Development of Products and Packaging for Use in Microwave Ovens

Development of packaging and products for use in microwave ovens

Related titles: Novel food packaging techniques (ISBN 978-1-85573-675-7) With its distinguished international team of contributors, Novel food packaging techniques summarises the key developments in the field. The first part of the book discusses general issues such as packaging design, consumer attitudes to novel packaging and the legislative context. Part II looks at new techniques such as the use of oxygen and other scavengers, freshness indicators and antimicrobial packaging. The final part of the book discusses packaging materials and considers how packaging can be used with other preservation techniques to improve the quality of particular foods. Chemical migration and food contact materials (ISBN 978-1-84569-029-8) Most food sold is packaged and although packaging has many positive benefits, constituents from it may migrate into the food, possibly exposing consumers to the chemicals, which may be carcinogenic or genotoxic. As demand for pre-packaged food and ready meals increases, the potential for consumer exposure to these chemicals may also increase. This collection surveys key research in the area. Parts I and II review regulation of food contact materials and the latest developments in analysis of food contact materials and exposure estimation. Part III covers different food contact materials in detail and includes case studies of specific packaging types. Environmentally compatible food packaging (ISBN 978-1-84569-194-3) Food packaging performs an essential function, but packaging materials can have a negative impact on the environment. This collection reviews bio-based, biodegradable and recycled materials and their current and potential applications for food protection and preservation. The first part of the book focuses on environmentally compatible food packaging materials. Part II discusses drivers for using alternative packaging materials, such as legislation and consumer preference, environmental assessment of food packaging and food packaging eco-design. Chapters on the applications of environmentally compatible materials for particular functions, such as active packaging, and in particular product sectors then follow. Details of these and other Woodhead Publishing materials books can be obtained by: · visiting our web site at www.woodheadpublishing.com · contacting Customer Services (e-mail: [email protected]; fax: +44 (0) 1223 893694; tel.: +44 (0) 1223 891358 ext. 130; address: Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington, Cambridge CB21 6AH, UK) If you would like to receive information on forthcoming titles, please send your address details to: Francis Dodds (address, tel. and fax as above; email: francis.dodds@woodhead publishing.com). Please confirm which subject areas you are interested in.

Development of packaging and products for use in microwave ovens Edited by Matthew W. Lorence and Peter S. Pesheck

Published by Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington, Cambridge CB21 6AH, UK www.woodheadpublishing.com Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi ± 110002, India Published in North America by CRC Press LLC, 6000 Broken Sound Parkway, NW, Suite 300, Boca Raton, FL 33487, USA First published 2009, Woodhead Publishing Limited and CRC Press LLC ß 2009 Woodhead Publishing Limited, except Chapters 3, 5, 6 and 15 which are ß Per Olov Risman The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publishers cannot assume responsibility for the validity of all materials. Neither the authors nor the publishers, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress. Woodhead Publishing Limited ISBN 978-1-84569-420-3 (book) Woodhead Publishing Limited ISBN 978-1-84569-657-3 (e-book) CRC Press ISBN 978-1-4398-0207-6 CRC Press order number: N10045 The publishers' policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acid-free and elemental chlorine-free practices. Furthermore, the publishers ensure that the text paper and cover board used have met acceptable environmental accreditation standards. Typeset by Godiva Publishing Services Limited, Coventry, West Midlands, UK Printed by TJ International Limited, Padstow, Cornwall, UK

Contents

Contributor contact details Introduction

xi xiii

Part I Principles 1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12

2

Electromagnetic basis of microwave heating

J T A N G and F P R E S U R R E C C I O N J R , Washington State University, USA

Introduction Microwaves EM waves General wave equations Propagation of microwaves in different media Propagation of electromagnetic wave between two media Standing waves Waveguide Field patterns in single-mode and multimode cavities Microwave heating of foods Conclusions References

Influence of food geometry and dielectric properties on heating performance

B W AÈ P P L I N G -R A A H O L T , SIK ± Swedish Institute for Food and Biotechnology, Sweden and T O H L S S O N , formerly of SIK ± Swedish Institute for Food and Biotechnology, Sweden 2.1 2.2 2.3

Introduction Microwave heating distribution and uniformity Heating phenomena which influence heating performance and uniformity

