h e n the w e t bulb is below the freezing point. A l t h o u g h reference m a y be m a d e to the latent heat and saturation pressure for ice, instead of water, the m e a s u r e m e n t becomes less accurate; the water s u p p l y is interrupted, and the water reservoir m a y be d a m a g e d . Second, as the R H drops below 20%, it becomes difficult to cool the wet bulb to the equilibrium depression, even w h e n the sensors are aspirated at an airstream rate of 10 m s -1. The reason for this is that the water of the wet bulb evaporates before the wet bulb reaches it m a x i m u m d e p r e s s i o n t e m p e r a t u r e (Fisher et al., 1981). For this r e a s o n the use of this i n s t r u m e n t is suggested in the range from 20 to 100%, which fortunately covers the m a i n parts of the practical cases. On the other hand, other sensors do not provide a w i d e r range of reliability. The most c o m m o n causes of error are the following ones. (i) Breathing in p r o x i m i t y of the sensor which m e a s u r e s an exceeding value of moisture. A n o t h e r frequent operator error is to h a n d l e a p s y c h r o m e t e r with the arm raised, as the air heated by the arm follows the u p w a r d heated p a t h a r o u n d the a r m and is then aspirated and m e a s u r e d by the p s y c h r o m e t e r . The correct

348 position is to handle the i n s t r u m e n t with a lowered

arm, or h u n g the

instrument to an extension pole. (ii) Reading the thermometers (in particular the wet bulb one) before it has reached equilibrium. It might be useful to remember that the fan does not affect the temperature of the dry bulb, but lowers that of the wet bulb. Although covering the bulb with a thin tubular cotton wick reduces the thermometer time constant, w h e n the fan is switched on, the dry sensor remains in the previous condition of equilibrium, but the wet sensor begins to lower its temperature and needs time to reach equilibrium. This error is frequent with sensors having a long time of response. (iii) Errors in the thermometer reading. This error may be i m p o r t a n t with mercury-in-glass thermometers as the operator must stay with his face close to the thermometers for a too long time to read the small scale divisions of both of them, and the face IR emission and the breath may warm the sensors. This problem has been eliminated in electronic psychrometers where the display is well visible and placed far from the sensors. Some of them have an automatic recording and there is no need to read the display, except for controlling if the equilibrium has been reached. (iv) Insufficient ventilation of the wet bulb. This error is frequent and becomes important for ventilation below 2 m s -1. Controlling the airspeed of ordinary psychrometers, it is very frequent to find insufficient ventilation speed. Often it is possible to remedy by diminishing the screen section to increase the airstream speed. In clockwork aspirated psychrometers, observations made too early (i.e. with reference to the instrument time response) are affected by error, as well as those made too late, when the spring is loosing its energy and the fan is slowing down. Electric fans avoid this problem. (v) Tubular cotton wick covering of the wet bulb not completely wet. (vi) Contaminated wet bulb wick covering, or use of non pure distilled water. After some times is elapsed, the forced ventilation causes contamination of the covering. Monitoring in polluted environments requires frequent changes of the wick covering. When a new cotton covering is used, it must before be boiled in distilled water to remove extraneous substances that may alter the surface tension of the absorbed water. (vii) Too thick covering (or freezing) of the wet bulb that may increase the time constant. (viii) Temperature below zero which causes the freezing of the wet bulb covering, so that the equilibrium is reached with ice instead of water. All the h y g r o m e t r i c p a r a m e t e r s can be obtained from the d r y bulb

349 t e m p e r a t u r e and wet bulb depression with the help of tables, d i a g r a m s or formulae, as discussed in Chapter 1, but the same can be obtained also from the air temperature and the RH. The p s y c h r o m e t e r gives v e r y accurate m e a s u r e m e n t s only w h e n the operation is made correctly. The effect of an error in the wet bulb reading varies with the temperature and humidity. An example of the propagation of errors is s h o w n in Fig.11.2 by supposing RH = 50% and measuring Tw. with an error of -0.1~

In the most frequent range of indoor climatology, i.e. 10 ___T < 30~

the

error is relatively small, i.e. less than 1% for RH, and one or a few tenths for SH,

AH, DP and e. In the meteorological range of variability, the error of RH increases exponentially with

decreasing

temperature

below

0~

but

in this s p a n

psychrometric measurements are avoided because the wet bulb freezes (although it is possible to compute the other variables either for wet bulb coated with supercooled water or covered with ice). For elevated temperatures the error of A H becomes important. However, it should be noted that this propagation of errors affects the accuracy of all the measurements, but systematic errors affect very little the reliability of the horizontal distributions of these parameters. It is very i m p o r t a n t to check before use if the two sensors, both dry, show exactly the same temperature. Also in the case that they measure the actual temperature with a small error (although identical for both sensors), the error is systematic and alters substantially in the same w a y all the readings, and is therefore negligible in the calculation of the variability of the hygrometric parameters. This is especially true w h e n plotting the distributions of the above variables in horizontal maps, as differential values are involved, and the departures from the average of the local minima and maxima remain practically unchanged. In order to obtain the distribution of the temperature and the h u m i d i t y in a horizontal cross section of a room, several dry and wet bulb observations should be made in a short time. This means that the instrument should have a very fast response and should be absolutely repetitive. Precision electronic psychrometers have been designed and built in our laboratory, with accuracy better than 0.1~ and fast response. Although sensors with a time constant better than 1 s were used, the overall time constant was 5 s, which is inclusive of the thermal inertia of the screen, m e c h a n i c a l p a r t s

and electronics. The c o m b i n a t i o n of some

different time constants reflects in the fact that plotting the n o r m a l i s e d t e m p e r a t u r e change for the step ambient variation versus t in a logarithmic paper, the plot departs from a straight line. This time constant limits the n u m b e r of observations for each run (e.g. 50 measuring points), which were m a d e with the fan u n i n t e r r u p t e d l y

switched-on

when

moving

from one m e a s u r i n g

350

1,5

RH 1,0

=,"

0,5

DP

r,,#3

SH

0,0

-0,5

-1,0 0

10

20

30

40

50

Temperature (~ Fig.11.2 An example of the error generated in computing the parameters: relative humidity (RH, %), specific humidity (SH, g/kg), absolute humidity (AH, g/m3), dew point (DP, ~ and vapour pressure (e, hPa), when the wet bulb temperatureTw, is measured with an error of-0.1~ at ambient RH = 50%.

351 position to the next one, in order to reduce the time elapsed before to reach equilibrium. In fact, when the operator arrives to the next position, the sensor is close to the equilibrium with the new values having already adapted to the values nearby during the path. All the c o m p o n e n t s

(i.e. sensors, screen, electronic circuits)

of the

p s y c h r o m e t e r s built to this aim, should be tested separately and then in conjunction to optimise the overall time constant and accuracy. Either linear or non-linear thermistors, or p l a t i n u m resistance sensors, are convenient fast sensors. Linear o u t p u t s avoid unnecessary electronic transformations of the signal, but miniaturised thermistors can equally be linearised and have a shorter time constant, which is a very i m p o r t a n t feature, especially w h e n several measurements are made in each run. Two types of screen are suggested: (i) a white polystyrene foam which is reflective, has a very low thermal capacity and is a good thermal insulator; its response time, measured with a radiometer, is less than 2 s; (ii) a thin aluminium foil reflecting outside and blackened inside. Low p o w e r c o n s u m p t i o n fans are utilised in order to reduce weight, volume and cost of rechargeable batteries. The velocity of the aspirated flow is regulated varying the internal section of the screen in correspondence of the wet bulb sensor, or operating on the fan. The dry and wet bulb sensors are placed side by side, or the wet bulb being midway between the dry one and the aspirating fan. The output should be clearly visible in a display and printed on paper or memorised in a computer.

11.1.3. Calibrating hygrometers All hygrometers need periodic calibrations. Psychrometers, being based on temperature measurements need a control of the temperature transducers, and especially of their matching. This is a clear advantage, as it is easier to do temperature than humidity calibrations. All the other devices need a comparison with a k n o w n h u m i d i t y level. Calibration is often m a d e in a closed, non absorbent box at controlled temperature where a super-saturated salt solution is spread in an area as large as possible, a n d a i r mixing ensures homogeneity inside the box. An excess of the solid salt is suggested, in order to ensure saturation also in the case that a huge amount of water vapour is absorbed by the solution with two possible negative consequences: (i) the excess of solid salt disappears and the solution is no more saturated; (ii) a density stratification forms, w i t h the upper layer enriched of absorbed water, non saturated and in equilibrium with a higher relative humidity. A list is here reported of substances (in addition to vacuum) that might be used to this aim, followed by their equilibrium RH at 20~

352 TABLE 11.1 Obtaining constant relative humidity within a closed space. When the super-saturated solution method is used, an excess of the listed substances should remain in solid phase in a saturated aqueous solution at 20~ saturated solution or other methods

RH

saturated solution

RH

saturated solution

RH

Air pump vacuum CaC12.6H20 Mg(NO3)2.6H20* KBr Na2SO4.10H20

0% 32% 56% 84% 93%

LiCI* Zn(NO3)2.6H20 NaBr.2H20 ZnS04.7H20 KNO3*

15% 42% 58% 90% 95%

MgC12.6H20* K2CO3.2H20 NaCI* Na2CO3.10H20 H20

32% 44% 76% 92% 100%

(Source: List, 1971; Weast, 1977/78; Green and Maloneyl 1984. Note: the substances suggested by the Smithsonian Institute are indicated with an asterisk).

However, it is better to consider this method as a crude approximation (i.e. within a few % RH) and a very effective way to obtain a steady state condition (i.e. constant RH) around an approximately k n o w n value, and pass to the second order approximation comparing the instrument with a reference hygrometer also located inside the box. In this case there is no need for temperature regulatiori, and this simplifies the procedures. The best home reference is a psychrometer, but w h e n this is placed inside the box, the continually evaporating water of the wet bulb causes a perturbation, generating an excess of vapour pressure and being a b s o r b e d by the s a t u r a t e d solution. In order to avoid this p r o b l e m , the p s y c h r o m e t e r should initially have the muslin dry and inserted into a glass or teflon capillary tube, e m p t y and connected with the box exterior, for the whole time needed to reach equilibrium, and only at the m o m e n t of the calibration test the muslin should receive and suck the water through the tube. In this way, the perturbation is very short and negligible, the whole volume in the box having already attained equilibrium, the water being supplied at the very last m i n u t e and the free surface of the muslin being extremely small compared with the free surface of the saturated solution. This practice is much more precise and cheap, as pure (and expensive) chemical products are not necessary. In fact, the principle is to k n o w (and adjust) the instrument output at exactly k n o w n h u m i d i t y levels, chosen at 4 or 5 different points in the humidity scale, and the knowledge of the h u m i d i t y level is based on the reading of a precise instrument, not on the reproduction of standard points by means of the use of chemical products at a precisely controlled temperature.

353 11.2. M E A S U R I N G INTERACTIONS

MONUMENT

HUMIDITY

AND

AIR-ARTEFACT

11.2.1. Measuring heat and moisture exchanges between air and monuments A fast psychrometer is also used to monitor exchanges of heat and vapour between the air and surfaces, e.g. between air and frescoed walls. In analogy with molecular diffusion, fluxes are proportional to the negative gradient of the diffused property. The same theory is applied as in Chapter 7 for the diffusivity of heat, i.e. the flux of heat H is 3T H - - K H 3n

(11.9)

where n is the normal to the surface and KH is the coefficient of heat exchange on the direction of n, and depends upon the physical mechanism responsible for the heat transport. In the case of still air in a closed environment, KH is determined by the thermal conductivity of air, i.e. KH = kT; when an internal dynamic boundary layer develops along the surface, the turbulent transport becomes dominant over the conductivity, and when turbulence is well developed, as in outdoor environments, KH is given by the eddy diffusivity KE. Of course, KE is a function of the Richardson number, increasing when Ri decreases (for experimental values see Plate, 1982). The eddy diffusion coefficient applies when the eddy motions are rapid enough and are the dominant factor in the heat transfer. However, if the wall is directly hit by solar radiation, or the temperature gradient is measured outside, in the convective boundary layer which forms over the ground overheated by the solar radiation, the mechanism of transfer changes, being characterised by the buoyancy and not by the momentum transfer. For this reason the subscript H reminds that the eddy diffusion coefficient for heat exchange may differ from that for momentum. When mechanical transfer dominates, the eddies preserve their properties over an average displacement l, called mixing length, and then mix with the surrounding environment. From the definition of eddy flux, i.e. the capability of transporting along the vertical (or the normal) mechanical mixing, the coefficient of eddy diffusivity K~ is given by KE ~ <w' t>

(11.10)

354 For a neutral shear flow, the parameters governing the mean flow are the surface stress, the distance from the surface, and the fluid density. Dimensional arguments lead to find the following equation in terms of the shearing stress r, which is linked with the dynamic viscosity and the wind shear

Ka = C~

~

T

(11.11)

P

where Ca is a constant (Goody, 1995). In conclusion, w h e n an observation of the temperature gradient near a surface is made, a quantitative evaluation of the heat exchange needs a careful examination of the dynamic state of the air motions, as the exchange coefficient varies. For this reason it might be better to limit the analysis to pinpoint the presence, the sign, the time of appearance, and the place where t e m p e r a t u r e gradients appear, and avoid the risk of macroscopic errors. The only reliable quantitative case is found in closed rooms, with calm, stable, stratified air. Under these circumstances, the quantitative value of the molecular heat exchange is obtained by substituting in eq.(11.9) the actual value of kT = 6.26 x 10-5 cal cm -1 s -1 K -1 (or 26.2 mW m -1 K -1) at T = 300K, i.e. 3T H = - 6.26 x 10-5 3n

(cal cm -2 s -1)

(11.12)

where the coefficient -6.26 x 10-5 gives the flux per unit gradient of T. Similarly, the flux of moisture Mv is given by

Mv = - pKw

3MR 3n

(11.13)

w h e r e p is the air density and Kw the diffusivity for water vapour. As in the previous case, Kw is not constant but varies between ~aw < Kw < KE where the extremes are the molecular diffusivity ~aw of vapour in still air in closed indoor e n v i r o n m e n t s , and the e d d y diffusivity KF. outdoors, where turbulence and mixing dominate. In order to get an idea of the numerical value of the moisture flux in a closed room with stable air, it is possible to substitute in the above equation the actual values of p = 1.16 x 10-3 g c m -3 and ~ w = 0.24 cm 2 s -1, i.e.

355

3MR My = - 2.77 x 10 -4 3n

(g cm-2

s-l)

(11.14)

where the coefficient -2.77 x 10 -4 gives the flux per unit gradient of MR. For example, a flux of moisture of this order of magnitude was m e a s u r e d with a Pich6 evaporimeter as potential evaporation rate (PER) in the Sistine Chapel at

RH = 50% (Camuffo and Bernardi, 1986). The Pichd evaporimeter is constituted of a vertical, reversed, graduated glass phial filled of water which supplies water to a porous ceramic disc or a blotting paper which adheres to the open bottom. Each hour it is possible to read on the graduated phial the amount of water that has been supplied to the disc and has evaporated, and is an index of the evaporation that might occur if a spot of damp surface were present. Exchanges of heat or moisture are always associated with gradients of T or

MR, but in m a n y cases exchanges are small and the gradients are difficult to measure as they are weak, close to the surface, easily dissipated by air motions and turbulence, and are easily perturbed by the experimental apparatus. For this reason it is not only very difficult to arrive at a precise quantitative evaluation of H and Mv, but it m a y be also difficult to individuate the occurrence of these fluxes. For this reason it is practically convenient to measure in finite terms AT and AMR close to the surface and far from it; although this m e a s u r e m e n t does not give the value of the actual gradient at the interface, it in any case furnishes an objective observation in finite terms. However, positioning the aspirated psychrometer near the surface, the local air is perturbed and the excess (or defect) of heat a n d / o r moisture is immediately aspirated by the fan; keeping in the same position the instrument for all the time necessary for the measurement, the new air that successively arrives into contact with the sensors is swallowed up by the suction depressure coming from the nearby air masses and is not in equilibrium with the wall. This problem can be partially overcome inserting on the psychrometer intake a thin, insulating disk, that obliges the air to converge from the edge of the disc to the aspiration cylinder passing through the thin layer between the disk and the wall surface (Fig.11.3). The air remains longer into contact with the wall surface exchanging heat and moisture and reaching a (partial) equilibrium before arriving into contact with the sensors. In order to avoid or minimise heat exchanges between the disc and the air, the disk must be made of a material both insulating and with low density, and polystyrene foam has both these characteristics. We have used polystyrene foam disks having 30 cm diameter and having attached three small distance

356 spacers m a d e of felt for two reasons: i.e. to ensure a constant distance (3 mm) between the disk and the wall, and to avoid damage leaning the disc against the wall.

=== ...= a m m ~ m a n m a n

i d a m i D

polystyrene disc

temp2r21 s re

II

suckingin fan

~

handle

~//////,/~ electronic ~ circuits

u g H m ~ u B u m lu~n m i D i ~ i | H i m i~in nmli l i i i m a n l i i l --an

wall surface

Fig.11.3 A polystyrene disc can be inserted on the psychrometer intake to oblige the air to remain more longer close to the wall surface passing through the thin layer between the disk and the surface (in this drawing a wall is sketched on the left); in this way the wall/air interactions are better evidenced. Another, but unreliable method, is applied by some people and has been recently utilised in the Giotto Chapel too. The claimed principle is that, leaning a cup against a wall, some air and moisture remains e n t r a p p e d and can be m o n i t o r e d in a larger interfacial volume, as this air has more o p p o r t u n i t y to interact with the wall, being not continually removed or perturbed by external factors. Just for this reason the entrapped air pocket is unable to reproduce the exchanges which occur at the free interface: after some time has elapsed, the still air entrapped reaches a new equilibrium and any change stops, or occurs in very

357 different conditions; on the other hand, at the free interface, w h e r e air is continually r e n e w e d by air m o v e m e n t s and diffusion, exchanges of heat and moisture occur at a rate which is determined by the turnover of the external air and IR radiation, in addition to the transport and diffusion inside the wall. The r e p r e s e n t a t i v i t y of this m e t h o d m i g h t be c o m p a r e d w i t h that of evaporimeters.

An evaporimeter consists in a pan filled of w a t e r w h e r e the

q u a n t i t y of liquid that has e v a p o r a t e d in a given time is m e a s u r e d . The evaporation rate is governed by the difference of vapour pressure in the free air and over the pan surface as well as by the rate at which the air which receives the evaporated

m o i s t u r e is r e m o v e d .

Suppose to expose an e v a p o r i m e t e r

in

s u m m e r t i m e after a rainfall, followed by some clear days. In the first day, w h e n the terrain is wet, the evaporation rate is all the same on the pan and the terrain. After a few days, the soil has lost most of the moisture in the surface layer and the evaporation is reduced to a minimum, or is stopped at all; on the other hand, the e v a p o r i m e t e r which is in a very dry e n v i r o n m e n t , shows an increased evaporation rate which is non representative of the real situation at that site. For this reason an evaporimeter m a y be representative of the evaporation from a lake, not a terrain. Another quaint error, typical of this i n s t r u m e n t , is an apparent, fast evaporation near sunset, when birds drink some water in the pane. Returning to the cup method, it might be supposed that it represents the e q u i l i b r i u m situation inside a pore in the inner of a wall. In reality, the entrapped air pocket is external to the wall where both the mixing ratio and the t e m p e r a t u r e and, consequently, the RH. have values different from the wall interior.

In fact, the air pocket entrapped between the wall surface and the cup

has a temperature which is affected by both these surfaces, and in addition the cup has a wider area, i.e. if the cup is a hemisphere with radius r, the ratio of the internal cup surface to the wall surface is 2rcr2/Trr2 = 2. The cup temperature is determined by the exchanges that occur with the wall and the air; the portion of wall covered with the cup has a temperature which is governed by both the inner wall and the interactions between the wall and the cup; this situation is very different from the free wall surface which interacts in another w a y w i t h the atmosphere. Finally, inside the pores, the saturation is governed by the Kelvin equation and the presence of hygroscopic salts: a situation which is totally different inside the cup.

11.2.2. Measuring humidity inside walls It is not easy to measure moisture inside walls (for a review of methods see N a p p i and C6te, 1997). C o m m o n l y used destructive m e t h o d s are to m e a s u r e

358 equilibrium air humidity in a hole performed into the wall or measure the difference of the weight of a sample just removed and after having dried it in an oven. An important non destructive method, originally devised for the soil moisture measurement, is based on the principle that high energy neutrons emitted from a radioactive source are slowed down to thermal energy by elastic collisions with other nuclei (WMO, 1983). The loss of energy depends upon the mass of the colliding nuclei, and increases by decreasing atomic number. The highest efficiency occurs with protons, i.e. hydrogen nuclei, which have the same mass as the impinging neutrons. A water molecule has two hydrogen atoms, and these atoms are practically absent in traditional building materials such as brick, stone, and mortar, except for some water which may be adsorbed, in the liquid state, or in hydrated crystals. However, non-water hydrogen is present in organic materials, and also crystalline structures, clay minerals, hydroxides and other substances have important neutron capture properties which add uncertainty to these measurements. After collision, neutrons are slowed down and scattered in all directions. Thus, the flux density of transmitted (or diffused) slow neutrons is nearly proportional to the water content over an approximately spherical volume with a radius of 15 to 35 cm. The count of thermal neutrons is made with either scintillation crystal detectors or gas filled detectors, and the standard error is proportional to the square root of the count. As a consequence, the error is larger at high water contents. In addition, changes in the air humidity and temperature cause drift to the equipment. The neutron interaction occurs across the whole thickness of the wall and the method cannot distinguish between surface and deep layers. Dealing with the risk Connected with radioactive materials, this method can be only applied with special precautions by authorised, well trained personnel. This method may give another information: part of the slow neutrons are captured by heavier nuclei with a gamma ray emission having an energy which is determined by the mass of the absorbing nuclei and ranges between 3.3 to 11.6 MeV. The analysis of the gamma ray spectrum detects the chemical elements. Another m e t h o d consists in measuring the speed of p r o p a g a t i o n of

ultrasonic pulses (typical frequency: 50 kHz) and also sonic pulses (typical frequency: 5 kHz) crossing a material, as the speed increases when water fills pores and capillaries (Mamillan, 1992; Murphy et al., 1996). Measurements can be taken either in the transmission, reflection and surface modes. In the first method, the receiver is in the same straight line as the emitted beam, on the other side of the wall; in the last two methods, the receiver is not aligned, and is

359 displaced in several positions at regular increasing distances. This allows to control if the delay in receiving the pulses is proportional to the increased distance. During the path, attenuations, dispersions and reflections of the signal occur, especially in the presence of discontinuities, defects and cracks. This method is more manageable and is currently used by technicians; the main limit is that it supplies a useful indication, but is unable to give a quantitative evaluation about the absorbed water. A similar comment could be addressed to the method based on the transmission of mono frequency radar waves, although it seems a more promising one. The most widely used method consists in measuring the current passing across two electrodes pressed against the wall. However, the current d e p e n d s u p o n the a m o u n t of liquid water, the presence of hygroscopic salts, the wall temperature

and

the mixing

ratio of the a t m o s p h e r e .

The n a t u r e

and

concentration of hygroscopic salts change for several reasons r e s p o n d i n g to external pollution (mainly NOx), past evaporation, infiltration or washing out of water

which

determine

efflorescences,

subflorescences,

salt

dissolution,

migration or removal. In addition, if the wall surface is close to the dew point, or the air is moist, or the wall is covered with deliquescent salts, as typically most of the NOx derived minerals are, the surface (not the interior) of the wall is very conductive and the measurement gives a non representative indication.

11.2.3. Measuring time of wetness It is well known that, when the junctions of a thermocouple are at different temperatures, an electromotive force is generated, or a current if the circuit is closed. The inverse p h e n o m e n o n is to cool junctions of a thermocouple array with a driving current (effect Peltier). Cooling by effect Peltier a m i r r o r e d reference surface, and recording the temperature in which the mirror begins to stream up, is a method which furnishes a direct measurement of the dew point, i.e. a dew point meter. The same technology used to detect the onset of droplets in a cooled mirror can be applied to detect the same p h e n o m e n o n , but on a mirror having the same temperature of an artefact. In this case, a dew point

signaller is obtained, useful to monitor the time of wetness (TOW), or to switch on a heating system when droplets begin to form on cold windows. In the latter case it is necessary to w a r m directly the glass by means of infrared radiation or electrical wire resistors, and not blowing heated air. The T O W is an important parameter in conservation science, as several physical, chemical and biological deterioration mechanisms are possible only in the presence of liquid water. However, it is always necessary to keep in mind that

360 the T O W is not an atmospheric variable only, but a variable which is determined by: the mixing ratio of the water vapour in air, the object surface temperature Ts and the surface contamination. Only w h e n Ts drops below the dew point the surface becomes wet and the T O W begins, independently of the ambient relative humidity. In reality, the T O W does not exactly coincide with the total time in which the surface temperature remains below the D P, but is (slightly) longer as w h e n Ts rises above D P, some time is still needed to evaporate the water from the surface. However, for non adsorbing materials the difference is small and the two variables are often assumed to be coincident, at least in a first approximation. Some dew point detectors can be found that are based on the conductivity (or dielectric capacity) of an adsorbing medium. The main problem is that they easily reach equilibrium during the wetting phase, but they retain water and remain d a m p for some time after the surface dries. They present hysteresis in drying and might be representative of some porous adsorbing materials but not of glass or polished metals.

lcrn

Fig.11.4 Dew point detector. The optical transducer (1) is composed of an IR emitting diode (2), a photo darlington (3), a balckened metal board with mirror (4), a shield (5) and four spacers (6). It may be attached to the surface or hung with a holder (7). (After Camuffo and Valcher, 1986, reprinted by permission of Kluwer Academic Publishers). A dew point detector which better responds to the b e h a v i o u r of non absorbing materials is based on the extinction (or attenuation) of a reflected IR b e a m w h e n dew droplets are forming on the surface of the b o d y u n d e r

361 examination. In fact, the IR radiation is absorbed and extinguished in a few micrometers of liquid water, so that when the first droplets begin to form and grow on the surface, the reflected beam is immediately attenuated and its intensity progressively diminishes until it is completely extinguished; this happens for a completely wet surface. However, as only metals and few other smooth surfaces are good reflectors, a tiny mirror is introduced as reference surface, which has the same temperature as the body. The mirror is put into thermal equilibrium with the artefact, but is part of the measuring device (Fig.11.4), being mechanically sealed at the appropriate distance to receive the IR beam from a LED emitter (i.e. an IR emitting diode) and to reflect it into the sensor (i.e. a photo Darlington). The mirror is at the centre of a small blackened metal board and a black plastic sheet to shield it against external interferences. The emitter is activated by a pulsed current in order to sensibly reduce the power supplied by the IR beam used in the detector and therefore the heating of the mirror. The output of the photo Darlington is amplified, transformed into a continuous level by a peak detector and then compared with a reference voltage which can be adjusted to calibrate the system that is triggered by a selected dimension of the growing droplets (Camuffo and Valcher, 1986).

363

C H A P T E R 12

Measuring Wind and Indoor Air Motions

12.1. METEOROLOGICAL WIND MEASUREMENTS

12.1.1. Anemometry For meteorological purposes, the wind speed and direction are measured with the anemometer and the wind vane, respectively. The two transducers may be separated or combined in only one instrument, e.g. the aerovane. For air pollution studies, another instrument, the U V W a n e m o m e t e r , m e a s u r e s separately the three wind vectors (two perpendicular in the horizontal plane and one vertical) by means of a set of three orthogonal propellers. For special studies other kinds of instruments are used. Anemometers are based on one of the following wind properties. Wind kinetic energy W i n d kinetic e n e r g y causes r o t a t i o n of c u p - w h e e l or p r o p e l l e r anemometers. The cup arms are supported by a vertical shaft and are insensitive to the wind direction; the propeller is continually oriented by a vane. The rotation is transformed into signal by means of photo choppers, contact switches, direct current generators (i.e. tachometers), or other systems. The threshold varies with the friction and the energy subtracted by the transducer: the photochopper does not subtract energy; the reed switch a very small amount; the tachometer a considerable one. This kind of anemometer has a low sensibility but is resistant to unfavourable environments and is reliable; for this reason it is typically used in synoptic meteorology and remote stations. Some miniature types are also used in micrometeorological studies for the dispersion of air pollution.

Cup anemometers are composed of three or four conical or hemispherical cups revolving about a vertical shaft. Originally, a four cup mounting was used, but the dynamic response of three cups is better, and the majority of instruments

364 follows this finding. The m a x i m u m torque produced by a single cup does not occur w h e n the wind blows directly into the concavity of the cup, but w h e n it forms an angle of about 45 ~. The output is essentially linear with constant wind speed up to about 30 m s -1 when the cup anemometer is calibrated in a wind tunnel but, in the field, with gusts and lulls, it overestimates the speed as the rotor is more sensitive to increasing than decreasing wind speed, so that it is practically

accelerated

during

fluctuating

wind

speeds

(Moses,

1968;

Ramachanddran, 1970; Hyson, 1972).

Propeller anemometers are composed of a propeller (or a windmill) which revolves about a pivoted horizontal shaft which is oriented into the direction from which the wind is blowing by vanes. The rate of rotation of the propeller is linearly proportional to the wind speed from 1 m s -1 up to 45 m s -1. The propeller responds in a different way as a function of the angle of attack, i.e. the angle between the axis of the anemometer and the wind direction, and indicates a lower wind speed when the angle of attack increases. As propellers are oriented by a vane, a fluctuating wind directions leads to an underestimate of the wind speed because the inertia of the system obliges the vane to smooth out and follow with delay the direction changes, and the angle of attack is generally different from zero. The inertia of the system is given not only by the friction and the distribution of the mass in the system, which dominates at low wind speed, but also by the moment of inertia of the blades under rotation, which dominates at high wind speed.

Fixed axis propellers should respond, to a good approximation, with a cosine law to the angle of attack. Only in this case they can be used to measure the orthogonal components of the wind vector (Camp et al., 1970; Horst, 1973). It should be noted that both cups and propeller blades are not symmetrical, w h e n observed d o w n w a r d s , on the same vertical. This means that rainfall impresses kinetic energy on initially motionless anemometers. On the contrary, rainfall slows d o w n the rotation at high wind speed, especially w h e n large droplets impact on the cups moving contrary to the wind field or on the uprising blades. Cups and propellers are generally made of metal in order to be rugged and resist to bad weather conditions, but thin aluminium or also plastic is often used to reduce the threshold. For low wind speed polycarbonate cups or foamed polystyrene propellers are used, with a threshold around 0.1 m s -1. Mechanical sensors cannot be employed for very low wind speed, i.e. below 0.1 m s -1.

Vanes can be flat or splayed, i.e. vanes composed of two divergent flat plates. Flat vanes offer the m i n i m u m resistance to the wind, whereas splayed vanes

365 increase the resistance to the wind and generate turbulence, and this helps the w i n d pressure to orient the vane. For this reason splayed vanes follow small changes in w i n d direction better than flat plates. However, the greater mass of these devices increases the inertia of the system which is unable to follow fast wind direction fluctuations. Flat vanes are preferred for micrometeorological and air pollution studies, splayed vanes for meteorological applications where the average wind direction is needed. The aerovane, i.e. the a e r o d y n a m i c shaped vane that seems an aircraft w i t h o u t wings, is very resistant but has a very high inertia due to both the distribution of mass (i.e. some 15% torque more than a flat vane with similar . physical dimensions) and the inertia m o m e n t of the rotating propeller. It operates as a low pass filter acting on the w i n d fluctuations and its use is appropriate only w h e n average values are needed.

Wind pressure Wind pressure is the physical principle on which the pressure tube (Pitot) or pressure-plate a n e m o m e t e r are based. The Pitot tube is based on the Bernoulli's law for m o v i n g airstreams, and consists in a m a n o m e t e r which measures the difference between the static and the dynamic pressure sampled at two orifices m a d e on the probe tube, made respectively in the stagnation point and where the wind field is unaffected. It is especially used into chimneys or in aeroplanes. The wind pressure is also used to orient wind vanes and measure the wind direction. The p r e s s u r e plate m e a s u r e s the deflection of a flat plate w h i c h is continually oriented along the wind direction by a vane. It was invented in the XVth century by Leonard and was used only in the past (Wildt anemometer). Wind turbulence, Reynolds stress and drag coefficient have been m e a s u r e d using a table-tennis ball as a sensor, pierced with a vertical metal axle whose tilting is measured with two orthogonal transducers (Smith, 1970).

Wind cooling power W i n d cooling p o w e r is used in hot wire or hot film a n e m o m e t r y . The principle is to measure the current required to keep constant the temperature of an overheated wire, or the change of temperature of a wire heated at constant current. As the wire is v e r y thin, the probe is very small, sensible and fast response, and is particularly suitable for microclimatic studies and to monitor low speed air m o v e m e n t s as well as short term fluctuations. The sensor is very fragile and m u s t be used with great care, and is more suitable for indoor studies.

366

Wind property of transmitting sounds The continuous-phase type sonic anemometer transmits across the path of interest a continuous beam of sonic energy; the phase of the received signal is compared with a fixed or reference phase. The pulse type sonic anemometer transmits sonic energy in bursts over the path of interest. Sonic pulses are transmitted

in opposite directions over the same path on each axis of

measurement.

Pulses travelling with the wind arrive sooner than those

travelling against the wind. The main advantages of this instrument are that it is linear and has a very fast response (i.e. a few milliseconds, so that it can respond to high frequency wind fluctuations), and has a very low threshold. This a n e m o m e t e r is particularly used in microphysical studies of the planetary boundary layer, e.g. to measure the exchanges of heat or momentum.

Wind property of transmitting light The Doppler effect is the change in the observed frequency of an (electromagnetic) wave due to relative motion of source and observer. Laser Doppler anemometry has developed different configurations. One of the most i m p o r t a n t is the differential Doppler or 'fringe' mode which concerns the interference fringe of two laser beams; suspended particles, transported by the air movement across the dark and light fringe pattern, determine the frequency of electric signals that are then processed to compute the airspeed. The velocity of the suspended particles causes a Doppler shift of the frequency of the light which is scattered and this is measured by a photo detector. In a relatively clean atmosphere, instruments need the introduction of tracer particles in the airstream. The main advantages are: direct method of measuring velocity leaving the flow undisturbed; very small sensing volume (e.g. a cube of 0.2 mm on a side); very high frequency (e.g. MHz) response, use for extremely low air speed. This system is expensive and is more suitable for scientific research than routine measurements.

12.1.2. Installing anemometers There

are

several

sources

of error

in wind

speed

and

direction

measurements, but the largest errors are due to the presence of the transducer which perturbs the wind field, or generates turbulence, or the presence of eddies generated by buildings, trees, or other obstacles; also the presence of the tower or the mast to which the instrument is attached cannot be neglected. Meteorological measurements of wind speed and direction are regulated by a normative which is extensively reported in many handbooks, and that can be

367 s u m m a r i s e d as follows. The anemometer should be placed on a mast at 10 m above the ground, over open, level terrain with no obstructions within 300 m. Obstacles, if any, should be at a distance not less than 10 times their height if they are u p w i n d , or 5 times if they are downwind. The aim is to observe the wind 'undisturbed', except for the action of the soil friction, i.e. the wind that an aeroplane experiences when is preparing to land or take-off. The same normative has been then applied for use in pollutant transport and dispersion. For pollution studies, the wind shear, i.e. the vertical change of wind speed and direction, is an important parameter. This vertical profile is obtained by installing some anemometers on a tower or tall mast, at heights increasing logarithmically from the soil. Also vertical profiles of the wind field are obtained launching pilot balloons and measuring their position with two theodolites at regular time intervals (e.g. every 15 s). The wind field is then calculated with trigonometry. 12.1.3. Measuring wind vector components

First of all, an anemometer measures the total amount of air masses that in the unit time is passed through the sensible part of the instrument,

supplying

part of its kinetic energy to the cups or propellers which are induced to rotate. The wind gustiness and the smaller scale turbulence oblige every air parcel to fly not in a straight line but with many vicious loops around the main direction. As a consequence, the space length computed by means of the integral ~u(t) dt, where u(t) is the instantaneous wind speed, is much greater than the real distance travelled by the air parcel from the sensor, and represented by the average wind vector. If this vector is needed to model the transport of pollutants, only three methods are appropriate, as follows. (i) To use a two component anemometer, which measures the two orthogonal vectors of the wind speed. The anemometer is composed of two tachometric generator transducers, mounted at right angle on a common mast. Each propeller measures the component of the wind which is parallel with is axis of rotation. Propellers have been studied in order to have a response to the wind angle which approximates the cosine law. When wind and propeller rotation reverse, also signal polarity reverses. The same principle is adopted for the so called U V W anemometer, which measures the three orthogonal wind vectors, U and V on the horizontal plane, and W along the vertical. The lateral and vertical fluctuations of the wind are important in micrometeorological investigations on the dispersion of airborne pollutants. (ii) To use a wind vane with a sine-cosine transducer supplied with a voltage

368 proportional to u(t). This method is much more convenient, but needs a special anemometer (Camuffo, 1976). This is substantially composed of a generating anemometer, e.g. a dynamo connected with the propellers (or the cups), which supplies an output proportional to u(t) and this output is used to feed the terminals of the sine-cosine potentiometer of the vane which measures the wind direction. This potentiometer has a continuous-rotation resistance element which varies with the sine function of the shaft rotation, and two independent brushes, spaced 90 ~ between them: consequently, one monitors sina(t) and the other sin(offt)+90 ~ = cosa(t), where o~(t) is the instantaneous wind direction. When the potentiometer is supplied with the tension u(t), the two potentiometer outputs

give respectively u(t) sina(t), u(t) cosa(t).

Continuous

resistance

elements, e.g. cermet, bi-film or conductive plastic should be preferred to wirewound ones, as the noise is reduced when the brushes oscillate following the wind fluctuations. Generating aerovanes are preferred, as they furnish only one compact and more strong instrument. The same result can be obtained also with ordinary anemometers by substituting the linear potentiometer with a sinecosine one and using the output of the airspeed transducer to supply the power to the potentiometer. (iii) To carry out a very frequent sampling of u(t) and a(t) and then compute per each instant the vector components u(t) sina(t), u(t) cosa(t). This method is less convenient, for it requires a huge amount of data to be monitored and processed, but can be made with ordinary anemometers.

12.1.4. Averaging wind direction Application of statistical formulae in meteorology needs particular care to avoid inappropriate calculations and misleading conclusions. For instance, during the first part of the summer nights in the plain of northern Italy, cold air flows from the mountain valleys on the southern lee of the Alps, and enter the plain, which is characterised by warmer and moister air masses. These cold tongues force the moist air of the plain to up rise generating local violent thunderstorms very similar to the thermoconvective ones which often occur in the early afternoon. By t h e way, beginning at midnight the meteorological observations of the day, some of these thunderstorms are apparently divided into two days and attributed half to the previous, and half to the next day, apparently increasing the frequency of occurrence. The above example helps to understand the behaviour of two air masses when they meet, when the physical nature is necessary to apply in a correct way the vector algebra. When two air masses meet, their dynamic state is represented

369 by two w i n d vectors, but in general the resultant is not the vector obtained as the algebraic s u m of the two original vectors. If the density of the two air masses is not the same, a frontal situation is generated and the denser one continues nearly unaffected its motion, whereas the lighter one slips above. It is useful to remember that a w i n d vane will always point a direction, with or w i t h o u t wind. When the w i n d drops, the vane remains oriented with the last direction. W h e n the average w i n d direction is c o m p u t e d , all the directions recorded in the absence of wind speed must be rejected. Another p r o b l e m occurs w h e n the mast or the vane shaft are not perfectly vertical. The distribution of the weight in a vane is not always balanced with the rotation axis passing across the centre of gravity of the vane. Out of balance, it shows a bias t o w a r d s the tilting direction, especially in presence of low w i n d speed or during calm. In climatology, the frequency d i s t r i b u t i o n makes m o r e sense than the arithmetic average represented by the

mean.