3

3 4 5 6 10 14 18 21 25 30 35 36

38

38 39 43

vi

Contents

2.4

2.6 2.7 2.8

Some remarks on methodology and applications of controlled microwave heating performance Modelling-based tools for improving microwave heating uniformity Future trends Sources of further information and advice Bibliography

53 59 61 61

3

Advanced topics in microwave heating uniformity

66

Introduction The microwave penetration depth Cavity modes Wave reflections at an external flat surface Internal vertical standing waves in large flat loads Underheating modes Simultaneous heating of loads with different permittivities Influences by different "00 , with the same "0 The edge overheating effect Heating of isolated rounded objects Combination effects Summary and conclusions Acknowledgement References

66 67 68 72 72 75 79 79 81 82 92 103 104 104

2.5

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14

4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

5

P R I S M A N , Microtrans AB, Sweden

Microwave ovens

N C O O P E R , Formative Solutions LLC, USA

Introduction History of the microwave oven Oven design and construction Heating uniformity Combination ovens Microwave oven safety Sources of further information and advice Bibliography

Measurements of dielectric properties of foods and associated materials P R I S M A N , Microtrans AB, Sweden

5.1 5.2 5.3 5.4

Introduction Historical developments and chapter outline Absolute and analytical methods A calibration method

50

105 105 105 108 113 122 125 127 127

129 129 130 131 134

Contents 5.5 5.6 5.7 5.8 5.9

6

Infinite MUT methods Retro-modelling techniques Summary and conclusions Acknowledgement References

Microwave dielectric properties of foods and some other substances P R I S M A N , Microtrans AB, Sweden

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12

7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11

vii 136 140 151 151 152

153

Introduction Absorption mechanisms in water Microwave dielectric data of water Contributions by ions Data of water and some other liquids at 2450 MHz Data of some food substances with high water content Data for some food substances with low water content Data for numerical modelling Mixture formulas Large particulate foods and limitations of the mixture equations Microwave transparency of food container materials, etc. References

153 154 156 159 160 162 166 167 167 171 172 173

Flavors and colors for microwave foods

176

Introduction What are flavors? Natural versus artificial flavors Sources of flavors Flavor creation Microwave versus conventional heating Flavor forms Browning reaction Product categories and challenges Conclusions References

176 176 177 178 179 180 181 182 187 190 191

S J R I S C H , Michigan State University, USA

Part II Microwave packaging materials and design 8 8.1

Rigid passive microwave packaging forms

A J G A L L O , Associated Packaging Technologies, USA Introduction

195 195

viii

Contents

8.2 8.3 8.4 8.5 8.6 8.7

Conditions of use 195 Operations 197 Application drives material choice/material choice drives design 199 Product 200 Tray geometry 203 Conclusions 206

9

9.1 9.2 9.3

Susceptors in microwave packaging

M R P E R R Y , General Mills, USA and R R L E N T Z , California Tube Laboratory, USA

207

207 207

9.4 9.5 9.6 9.7 9.8 9.9

Introduction History Reflection, transmission, and absorption of microwave power by a susceptor Temperature limiting in PET susceptors Measurement methods Manufacture Use and application Conclusions References

10

Shielding and field modification ± thick metal films

237

10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9

Introduction History Physics and design principles Patterning thick metal films Antennas Application examples Conclusions Sources of further information and advice References

T H B O H R E R , Pac Advantage Consulting, LLC, USA

209 213 218 220 225 234 235

237 238 245 254 258 260 261 263 264

Part III Product development, food, packaging and oven safety 11

Package and product development testing in a microwave oven

M W L O R E N C E , General Mills Inc., USA 11.1 11.2 11.3

Introduction Realities of heating food in microwave ovens Consumer microwave oven variability

269 269 270 270

Contents 11.4 11.5 11.6 11.7 11.8 11.9

12 12.1 12.2 12.3 12.4

13 13.1 13.2 13.3

Commercial microwave oven variability Consumer variability Product variability Measurable responses Basic experimentation in microwave ovens References

Regulatory issues in microwave packaging

S J R I S C H , Michigan State University, USA Introduction History of microwave package regulations Current regulations References

Microwave oven safety

D B A R O N , dBEMF, USA

Microwave safety basics Microwave ovens and pacemakers Electromagnetic field exposure ± industrial applications Appendix: Microwave oven survey meters

ix 271 272 274 275 276 282

283 283 284 287 289

290 290 294 294 300

Part IV Modelling of microwave heating 14

Modeling microwave heating in foods

M C E L U C H and P K O P Y T , Warsaw University of Technology, Poland

305

14.1 14.2 14.3 14.4 14.5 14.6 14.7

Introduction FDTD versus FEM Coupled electromagnetic±thermodynamic simulation Computational examples Conclusions Acknowledgements References