Consider e.g. the case of a coastal

site, with the sea breeze from east (90 ~) and the land breeze from west (270~ The distribution of the w i n d direction is bi-modal with two peaks at 90 ~ and 270 ~ whereas the mean gives the dominance of a non-existing w i n d from south (180~ However, although on the long term frequency distributions are necessarily used, in the short term of a sampling interval (e.g. 10 min), the w i n d is considered to oscillate a r o u n d a main direction, and an arithmetic average is used to c o m p u t e the m e a n value. A c o m m o n p r o b l e m , not statistical b u t technological, is averaging the w i n d direction with fluctuations in the n o r t h e r n sector. In fact, ordinary potentiometers present a discontinuity between 0 ~ and 360 ~ so that in the case the w i n d fluctuates symmetrically around north, averaging the data one obtains 180 ~, i.e. exactly the opposite direction. If recording is being performed in a strip chart recorder, the trace is a line going back and forth across the whole chart width. Several solutions have been devised to overcome this d r a w b a c k . Here only a few of them will be presented for their practical interest. Other original devices have been described elsewhere (Camuffo, 1979). The first system is composed of two identical potentiometers connected with the same vane, the first h a v i n g the range 0-360 ~, the second 180-540 ~ being assembled rotated of 180 ~, i.e. w h e n the b r u s h of the first one reaches the discontinuity 0-360 ~, the brush of the second is positioned in the m i d d l e of the second p o t e n t i o m e t e r , on the opposite side of the discontinuity. W h e n this happens, the o u t p u t is switched from the first potentiometer to the second one, so that continuity is ensured for 1 1/2 revolution. The range extension can also be p e r f o r m e d with only one potentiometer and an electronic translator, in order to

370 reduce friction and w i n d threshold. The range extension 0-540 ~ ensures continuity for most of the cases, except when the upper limit 540 ~ is reached and the output is switched to 180 ~ and as well as the lower limit 0 ~ is reached, and the output is switched to 360 ~. The second system (Camuffo and Denegri, 1976) can be applied to standard instruments, i.e. a vane coupled to an ordinary potentiometer and only one sliding contact. The principle is as follows. Suppose that the compass is divided into 100 parts, so that each one is represented by a two-digit number from 00 to 99. By s u m m i n g 1000 of these numbers, a five-digit number is obtained, and the first two figures represent the mean value within the above resolution. If three-digit numbers are used, and the first figure is considered as an index of periodicity, then the two figures following the first one in the sum of 1000 numbers, represent the mean value related to the compass card. The index of periodicity disappears if the first figure is neglected, even if has been used to compute the sum. In this example an index of periodicity from 0 to 2 can be used, which is sufficient to allow complete rotations of the wind vane during the averaging period; in practice only one extension is necessary in order to avoid the discontinuity around north. The method consists in adding or subtracting only one unit to the index, d e p e n d i n g whether the wind vane is arrived to the discontinuity rotating clockwise or counter clockwise, i. e. from west or from east. Actually, at the beginning, the index is put equal to 1 and becomes 0 or 2 during the addition. Therefore, when the wind is rotating from the direction labelled 9900, the c o r r e s p o n d i n g n u m b e r s are 199-200, without discontinuity. In our example,

making

potentiometer

1000 s a m p l i n g s equally distributed

discontinuity,

i.e.

199-200, the

total

around

the former

199500 is obtained.

Disregarding the first figure, and considering the last three as decimal values, the mean direction 99.5 is got. The resolution may be increased dividing the compass into 1000 parts. This principle can be applied to ordinary potentiometric wind vanes in two ways. The first is to supply the potentiometer with a fixed voltage and convert the brush output into digital numbers. These numbers, with the proper index, can be s u m m e d to obtain the mean value as explained. The second method is obtained with the help of a tension to frequency converter, and counting the pulses during the sampling interval. In this case, before conversion, the voltage applied to the terminals of the potentiometer must be a d d e d to the signal measured

at the b r u s h if this has m o v e d to the lower value across the

discontinuity, or subtracted for the opposite rotation. Another method is based on the principle that in climatology frequency

371 statistics are better than p e r f o r m i n g averages. On this ground, the i n s t a n t a n e o u s direction is m o n i t o r e d at regular time intervals, and after the s a m p l i n g time the p r e v a l e n t d i r e c t i o n is f o u n d as the m i d d l e of the sector w i t h the l a r g e s t population, i.e. w h e r e the m o d e is located; sometimes the m o d e is found looking at the frequency distribution.

12.1.5. Measuring wind variance Following the definition, the s t a n d a r d deviation ry0 of the w i n d direction can be m e a s u r e d as

ry0 -

~(~

0 '2) (n-l)

where

(12.1)

8' are the a n g u l a r w i n d fluctuations d e t e r m i n e d after a record of n

m e a s u r e m e n t s of 0(t), taken with very short s a m p l i n g time, for a certain time interval. The d e t e r m i n a t i o n of the variance, m a d e by m e a n s of the above m a t h e m a t i c a l definition of ry0 has a negative aspect: it needs a h u g e a m o u n t s of data, which should be recorded on a data logger having a very large capacity and, therefore, being expensive. For this reason other m e t h o d s m a y be preferred, and one of t h e m is here described (Camuffo, 1976). In general, f l u c t u a t i o n s are symmetrically

distributed

around

the m e a n

wind

direction

, a n d the

distribution function is fairly well approximated by a Gaussian. As a consequence, the third spectral m o m e n t of the fluctuations, called skewness, is zero. As 0 = <8> + O' a n d recalling the f o r m u l a for the s u m of angles in trigonometric functions, <sino> = < s i n ( < o > + 0 ' ) > = < s i n < o > cos0' + cos sin0'> = sin + cos <sin0'> = sin - sin

(12.2)

= +O')> - cosO' - sin sinO'> = cos - sin <sin0'> = cos<0> = cos

(12.3)

as sin<0'> = 0 in that the sine is an o d d function and the fluctuations are randomly distributed around 0 and < c o s 0 ' > Therefore,

1 for the s y m m e t r i c a l reason.

372 <sin 8> - - =

tan<0>

(12.4)

where the mean direction is related to the average values of the trigonometric functions sine and cosine. Also in the case of non symmetrical distribution of the fluctuations, i.e. near an obstacle or other disturbing factors, by expanding the sine function in MacLaurin series, i.e. <8'3>

sin<0'> = < 8 ' > -

3!

<8'5>

+

5~-

<8'7>

7~

+''"

(12.5)

it can be recognised that the error is very small, i.e. less than 1%. W h e n the fluctuations are randomly distributed, then the central m o m e n t s are 2n

<0'2n> = lx3x5x...x(2n-1) cr0

(12.6)

and substituting this equation in the MacLaurin expansion of cos0' in eq.(12.2) and eq.(12.3), 2

<sin0>

~ = cos<0'>

sin< 0'>

exp(- 2_?o)

(12.7)

and finally the variance of the wind fluctuations is obtained: 2

~ 0 - -2 In

<sin 8> sin<

0'

>

= -2 In

cos<0'>

(12.8)

so that the coefficient of dispersion can be simply obtained from average values m e a s u r e d with a sine cosine transducer, or c o m p u t i n g these trigonometric functions. 12.2. MEASURING INSIDE AIR MOTIONS In conservation studies the point of view is far from that of the w e a t h e r analysis: the interest is not focused on the unperturbed wind far from obstacles but on its interaction with the m o n u m e n t . On a free site the w i n d speed is a function of time only, v(t), but around a m o n u m e n t it is v(x, y, z, 0;t), as this variable changes point by point on the m o n u m e n t surface for the aerodynamic interactions and depends also upon the attack angle 8. This means that a standard

373 normative on the best m e t h o d of taking m e a s u r e m e n t s cannot be applied and field observations should be m a d e only after a p r e l i m i n a r y analysis of the problem, the site t o p o g r a p h y and m o n u m e n t geometry, in order to determine

why, what, where, when and how to measure. 12.2.1. Hot wire anemometry Observations of: low air speed, turbulence, thin airstream on a developing surface b o u n d a r y layer or thin airstream passing below a closed door, cannot be taken with ordinary mechanical anemometers (e.g. cup or propeller types), due to their elevated inertia and threshold, or for the unbalanced effect on the opposed cups or the i n h o m o g e n e o u s pressure distribution on the blades. Miniature hot wire (or film) a n e m o m e t r y responds (although not completely) to this d e m a n d and is extensively used for its simple use and low cost. The size of the sensor is of the order of one or few m m in length, and the diameter is of the order of 5 ~tm. The hot wire measures airspeeds above 10 cm s -1 and the time constant is of the order of 0.001 s. A lower threshold, i.e. 5 cm s -i, is obtained with a nickel thin film deposited by sputtering on a spherical glass sensor, with a diameter of 3 m m (Dantec, 1996). The relatively larger mass increases the time constant to 0.08 s and the overheating generates a convective motion which interferes with the air m o v e m e n t at low air speeds. This interference determines the lower limit of reliable measurements which is around 3 cm s -1 As a single wire responds to the velocity component perpendicular to it, a variety of probe exists, m o u n t e d either single, or coupled orthogonally in a plane or three-dimensionally, s u s p e n d e d between the tips of a fork-like support, for detecting one, two or three c o m p o n e n t s of the airstream. Some probes are inserted into a cylindrical shield (a tube) in order to m e a s u r e the s t r e a m component along the cylinder axis. However, the edges of the tube disturb the flow field and generate turbulence. It is convenient to remove this shield and insert the bare probe into the airstream, with the wire n o r m a l to the flow direction. The physical principle (DISA, 1976; Doebelin, 1990) is the thermal loss of a heated resistance sensor which is an overheated wire. The heat loss is not only dependent upon the air speed but also upon a number of parameters such as air temperature and pressure. If only the air speed changes, or the influence of the other parameters is compensated through the use of other sensors and suitable electronic units, the o u t p u t gives the air speed. The characteristic transfer function is in first approximation composed of an exponential and a square root function, but the signal can be linearised, so that the processed output is simply

374 proportional to the airspeed. Two different circuits are available for this kind of sensors: the constanttemperature and the constant-current anemometer. The c o n s t a n t - t e m p e r a t u r e type consists of a Wheatstone bridge and a servo amplifier and the sensor acts as active arm of the bridge. The current through the wire is adjusted to keep the wire temperature constant and is a measure of the flow velocity. The constantcurrent type has the sensor powered by a constant current supplied by a generator having high internal resistance in order to be independent of any resistance changes in the bridge. The wire attains a temperature which is in equilibrium with the convective heat loss due to the airstream. The heat generated is the product of the electrical resistance by the square of the current intensity, the wire temperature, and hence the airspeed is measured in terms of the electrical resistance. In practice, the constant-temperature anemometers are preferable and are effectively popular for their easy use, fast response and low cost. 12.2.2. Sonic anemometry The velocity of a sonic wave in a medium is known and depends upon the elastic properties of the medium. When a sonic wave is superimposed upon an air stream, its transmission speed is equal to the sum of the velocity of the sound with respect to the medium, plus the velocity of the medium. Sonic pulses are transmitted

in opposite directions over the same path on each axis of

measurement. The pulses are exchanged between two miniature piezoelectric transducers which are used to alternatively transmit and receive, and the sonic anemometer measures the average value of the speed of propagation of these pulses. The measurement is representative of the average airflow which crosses a cylinder, i.e. the sonic beam having the cross section determined by the transducer size and the path length L equal to the transducers spacing. The space resolution is determined by the transducer size (typically of the order of 1 cm diameter) and the value of L which varies with the model, e.g. 15 cm, 40 cm. However, the higher the space resolution, the greater the perturbation caused by the transducers to the fluid motion. The operating principle (Beaubien and Bisberg, 1968) is that the sound wave transmitted in still, or moving air, introduces a time lag which depends upon the air speed and direction. The first equation which governs the operating principle is the definition of the velocity C of sound which propagates in still air, i.e.

1

C = "~[

T M

(12.9)

375 where 7 is the ratio between the specific heats at constant pressure and volume, and M the molecular mass of the gas. At T - 273K, the speed in the air is 33,145 cm s -1. Therefore, a sonic a n e m o m e t e r is always associated with a precise t h e r m o m e t e r w h o s e m e a s u r e m e n t s are necessary to enter the formulae and compute the sonic velocity. However, also the elevate presence of moisture may cause d e p a r t u r e s to the m e a s u r e m e n t s increasing the sonic speed. As water v a p o u r has a mass noticeably different from the other gases constituting the atmosphere, the following empirical equation holds for humid air

C = 2006.7

e

T (1 + 0.3192~ )

(cm s -1)

(12.10)

w h e r e e is the water v a p o u r pressure and p the atmospheric pressure. The variable vapour pressure is a source of error and the m a x i m u m error is found in s u m m e r ; e.g. at T = 303 K and RH = 70%, e = 30 hPa and this variation is equivalent to 0.3~

shift in air temperature. The error is smaller in the cold

season. When the airstream is moving at the speed u and with an angle 0 with reference to the transducer alignment, the sonic anemometer measures the speed component u cos0 by means of the sonic transit time At which is given by

At =

2L u cos0 u2

(12.11)

ca(I-v)

which is the basic equation for sonic anemometry. The main interest for the sonic anemometer is that it has no threshold and is a totally passive instrument, which does not interfere with the fluid motion, except for the presence of the transducers which can generate turbulence. The experimental array can be composed of only one, two or three axes, each having a pair of aligned transducers, depending upon the n u m b e r of dimensions that should be taken into account. For the above reasons the measurements are not so punctual as with a hot wire, and cannot go close to a surface as a hot wire, but these goals are much better attained with a laser-Doppler anemometer.

12.2.3. Laser-Doppler anemometry The laser Doppler anemometry is based on the well k n o w n principle that a

376 moving source emitting or reflecting a wave generates a frequency shift. A number of different configurations exist, but the mostly used is the differential Doppler, also called fringe mode. The air is transparent to laser light, but a number of reflecting particles introduced in the airflow may diffuse light, introducing a Doppler shift generated by their movement. By crossing two coherent light beams having plane wave fronts (i.e. two laser beams generated by the same source), an interference fringe is generated in the crossing area. The fringe spacing is proportional to the wavelength of the light )v and inversely proportional to the angle 20 between the two beams. A particle moving in the intersection of the two beams will scatter light whose intensity will vary according to the intensity pattern of the light as determined by the brightness of the interference fringe. The frequency of the light scattered by the particles transported by the airflow is characterised by a Doppler shift generated by the velocity of the particles. A photomultiplier detects these variations and the frequency of the resulting signal is determined from the Doppler analysis (Durst et al., 1981). The frequency f of the electric signal generated by a particle moving across the fringe volume with a velocity component u normal to the fringes is u

f=2

sin0 )v

(12.12)

so that for a typical wavelength and 0 = 30 ~ f is of the order of 105 Hz (Doebelin, 1990). The method is more sensitive when the fringe pattern is perpendicular to the airflow, and for this reason the fringe can be rotated to obtain the highest sensitivity (and find the flow direction), or to obtain the two components of the velocity vector in the plane parallel to the surface. This method is very accurate as the interference fringe area can be very small (i.e. with size of the order of a tenth of millimetre) and can be sited very close to the surface, or in contact with the surface, i.e. within the internal boundary layer which forms on the surface. This is the only instrument able to measure air motions very close to a surface and is potentially very useful for s t u d y i n g air-surface interactions and aerodynamic deposition. Another important advantage is that the measure is direct, the flow remaining undisturbed by measurement, without needing the introduction of solid probes or mobile items into the flow. The response is immediate. The negative aspects are substantially three. The first is that the air must be seeded with tracers, i.e. particles that may deposit on the surface, soiling and damaging it. The second is that the introduction of these tracers near the surface

377 perturbs the natural dynamic equilibrium under investigation. Last but not least, these devices are very expensive. 12.2.4. A simple analysis of atmospheric turbulence

Several approaches exist to study the atmospheric turbulence, and several books have been written on this subject, e.g. Sutton (1960), Pasquill (1962, 1974), Lumley and Panofsky (1964), Tennekes and Lumley (1973), C s a n a d y (1980), Vinnichenko et al. (1980), N e w s t a d t et van Dop (1984), Landahl and MolloChristensen (1986), Clifford et al. (1993) and many others exist on the statistical analysis of time series. However, it may be useful to report some notes on a statistical m e t h o d that was originally introduced by Rice (1944; 1945) for the telephone r a n d o m noise and then adapted by some oceanographers (Cartwright and Longuett-Higgins, 1956; Longuett-Higgins 1957; 1962; Kinsman, 1965) to the analysis of the sea waves. The results can be applied to the a t m o s p h e r i c turbulence, as the instrumental records of the instantaneous sea level and the wind speed are very similar: the average sea level is substituted by the mean wind speed and the fluctuating waves by the eddies. Although the theory is quite complex, the application is very simple, and needs only counting the n u m b e r of times the signal crosses the mean level, and the total number of fluctuations. It gives the mean airspeed, average period of eddies, the modes of the gusts and the lulls, the spectral width parameter, the first three even spectral moments. The zero-crossing period is defined as the average period ~:(0) for which a sensor placed at the average sea level (which is a s s u m e d as zero level) is alternatively submersed by waves and then emerged, and is expressed as r(O) = Ti/N(O) where Ti is the observing time interval and N(O) represents the n u m b e r of times that the waves have exceeded the calm sea level. In the same way the

crossing period ~:(r/) is defined as well as the number of crossings N(rl) for any arbitrary level 7/, i.e.:

r(rl) -

Ti

N(O) - "c(O)- N(ll) N(ll)

(12.13)

and the m e a n zero-crossing frequency F(O), or the 7/ level frequency F(rl), are obviously defined as the inverse of ~:(0) and ~:(,/), respectively. To apply this statistical method to our case, some obvious substitutions are required: the eddy turbulence for the waves; the airspeed or wind direction for the sea level; the mode of the instantaneous air velocity or direction for the average sea level. If mo is the zero-order moment, i.e. the standard deviation of the wave

378

height, the second order moment of the spectrum is m2 = mo (2rr f(O)) 2. The plot of the distribution N(rl) versus r/(Fig.12.1) is bell shaped with the m a x i m u m at N(O), and the standard deviation can be graphically obtained by measuring the half of the segment which intercepts the plot of N(r/) at the frequency level "~N(O) = 0.607 N(O). Please note that the maximum at N(O), i.e. the mode, is determined as a first approximation, being conditioned by the choice of the crossing levels, the resolution being the step between two levels. The distribution

N(rl) lies between two limit distributions, i.e. the symmetric Gaussian one 7"/2 N(71) = N(O) exp(-2-~o)

(12.14)

for a wide-band spectrum, i.e. random components, and the asymmetric Rayleigh distribution

N(n) = N(O)

mo

7-/2 exp(-~-G--)

(12.15)

for a narrow-band spectrum, i.e. when the spectrum is sharply peaked around a definite frequency. Cartwright and Longuett-Higgins (1956) found a general analytical expression for the distribution of any shape of spectrum, given by the probability distribution Pr(~) of the maxima between the levels r/and rl + 6r/ 1

~2

co

~2

PF(~) = ~ [ e x p ( - 2 - ~ 2) + ~ql-l;2exp(--~ -) fexp(-~)dx]

(12.16)

-oo

where m = (~/~)~ 1-~2. The transition from the two limit distributions (Gaussian and Rayleigh) is determined by the value of the spectral width parameter ~ which ranges from 0 and 1 and is defined by the 0th, 2nd and 4th order moments, 2 mo m4 - m2 mo m4

(12.17/

The Gaussian distribution is obtained with ~ = 1 and the Rayleigh one with a = 0. The above authors demonstrated that the value of e can be simply determined by counting the number of the zero crossings and the number of maxima Nm which have occurred in the same interval, i.e.

379

0,8

0,6

olml

0,4

r~

0

0,2

0

imP"9

v

9

l

0

,

!

10

'

'

u

30

20

1-

40

Velocity (cm/s) Fig.12.1 Normalised crossing frequency of the velocity levels 0, 2, 4, 6.... c m / s in an internal boundary layer along a wall. The distribution is skew, being slowed down by entertainment of calm air.

0,4 I 0,2

rO

~ t~

-0,2

0

-0,4

-0,6

I 0

.

. . 10

.

. 20

.

. 30

40

Velocity .(cm/s)

Fig.12.2 Plot of the incremental values N(Th) - N(11i-1), i.e. the number of times the speed has exceeded the velocity level rM but not the level rli, plotted versus the airspeed.

380 ~/

N(O)2

~=

1-

(12.18)

2

Nm and in addition the mean frequency of the zero crossings F(O) and the mean frequency of the maxima F(max), are linked with the even moments as follows

lq

F (O) - ~ j ~

mo

lqm4

F (m ax ) = T i - X [ ~

m---2

(12.19)

The graphs of the incremental values N ( r l i ) - N(rli-1), i.e. the number of times the fluctuations (originally: the waves) have exceeded the level r/i-1 but not the level r/i, plotted versus 77 are more or less symmetrical with reference to the origin and are characterised by two peaks, one positive and one negative (Fig.12.2). The intercept between

the line 0 crossings increment

(which

corresponds to the maximum of the crossing frequency) with the plot gives a better approximation of the mode. The peaks provide a useful information about the distribution of the fluctuations which recur most frequently, i.e. the mode of the gusts and the lulls. The method simply requires to count the number of times some arbitrarily chosen

levels of speed

(or some directions) have been crossed by the

instantaneous wind speed (or direction) and the number of maxima of this i n d e p e n d e n t variable during the same observing interval. There are two operational procedures: (i) to measure continually or to sample with a high frequency the variable, and the arbitrary crossing levels can be chosen after the measurement, by subdividing in equal intervals the range of variability of the measured variable; (ii) to select the crossing levels before the measurement, and simply record the number of crossings and the number of maxima. The former method requires to store a huge amount of data and the memory of the recording instrument should have an elevated capacity. The latter requires a special device, or a data acquisition system programmed to this aim; the advantage is that a much more smaller memory capacity is sufficient, and the data processing is much simpler. By the way, this is a further method to measure the time distribution of the wind direction, based on the principle of dividing the compass in a number of equally spaced directions, and counting the number of times these directions have been crossed, which avoids the problem of averaging a r o u n d discontinuity 0-360 ~.

the

381

C H A P T E R 13

Measuring Rainfall and Windborne Droplets

Precipitation is defined as a hydrometeor made up of an aggregate of aqueous particles, liquid or solid, crystallised or amorphous, which fall from a cloud or a group of clouds and reach the ground (WMO, 1966). This definition, which is the most accredited one, includes drizzle, rain, shower, snow, sleet and hail, but does not include dew, rime, hoar frost and mist because: they form for direct condensation or sublimation, they are not associated with a cloud and, finally, they do not fall. However, these latter h y d r o m e t e o r s are s o m e t i m e s found included, as e.g. (WMO, 1983) or are called occult precipitation. The first obvious, but never sufficiently remembered consideration, is that precipitation is not h o m o g e n e o u s l y distributed in time and space, but is a variable amount of water or ice which falls as a consequence of the type of cloud, its past and present history (which determines the droplets or ice crystals size), the cloud vertical development, transit speed and path. C u m u l u s clouds develop vertically, with strong convective currents in the interior, which make faster the growth of droplets or hail, and in this case the precipitation occurs abruptly and violently, forming patches which displace with the cloud passage and w i n d transport. On the other hand, stratus clouds spread horizontally, are rather u n i f o r m and s u p p l y droplets more regularly, with a m o r e h o m o g e n e o u s distribution in time and space. A rain gauge sited below the centre of a cumulus cloud w h e n it is passing, or one collecting rainfall w h e n the w i n d aloft drops, will m e a s u r e a precipitation a m o u n t m u c h greater than other gauges sited in different places nearby, so that rainfall can vary significantly over distances of a few kilometres or less. The same occurs for the passage of fronts. With stratus clouds the departures are much smaller and measurements are representative of a more general phenomenon.

382 13.1. METEOROLOGICAL PRECIPITATION MEASUREMENTS Although weather data are not directly useful to evaluate the total a m o u n t of water fallen on monuments, they are in any case representative of the climate in which m o n u m e n t live, and constitute an environmental information that is useful in u n d e r s t a n d i n g the causes of the m o n u m e n t decay in their natural context. In meteorology, precipitation gauges (UK Meteorological Office, 1981; WMO, 1983; 1984; 1986; 1994) are used to monitor the precipitation that has fallen in a given time interval or to monitor the instantaneous rate of fall. The gauges are m a d e of a collecting receiver in the form of a funnel, with a horizontal circular aperture of known size, and the collected water is then measured in one of the following ways. (i) The tipping bucket rain recorder is based on a bucket divided into two equal compartments,

mounted

on a spindle in the m i d d l e

(Fig.13.1). The two

water inlet pipe

tipping bucket

l!iii

i

iil

i iii iiiiii

@ @

................I iiii iii iii i i~ii ii iiiii

Fig.13.1 Mechanism of the tilting bucket rain gauge transducer

c o m p a r t m e n t s are symmetrically disposed so that the bucket is balanced in unstable equilibrium about a horizontal axis. In its normal position it rests against one of the two stops, which prevent it tipping over completely. Rain

383

flowing out of the funnel falls into the uppermost compartment and w h e n has filled it, the centre of gravity is displaced and the bucket overbalances, tips and empties

the precipitation.

This p i v o t i n g m o v e m e n t

displaces the second

compartment in the uppermost position in which it receives the rainwater until is filled and tips discharging the water in it. Counting with a magnetic reedswitch the n u m b e r of tips, it is possible to know the amount of water that has been collected and discharged. Of course, this method does n o t s u p p l y a continuous record, but only proceeds by counting increments of precipitation with resolution 0.2 mm. An error is due for the rainfall lost during the time employed in the tipping motion, which m a y be appreciable during heavy precipitation. The time of the very beginning and ending of drizzle or very light rain cannot be accurately measured. N o t w i t h s t a n d i n g these limits, this kind of gauge is the most convenient and popularly used as it is the most suitable for recording rainfall automatically with an electronic datalogger. (ii) The

float type, w i t h a u t o m a t i c s i p h o n i n g a r r a n g e m e n t s , r e c o r d s the

movement of a light float in a float chamber which receives the rain collected by the funnel. The float is connected with a pen which registers on a d r u m or a strip chart the level, i.e. the rainfall amount. When the chamber is full of water a natural, or a tilting siphon system, makes water to flow out of the float chamber until the level falls to the zero level; the siphoning action ceases, and the cycle starts again. Some rainfall is lost during the siphoning action. This type is used in the British Isles. (iii) The

weighing type operates by recording the total Weight of the water

collected in a can. The weight of the collecting can is recorded continuously, either by means of a spring mechanism (e.g. the can descends against the compression of a spring) or the displacement of a weight. This system is accurate and continuous, but normally it has no provisions for emptying itself. This is used in cold climates where it is desired to record either snow, hail or rainfall, and the solid precipitation does not have to be melted in order to be measured. In mild or w a r m climates evaporation losses are reduced by adding oil to form a film 1 m m thick over the free water surface in the container. In regions where snow or sleet are common, automatic measurements are possible only with gauges provided of a heater to melt ice and measure it as liquid water. If the funnel is not heated, surface condensation such as dew, hoar frost, rime and also fog can provide some water, which is neither rainfall, nor

384 strictly precipitation, but the gauge interprets and measures it in the same way. In the case of hail, the bouncing of hailstones on the funnel causes an important loss of ice precipitated. A number of other causes of error can be found in measuring precipitation, and the minor ones are: evaporation, which may contribute for-1% of the total and may be also more important in hot regions; droplets adhesion, i.e. -0.5%; colour, -0.5%; funnel inclination, -0.5%; large droplets splashing, +1%, with a total error -1.5%. However, the main error is due to exposure, and this error cannot be exactly evaluated. The World Meteorological Organisation suggests that the amount of precipitation collected by a rain gauge may be 3 to 30% less than the actual precipitation reaching the ground (WMO, 1981) and the UK Meteorological Office suggests a much wider range, i.e. 5 to 80% less (UK Meteorological Office, 1981). Such a large error is especially made when the wind is strong, and the droplets tend to be transported parallel to the horizontal plane of the funnel mouth and the turbulence generated near the funnel may disperse the droplets loosing them and decreasing the collection efficiency. This effect becomes especially important with snow-flakes that are more sensitive to wind transport and departures in the wind field. In order to minimise the effect on the wind field disturbance, the site should be chosen accurately, which should be actually representative of the area u n d e r consideration. To this aim the gauge should be free of o v e r h a n g i n g obstructions. If the area has vegetation, this should be uniformly distributed, and the funnel should be at the average height of the vegetation. Some appropriate fence structures could be installed to homogenise the area characteristics. Wind shields are suggested around the gauge orifice to shelter it from high wind speed parallel to the mouth, generating an appropriate turbulence. These shields are built with metal strips forming a truncated cone with the vertex pointing at the base of the gauge, but leaving some free space between strip and strip. The gauge should be at a sufficient distance from obstacles to avoid local eddies. In order to avoid interferences with the wind field, the m i n i m u m distance allowable for obstructions should be twice their height. Sometimes a greater distance is suggested, e.g. the WMO report No 266 (1984) suggests four times their height. Observation of precipitation using radar or satellite remote sensing are used for general weather purposes, but are not of interest for m o n u m e n t preservation, except in the case of forecast and alert for large and important storm systems. However, also in this case the attention is focused in the civil protection, and not in undertaking safety measures for monuments.

385 13.2. PRECIPITATION ON MONUMENTS Standard weather m e a s u r e m e n t s are taken in the u n d i s t u r b e d ,

open

country, and the precipitation is not the same than in towns. Towns are generally warmer and the higher temperature generates convective motions which favour the formation of clouds; the turbulence induced by buildings exchanges momentum and mixing with the effect of slowing down the wind field, making colder the lower layers and transporting heat aloft; traffic and domestic heating are a source of pollutants which act as condensation nuclei. All these factors contribute to increase the frequency of precipitation, and in particular with showers and thunderstorms over the large towns. It has been demonstrated that the precipitation over towns is greater than over the surrounding country, and that the average frequency of precipitation in working days is higher than during Saturday and Sunday (Landsberg, 1981). Weather measurements are not much representative of the rainfall which has fallen on monuments located in the centre of a town, where the situation is complicated by the shielding of buildings, the street channelling of the wind field, or m a n y other aerodynamic disturbances. In addition, metal domes or also wetted buildings may generate strong anomalies in the electric field in the presence of charged clouds. As the water molecule is a dipole, droplets may be charged by induction and attracted. In addition, all the droplets and aerosols formed by raindrop splashing are charged and their behaviour depends upon the wind drag, gravity force and electric field. Weather measurements are representative of the undisturbed rainfall. On monuments, the rainfall intensity is relevant because intense rainfall is more effective in washing the surface and in causing erosion. This situation totally changes in windward and leeward surfaces. The airflow and the electric field may reduce the precipitation in one place and increase it in another. Weather observations

are representative

of the water fallen into a

horizontal circular aperture, whereas monuments mainly have a vertical extent, and the number of raindrops intercepted by the monument varies with the wind speed, direction and local aerodynamic disturbance. For this reason vertical collectors are sometimes used in proximity of a monument surface, and they are representative only of the rainfall that hits a vertical surface having their particular orientation in the specific point where they are located. No normative exists for these methods or other similar experiments. Another possibility is to collect the water flowing down the monument and

386 measure it, if the m o n u m e n t is not constituted of a porous material which absorbs water. In any case the run-off is sometimes collected in order to perform chemical analyses on leached ions and dissolved stone. A third method, based on standard instruments, is to collect precipitation on the horizontal plane with a recording rain gauge and associate the measurement with the wind speed and direction. As the trajectory of a falling raindrop is determined by the combined action of the falling velocity (Fig.13.2) and wind drag, the impact on a vertical surface can be calculated once the droplet diameter and the wind speed are known. Unfortunately, there are not easy methods to measure the droplet diameter, and only approximate evaluations can be made with a crude estimate of the drop diameter and the other variables.

10 or3

8

-~ 6 @

4 2 ,

0

!

1

,

i

2

,

!

3

'

!

'

4

i

5

|

!

,

6

7

Drop Diameter (mm)

Fig.13.2 Terminal velocity of free falling droplets. (Source: Houghton, 1985)

However, even in the case of a successful tentative of knowing the rainfall which crosses a vertical plane, this result can be hardly applied to the actual case of a true surface, although with a very simple geometry, e.g. the facade of a building. In fact, in the case of a calculation of raindrops crossing a vertical plane, there is no interference between the chosen area and the wind; in the actual case of a building surface, the wind field is perturbed by the architectural shape and, consequently, the horizontal drag changes as well as the resulting path of raindrops. For instance, the top part of the building is hit by raindrops that have been dragged till the last few seconds by a wind stream that is passed nearly

387 undisturbed above the obstacle; the lower part is hit by droplets that in the last part of their path have been dragged by an air stream travelling not against the surface, but parallel to it, so that the droplets are deviated laterally and dispersed, and those which reach the surface for their inertia are only a very small fraction. This is the reason w h y the upper side of buildings is generally washed out better than the lower one (Fig.13.3). In the case of a m o n u m e n t the situation is also worse, as the more complex shape and all the local changes in the surface relief, orientation and so on make extremely difficult to evaluate the interactions with raindrops and run-off.

Fig.13.3 The efficiency of windborne droplets in washing the top of monuments is evident at the Colosseum, Rome. The upper part is washed out by rainfall, whereas in the intermediate and lower part, dust and soot accumulate.

The run-off on historical buildings was measured in several occasions and in a number of ways, either collecting directly running water into a funnel placed under an edge, or building simple devices to this aim. For instance, Leysen et al. (1989) placed longitudinally against the wall of the Mechelen Cathedral a plastic cylinder with a longitudinal slit 3 cm wide, with the lower edge firmly fixed against the wall. The running water was collected into the cylinder and flowed through a hole in the bottom and a tube, arriving into a plastic bottle to be taken

388 away and analysed in the laboratory. The same authors used also gutters pressed against the wall to collect water running off the cathedral walls, i.e. 'runoff water' and 'washout water' with different content of eroded material, arriving at a r o u g h estimate of the annual material loss and surface recession rate.

13.3. WET AND DRY DEPOSITION SAMPLERS It is evident that m o n u m e n t s react with the chemical substances which deposit on them and not with the gases and particles which are simply suspended in the atmosphere. Most gases and aerosols may remain in the a t m o s p h e r e because they have a very low deposition rate, so that a measurement in the air is useful for studies on health (in fact lungs p u m p and filter air with s u s p e n d e d pollution), but not for m o n u m e n t decay. For this reason, the ! so called wet-anddry deposition sampler has been invented to measure, separately, the acid rain and the airborne particles which deposit on a horizontal surface d u r i n g dry periods. Some slightly different devices have been invented (e.g. Georgii and Pankrath, 1982; Munn and Rodhe, 1985), but the most widespread type consist in two equal buckets, made of glass, plastic (e.g. PVC, polyethylene), stainless steel or other non reactive materials, one to collect dry deposition and one for the wet one, with only one lid, which is alternatively displaced over the dry or the wet bucket, driven by a rainfall sensor. The rainfall sensor is constituted of a resistance sensor with several parallel unshielded metal resistors which are t r a n s f o r m e d in a short circuit by rainwater; another c o m m o n sensor is a capacitive one, where absorbed water changes the dielectric capacity in a condenser; another system is to interrupt an IR beam emitted by a diode, but several other possibilities exist. After a week, or another chosen time interval, it is possible to pick up the two buckets and analyse separately the content of the dry bucket, i.e. dust and particles, and the acid rain collected in the wet one. This device is obviously located in an open area, far from obstacles or pollution sources. The collection vessels are equipped with an external metal ring with needles, or crossed wires, in order to avoid that birds can land and stay on the funnel edge and contaminate the sample with their droppings. This crude device has been largely used in the last two decades, but presents several problems, as follows. Although the lid is over the wet bucket during the sunshine, the bucket becomes hot and some water evaporates, changing the p H of the wet sample. In addition, condensation nuclei, dust (especially Saharan dust

389

in Europe) or other solid particles fallen with the rainfall may eventually dissolve and buffer the solution changing the pH and the ionic composition. Real-time measurements automatically carried out during the precipitation event are preferable (Camuffo et al., 1984; 1988; Camuffo, 1990). Also biological life, especially algae, may develop in the rainwater perturbing the chemical equilibrium. The w e t / d r y sensor which displaces the lid is not very fast and is provided of a selected lag to confirm the signal and avoid false alarms; therefore the dry bucket receives the very first rain droplets, which often are the most polluted ones. A problem is that the d r y / w e t sensor may respond also to dew, frost and fog, inappropriately opening the cover of the wet bucket and collecting there, for many hours, especially during the night-time, the dry deposition. It is not clear what the dry bucket collects. Substantially, it gather in the bottom all the coarse particles which deposit via gravitational settling, and in the outer and inner surface it attracts the charged particles that are driven by the electric field generated by the bucket when it is hit by solar radiation or is rubbed by the wind friction. In sunny days the bucket is always heated by solar radiation; it becomes hot and thermophoresis tends to w e a k l y counteract the other deposition mechanisms. For this reason the bucket interacts with the suspended particles with a variable selective action on the deposition mechanisms. In any case, the dry deposit which is collected with this method is in some way representative of the coarse and giant particles, i.e. the so called dustfall, which accumulates on the upward horizontal surface of monument and is mainly composed of soot, dust, pollens, fibres). This is very different from the measurement of the suspended particulate matter performed with high-volume samplers which are composed of filter, motor blower and flow meter. The latter measurement practically samples all the suspended particles which are larger than the average aerodynamic size of the filter pores, independently these particles will later deposit or not. A simpler, earlier version of the wet-and-dry deposition sampler is the so called bulk precipitation sampler constituted of only one funnel and precipitation collector which remains uncovered for the whole sampling period, collecting whatever is depositing, either in the dry or the wet phase. This instrument is intended to monitor the deposit which forms on a monument, or a plant, irrespective of approximation being without hot climates or

the distinction between the dry or the wet phase. However, the is very crude and the representativity uncertain. In addition, automatic cover, the evaporation loss may be very important in dry periods. Likethe dry collector of the wet-and-dry sampler, the

390 bulk sampler m a y be contaminated by local dust, which m a y significantly alter the

pH.

Although this method had some success in the past, the data are vague

and difficult to interpret. This kind of information is very difficult to obtain, and f u r t h e r research is n e e d e d monitoring.

to devise a reliable i n s t r u m e n t for a u t o m a t i c

391

References CHAPTER 1

1.1. Theory and general applications Maunder, W.J., 1994: Dictionary of Global Climate Change. UCL Press, London, 257 pp. Michalski, L., Eckersdorf, K. and McGee, J., 1991: Temperature Measurement. Wiley, New York, 514 pp. Porges, F., 1995: HVAC Engineer's Handbook. Butterworth Heinemann, Oxford, 278 pp. Rosenhow, W.M., Hartnett, J.P., and Ganic', E.N., 1985: Handbook of Heat Transfer Applications, Mc Graw-Hill, New York. Saint-Gobain, 1977: Manuale Tecnico del Vetro. Fabbrica Pisana, Milano, 331 pp. Touloukian Y.S. and DeWitt D.P., 1972: Thermal Radiative Properties of Nonmetallic Solids. Thermophysical Properties of Matter, Vol.8. IFI/Plenum, New York.