305 308 323 326 344 346 346

15

Modelling the effects of active packaging of microwaved foods

349

P R I S M A N , Microtrans AB, Sweden 15.1 15.2 15.3 15.4

Introduction Microwave properties of metals Shielding devices Ameliorators

349 350 352 354

x

Contents

15.5 15.6 15.7

Susceptors Final comments References

361 370 371

Index

372

Contributor contact details

(* = main contact) Editors Matthew W. Lorence* and Peter S. Pesheck One General Mills Boulevard Minneapolis, MN 55426 USA E-mail: [email protected]; [email protected] Chapter 1 Professor J. Tang* and F.P. Resurreccion Jr Department of Biological Systems Engineering Washington State University Pullman, WA USA E-mail: [email protected] Chapter 2 B. WaÈppling-Raaholt* SIK ± the Swedish Institute for Food and Biotechnology Box 5401 SE-402 29 GoÈteborg Sweden E-mail: [email protected]

Professor T. Ohlsson Formerly of: SIK ± the Swedish Institute for Food and Biotechnology Box 5401 SE-402 29 GoÈteborg Sweden Chapters 3, 5, 6 and 15 Per O. Risman Microtrans AB SandsjoÈn 800 SE-43892 HaÈrryda Sweden E-mail: [email protected]; [email protected] Chapter 4 N. Cooper Formative Solutions LLC Dallas, TX 75135 USA E-mail: [email protected] Chapters 7 and 12 Dr S.J. Risch Michigan State University USA E-mail: [email protected]

xii

Contributor contact details

Chapter 8 A.J. Gallo Director of Applications Development Associated Packaging Technologies 1 Dickinson Drive Suite 100 Chadds Ford, PA 19317 USA E-mail: [email protected] Chapter 9 Ronald R. Lentz* 1471 Farragot Dr. Hollister, Ca 95023 USA E-mail: [email protected] Michael R. Perry 502 Lanewood Lane Plymouth, MN 55447 USA E-mail: [email protected] Chapter 10 Timothy H. Bohrer Pac Advantage Consulting, LLC 5012 S. Woodlawn Ave #1 Chicago, IL 60615-2814 USA E-mail: [email protected]

Chapter 11 Matthew W. Lorence One General Mills Boulevard Minneapolis, MN 55426 USA E-mail: [email protected] Chapter 13 Dave Baron dBEMF Austin, TX USA E-mail: [email protected] Chapter 14 M. Celuch* and P. Kopyt Institute of Radioelectronics Warsaw University of Technology ul. Nowowiejska 15/19 00-665 Warsaw Poland E-mail: [email protected]; [email protected]

Introduction

Developing food products (and associated packaging) intended to be prepared in the common microwave oven presents numerous and familiar challenges. This book was written to help developers understand the science underlying these difficulties and to provide insight and suggest tools to address them. The book is intended for those with some introductory training in electromagnetics or who have microwave development experience and are motivated to understand and apply modern development tools. For those needing an introduction which starts from the very beginning, we recommend Buffler's excellent little book (Buffler, 1993). Electromagnetics is a difficult subject, and microwave heating (in which the electric field strength is high enough and the food or packaging is `lossy' enough to heat) is even more so. Useful introductory material is scattered through the academic, trade, and patent literature and can be difficult to locate. Further, introductory material by definition is simplified, and unfortunately is sometimes oversimplified. Our guiding principle has been to provide a comprehensive survey, written with clarity, at a level needed to efficiently and effectively design products and packaging intended for use in microwave ovens. We have done our best to make this book an effective learning tool. We wish to thank all of the authors who worked under tight deadlines and tolerated the editors' multiple requests for yet another revision to (we hope) further improve clarity, our colleagues at General Mills for their support and encouragement, and our families for their patience and understanding over the two years we devoted to this project. Matt Lorence Peter Pesheck

Reference Buffler, C.R. (1993) Microwave Cooking and Processing: Engineering Fundamentals for the Food Scientist, Aspen Publishers, Gaithersburg, MD.