1.2. Applications to conservation Benoist, L., 1960: Musdes et Musdologie. Presses Universitaires de France, Paris, 128 pp. Bernardi, A., Camuffo, D., Del Monte, M., and Sabbioni, C., 1985: Microclimate and Weathering of an Historical Building: the Ducal Palace in Urbino. Science Total Environment, 46, 243-260. Bernardi, A. and Camuffo, D., 1995a: Uffizi Gallery in Florence: a Comparison between two Different Air Conditioning Systems. Science and Technology for Cultural Heritage 4,2, 1122. Bernardi, A. and Camuffo, D., 1995b: Microclimate in the Chiericati Palace Municipal Museum, Vicenza. Museum Management and Curatorship, 14, 5-18. Camuffo, D., 1981: Hot-Horse Anemometry. Atmospheric Environment, 15, 1767. Camuffo, D., 1983: Indoor Dynamic Climatology: Investigations on the Interactions between Walls and Indoor Environment. Atmospheric Environment, 17, 1803-1809. Camuffo, D., 1986: Deterioration Processes of Historical Buildings, pp. 189-221 in: T. Schneider (ed.): Acidification and its Policy Implications, Elsevier, Amsterdam. Camuffo, D., 1991: Environment and Microclimate; pp. 37-50 in: N. Baer, C. Sabbioni and A. Sors (ed.s): Science Technology and European Cultural Heritage Butterworth, Oxford. Camuffo, D., 1994: Effects of Air Pollution on Historic Buildings and Monuments. Scientific Basis for Conservation: Case Studies in the Deterioration of Stone Monuments in Italy. European Cultural Heritage Newsletter on Research, 8,1, 7-15. Camuffo, D. and Bernardi, A., 1986: Dinamica del microclima e scambi termoigrometrici tra pareti e atmosfera interna nella Cappella Sistina. Bollettino dei Monumenti, Musei e Gallerie Pontificie, 6, 211-257. Camuffo, D. and Bernardi, A., 1988: Microclimate and Interactions between Atmosphere and the Orvieto Cathedral. Science Total Environment, 68, 1-10. Camuffo, D. and Bernardi, A., 1991a: The microclimate of Leonardo's "Last Supper"; joint edition European Cultural Heritage Newsletter on Research, and Bollettino Geofisico, special issue, 14, 3, 1-123. Camuffo, D. and Bernardi, A., 1991b: Indoor and Outdoor Microclimate: the Trajan Column and Sistine Chapel; pp. 295-305 in: N. Baer, C. Sabbioni and A. Sors (editors): Science Technology and European Cultural Heritage Butterworth, Oxford. Camuffo, D. and Bernardi, A., 1993: Microclimatic Factors affecting the Trajan Column. Science Total Environment, 128, 227-255. Camuffo, D. and Bernardi, A., 1995a: The Microclimate of the Sistine Chapel, Joint edition European Cultural Heritage Newsletter on Research, 9, 7-32 and Bollettino Geofisico, 18 (2) 7-32.

392 Camuffo, D. and Bernardi, A., 1995b: Study of the Microclimate of the Giant Hall of the Da Carrara's Royal Palace, Padova. Studies in Conservation, 40, 237-249. Camuffo, D. and Bernardi, A., 1996: Deposition of Urban Pollution on the Ara Pacis, Rome. Science Total Environment, 189/190, 235-245. Camuffo, D. and Bernardi, A., 1997: Controlling the Microclimate and the Particulate Matter inside the Historic Anatomic Theatre, Padova. Museum Management and Curatorship, 15, 285-298. Camuffo, D. and Schenal, P., 1982: Microclima all'interno della Cappella degli Scrovegni: scambi termodinamici tra gli affreschi e l'ambiente, pp. 107-209 in: Ministero dei Beni Culturali ed Ambientali: Giotto a Padova, special issue of Bollettino d'Arte, Poligrafico dello Stato, Rome. Camuffo, D., Sturaro, G. Valentino, A., Gattolin, M., Enzi, S., and Bernardi, A., 1996: Analisi del Microclima e delle interazioni ambiente-manufatto per la conservazione della Torre di Pisa. Report to Consorzio della Torre di Pisa, Pisa. Camuffo, D., Vincenzi, S. and Pilan, L., 1984: A First-Order Analysis of the Heat Wave in the Soil. Water, Air and Soil Pollution, 23, 441-454. De Guichen, G., 1984: Climate in Museums. ICCROM, Rome. Jamiolkowski, M., 1995: Leaning Tower of Pisa - Description of the Behaviour, pp. 203-226 in: F. Zezza (ed.): The Conservation Project: Knowledge of the Functional Elements for the Planning of the Interventions and Geotechnical Aspects of the Protection. Community of Mediterranean Universities, Adda, Bari. Jenkins, K.A. and Smith, B.J., 1990: Daytime Rock Surface Temperature Variability and Its Implications for Mechanical Rock Weathering: Tenerife, Canary Islands. Catena, 17, 449-459. Michalski, S., 1993: Relative Humidity: a Discussion of Correct/Incorrect Values. ICOM Committeee for Conservation,, 336.C. Padfield, T., 1994: Role of Standards and Guidelines, pp. 191-199 in W.E. Krumbein, P. Brimblecombe, D.E. Cosgrove and S. Stainforth (ed.s): Durability and Change, Wiley, New York, 307 pp. Smith, B.J., 1978: The Origin and Geomorphic Implications of Cliff Foot Recesses and Tafoni on Limestone Hamadas in the Northwest Sahara. Z. Geomorph. N.F. 22 (1), 21-43. Veniale, F., 1995: Minerali costituenti le rocce: processi e sequenze di alterazione, pp. 11- 32 in: R.A. Lef6vre (ed.): La pietra dei monumenti nel suo ambiente fisico. Istituto Poligrafico e Zecca dello Stato, Rome. Warscheid, T. and Krumbein, W.E., 1996: Biodeterioration of Inorganic Nonmetallic Materials - General Aspects and Selected Cases, pp. 273-295 in: E. Heitz, W. Sand and H.C. Flemming (ed.s): Microbiatly Induced Corrosion of Materials. Springer Verlag, New York. Warke, P.A. and Smith, B.J., 1994: Short Term Rock Temperature Fluctuations under Simulated Hot Desert Conditions: Some Preliminary Data, pp. 57-70 in: D.A. Robinson and R.B.G. Williams (ed.s): Rock Weathering and Landform Evolution, Wiley, New York. CHAPTER 2

2.1. Theory and general applications Fermi, E., 1958: Termodinamica. Boringhieri, Torino, 179 pp. Giordano, G., 1993: Tecnica delle costruzioni in legno. Hoepli, Milano, 826 pp. Jones, D.A., 1996: Principles and prevention of Corrosion. Prentice Hall, Upper Saddle River, N.J., 572 pp. Plank, M., 1926: Treatise on Thermodynamics, Dover, New York, 297 pp. Summit, R. and Slicker, A., 1980: Handbook of Material Science, Vol. IV: Wood. CRC Press, Boca Raton, Florida, 459 pp.

393

2.2. Applications to conservation Bernardi, A. and Camuffo, D., 1995: Uffizi Gallery in Florence: a Comparison between two Different Air Conditioning Systems. Science and Technology for Cultural Heritage 4,2, 1122. Coped6, M., 1991: La carta e il suo degrado. Nardini, Florence, 165 pp. Laurenzi Tabasso, M. and Marabelli, M., 1992: II degrado dei monumenti in Roma in rapporto all'inquinamento atmosferico. Betagamma, Viterbo, 169 pp. Massari, G., 1959: Risanamento igienico dei locali umidi. Hoepli, Milan, 437 pp. Massari, G., 1971: Batiments humides et insalubres - Pratique de leur assainissement. Eyrolles, Paris, 526 pp. Massari, G., 1977: Humidity in monuments. ICCROM, Rome, 47 pp. Newton, R. and Davison, S., 1989: Conservation of Glass. Butterworths, London, 322 pp. Padfield, T., 1994: Role of Standards and Guidelines, pp. 191-199 in W.E. Krumbein, P. Brimblecombe, D.E. Cosgrove and S. Stainforth (ed.s): Durability and Change, Wiley, New York, 307 pp. Richardson, B.A., 1993: Wood Preservation. E & FN Spon (Chapman & Hall), London, 226 PP. Thomson, G., 1986: The Museum Environment. Butterworths, London, 293 pp. Warscheid, T. and Kuroczkin, J., 1997: Biodeterioration of Stones, in Studies in Museology, Biodeterioration of Cultural Properties, ed. R.J. Koestler and A.E. Charola. ButterworthHeinemann, London, in press.

2.3. Books consulted for the definitions of the meteorological variables in this and the next chapter Harrison, L.P., 1965: Fundamental Concepts and Definitions Relating to Humidity, pp. 3-69 in: A. Wexler (editor): Humidity and Moisture, Measurement and Control in Science and Industry, Vol 3: Fundamentals and Standards. Rehinold, New York. Huschke, R.E., 1959: Glossary of Meteorology. American Meteorological Society, Boston, 638 PP. List, R.J., 1971: Smithsonian Meteorological Tables. Smithsonian Institution, Washington DC, 527 pp. Parker, S.P., 1988: Meteorology Source Book. McGraw-Hill, New York, 304 pp. Saucier, W.J., 1989: Principles of Meteorological Analysis, Dover, New York, 438 pp. UK Meteorological Office, 1991: Meteorological Glossary. HMSO, London, 335 pp. World Meteorological Organization, 1966: International Meteorological Vocabulary. WMO N.182, Geneva, 276 pp. World Meteorological Organization, 1987: International Cloud Atlas, Vol.II. WMO, Geneva, 212 pp. CHAPTER 3

3.1. Theory and general applications Goody, R., 1995: Principles of Atmospheric Physics and Chemistry. Oxford University, New York, 324 pp. Kasahara, A., 1974: Various Vertical Coordinate Systems Used for Numerical Weather Prediction. Monthly Weather Review, 102, 509-522.

3.2 Further reading Belinski, V.A., 1948: Dynamic Meteorology. Ogiz, Moscow, 591 pp. Brutsaert, W.H., 1982: Evaporation in the Atmosphere. Reidel, Dordrecht, 299 pp. Byers, H.R., 1974-General Meteorology, McGraw-Hill, New York, 461 pp.

394 Haltiner, G.J. and Martin, F.L., 1957: Dynamical and Physical Meteorology. McGraw-Hill, New York, 454 pp. Houghton, D.D., 1985: Handbook of Applied Meteorology. Wiley, New York, 1461 pp. Iribarne, J.V. and Godson, W.L., 1981: Atmospheric Thermodynamics. Reidel, Dordrecht, 259 PP. Matveev, L.T., 1967: Physics of the Atmosphere. Israel Program for Scientific Translations, Jerusalem, 699 pp. Petterssen, S., 1956: Weather Analysis and Forecasting, Vol.II. McGraw-Hill, New York, 265 PP. CHAPTER 4

4.1. Theory and general applications Andrews, J.E., Brimblecombe, P., Jickells, T.D. and Liss, P.S., 1996: An Introduction to Environmental Chemistry. Blackwell, Oxford, 209 pp. Born, M., 1952: Atomic Physics. Blackie & Son, London, 437 pp. Einstein, A., 1905: Ueber einen die Erzegung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, Annalen der Physik, 17, 132-148. Kondratyev, Ya, 1969: Radiation in the Atmosphere. Academic Press, New York, 912 pp. Robinson, N., 1966: Solar Radiation, Elsevier, Amsterdam, 347 pp. Varshneya, A.K., 1994: Fundamentals of Inorganic Glasses. Academic Press, Boston, 570 pp.

4.2. Applications to conservation Bernardi, A. and Vincenzi, S., 1994: Diurnal Variation of Solar Radiation on Differently Orientated Surfaces of Monuments. Nuovo Cimento 17C (4), 431-442. Camuffo, D. and Bernardi, A., 1991: The microclimate of Leonardo's "Last Supper"; joint edition European Cultural Heritage Newsletter on Research, and Bollettino Geofisico, special issue, 14 (3), 1-123. Camuffo, D. and Bernardi, A., 1986: Dinamica del microclima e scambi termoigrometrici tra pareti e atmosfera interna nella Cappella Sistina. Bollettino dei Monumenti, Musei e Gallerie Pontificie, 6, 211-257. Ortega-Calvo, J.J., Hernandez-Marine, M. and Saiz-Jimenez, C., 1991: Biodeterioration of Building Materials by Cyanobacteria and Algae. International Biodeterioration 28, 165186. Vittori, O. and Mestitz, A., 1975: Artistic Purposes of some Features of Corrosion on the Golden Horses of Venice. Burlington Magazine, 864 (98), 132-139. Warscheid, T. and Kuroczkin, J., 1997: Biodeterioration of Stones, in: R.J. Koestler and A.E. Charola (ed.s): Studies in Museology, Biodeterioration of Cultural Properties. ButtherworthHeinemann, Oxford (in print). Wypych, G., 1995: Handbook of Material Weathering. Chem Tec, Toronto, 564 pp.

4.3. Further reading Liou, K.N., 1980: An Introduction to Atmospheric Radiation. Academic Press, San Diego, 392 PP. Liou, K.N., 1992: Radiation and Cloud Processes in the Atmosphere. Oxford University Press, New York, 487 pp. List, R.J., 1971: Smithsonian Meteorological Tables. Smithsonian Institution, Washington DC, 527 pp. Platridge, G.W. and Platt, C.M.R., 1976: Radiative Processes in Meteorology and Climatology. Elsevier, Amsterdam, 318 pp.

395 CHAPTER 5

5.1. Theory and general applications Adamson, A. W., 1986: A Textbook of Physical Chemistry, Academic Press, San Diego 972 pp. Brunauer, S., 1945: The Adsorption of Gases and Vapors. Princeton University Press, Princeton, 511 pp. Byers, H.R., 1959: General Meteorology. McGraw-Hill, New York, 461 pp. Byers, H.R., 1965: Elements of Cloud Physics. University of Chicago Press, Chicago, 191 pp. Camuffo, D., 1984: Condensation-Evaporation Cycles in Pore and Capillary Systems According to the Kelvin Model. Water, Air and Soil Pollution, 21, 151-159. Clifford, J., 1981: Properties of Water in Capillary and Thin Films, in F. Franks (ed.): Water, a Comprehensive Treatise, Vol.5, Water in Disperse Systems. Plenum, New York, 366 pp. Everett, D.H., 1961: The Thermodynamics of Frost Damage to Porous Solids. Trans. Faraday Soc., 57, 1541-1551. Fagerlund, G., 1973: Determinations of Pore-Size Distribution from Freezing Point Depression, Materiaux et Constructions, 6, 215-225. Gregg, S.J. and Sing, K.S.W., 1967: Adsorption, Surface Area and Porosity, Academic Press, London, 371 pp. Iribarne, J.V. and Godson, W.L., 1986: Atmospheric Thermodynamics. Reidel, Dordrecht, 259 PP. Kikoin, A. and Kikoin, I., 1978: Molecular Physics, Mir, Moscow, 480 pp. Madonna, L.A., Sciulli, C.M., Canjar, L.N. and Pound, G.M., 1961: Low Temperature Cloud Chamner Studies on Water Vapour, Proc. Phys. Soc. 78, 1218-1222. Mason, B.J., 1951: Spontaneous Condensation of Water vapour in Expansion Chamber Experiments, Proc. Phys. Soc. B64, 773-779. Mason, B.J., 1971: The Physics of Clouds, Clarendon Press, Oxford, 671 pp. Matveev, L.T., 1984: Cloud Dynamics, Reidel, Dordrecht, 340 pp. Matveev, A.N., 1985: Molecular Physics, Mir, Moscow, 448 pp. Mikhail, R.S. and Robens, E., 1983: Microstructure and Thermal Analysis of Solid Surfaces, Wiley, New York, 496 pp. Pruppacher, H.R. and Klett, J.D., 1980: Microphysics of Clouds and Precipitation. Reidel, Dordrecht, 714 pp. Sedunov, Yu.S., 1974: Physics of Drop Formation in the Atmosphere, Wiley, New York, 234 pp. Sivuchin, D.V., 1986: Corso di Fisica Generale, Vol.2, Mir, Moscow, 583 pp. Thomson, W. (Lord Kelvin), 1870: On the Equilibrium of Vapour at a Curved Surface of Liquid. Proc. Roy. Soc. Edinburgh, 7, 63-69. Weast, R.C., 1985 CRC Handbook of Chemistry and Physics 1985-86, 66th ed., CRC Press, Boca Raton, Florida, pp.D213-D214. Wright, H.L., 1936: The Size of Atmospheric Nuclei: Some Deductions from Measurements of the Number of Charged and Uncharged Nuclei at Kew Observatory. Proc. Phys. Soc. 48, 675-699. Young, K.C., 1993: MicrophysicaI Processes in Clouds. Oxford University Press, New York, 427 PP.

5.2. Applications to conservation Biscontin, G., Driussi, G., Maravelaki, P. and Zendri, E., 1993: Physico-Chemical Investigations of Stone Architectonic Surfaces in Venice: the Scuola Grande dei Carmini; pp. 125-136 in G. Biscontin and L. Graziano (ed.s): Conservation of Architectural Surfaces: Stones and Wall Covering. I1 Cardo, Venice. Camuffo, D., 1988: Surface Moisture and Conservation. European Cultural Heritage Newsletter on Research, 2,5, 6-10.

396 De Quervain, F., 1967: Technische Gesteinskunde. 2 Aufl. Min. Geotechn. Reihe, Bd 1, Birkh~iuser Verlag, Basel. DIN 66131, 1973: Bestimmung der spezifischen Oberfl~iche von Festoffen durch Gasadsorption nach Brunauer, Emmett und Teller (BET), Grundlagen. Fitzner, B., 1994: Porosity Properties and Weathering Behaviour of Natural Stones, pp. 43-54 in F. Zezza (ed.): Stone Material in Monuments: Diagnosis and Conservation, 2nd International Corurse on Monument Conservation, Adda, Bari, 222 pp. Ginell, W.S., 1994: The Nature of Changes Caused by Physical Factors, pp. 81-94 in W.E. Krumbein, P. Brimblecombe, D.E. Cosgrove and S. Stainforth (ed.s): Durability and Change, Wiley, New York, 307 pp. Graedel, T.E., 1994: Mechanisms of Chemical Change in Metals Exposed to the Atmosphere, pp. 95-105 in W.E. Krumbein, P. Brimblecombe, D.E. Cosgrove and S. Stainforth (ed.s): Durability and Change, Wiley, New York, 307 pp. Klopfer, H., 1985: Feuchte, in Lutz et al., Lehrbuch der Bauphysik; 265-434 and 628-635 (Lit.). Teubner, Stuttgart. Jeannette, D., 1997: Structures de porosit6, m6canismes de transfert des solution et principales alt6rations des monuments, pp. 49-77 in: R.A. Lef6vre (ed.): La pietra dei monumenti in ambiente fisico e culturale, European University Centre for Cultural Heritage, Ravello. Laurenzi Tabasso, M. and Marabelli, M., 1992: II degrado dei monumenti a Roma in rapporto all'inquinamento atmosferico. Betagamma, Viterbo, 169 pp. Torraca, G., 1981: Porous Building Materials. ICCROM, Rome. 141 pp. Torraca, G., 1994: Physical Condition. A Primary Factor in the Durability of Stone, pp. 52-57 in F. Zezza (ed.): Stone Material in Monuments: Diagnosis and Conservation, 2nd International Corurse on Monument Conservation, Adda, Bari, 222 pp. Waller, R., 1992: Temperature- and Humidity-Sensitive Mineralogical and Petrological Specimens, pp. 25-50 in F.M. Howie (ed.): The Care and Conservation of Geological Material: Minerals, Rocks, Meteorites and Lunar Finds. Butterworth Heinemann, Oxford. Warscheid, T., Becker, T.W., Braams, J., Gehrmann, C., Krumbein, W.E. and Petersen, K., 1993: Studies on the Temporal Development of Microbial Infection of Different Types of Sedimentary Rocks and Its Effects on the Alteration of the Physico-Chemical Properties in Building Materials, pp. 303-310 in M.J. Thiel (ed.): Proceedings of the International RILEM/UNESCO Congress "Conservation of Stone and Other Materials" Vol.l: Causes of Disorders and Diagnosis, E&FN Spon, London. Wendler, E., 1997: New Materials and Approaches for Conservation, pp. 181-196 in N.S. Baer and R. Snethlage (ed.s):Saving Our Architectural Heritage: The Conservation of Historic Stoine Structures. Wiley, Chichester. Winkler, E.M., 1986: A Durability Index for Stone. Bull. Assoc. Engin. Geol. 23, 344-347. CHAPTER 6

6.1. Theory and general applications Adamson, A. W., 1986: A Textbook of Physical Chemistry, Academic Press, San Diego 972 pp. Blanchard, D.C. and Woodcock, A.H., 1980: The Production, Concentration, and Vertical Distribution of the Sea-Salt Aerosol, pp. 330-347 in T.J. Kneip and P.J. Lioy (Eds.): Aerosols: Anthropogenic and Natural, Sources and Transport, Annals of the New York Academy of Sciences, Vol. 338, New York, 618 pp. Brimblecombe, P., 1987: The Big Smoke. Methuen, London, 185 pp. Brimblecombe, P., 1992: History. of Atmospheric Acidity, pp. 267-304 in M. Radojevic and R.M. Harrison (Eds.): Atmospheric Acidity, Elsevier, London. Brimblecombe, P., 1995: History of Air Pollution, pp. 1-18 in H.B. Singh (Ed.): Composition, Chemistry and Climate of the Atmosphere. Van Nostrand Rehinold, New York.

397 Camuffo, D., 1984: Condensation-Evaporation Cycles in Pore and Capillary Systems According to the Kelvin Model. Water, Air and Soil Pollution, 21, 151-159. Camuffo, D., 1990: Acidic Precipitation Research in Italy, pp 229-265 in: A.H.M. Bresser and W. Salomons (eds): Acidic Precipitation Vol.5, Springer Verlag, New York. Camuffo, D. and Enzi, S., 1995: Impact of Clouds of Volcanic Aerosols in Italy in the past Centuries. Natural Hazards, 11, 135-161. Dullen, F.A.L., 1979: Porous Media. Fluid Transport and Structure. Academic Press, New York. 396 pp. Gordon, J. and MacDonald, F., 1953: Anhydrite-Gypsum Equilibrium Relations. American Journal of Science, 251, 884-898. Kireev, V., 1977: Physical Chemistry. Mir, Moscow, 572 pp. Price, C. and Brimblecombe, P., 1994: Preventing Salt Damage in Porous Materials, pp.90-93 in Proc. Preventive Conservation, Ottawa. Prodi, F. and Fea, G., 1979: A Case of Transport and Deposition of Saharan Dust over the Italian Peninsula and Southern Europe. J. Geoph. Res. 84, 6951-6960. 6.2. Applications to conservation Arnold, A., 1983: Determination of Mineral salts from Monuments. Studies in Conservation, 29, 129-138. Arnold, A. and Zehnder, K., 1990: Salt Weathering on Monuments. pp. 31-58 in F. Zezza (ed.): The Conservation of Monuments in the Mediterranean Basin. Grafo, Bari. Arnold, A. and Zehnder, K., 1991: Monitoring Wall Paintings Affected by Soluble Salts, pp. 103-135 in S. Cather (ed.): The Conservation od Wall Paintings, Paul Getty TrUst, Thien Wah Press, Singapore. Beadecker, P.A. and Reddy, M.M., 1993: The Erosion of Carbonate Stone by Acid Rain. Journal Chemical Education, 70 (3), 104-108. Becker, T.W., Krumbein, W.E., Warscheid, T. and Resende, M.A., 1994: Investigations into Microbiology, pp. 147-190, in H.K. Bianchi (ed.): IDEAS - Investigations into Devices against Environmental Attack on Stones. GKSS-Forschungszentrum, Geesthacht (F.R.G.). Bernardi, A., Camuffo, D., Del Monte, M. and Sabbioni, C., 1985: Microclimate and Weathering of a Historical Building: the Ducal Palace in Urbino, Science Total Environment, 46, 243-260. Camuffo, D., 1984: The Influence of Run-Off in Weathering of Monuments. Atmospheric Environment, 18, 2273-2275. Camuffo, D., 1986: Deterioration Processes of Historical Monuments, pp. 189-221 in: T. Schneider (ed.): Acidification and its Policy Implication, Elsevier, Amsterdam. Camuffo, D., 1991a: Aspetti microfisici delle precipitazioni acide in relazione al degrado dei monumenti, pp 339-350 in L. Morselli (ed.): Deposizioni acide, i precursori, l'interazione con l'ambiente e i materiati, Maggioli Editore, Rimini. Camuffo, D., 1991b: Environment and Microclimate; pp. 37-50 in: N.S. Baer, C. Sabbioni and A.I. Sors (ed.): Science, Technology and European Cultural Heritage, ButterworthHeinemann, London. Camuffo, D., 1992: Acid Rain and Deterioration of Monuments: How Old Is the Phenomenon? Atmospheric Environment, 26B, 241-247. Camuffo, D., 1994: Aspetti meteorologici e microclimatici nel degrado dei materiali lapidei. Accademia Nazionale dei Lincei, Contributi del Centro Linceo Interdisciplinare ~Beniamino Segre~, 88, 9-27. Camuffo, D., 1995: Physical Weathering of Stones. Science Total Environment, 167, 1-14. Camuffo, D., Del Monte, M. and Ongaro, A., 1984: The pH of Atmospheric Precipitation in Venice, Related to both the Dynamics of Precipitation Events and the Weathering of Monuments. Science Total Environment, 40, 125-139. Camuffo, D., Del Monte, M. and Sabbioni, C., 1987: Influenza delle precipitazioni e della condensazione sul degrado superficiale dei monumenti in marmo e calcare, pp 15-36 in:

398 Ministero dei Beni Culturali ed Ambientali: "Materiali Lapidei", special issue of Bollettino

d'Arte, Poligrafico dello Stato, Rome. Camuffo, D., Del Monte, M., Sabbioni, C. and Vittori, O., 1982: Wetting, Deterioration and Visual Features of Stone Surfaces in an Urban Area. Atmospheric Environment, 16, 2253-2259. Camuffo, D. and Valcher, S., 1986: A Dew Point Signaller for Conservation of Works of Art. Environmental Monitoring and Assessment, 6, 165-170. Del Monte, M. and Sabbioni, C., 1980: Authigenic Dolomite on Marble Surface. Nature, 228, 350-351. Del Monte, M. and Sabbioni, C., 1984a: Morphology and Mineralogy of Fly Ash from a CoalFlueded Power Plant. Arch. Met. Geoph. Bioclim., 35, 93-104. Del Monte, M., Marcazzan, G.M., Sabbioni, C. and Ventura, A., 1984b: Morphological, Physical and Chemical Characterisation of Particles Emitted by a Coal-Fired Power Plant. J. Aerosol Sci. 15, 325-327. Gummerson, R.J., Hall, C. and Hoff, W.D., 1980: Water Movement in Porous Building Materials - II Hydraulic Suction and Sorptivity of Brick and Other Masonry Materials. Building and Environment, 15, 101-108. Hall, C., 1981: Water Movement in Porous Building Materials - IV The Initial Surface Absorption and the Sorptivity. Building and Environment, 16, 201-207. Padfield, T., 1995-97: An Introduction to the Physics of the Museum Environment. Natural Museum, Danmark, published in the website http://www.natmus.min.dk/cons/tp. Sabbioni, C., Zappia, G., Gobbi, G. and Pauri, M.G., 1993: Deterioration of Ancient and Modern Buildings Materials Due to Environmental Factors, pp. 235-242 in: C.A. Brebbia and R.J.B Frewer (ed.s): Structural Repair and Maintenance of Historical Buildings. Computational Mechanics Publications, Southampton. Saiz-Jimenez, C., 1995: Microbial Melanins in Stone Monuments. Science Total Environment 167, 273-286. Warscheid, T. and Kuroczkin, J., 1997: Biodeterioration of Stones, in: R.J. Koestler and A.E. Charola (ed.s): Studies in Museology, Biodeterioration of Cultural Properties. ButtherworthHeinemann, London. (in print). Warscheid, T., Oelting., M. and Krumbein, W.E., 1991: Physico-Chemical Aspects of Biodeterioration Processes on Rocks with Special Regard to Organic Pollution. International Biodeterioration 28, 37-48. Winkler, E.M., 1994: Stone in Architecture. Springer Verlag, Berlin, 313 pp. Wittenburg, C., 1994: Trokene Schadgas- und Partkeldeposition auf vershiedenen Sandsteinvariet~iten unter besonderer Ber~icksichtigung atmosph~irischer Einftut~gr6t~en. PhD Thesis, Hamburg. CHAPTER 7

7.1. Theory and general applications Anfossi, D., Bacci, P., Giraud, C., Longhetto, A. and Piano, A., 1976: Meteorological Surveys at La Spezia Site. In A. Longhetto (ed.): Atmospheric Pollution, Elsevier, Amsterdam, 531-54. Berlyland, M.E., 1991: Prediction and Regulation of Air Pollution. Kluwer, Dordrecht, 312 PP. Brimblecombe, P., 1987: The Big Smoke, Methuen, London, 185 pp. Brown, R.A., 1991: Fluid Mechanics of the Atmosphere, Academic Press, San Diego, 486 PP. Camuffo, D., 1980: Fog and Related Diffusion Potential at Venice: Two Case Studies. Boundary Layer Meteorology, 18, 453-471. Camuffo, D., 1981b: Fluctuations in Wind Direction at Venice, Related to the Origin of the Air Masses. Atmospheric Environment, 15, 1543-1551.

399 Camuffo, D., 1984: Anlysis of the series of precipitation at Padova, Italy, Climatic Change, 6, pp.57-77. Camuffo, D., 1990: Clima e uomo. Garzanti, Milano, 207 pp. Camuffo, D. and Bernardi, A., 1982: The Diurnal Trend in Surface Mixing Ratio at Padova, Italy. Boundary Layer Meteorology, 22, 273-282. Camuffo, D. and Bernardi, A., 1982: An Observational Study of Heat Fluxes and their Relationships with Net Radiation. Boundary Layer Meteorology, 23, 359-368. Camuffo, D., Bernardi, A. and Bacci, P., 1982: Computing the Flux of Moisture from Net Radiation and Soil Wetness. Boundary Layer Meteorology, 22, 503-510. Camuffo, D. and Zardini, F., 1996: Controlling the Homogeneity of a Long Meteorological Series: the Series of Padova (1725-today), 12 pp. in: Subba Rao (editor): Applications of Time Seriesfor Meteorology and Astronomy, Chapman & Hall, London (in print). Cayan, D.R. and Douglas, A.V., 1984: Urban Influences on Surface Temperatures in Southwestern United States during Recent Decades. J. Clim. Appl. Meteorol., 23, 1520-1530. Deacon, E.L., 1949: Vertical Diffusion in the Lowest Layers of the Atmosphere. Quart J. Roy. Meteor. Soc., 75, 89-103. Dobbins, R.A., 1979: Atmospheric Motion and Air Pollution. Wiley, New York, 323 pp. Echols, W.T. and Wagner, N.K., 1972: Sourface Roughness and Internal Boundary Layer near a Coastline. J. Appl. Meteor., 11, 658-662. Elliot, W.P., 1958: The Growth of the Atmospheric Internal Boundary Layer. Trans. Amer. Geophys. Union, 39, 1948-1954. Gifford, F.A., 1961: Uses of Routine Meteorological Observations for Estimations of Atmospheric Dispersion. Nuclear Safety, 2, 47-51. Gifford, F.A., 1976: Turbulent Diffusion Typing Schemes: a Review. Nuclear Safety, 17, 68-86. H6gstr6m, U., 1964: An Experimental Study on Atmospheric Diffusion. Tellus, 16 (2), 205-251. Jones, P.D., Raper, S.C.B., Bradley, R.S., Diaz, H.F., Kelly, P.M. and Wigley, T.M.L., 1986: Northern Hemisphere Surface Air Temperature Variations: 1851-1984. J. Climate Appl. Meteorol., 25, 161-179. Landsberg, H.E., 1981: The Urban Climate. Academic Press, New York, 275 pp. Lee, D.O., 1992: Urban Warming? - An Analysis of Recent Trends in London's Heat Island. Weather, 47 (2), 50-56. Lumley, J.L. and Panofsky, H.A., 1964: The Structure of Atmospheric Turbulence. Interscience, New York, 239 pp. Mc Elroy, J.L., 1969: A Comparative Study of Urban and Rural Diffusion. J. Appl. Meteor., 8, 19-31. Mc Vehil, G.E., 1964: Wind and Temperature Profiles near the Ground in Stable Stratification. Quart. J.Roy. Meteor. Soc., 90, 136-146. Monin, A.S. and Obukov, A.M., 1953: Dimensionless Characteristics of Turbulence in the Layer of Atmosphere near the Ground. Doklady Akademii Nauk SSSR, 93, 257-267. Munn, R.E., 1966: Descriptive Micrometeorology, Academic Press, New York, 245 pp. Munn, R.E. and Rodhe, H., 1985: Compendium of Meteorology Vol.II, Part 6 - Air Chemistry and Air Pollution Meteorology. World Meteorological Organisation, WMO No.364, Geneva, 209 pp. Panofsky, H.A. and Townsend, A.A., 1964: Change of Terrain Roughness and the Wind Profile. Quart. J. Roy. Meteor. Soc., 90, 147-155. Pasquill, F., 1961: The Estimation of the Dispersion of Windborne Material. Meteorological Magazine, 90, 33-49. Pasquill, F., 1962: Atmospheric Diffusion, first ed., Van Nostrand, London, 297 pp. Pasquill, F., 1974: Atmospheric Diffusion, second ed., Wiley, New York, 429 pp. Plate, E.J., 1982: Engineering Meteorology. Elsevier, Amsterdam, 740 pp.

400

Richardson, L.F., 1920: Some Measurements of Atmospheric Turbulence. Phil. Trans. Roy. Soc., London, Ser A, 221, 1-28. Schlicting, H., 1955: Boundary Layer Theory, NewYork, Mc Graw-Hill, 535 pp. Simiu, E. and Scanlan, R.H., 1986: Wind Effects on Structures. Wiley, New York, 589 pp. Singer, I.A. and Smith, M.E., 1953: Relation of Gustiness to Other Meteorological Parameters. Journal of Meteorol., 10, 121-126. Smith, F.B., 1972: A Schema for Estimating the Vertical Dispersion of a Plume from a Source near Ground Level. In NATO/CCMS Proceedings of the 3rd Meeting of the Expert Panel on air pollution modeling, Tech. Report N. 14, XVII, 1-14. Smith, M., 1970: Recommended Guidefor the Prediction of the Dispersion of Airborne Effluents. American Soc. Mechanical Engineers, New York. 85 pp. Sutton, O.G., 1947: The Theoretical Distribution of Airborne Pollution from Factory Chimneys. Quart. J. Roy. Meteor. Soc., 73, 426-436. Turner, D.B., 1964: A Diffusion Model for an Urban Area. J. Appl. Meteor., 3 (1), 83-91 Van Der Hoven, I., 1967: Atmospheric Transport and Diffusion at Coastal Sites. Nuclear Safety, 490-499.

7.2. Applications to conservation Camuffo, D., 1981a: Hot-Horse Anemometry. Atmospheric Environment, 15, 1767. Camuffo, D., 1993: Reconstructing the Climate and the Air Pollution of Ancient Rome During the Life of the Trajan Column. Science Total Environ. 128, 205-226. Camuffo, D. and Bernardi, A., 1993: Microclimatic Factors affecting the Trajan Column. Science Total Environ., 128, 227-255. Camuffo, D., Vincenzi, S. and Pilan, L., 1984: A First-Order Analysis of the Heat Wave in the Soil. Water, Air Soil Pollution, 23, 441-454. Camuffo, D. and Vincenzi, S., 1985: Computing the Energy Balance of a Statue of Bronze: the San Marco's Horses as a Case Study. Science Total Environ., 44, 147158. CHAPTER 8

8.1. Theory and general applications Bagnold, R.A., 1941: The Physics of Blown Sand and Desert Dunes, Chapman and Hall, London (3rd ed.1984). Barndorff-Nielsen, O.E. and Willetts, B.B., 1991: Aeolian Grain Transport, 1: Mechanics, 2: The Erosional Environment. Acta Mechanica Supplementums 1 and 2, SpringerVerlag, Wien. Bouma, P.J., 1947: Physical Aspects of Colour. Philips Gloeilampenfabrieken, Eindhoven, 312 pp. Buffle, J. and Van Leeuwen, H.P., 1992: Environmental Particles. Lewis, Boca Ration, Vol.I: 554 p., Vol.II: 426 pp. Cadle, R., 1965: Particle Size, Theory and Industrial Applications. Reinhold, New York, 158 PP. Caporaloni, M., Tampieri, F., Trombetti, F. and Vittori, O., 1975: Transfer of Particles in Nonisotropic Air Turbulence, J. Atmos. Sciences, 32, 565-568. Chandrasekhar, S., 1943: Stochastics Problems in Physics and Astronomy. Rev. Modern Phys., 15 (1), 2-89. Einstein, A., 1905: Uber die von der molekularischen Theorie der W~irme gefordete Bewegung, von in ruhenden Fltissigkeiten suspendierten Teilchen. Ann. d. Physik 17, 549-560. This and other related papers have been translated and reprinted in A. Einstein, 1956: Investigations on the Theory of the Brownian Movement, edited with notes by R. Ftirth, Dover, New York, 119 pp.

401 Epstein, P.S., 1924: On the Resistance Experienced by Spheres in their Motion through Gases. Phys. Rev. 23, 710-733. Fletcher, B., 1976: The Incipient Motion of Granular Materials. J. Phys. D: Appl. Phys., 9, 2471-2478. Friedlander, S.K., 1977: Smoke, Dust and Haze. Wiley, New York, 317 pp. Gillette, D., 1980: Major Contributions of Natural Primary Continental Aerosols: Source Mechanisms, pp. 348-358 in T.J. Kneip and J. Lioy (ed.s): Aerosols: Anthropogenic and Natural, Sources and Transport. New York Academy of Sciences, New York, 618 PP. Goldsmith, P., Delafield, H.J. and Cox, L.C., 1963: The Role of Diffusiophoresis in the Scavenging of Radioactive Particles from the Atmosphere. Q. J. R. Met. Soc. 89, 43. Hidy, G.M., 1984: Aerosols, an Industrial and Environmental Science. Academic Press, San Diego, 774 pp. Hidy, G.M. and Brock, J.R., 1970: The Dynamics of Aerocolloidal Systems. Pergamon, Oxford Hidy, G.M. and Brock, J.R., 1972: Topics in Current Aerosol Research. Pergamon, Oxford, 384 pp. Hicks, S.B.B., 1982: Wet and Dry Surface Deposition of Air Pollutants and their Modeling, pp. 183-196 in: N.S. Baer (ed.): Conservation of Historic Stone Buildings and Monuments, National Academy Press, Washington D.C., 365 pp. Hinds, W.C., 1982: Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles. Wiley, New York, 424 pp. Isachenko, V.P., Osipova, V.A. and Sukomel, A.S., 1977: Heat Transfer. Mir, Moscow. Landsberg, G.S., 1979: Ottica, Vol.2 MIR, Moscow, 478 pp. Ming Chen Wang and Uhlenbeck, G.E., 1945: On the Theory of the Brownian Motion II. Rev. Modern Phys., 17 (2/3), 323-341. Nazaroff, W.W. and Cass, G.R., 1987: Particle Deposition from a Natural Convection Flow onto a Vertical Isothermal Plate, J. Aerosol Science, 18, 445-455. Phenix, A. and Burnstaock, A., 1990: The Deposition of Dirt: a Review of Literature, pp. 11-18 in S. Hckney et al. (eds.): Dirt and Pictures Separated, the U.K. Institute for Conservation, Belton, England, 56 pp. Prodi, F. and Tampieri, F., 1982: The Removal of Particulate Matter from the Atmosphere: the Physical Mechanisms. Pageoph, 120, 286-325. Pruppacher, H.R. and Klett, J.D., 1980: Microphysics of Clouds and Precipitation, Reidel, Dordrecht, 714 pp. Pye, K., 1987: Aeolian Dust and Dust Deposits. Academic Press, London, 334 pp. Schlichting, H., 1979: Boundary-Layer Theory. McGraw-Hill, New York, 817 pp. Sehmel, G., 1980: Particle and Gas Deposition: a Review. Atmospheric Environment, 14, 983-1011. Seinfeld, J.H., 1986: Atmospheric Chemistry and Physics of Air Pollution. Wiley, New York, 738 pp. Slinn, W.G.N. and Hales, J.M., 1970: Phoretic Processes in Scavenging, Atomic Energy Commission Symp. Ser. 22, U.S. Atomic Energy Committee, pp. 411-422. Smith, B.J. and McAlister, J.J., 1986: Observations on the Occurrence and Origins of Salt Weathering Phenomena near Lake Magadi, Southern Kenia. Z. Geomorph. N.F., 30 (4), 445-460. Talbot, L., Cheng, R.K., Schefer, R.W. and Willis, D.R., 1980: Thermophoresis of Particles in a Heated Boundary Layer. J. Fluid Mechanics 1014, 737-758. Tritton, D.J., 1988: Physical Fluid Dynamics. Clarendon, Oxford, 519 pp. Vercelli, F., 1933: L'Aria. UTET, Torino, 711 pp. Vittori, O., 1973: Scavenging of Atmospheric Particles by Growing Ice Crystals: a Contribution to a Proposed Mechanism. J. Atmos. Sci., 30 (2), 321-324. Vittori, O., 1984: Transient Stefan Flow and Thermophoresis around an Evaporating Droplet. Nuovo Cimento, 7C (2), 254-269

402

W a l d m a n n , L. and Schmitt, K.H., 1966: Thermophoresis and Diffusophoresis of Aerosols in C.N. Davies (ed.): Aerosol Science, Academic, New York. Wax, N., 1954: Noise and Stochastic Processes, Dover, New York, 345 pp. Zimon, A., 1982: Adhesion of Dust and Powder, Consultants Bureau - Plenum, New York.