1

Electromagnetic basis of microwave heating J T A N G and F P R E S U R R E C C I O N J R , Washington State University, USA

Abstract: This chapter provides the fundamentals of electromagnetic (EM) waves relating to microwave heating and processing of foods. Included are broad discussions on the characteristics of EM waves generated from the source and on to food materials in accordance with Maxwell equations. Important concepts such as electromagnetic wave propagation and penetration, energy associated with EM waves, and conversion to heat relating to the dielectric properties of food materials are discussed in preparation for more detailed discussions in other chapters. In particular, important information relating to electromagnetic field distributions in waveguides, microwave cavities, and foods are presented to the readers to allow a general understanding of complicated physical phenomena associated with heating uniformity in both domestic ovens and industrial scale microwave systems. Key words: microwaves, electromagnetic, wave equation, dielectric property, oven cavity, microwave heating.

1.1

Introduction

Microwave heating of foods results from conversion of electromagnetic energy to thermal energy through increased agitation of water molecules and charged ions when exposed to microwaves. Direct penetration of microwaves into food materials enables us to heat foods much faster than conventional heating methods that rely on surface heating such as countertop stoves or baking ovens. The convenience brought about by fast microwave heating makes microwave ovens a household necessity in modern society. Microwave heating systems are also commonly used in the food service and processing industry for fast heating applications. However, users of microwave ovens or industrial microwave systems also experience various frustrations, in particular non-uniform heating. Factors that influence uneven microwave heating include microwave cavity design, food physical properties, and food geometry. Those factors determine how the microwave field is distributed in ovens and within foods. This chapter will discuss fundamental principles which underlie the unique characteristics of microwaves in air and in foods, thus laying a foundation for discussions in other chapters of the book. This chapter includes an introduction to microwave heating in a broad context of electromagnetic (EM) energy and Maxwell equations that govern the

4

Packaging and products for use in microwave ovens

fundamental behavior of EM waves in air, in microwave cavities and in foods. Several very important equations derived from Maxwell equations, including wave equations, power equation, and Snell's law, are presented. Those equations provide insights into microwave heating behavior in domestic and industrial microwave ovens and in foods. Finally dielectric properties of foods are briefly discussed in connection with microwave heating and heating uniformity.

1.2

Microwaves

Microwaves are electromagnetic waves at frequencies between 300 and 300,000 MHz (Decareau, 1985), with corresponding wavelengths of 1 to 0.001 m, respectively. Microwaves are used in communication systems and radar (Radio Detection and Ranging). Radar systems were first developed during World War II for detecting enemy aircraft, and are now used for a wide range of remote sensing and motion detection applications, including air-traffic control, missile tracking, weather forecasting, and automobile motion sensing. Microwave communication systems include wireless computer networks, global positioning satellite systems, and cellular video systems (Pozar, 1998). Owing to heavy uses for radar and wireless communication applications, only a limited number of microwave frequency bands are allocated in different countries (in the US by the Federal Communications Commission or FCC) for industrial, scientific, and medical (ISM) applications to avoid interference to radar and wireless communication. Table 1.1 lists ISM bands used in different food applications. Industrial equipment for the listed frequency bands is readily available from commercial suppliers. Table 1.1 Important microwave frequency allocations for industrial, scientific and medical (ISM) use (Decareau, 1985; Metaxas and Meredith, 1993; Buffler, 1993) Frequency (MHz)

Frequency tolerance (MHz)

896 915

10 13

2375

50

2450

50

Example of industrial applications

Countries

Tempering of frozen products Precooking of bacon, tempering of frozen products Domestic microwave ovens

Great Britain North and South America, China Albania, Bulgaria, Hungary, Romania, Czechoslovakia, former USSR Worldwide, except where 2375 MHz is used

Domestic microwave ovens, industrial precooking of bacon, pasteurization and sterilization of packaged foods

Electromagnetic basis of microwave heating

1.3

5

EM waves

EM waves propagate in space at the speed of light ( 3  109 m/s). X-rays, visible light, microwave, radio waves, and light are some of the different forms of electromagnetic waves characterized by wavelength and frequency (Fig. 1.1). The microwave portion of the spectrum lies in the frequency range 300±300,000 MHz and is therefore a non-ionizing form of electromagnetic energy (Schubert and Riegel, 2005). EM waves traveling in space without obstruction approximate the behavior of plane waves. Electromagnetic waves have an electric (E) field component and a magnetic (H) field component that oscillate in phase and in directions perpendicular to each other. The behavior of each quantity in a specified region in space is described by the wave equations that we will discuss later in this section. For plane waves, also called transverse electromagnetic (TEM) waves, both E and H components are in transverse planes (perpendicular) to the traveling direction of the electromagnetic wave. In mathematical terms, an electromagnetic wave propagates in the direction of the cross-product of two vectors E  H. That is, assuming that the direction of the propagation of EM waves is in the z direction as illustrated in Fig. 1.2, the x-z plane contains the electric component E with the electric field components directed towards the x-axis, while the y-z plane contains the magnetic component H with magnetic field components directed towards the y-axis. The amplitude of an electromagnetic wave determines the maximum intensity of its field quantities. The amplitude of the electric field (Eo) is measured in

1.1 Electromagnetic wave spectrum (The National Physical Laboratory, NPL).

6

Packaging and products for use in microwave ovens

1.2 Electromagnetic wave propagation.

volts per meter (V/m) and the magnetic field (Ho) in amperes per meter (A/m). A peak to peak value covers one complete cycle of a wave (Fig. 1.2). A complete cycle can also be measured from a given point of intersection on an axis up to a second point of intersection. The wavelength () of an EM wave is the distance between two peaks of either electric or magnetic field. The number of cycles per second is called temporal frequency (f). The unit of temporal frequency is expressed in hertz (Hz) which is equal to cycle/s. The time required for a wave to complete a cycle is referred as period (T, in second), and T ˆ 1=f . Wavelength and temporal frequency are quantities that are inversely proportional. The proportionality constant is the velocity, or speed of propagation (Up) in m/s and is given in the equation as f ˆ Up …1=†. In free space, the speed of propagation is equal to the speed of light (c): c ˆ f

1:1

The speed of light in free space, which is a constant value, is a meter traveled by light at an interval of 1 per 299 792 548ths of a second which is approximately 3  108 m/s (Sullivan, 1983). Angular frequency (!) is the ratio of one complete cycle (2) to the period (T) of a sinusoidal EM wave. It is expressed as: 2 T ! ˆ 2 f

!ˆ

1.4

General wave equations

1.4.1

Maxwell equations

1:2 1:3

A set of four Maxwell equations governs the general characteristics of electromagnetic waves traveling in a medium. These equations are:

Electromagnetic basis of microwave heating

7

rDˆ

1:4

rBˆ0

1:5

r  E ˆ ÿ

@H @t

1:6

@E 1:7 @t where the symbols are as explained in Table 1.2. For the above equations to be valid, the medium should have a uniform property that is linear, homogeneous, and isotropic. Linearity means the electric flux density D is directly proportional to the electric field intensity …D ˆ "E† and magnetic flux density B is directly proportional to the magnetic field intensity …B ˆ H†. Homogeneity means that the dielectric properties of the medium (permittivity, permeability, and conductivity) at all points in the path of the EM wave are the same. Isotropicity means permittivity (") and permeability () are independent of orientation of the EM wave (Guru and Hiziroglu, 2004). Equation 1.4 describes that the source of an electric field is from the charge density in a given volume, while equation 1.5 denotes that magnetic monopole does not exist. They are collectively known as Gauss's law. Equation 1.6 or Faraday's law explains that a time-varying magnetic field would induce a timevarying electric field. Finally, equation 1.7 or Ampere's circuit law describes the conservation of charge in terms of magnetic field, current flow, and variable electric field. Those laws had been discovered from experimental observations 40±50 years before James Clerk Maxwell published a unified electromagnetic theory in 1873 (Pozar, 1998). r  H ˆ E ‡ "

Table 1.2 Description of symbols Variable

Description

Type

Common unit*

E D H B   "  t r


Electric field intensity Electric flux density Magnetic field intensity Magnetic flux density Volume charge density Permeability Permittivity Conductivity Time Del operator Dot product Cross-product

Vector Vector Vector Vector Scalar Scalar Scalar Scalar Scalar Vector/Scalar Scalar Vector

V/m C/m2 A/m Wb/m2 C/m3 H/m F/m S/m second

*V = volts, C = coulomb, A = amperes,Wb = weber, H = henry, F = farad, S = siemen.