8.2. Applications to conservation Ashurst, J. and Ashurst, N., 1989: Practical Building Conservation. Volume 1 Stone Masonry. Gower, Aldershot (U.K.), 100 pp. Camuffo, D., 1987: L'illuminazione negli ambienti di conservazione; First part Rassegna Beni Culturati, 3 (4), 40-44 and second part, item 3 (6), 38-40. Camuffo, D., 1990: Ambiente e monumenti: microclimatologia di ambienti chiusi e c o n s e r v a z i o n e di opere pittoriche. Accademia Nazionale Lincei, Giornata dell'Ambiente, 82, 157-166. Camuffo, D., 1991: Wall Temperature and Soiling of Murals. Museum Management and Curatorship 10, 373-383. Camuffo, D. and Bernardi, A. 1986: Dinamica del microclima e scambi termoigrometrici tra pareti e atmosfera interna nella Cappella Sistina. Bollettino Monumenti Musei Gallerie Pontificie, 6, 211-257. Camuffo, D., 1993: Controlling the Aeolian Erosion of the Great Sphinx. Studies in Conservation, 38, 198-205. Camuffo, D. and Bernardi, A., 1991: The Microclimate of Leonardo's "Last Supper"; joint edition European Cultural Heritage Newsletter on Research, and Bollettino Geofisico, special issue, 14 (3), 1-123. Camuffo, D. and Bernardi, A., 1995: The Microclimate of the Sistine Chapel, Joint edition European Cultural Heritage Newsletter on Research, 9, 7-32 and Bollettino Geofisico, 18 (2), 7-32. Camuffo, D., Del Monte, M. and Sabbioni, C., 1987: Influenza delle precipitazioni e della condensazione sul degrado superficiale dei monumenti in marmo e calcare, pp. 1536 in Ministero Beni Culturali ed Ambientali "Materiali lapidei", special issue of Bollettino d'Arte, Poligrafico dello Stato, Rome. Camuffo, D. and Schenal, P., 1982: Microclima all'interno della Cappella degli Scrovegni scambi termodinamici tra gli affreschi e l'ambiente, pp. 107-209 in Ministero dei Beni Culturali ed Ambientali "Giotto a Padova", special issue of Bollettino d'Arte, Poligrafico dello Stato, Rome. Eastaugh, N., 1990: The Visual Effects of Dirt on Paintings pp. 19-23 in S. Hackney et al. (eds.): Dirt and Pictures Separated, the U.K. Institute for Conservation, Belton, England, 56 pp. Getty Conservation Institute, 1990: Conservation Research Proposal for the Great Sphinx Presented in Cairo. Getty Conservation Institute Newsletter, 5 (8.2), 1-2. Koestler, R.J., Warsheid, T. and Nieto, F., 1996: Biodeterioration: Risk Factors and Their Management, pp. 25-36 in: N.S. Baer and R. Snethlage (editors): Saving Our Architectural Heritage: the Conservation of Historic Stone Structures. Wiley, Chichester. Lazzarini, L. and Laurenzi-Tabasso, M., 1986: II restauro della pietra. Cedam, Padova, 320 pp. Marshall, K.C., 1984: Microbial Adhesion and Aggregation. Springer Verlag, Berlin, 424 pp. Thomson, G., 1986: The Museum Environment. Buttherwords, London, 293 pp. Zezza, F., 1976: Caratteristiche litogenetiche e forme della degradazione delle pietre da costruzione calcaree di origine biochimica e detritica. Rassegna Tecnica Pugliese Continuit?z, 10 (2), 3-28. Zezza, F., 1994: Evaluation Criteria of the Effectiveness of Treatments by Non Destructive Analysis, pp. 198-212 in: F. Zezza (ed.): Stone Material in Monuments: Diagnosis and Conservation, 2nd Course of the Community of Mediterranean Universities. Adda, Bari.

403 CHAPTER 9

9.1. General theory on sampling and turbulence Lumley, J.L. and Panofsky, H.A. 1964: The Structure of Atmospheric Turbulence. Wiley, New York, 239 pp. Munn, R.E., 1970: Biometeorological Methods. Academic Press, New York, 336 pp. Pasquill, F., 1962: Atmospheric Diffusion, 1st ed., Van Nostrand, London, 297 pp. Pasquill, F., 1974: Atmospheric Diffusion, 2nd ed., Wiley, New York, 429 pp. Plate, E.J., 1982: Engineering Meteorology, Elsevier, Amsterdam, 740 pp. Tennekes, H. and Lumley, J.L., 1973: A First Course in Turbulence. MIT Press, Cambridge, Mass., 298 pp. Vinnichenko, N.K., Pinus, N.Z., Shmeter, S.M. and Shur, G.N., 1980: Turbulence in the Free Atmosphere. Consultants Bureau, New York, 310 pp. Wei, W.W., 1990: Time Series Analysis. Addison Wesley, Redwood City, Ca., 478 pp.

9.2. Instruments and measuring techniques Doebelin, E.O., 1990: Measurement Systems - Application and Design. McGraw Hill, New York, 960 pp. Linacre, E., 1992: Climate Data and Resources. Routledge, London, 366 pp. Moses, H., 1968: Meteorological Instruments for Use in Atomic Energy Industry, pp. 257-300 in D.H. Slade (Ed.): Meteorology and Atomic Energy 1968. U.S. Atomic Energy Commission, Div. Tech. Info. World Meteorological Organisation, 1983: The Guide to Instrument and Methods of Observation, WMO Technical Publication No 8, Geneva. World Meteorological Organisation, 1986: Compendium of Lecture Notes on Meteorological Instruments for Training Class III and Class IV Meteorological Personnel, WMO Technical Publication No 622, Geneva. CHAPTER 10 Benedict, R., 1984: Fundamentals of Temperature, Pressure, and Flow Measurements. Wiley, New York, 532 pp. Camuffo, D., 1980: Fog and Related Diffusion Potential at Venice: two Case Studies. Boundary Layer Meteorology 18, 453-471. Camuffo, D., 1982: The Nocturnal IBL over an Hilly Island with Reference to the Diffusion of Radioactive Nuclei. Boundary Layer Meteorology, 22, 233-240. Camuffo, D. and Bernardi, A., 1993: Microclimatic Factors affecting the Trajan Column. Science Total Environment 128, 227-255. Camuffo, D. and Schenal, P., 1982: Microclima all'interno della Cappella degli Scrovegni: scambi termodinamici tra gli affreschi e l'ambiente, pp. 107-209 in: Ministero dei Beni Culturali ed Ambientali: Giotto a Padova, special issue of Botlettino d'Arte, Poligrafico dello Stato, Rome. Green, W. and Maloney, G.O. (ed.s), 1984: Perry's Chemical, Engineers Handbook, Sisth Ed., McGraw-Hill, Singapore. Hadlock, R., Seguin, W.R. and Garstang, M., 1972: A Radiation Shield for Thermistor Development in the Atmospheric Boundary Layer. J. Appl. Meteorol.,11, 393-399. Lide, D.R. (ed.), 1990: CRC Handbook of Chemistry and Physics, 71 Ed. CRC Press, Boca Raton, Fla. Kondratyev, K.Y., Kozoderov, V.V., Smokty, O.I., 1992: Remote Sensing of the Earth from Space: Atmospheric Correction. Springer-Verlag, Berlin, 478 pp. Michalski, L., Eckersdorf, K. and J. McGee, 1991: Temperature Measurement. Wiley, New York, 514 pp.

404 Nicholas, J.V. and White, D.R., 1994: Traceable Temperatures - An Introduction to Temperature Measurement and Calibration. Wiley, New York, 358 pp. Oke, T.R., 1978: Boundary Layer Climates, Methuen, London, 372 pp. Platridge, G.W. and Platt, C.M.R., 1976: Radiative Processes in Meteorology and Climatology. Elsevier, Amsterdam, 318 pp. Schooley, J.F., 1986: Thermometry. CRC Press, Boca Raton, Fla., 245 pp. UK Meteorological Office, 1981: Handbook of Meteorologicat Instruments- VoI.2 Measurement of Temperature. Her Majesty's Stationary Office, London. Wolfe, W.L. and Zissis, G.J., 1989: The Infrared Handbook. Environmental Research Institute of Michigan. World Meteorological Organisation, 1983: The Guide to Instrument and Methods of Observation, WMO Technical Publication No 8, Geneva. World Meteorological Organisation, 1986: Compendium of Lecture Notes on Meteorological Instruments for Training Class III and Class IV Meteorological Personnel, WMO Technical Publication No 622, Geneva. CHAPTER 11 Camuffo, D. and Bernardi, A., 1986: Dinamica del microclima e scambi termoigrometrici tra pareti e atmosfera interna nella Cappella Sistina. Bollettino dei Monumenti, Musei e Gallerie Pontificie, 6, 211-257. Camuffo, D. and Valcher, S., 1986: A Dew Point Signaller for Conservation of Works of Art. Environmental Monitoring and Assessment 6, 165-170. Davey, F.K., 1965: Hair Humidity Elements, pp. 571-573 in A. Wexler (ed.): Humidity and Moisture Vol. 1: Principles and Methods of Measuring Humidity in Gases. Rehinold, New York, 687 pp. Fisher, P.D., Lillevik, S.L. and Jones, A.L., 1981: Microprocessors Simplify Humidity Measurements. Transactions on Instrumentation and Measurements IM 30 (1), 57-63. Harriman, L.G., 1990: The Deumidification Handbook, Munters, Cargocaire, 186 pp. List, R.J., 1971: Smithsonian Meteorological Tables, Smithsonian Institution, Washington D.C., 527 pp. Mamillan, M, 1992: Mdthodes d'dvaluation des ddgradations des monuments en pierre, pp. 175-181 in F. Zezza (ed.): Weathering and Air Pollution. Adda, Bari. Murphy, W., Smith, J.D. and Inkpen, R.J., 1996: Errors Associated with Determining P and S Acoustic Wave Velocities for Stone Weathering Studies, pp. 228-244 in: B.J. Smith and P.A. Warke (ed.s): Processes of Urban Stone Decay, Donhead, London. Nappi, A. and C6te P., 1997: Non-Destructive Methods Applicable to Historic Stone Structures, pp. 151-166 in N.S. Baer and R. Snethlage (ed.s): Saving Our Architectural Heritage: The Conservation of Historic Stone Structures, Wiley, Chichester. UK Meteorological Office, 1981: Handbook of Meteorological Instruments, Vol.3: Measurement of Humidity. Her Majesty's Stationary Office, London, 43 pp. Weast, R.C., 1977/78: CRC Handbook of Chemistry and Physics, CRC Press, West Palm Beach, Fla. Wexler, A., 1965: Humidity and Moisture Vol. 1: Principles and Methods of Measuring Humidity in Gases. Rehinold, New York, 687 pp. Wiederhold, P.R., 1975: Humidity Measurements part I: Psychrometers and Percent RH Sensors. Instrum. Technol. 22, 31-37.

405 CHAPTER 12

12.1. Anemometry Beaubien, D.J. and Bisberg, A., 1968: The sonic Anemometer. Cambridge System, Newton, Mass., 5 pp. Camp, D.W., Turner, R.E. and Glichrist, L.P., 1970: Response Tests of Cup, Vane and Propeller Wind Sensors. J. Geophysical Research 75, 5265-5270. Camuffo, D., 1976: How to Obtain Mean Value and Variance of Wind Direction by Using a Sine-Cosine Transducer. Atmospheric Environment 10, 167-168. Camuffo, D. and Denegri, A., 1976: A Method for Measurement of Mean Wind Direction with the use of Standard Potentiometric Transducers. Atmospheric Environment 10, 415. Camuffo, D., 1979: Graphic Recording and Averaging the Wind Direction. II Nuovo Cimento 2C, 607-618. Dantec, I996:54N50 Low Velocity Flow Analyzer Mark II, Dantec Electronics, Skovlunde, Denmark, 8 pp. DISA, 1976: Description of the DISA Constant Temperature Anemometry System, DISA Electronics, Skovlunde, Denmark, 56 pp. Doebelin, E.O., 1990: Measurement Systems - Application and Design. McGraw Hill, New York, 960 pp. Durst, F., Melling, A. and Whitelaw, J.H., 1981: Principles and Practice of Laser-Doppler Anemometry. Academic Press, London, 437 pp. Horst, T.W., 1973: Corrections for Response Errors in a Three-Component Propeller Anemometer. J. Appl. Meteorol. 12, 716-725. Hyson, P., 1972: Cup Anemometer Response to Fluctuating Wind.Speeds. J. Appl. Meteorol., 11, 843-848. Moses, H., 1968: Meteorological Instruments for Use in Atomic Energy Industry, pp. 257-300 in D.H. Slade (Ed.): Meteorology and Atomic Energy 1968. U.S. Atomic Energy Commission, Div. Tech. Info. Newstadt, F.T.M. and Van Dop, N., 1984: Atmospheric Turbulence and Air Pollution Modelling. Reidel, Dordrecht, 358 pp. Ramachandran, S., 1970: A Theoretical Study of Cup and Vane Anemometers. Quart. J. R. Met. Soc. 96, 115-123 Smith, S., 1970: Thrust-Anemometer Measurements of Wind Turbulence, Reynold Stress, and Drag Coefficient over the Sea. J. Geophys. Research, 75, 6758-6770. UK Meteorological Office, 1981: Handbook of Meteorologicat Instruments, Vol.4: Measurement of Surface Wind. Her Majesty's Stationary Office, London, 43 pp.

12.2. General theory on turbulence Cartwright, D.E. and Longuett-Higgins, M.S., 1956: The Statistical Distribution of the Maxima of a Random Function.Phil. Trans. Roy. Met. Soc., Ser. A 237, 212-232. Clifford, N.J., French, J.R. and Hardisty, J., 1993: Turbulence. Wiley, Chichester, 360 pp. Csanady, G.T., 1980: Turbulent Diffusion in the Environment. Reidel, Dordrecht, 248 pp. Goody, R., 1995: Principles of Atmospheric Physics and Chemistry. Oxford University Press, New York, 324 pp. Kinsman, B., 1965: Wind Waves, Prentice Hall, Englewood Cliffs, N.J., Landahl, M.T. and Mollo-Christensen, E., 1986: Turbulence and Random Processes in Fluid Mechanics Cambridge, Cambridge, 154 pp. Longuett-Higgins, M.S., 1957: The Statistical Analysis of a Random, Moving Surface.Phil. Trans. Roy. Met. Soc., Ser. A 249, 321-387. Longuett-Higgins, M.S., 1962: The Distribution of Intervals between Zeros of a Stationary Random Function. Phil. Trans. Roy. Met. Soc., Ser. A 254, 557-599. Rice, S.O., 1944: Mathematical Analysis of Random Noise. Bell System Tech. J., 23, 282-332. Rice, S.O., 1945: Mathematical Analysis of Random Noise. Bell System Tech. J., 24, 46-156.

406 Sutton, O.G., 1960: Atmospheric Turbulence. Methuen, London, 111 pp. CHAPTER 13

13.1. Weather precipitation measurements Houghton, D.D., 1985: Handbook of Applied Meteorology. Wiley, New York, 1461 pp. Landsberg, H.E., 1981: The Urban Climate. Academic Press, New York, 275 pp. UK Meteorological Office, 1981: Handbook of Meteorological Instruments - Vol.5 Measurement of Precipitation and Evaporation Her Majesty's Stationary Office, London. World Meteorological Organisation, 1966: International Meteorological Vocabulary, WMO Technical Publication No 182 TP.91, Geneva. World Meteorological Organisation, 1983: The Guide to Instrument and Methods of Observation, WMO Technical Publication No 8, Geneva. World Meteorological Organisation, 1984: Compendium of Lecture Notes for Training Class IV Meteorological Personnel, Vol.2 Meteorology. WMO Technical Publication N o 266, Geneva, 455 pp. World Meteorological Organisation, 1986: Compendium of Lecture Notes on Meteorological Instruments for Training Class III and Class IV Meteorological Personnel, Vol.1 WMO Technical Publication No 622, Geneva. World Meteorological Organisation, 1994: Guide to Hydrological Practices. WMO Technical Publication No 168, Geneva.

13.2. Precipitation on monuments and wet and dry deposition samplers Georgii, H.W. and Pankrath, J., 1982: Deposition of Atmospheric Pollutants. Reidel, Dordrecht, 217 pp. Camuffo, D., 1990: Acidic Precipitation Research in Italy, pp. 229-265 in: A.H.M. Bresser and W. Salomons (editors): "Acidic Precipitation", Vol.5, Advances in Environmental Science, Springer Verlag, New York. Camuffo, D., Del Monte, M. and Ongaro, A., 1984: The pH of Atmospheric Precipitation at Venice, Related to both the Dynamics of Precipitation Events and Weathering of Monuments. Science Total Environment, 40, 125-140. Camuffo, D., Bernardi, A. and Zannetti, M., 1988: Analysis of the Real-Time Measurement of the pH of Rainfall at Padova, Italy: Seasonal Variation and Meteorological Aspects. Science Total Environment, 71, 187-200. Leysen, L., Roekens, E. and Van Grieken, R., 1989: Air-Pollution-Induced Chemical Decay of a Sandy Limestone Cathedral in Belgium. Science Total Environment, 78, 263-287. Munn, R.E. and Rodhe, H., 1985: Compendium of Meteorology Vol.II, Part 6 - Air Chemistry and Air Pollution Meteorology. World Meteorological Organisation, WMO No.364, Geneva, 209.