8

1.4.2

Packaging and products for use in microwave ovens

Wave equations

Specific wave equations can be derived from Maxwell's equations. For simplification, the medium in which the EM wave travels is assumed to have no charge density and current density (Sadiku, 2006). By applying curloperation on equations 1.6 and 1.7, wave equations in terms of electric field intensity or magnetic field intensity are expressed as (Metaxas, 1996): r2 E ˆ 

@E @2E ‡ " 2 @t @t

1:8

@H @2H ‡ " 2 1:9 @t @t The above two equations are not independent; the knowledge of electric field intensity leads to the magnetic field intensity, or vice versa, as indicated in the Maxwell equations 1.6 and 1.7. For simplicity, we only consider sinusoidal time-varying fields (referred to as time-harmonic fields). Equations 1.8 and 1.9 can then be written in the following forms: r2 H ˆ 

r2 E ˆ 2 E 2

2

r Hˆ H where is referred to as propagation constant and p

ˆ j!… ‡ j!"† ˆ  ‡ j

1:10 1:11 1:12

In equation 1.12, ! is the angular frequency of the sine wave (! ˆ 2f ) and j p denotes imaginary number (j ˆ ÿ1). Metaxas (1996) shows detailed derivation of the general Maxwell's equations to obtain the above two equations for time-harmonic fields. The propagation constant is a complex number. The real part (), referred to as the attenuation constant, describes the decrease in the amplitude of the wave (due to absorption and thus generation of heat) as it travels in a certain medium. The imaginary part ( ), referred to as phase constant, characterizes the propagation of the wave. Both parts are related to the permittivity, permeability and electric conductivity of the medium in question (Sadiku, 2006): v # u "r   2 u" ÿ1 1:13a  ˆ 2 f t 1‡ 2 !" v # u "r   2 u" ˆ 2 f t ‡1 1‡ 2 !" The wave velocity is related to the phase constant by

1:13b

Electromagnetic basis of microwave heating Up ˆ

2 f

9 1:13c

and wavelength by ˆ

2

1:13d

The magnitude of the electric field in an EM wave is proportional to that of the magnetic field. The proportionality constant is the intrinsic impedance (), and is a function of the medium properties " and . The intrinsic impedance is a complex number (consisting of real and imaginary parts) with corresponding magnitude and angle: s E j! j! 1:14 ˆ ˆ ˆ ˆ jj€ H

 ‡ j!" where: jj ˆ 

p ="   2 1=4 1‡ !"

1:14a

 1:14b !" With the propagation constants and intrinsic impedance parameters described above, both electric field intensity and magnetic field intensity for the EM wave traveling along the z-axis (Fig. 1.2) can be expressed in the phasor form (for explanation of phasor notation see Sadiku, 2006) tan2 ˆ

Ex …‡z† ˆ Ex0 eÿz eÿj z Hy …‡z† ˆ

1 Ex0 eÿz eÿj z eÿj jj

Ex …ÿz† ˆ Ex0 ez ej z Hy …ÿz† ˆ ÿ

1 Ex0 ez ej z eÿj jj

1:15 1:16 1:17 1:18

where Ex0 indicates the amplitude of EM wave at z ˆ 0, while Ex(z) and Hy(z) denote electric field and magnetic field which propagate in the z-axis while oscillating in the direction of x-axis and y-axis, respectively. Ex(+z) and Hy(+z) are forward moving waves, while Ex(ÿz) and Hy(ÿz) are the backward moving waves. The quantities eÿz and ez determine if, or how fast, the amplitude decays with distance into the medium; the quantities e j z eÿj and ej z eÿj describe the other characteristics of the wave such as phase, wavelength, and velocity.

10

Packaging and products for use in microwave ovens

1.4.3

Energy and power

Microwave carries electromagnetic energy as it travels through a medium. A measure of the microwave power across a unit area is the Poynting vector (in w/m2) defined as (Sadiku, 2006): PˆEH

1:19

It is an instantaneous power density vector in the direction of microwave propagation and is a function of time and location. The Poynting vector for a plane wave traveling in the z direction, as shown in Fig. 1.2, can be expressed as P…z; t†. Its time average value, a more commonly used value to indicate the changes in microwave power with distance, is calculated as: Z 1 T Pave …z† ˆ P…z; t†dt 1:20 T 0 For time-harmonic waves and using equations 1.15 and 1.16, the magnitude of microwave power as a function z can be written in terms of electric field intensity: Pave …z† ˆ

1 2 ÿ2z E e cos 2jj x0

1:21

or simply: Pave …z† ˆ Pave …0†eÿ2z

1:22

where Pave …0† is the microwave power flux intensity (w/m2 ) at z ˆ 0. Equation 1.22 resembles the form of the Beer±Lambert law developed empirically for reduction of light intensity as it travels through different materials (Ingle and Crouch, 1988).

1.5

Propagation of microwaves in different media

For convenience, the discussion of EM wave characteristics is made in connection with different media classified into four different general categories: (1) free space, (2) lossless dielectric; (3) lossy dielectric; and (4) good conductor (Guru and Hiziroglu, 2004). As will be seen later, categories 1, 2, and 4 can all be considered as special cases of category 3.

1.5.1

Free space

Free space is defined as a perfect vacuum or, at microwave frequencies, air. The permittivity, permeability, and conductivity of a free space have the following values:

Electromagnetic basis of microwave heating

11

"0 ˆ 10ÿ9 =36 F/m 0 ˆ 4  10ÿ7 H/m 0 ˆ 0 S/m

1:23

The permittivity and permeability of all other media are given relative to the dielectric properties of free space: " ˆ "r "0  ˆ r 0

1:24 1:25

where "r and r are dimensionless numbers, referred to as relative permittivity and relative permeability respectively. For free space, "r ˆ 1, and r ˆ 1. Food materials are generally non-magnetic in nature, the relative permeability approximates a value of one (r ˆ 1). Using the values provided by equations 1.23, the intrinsic impedance of a free space (0 ) can be calculated from equation 1.14: r 0 ˆ 120  377

1:26 0 ˆ "0 The velocity (Up) for the EM wave traveling in free space is calculated from equation 1.13c as: Up ˆ

2 f 2 f 1 m ˆ p ˆ p ˆ 299 792 548  3  108 m/s 2 f 0 "0 0 "0 s 1:26a

The above value is indeed the speed of light. Thus, often the more conventionally used symbol c is used, instead of Up. Likewise, the wavelength in free space (and air) is calculated using Equation 1.13d: 0 ˆ

1.5.2

2 2 1 c ˆ p ˆ p ˆ 2 f 0 "0 f 0 "0 f

1:26b

Lossless dielectric media

In a lossless dielectric medium (e.g., plastics, glasses, and other electrically nonconductive materials) the conduction current is negligible compared with the displacement current (expressed as the second term on the right-hand side of Equation 1.7). Thus conductivity can be assumed approximately zero ( ˆ 0). The parameters that determine wave propagation, impedance, and phase angles expressed in the general Equations 1.12 and 1.14 can be simplified into: ˆ0

1:27

p ˆ 2 f r 0 "r "0

1:28

12

Packaging and products for use in microwave ovens r r r 0  ˆ ˆ "r "0 "  ˆ 0

1:29 1:30

The general form for a transverse EM wave (Equations 1.15 and 1.16) traveling in a lossless dielectric medium in the direction z can also be simplified into: Ex …‡z† ˆ Ex0 eÿj z 1 Hy …‡z† ˆ Ex0 eÿj z 

1:31 1:32

The above wave equations suggest no reduction in intensity as EM wave travels in the z direction.

1.5.3

Lossy dielectric media

A lossy dielectric medium is defined as a medium in which the electric conductivity is not equal to zero yet it is not a good conductor. Setting  6ˆ 0 in Equation 1.12 leads to a non-zero attenuation constant ( 6ˆ 0). The general wave equations and the associated parameters expressed in Equations 1.12 to 1.22 therefore apply to lossy dielectric media. According to Equations 1.15 and 1.16, the amplitude of electric and magnetic fields decreases exponentially with travel distance (Fig. 1.3). The changes in the amplitudes are quantified by the attenuation constant (). Microwave power was lost (i.e., converted to heat) according to Equation 1.22: Pave …z† ˆ Pave …0†eÿ2z

1:33

This is illustrated in Figure 1.4 as an EM wave enters into a lossy dielectric medium. The larger the value of the attenuation constant (), the more rapidly the EM wave loses its power along the path of transmission. The ability of EM to penetrate a lossy dielectric material is indicated by power penetration depth,

1.3 Reduction in wave amplitude with travel distance.

Electromagnetic basis of microwave heating

13

1.4 Attenuation of EM wave in a lossy dielectric medium and definition of power penetration depth.

commonly (in contrast to the half power depth) defined as the distance over which the EM power decreases to 0.368 (1/e) of the original value (Metexas and Meredith, 1993). From this definition, one can derive the expression for the power penetration depth (dp) using Equation 1.22: 1 Pave …dp † ˆ Pave …0†eÿ2dp ˆ Pave …0† e Using the last two terms in the above equation yields: 1 2 Substituting in Equation 1.13a yields: dp ˆ

dp ˆ

1 s r    2 ÿ1 2 f 2" 1‡ !"