407

References index Adamson, A. W., 159, 180 Andrews, J.E., 126 Anfossi, D., 206 Arnold, A., 179, 181, 182 Ashurst, J., 290 Ashurst, N., 290 Bagnold, R.A., 284, 287 Barndorff-Nielsen, O.E., 287 Beadecker, P.A., 163 Beaubien, D.J., 374 Becker, T.W., 169 Benedict, R., 316 Benoist, L., 6 Berlyland, M.E., 234 Bernardi, A., 6, 18, 19, 27, 32, 33, 34, 53, 71, 111, 118120, 164, 192, 217, 273, 335, 355 Bisberg, A., 374 Biscontin, G., 149 Blanchard, D.C., 183 Born, M., 105 Bouma, P.J., 270 Brimblecombe, P., 162, 183, 207 Brock, J.R., 247 Brown, R.A., 222 Brunauer, S., 151 Buffle, J., 237, 258 Burnstaock, A., 258, 266, 270 Byers, H.R., 132, 137 Cadle, R., 257, 259 Camp, D.W., 364 Camuffo, D., 6, 11, 12, 18, 19, 27, 32, 33, 34, 35, 36, 53, 71, 118, 120, 149, 161, 162, 163, 165, 166, 172, 178, 187, 210, 217, 218, 234, 263, 273, 275, 281, 287, 330, 332, 335, 355, 360, 361, 368, 369, 370, 371, 389 Caporaloni, M., 261 Cartwright, D.E., 377, 378 Cass, G.R., 274 Cayan, D.R., 209 Chandrasekhar, S., 238 Clifford, J., 157 Clifford, N.J., 377 Coped6, M., 66 C6te P., 357 Csanady, G.T., 377 Dantec, 373

Davey, F.K., 342 Davison, S., 65 Deacon, E.L., 227 De Guichen, G., 6 Del Monte, M., 163, 164 Denegri, A., 370 De Quervain, F., 131 DeWitt, D.P., 22 DIN 66131, 131 DISA, 373 Dobbins, R.A., 234 Doebelin, E.O., 295, 321, 342, 373, 376 Douglas, A.V., 209 Dullen, F.A.L., 172 Durst, F., 376 Eastaugh, N., 270 Echols, W.T., 206 Einstein, A., 103, 238, 240, 241, 245 Elliot, W.P., 206 Enzi, S., 162 Epstein, P.S., 245, 246 Everett, D.H., 156, 158 Fagerlund, G., 157 Fea, G., 162 Fermi, E., 46 Fisher, P.D., 347 Fitzner, B., 131, 149 Fletcher, B., 284 Friedlander, S.K., 237, 247 Georgii, H.W., 388 Getty Conservation Institute, 287 Gifford, F.A., 232 Gillette, D., 284 Ginell, W.S., 159 Giordano, G., 61 Godson, W.L., 157 Goldsmith, P., 250, 253 Goody, R., 98, 354 Gordon, J., 184, 185 Graedel, T.E., 155 Green, W., 340, 352 Gregg, S.J., 151 Gummerson, R.J., 178 Hadlock, R., 325 Hales, J.M., 247, 250 Hall, C., 178 Harriman, L.G., 342

408 Hicks, S.B.B., 261 Hidy, G.M., 237, 247 Hinds, W.C., 237 HOgstrOm, U., 225 Horst, T.W., 364 Houghton, D.D., 386 Hyson, P., 364 Iribarne, J.V., 157 Isachenko, V.P., 263 Jamiolkowski, M., 12 Jeannette, D., 149 Jenkins, K.A., 12 Jones, D.A., 65, 209 Jones, P.D., 209 Kasahara, A., 97 Kikoin, A., 132 Kikoin, I., 132 Kinsman, B., 377 Kireev, V., 180 Klett, J.D., 137, 237, 247, 250 Klopfer, H., 131 Koestler, R.J., 267 Kondratyev, K.Y., 336 Kondratyev, Ya., 111 Krumbein, W.E., 14 Kuroczkin, J., 14, 67, 127, 169 Landahl, M.T., 377 Landsberg, G.S., 259 Landsberg, H.E., 207, 385 Laurenzi Tabasso, M., 65, 148, 290 Lazzarini, L., 290 Lee, D.O., 209 Leysen, L., 387 Lide, D.R., 340 Linacre, E., 295 List, R.J., 352 Longuett-Higgins, M.S., 377, 378 Lumley, J.L., 211, 214, 224, 377 MacDonald, F., 184, 185 Madonna, L.A., 141 Maloney, G.O., 340, 352 Mamillan, M., 358 Marabelli, M., 65, 148 Marshall, K.C., 258 Mason, B.J., 132, 137, 141, 142 Massari, G., 77 Matveev, A.N., 146 Matveev, L.T., 132 Maunder, W.J., 4 McAlister, J.J., 284

McElroy, J.L., 234 McVehil, G.E., 223 Mestitz, A., 108 Michalski, S., 6 Michalski, L., 22, 316, 321, 325 Mikhail, R.S., 151 Ming Chen Wang, 238 Mollo-Christensen, E., 377 Monin, A.S., 224 Moses, H., 298, 364 Munn, R.E., 209, 295, 388 Murphy, W., 358 Nappi, A., 357 Nazaroff, W.W., 274 Newstadt, F.T.M., 377 Newton, R., 65 Nicholas, J.V., 321, 338, 339 Obukov, A.M., 224 Oke, T.R., 340 Ortega-Calvo, JJ., 127 Padfield, T., 6, 69, 189 Pankrath, J., 388 Panofsky, H.A., 206, 211, 214, 224, 377 Pasquill, F., 231, 377 Phenix, A., 258, 266, 270 Plank, M., 47 Plate, E.J., 208, 219, 353 Platridge, G.W., 340 Platt, C.M.R., 340 Porges, F., 25 Price, C., 183 Prodi, F., 162, 247, 250 Pruppacher, H.R., 137, 237, 247, 250 Pye, K., 287 Ramachandran, S., 364 Reddy, M.M., 163 Rice, S.O., 377 Richardson, B.A., 66 Richardson, L.F., 223 Robens, E., 151 Robinson, N., 111 Rodhe, H., 209, 388 Rosenhow, W.M., 7 Sabbioni, C., 164, 167 Saint-Gobain, 22 Saiz-Jimenez, C., 167 Scanlan, R.H., 208 Schenal, P., 32, 35, 36, 281, 332 Schlichting, H., 206, 262 Schmitt, K.H., 246

409 Schooley, J.F., 316, 321 Sedunov, Yu.S., 132 Sehmel, G., 237, 261 Seinfeld, J.H., 237, 240 Simiu, E., 208 Sing, K.S.W., 151 Singer, I.A., 230 Sivuchin, D.V., 132 Slicker, A., 63 Slinn, W.G.N., 247, 250 Smith, B.J., 12, 13, 284 Smith, F.B., 234 Smith, M.E, 230 Smith, S., 365 Summit, R., 63 Sutton, O.G., 226, 377 Talbot, L., 246, 247 Tampieri, F., 247, 250 Tennekes, H., 377 Thomson, G., 6, 64, 74, 270 Thomson, W. (Lord Kelvin), 135 Torraca, G., 148, 156 Touloukian Y.S., 22 Townsend, A.A., 206 Tritton, D.J., 290 Turner, D.B., 234 Uhlenbeck, G.E., 238 UK Meteorological Office, 295, 316, 342, 346, 347, 382, 384 Valcher, S., 187, 360, 361 Van Der Hoven, I., 206 Van Dop, N., 377 Van Leeuwen, H.P., 237, 258

Varshneya, A.K., 122 Vercelli, F., 289 Vincenzi, S., 111, 218 Vinnichenko, N.K., 377 Vittori, O., 108, 250, 253 Wagner, N.K., 206 Waldmann, L., 246 Waller, R., 155 Warke, P.A., 13 Warscheid, T., 14, 67, 127, 148, 169, 173 Wax, N., 238 Weast, R.C., 160, 352 Wei, W.W., 304 Wendler, E., 148 Wexler, A., 295, 342 White, D.R., 321, 338, 339 Wiederhold, P.R., 347 Willetts, B.B., 287 Winkler, E.M., 147, 177 Wittenburg, C., 169 Wolfe, W.L., 336, 340 Woodcock, A.H., 183 World Meteorological Organization, 295, 316, 324, 325, 342, 346, 347, 358, 381, 382, 384 Wright, H.L., 143 Wypych, G., 104, 124 Young, K.C., 137 Zardini, F., 210 Zehnder, K., 179, 181, 182 Zezza, F., 284 Zimon, A., 266 Zissis, G.J., 336, 340

411

Subject index absolute humidity, 55-58 absolute temperature, 9-10 absorbivity, 109 acid rain, 161-164 adhesive forces, 266 adiabatic (atmosphere, expansion, gradient), 93-96, 200-201 adsorption isotherm, 151-156 advection hoar frost, 79 aerodynamic deposition, 260-265 aerovane, 365 air-surface interactions, 30-37, 51-54, 353357 aliasing, 303 altitude of the sun, 110 anemometer location, 366-367 anemometry, 363-366 Archimedes hydrostatic balance, 254-255 artificial microclimate, 6-7 atmospheric stability, 198-205, 221, 332333 atmospheric variables needed for conservation, 296-298 averaging wind direction, 368-371 Avogadro number, 9 azimuth of the sun, 110 barometric formula, 134; particle distribution, 268-269 Bernoulli equation, 173 bimetallic thermograph, 318-319 biodegradation, 67 biological patina 2, 31-32, 167-169 black crust, 164-168 black surface, 267 boiling point, 144-146 Boltzmann constant, 9 Bouguer-Lambert law, 108-109 breaking white area, 169-170 Brookhaven stability categories, 230-231 Brown motion, 237-244 Brunt V~iis/il/i frequency, 206 bubbles, 143-146 bulk deposition sampler, 389-390 bulk IR reflection, 337 Cantor law, 151 canyon effect, 209 capillary force, 267; suction, 175-179 Carnot efficiency, 45 cellulose degradation, 66 church heating, 24-30

Clausius Clapeyron equation, 44-46 climate, 4 cloud condensation level, 100 cold light, 119 colour of natural light, 115-116; of sunlight, 116 colour temperature, 105 coning, 199, 201 constant stress layer, 226 contact charging, 257 contact sensors, 334-335 continuum regime, 236 corrasion, 284-285 corrosion, 65 Coulomb field of a drop, 141; attraction of particles, 266 crossings analysis of turbulence, 377-380 crusts (white, black, gray, soot deposit), 164-172 Cunningham slip factor, 240-241 cup anemometer, 363-364 Dalton law, 42, 267-268 daylight duration, 110 Deacon number, 227 declination of the sun, 109-110 degree of saturation of vapour, 58 deliquescent salts, 141, 185 density of water vapour, 55 deposition velocity, 236-237 dew, 76 dew point meter, 359; signaller, 359-361 dew point spread, 76, 145-147 dew point temperature, 74-79 diffuse solar radiation, 109 diffusion, 248-249; charging, 257; slip factor, 250 diffusiophoresis, 248-250 diffusivity (Brownian), 240-241 direct solar radiation, 109 donor-acceptor forces, 266-267 Doppler anemometry, 366, 375-377 drainage of large particles, 269 drizzle, 297 drunk's walk, 237-238 dry adiabatic atmosphere, 95-96 dry air (composition), 7-8 dry bulb temperature, 10 drying monuments, 174-175, 192-193 dynamic pressure, 173 eccentricity of the earth orbit, 110

412 eddies, 197 eddy diffusivity: coefficient, 353-354; heat, 214-215; momentum, 215, 353-354 eddy velocity, 211-212; viscgsity, 215 effective height, 229 effective radiation temperature, 340 Einstein equation, 103-104, 239-240 electric hygrometer, 346 electrical forces on a particle, 266-267 electrophoresis, 257-258 embryo, critical radius, 140 emissivity, 106-107, 338-340 enthalpy, 86, 137 entropy, 86-87, 98 Epstein equation, 239, 246-247 equation of state for perfect gases, 8-9 equilibrium moisture content, 61-64 equilibrium pressure (RH) over a solution, 179-181,351-352 equivalent temperature (isobaric), 92-93 equivalent-potential temperature, 99-100 error generated by uncorrect psychrometric readings, 350 Eulerian frame, 91 evaporimeter, 357 falling droplets, terminal velocity, 386 fanning, 199, 202 Fick equation, 249 film capacitor hygrometer, 345-346 fixed axis propeller, 364 flash light, 125 float type rain recorder, 383 floor heating, 25-27 foen, 100 fog, 297-298, dry fog, 162 free convection layer, thickness of, 263-264 freezing point depression (hygroscopic salts), 159-160; (Kelvin effect), 157-158 freezing-thawing cycles, 156-160 friction velocity, 212-213 fringe mode, 366, 376 frost (hoar, crystalline, white), 79 frost point temperature, 79 fumigation, 199, 202 gas constant, 9 Gaussian plume dispersion, 227-229 geopotential height, 134 Gibbs free energy of a surface, 132, 137 glass degradation, 65-66 glaze, 79 global climate, 3 globe thermometer, 315 Goldsmith equation, 253

granular disgregation, 12-13 Grashof number, 262-263 gravitational settling, 254-256 Great Sphinx, 287-290 ground ice, 79 gypsum (formation), 65 hail, hailstones, 297 hair hygrometer, 342-345 heat balance, 215-219 heat flux in atmosphere, 213-219, 353-354 heat flux into the ground, 216-219 heat island, 207-208 HVAC to avoid soiling, 270-279 heating buildings used at times, 24-30 height of the sun, 110 Helmoltz free energy, 138 Henry law, 180 heterogeneous nucleation, 141 Hettner formula, 259 hoar (frost, air), 79 H6gstr6m ratio, 225 homogeneous nucleation, 140-141 hot air heating, 27-29 hot wire anemometer, 373-374 hour angle, 110 humidifiers, 51-53, 281 humidity (deterioration mechanisms), 6467, 147-148; in rooms and show cases, 70-74; measurements, 341-361 hydration-dehydration cycles, 181-186 hydrometeor roses, 297-299 hygrometer, calibration, 351-352 hypsometric formula, 134 ice fog, 79 imaging instruments, 336 inertial impaction, 260 inertial interception, 260 ink-bottle pore, 150-151, 155 instrument location, 327-328 intensity of solar radiation, 111-115 internal boundary layer, 205-206 internal pore, 150-151 interstitial condensation, 187-190 inversion, 201 mviscid flow, 173 irradiation, 111-115 isentropic surface, 97-98 lsochoric lines, 87 isolines, 38-41 isothermy, 201 Kelvin equation, 130-138; paradox and experiment, 135-137

413 kinematic coefficient of eddy viscosity, 215 kinematic viscosity, 221-222 kinetic energy of gas molecules, 9; in sand blasting, 290-292 Knudsen number, 235 kytoon, 328-329 Lagrangian frame, 91 Lambert law, 107-108 Lambertian surface, 107-108 lamps, 117-119 Langevin equation, 238 Laplace pressure, 133-134 lapse rate, 198 laser Doppler anemometer, 366, 375-377 latent heat flux, 213-215, 216-219, 353-355 latent heats of vaporisation, fusion, sublimation, 44-48, 86 length of observations, 304-305 light (deterioration mechanism), 122-127 limits of HVAC, 7 liquid-film adhesion, 267 liquid-in-metal thermometer, 318 local climate, 3 lofting, 199, 202 logarithmic wind profile, 226 looping, 198-199 luminance, 107-108 macropores, 131 Magnus (or Tetens) formula, 42; coefficients for water or ice, 42 mantle heating, 29 Mason formula, 142-143 mass concentration of moist air, 54 mature droplet, 140 McVehil ratio, 223-224 mean Maxwell-Boltzmann velocity, 243244 mercury-in-glass thermometer, 316-318 microclimate (definition), 3-4 microclimate diagnostics, 30-37, 51-54; for conservation, 68-69 micropores, 131, 146-151 mixing ratio, 48-50 mode, 302 moisture capacity, 58; content of moist air, ",~\54 . moasture flux in atmosphere, 213-215, 21621'9, 353-355 mole, 9 molecular diffusivity, 354 molecular regime, 236 molecular temperature, 10 molecular viscosity, 211

Monin-Obukov length, 224-225 nanoclimate, 3 Neper number, 48 neutrons method to measure wall dampness, 358 non-imaging instruments, 336-337 normative on microclimate, 69, 295 Nyquist frequency, 304 occult precipitation, 381 open pore, 149-151 optical fibers, 122; filters, 121-122 optical path length, 111-113 osmotic pressure, 142 overpressure in a closed capillary, 178-179 particle diameter, 235 Pasquill Gifford diagrams, 233 Pasquill stability categories, 231-234 Peltier effect, 359 percentiles, 302 perfect gas, 8 pew heating, 25 pH of rain, 163, 171-172 photochemical smog, 126 photophoresis, 258-259 phototrophic organisms, 126-127 Pich6 evaporimeter, 355 picoclimate, 3 Pitot tube, 365 planetary boundary layer, 196 Plank formula, 103 platinum resistance sensor, 319-320 plume concentration, 228-229; dispersion, 227-229 Poisson equation, 95 position of light sources, 125-126; of paintings, 279-282 potential temperature, 96-99 Prandtl number, 262-263 precipitation measurement, 382-384 precipitation, 297, 381 pressure of a light beam, 258-259 pressure of water vapour, 42-44 propeller anemometer, 364 Pruppacher and Klett equation, 247-248 pseudo-adiabatic process, 100 psychrometer, 81, 346-351,355-356; coefficient, 82, 346-347 psychrometric chart, 83-89 Purkinje effect, 116 quartz thermometer, 324-325

414

R parameter, 227 radiant emission, radiance, 107-108 radiation laws, 103-105 radiometers, 336-340 radiometric temperature, 105-107 radiosionde, 328-331 rainfall, 297 rainout, 161 random walk, 237-238 Raolut law, 180 Rayleigh number, 262; distribution, 378 reflectivity, 107, 109 regional climate, 3 relative humidity, 58-60 remote sensing, 336-340 response time of a sensor, 305-312 Reynolds number, 222 Richardson flux number, 224; gradient number, 223 rime (soft, hard, fog), 79 roughness length, 226 rounding off of a number, 41 Rubinowitz formula, 259 runoff collector, 387-388 saltating granules, 286-287 sampling frequency, 302-304 sand blasting, 290-292 saturation pressure, 42 Schmidt number, 243 screen, 325-327 sea spray and salt damage, 181-186; and wind speed, 183 Seebeck effect, 323 sensible heat, 86 sensors with different time constant, 308 shearing stress, 210-211 show case (overheating), 21-24; lighting, 122 shower, 297 silica gel, 73-74, 155 similarity theory, 226 sine-cosine transducer, 367-368, 372 skewness, 371 snow, 297 soiling, 270-273 solar coordinates, 110 solar radiation on a surface, 109-114 sonic anemometer, 374-375 sound velocity, 374-375 specific free energy, 132 specific humidity, 54-55 speed of the free convection layer, 263-264 spread, 76 stable atmosphere, 201

statistical data representation, 298-302 stau, 100 Stefan Boltzmann law, 105-107 Stefan constant, 106 Stefan flow, 250-254 Stevenson screen, 326 Stevin law, 132-133 Stokes law, 239 Stokes-Einstein equation, 240-242 subadiabatic gradient, 200-202 sunrise and sunset, 110 superadiabatic gradient, 198-200 surface adhesion, 265-267 surface IR reflection, 337 surface layer, 226 surface temperature, 333-340 9surface tension, 132 Sutton turbulence index, 225-226 tafoni, 284 Talbot equation, 247-248 temperature (definition), 9-10; (deterioration mechanisms), 10-14; (habitat for biological life), 13-14 temperature cycles, 10-11; in a building, a room, 14-21; in a show cases, 21-24 temperature measurements, 315-340 Tetens (or Magnus) formula, 42 thermal, 198, 214 thermal conductivity, 216; diffusivity, 217; speed, 243 thermistor, 320-323 thermocuple, 323-324 thermophoresis, 245-248 thetered balloon, 330 time constant, 305-307, 314 time-of-wetness, 148, 296, 359-361 tipping bucket rain recorder, 382-383 transition regime, 236 transmissivity, 109 truncating a number, 41 turbulence, 219-221; turbulent transfer,211 two electrodes method to measure wall dampness, 359 ultrasonic pulses method to measure wall dampness, 358-359 uncertainty principle, 32 uplifting granules, 284-286 urban climate, 207-208 vacuum cleaners, 269-270 van der Hoven formula, 206 van't Hoff factor, 142 vane, 364-365

415 vapour tension, 42 ; over a solution, 179181 vertical fluxes of heat, moisture and momentum, 213-215 vertical temperature profile, 328-333 virtual temperature, 101-102 viscosity (molecular or dynamic), 211 Waldmann and Scmitt equation, 246 wall dampness, 357-359 Washburn equation, 177 washing white area 2, 30 washout, 161 water in capillary, 172, 177-178 water molecule, 8, 176 wavelength of solar radiation, 104 weighing-type rain recorder, 383 wet and dry deposition sampler, 388-389 wet bulb temperature (isobaric), 79-83; depression, 80-81

whashing white area, 164-171 Wheatstone bridge, 321-322 whiskers, 182 Wien displacement law, 105 Wildt anemometer, 365 wind drag, 174; lift, 174; shear, 202, 211, 367 wind erosion, 282-290 wind kinetic energy, 363; pressure, 365 wind measurement, 363-380 wind property of transmitting light, 366; sounds, 366; cooling power, 365; wind standard deviation, 227, 371-372 wind vector components, 197, 367-368 windscreen effect, 76 wood deformation (tangential, radial, longitudinal), 61-64 Wright formula, 143 zenith angle, 110