1:34

1:35

1:36

The above equation will be used in a later section to discuss microwave power penetration in foods in connection with microwave heating uniformity.

1.5.4

Good conductor

Good conductors, such as metals, are characterized by extremely large electric conductivities (i.e., copper ˆ 6  107 S/m). Thus, setting  ˆ 1 in Equations 1.12 and 1.14 leads to  ˆ 1, ˆ 1, and Up ˆ 0. These values suggest that microwaves do not transmit in good conductors. In reality, all metals are not perfect conductors, and electric conductivity is not infinitely large. The electromagnetic wave does penetrate several micrometers, depending upon the electric conductivity of the materials. But for practical reasons, we consider all metals to be perfect dielectric conductors (PEC). Metals

14

Packaging and products for use in microwave ovens

are used to confine microwave energy in a space (i.e., in a microwave cavity) or to guide microwave (i.e., in a waveguide) to a specific application location.

1.6

Propagation of electromagnetic wave between two media

This section provides a brief description of the general characteristics of electromagnetic waves when traveling through two different yet adjacent media (e.g., from medium 1 to medium 2). The wave traveling in medium 1 before encountering medium 2 is called the incident wave. At the interface between medium 1 and 2, a portion of the incident wave will enter medium 2 and be transmitted at a certain angle (t ) referred to as the angle of transmission (Fig. 1.5a). This wave is called the transmitted wave. The rest of the incident wave will be reflected back to medium 1 at a certain angle called the angle of reflection (r ). This wave is called the reflected wave. If the direction of the incident wave is perpendicular to the interface of the two media (i ˆ 0), the resulting angle of transmission and reflection will be equal to zero (t ˆ r ˆ 0) (Fig. 1.5b). This condition is called normal penetration of EM waves, since the direction of propagation is normal to the interface. In a more general case in which an incident wave travels at a certain angle to the interface between the two media (i > 0), the angle of transmission and reflection will no longer be equal to zero. This condition is called oblique penetration of EM waves. The portion of an incident wave being transmitted is quantified by the transmission coefficient () defined as the ratio of the amplitude of the transmitted electric field over the amplitude of the incident electric field: ˆ

Ex0…transmitted† Ex0…incident†

1:37

1.5 Propagation of electromagnetic wave at the interface of two different media: (a) general case, and (b) normal penetration.

Electromagnetic basis of microwave heating

15

The portion of an incident wave being reflected is quantified by the reflection coefficient (%) defined as the ratio of the amplitude of the reflected electric field over the amplitude of the incident electric field: %ˆ

1.6.1

Ex0…reflected† Ex0…incident†

1:38

Normal penetration

For normal penetration of electromagnetic wave, the transmission and reflection coefficients can be expressed in terms of intrinsic impedances of the two media (1 , 2 ) (Guru and Hiziroglu, 2004): ˆ

Ex0…transmitted† 22 ˆ Ex0…incident†  2 ‡ 1

1:39

%ˆ

Ex0…reflected† 2 ÿ 1 ˆ Ex0…incident† 2 ‡ 1

1:40

where subscripts 1 and 2 denote the first and second media, respectively. The above equations were derived from the assumption that there is no current density at the interface of the two media and that the tangential component of electric and magnetic field are continuous. In an air±dielectric medium interface, the equations of incident, reflected, and transmitted waves are as follows: Ex …‡z†incident ˆ Ex0…incident† eÿj 1 z Hy …‡z†incident ˆ

1 Ex0…incident† eÿj 1 z 1

Ex …ÿz†reflected ˆ %Ex0…incident† ej 1 z Hy …ÿz†reflected ˆ ÿ

% Ex0…incident† ej 1 z 1

Ex …‡z†transmitted ˆ Ex0…incident† eÿj 2 z Hy …‡z†transmitted ˆ

 Ex0…incident† eÿj 2 z 1

1:41 1:42 1:43 1:44 1:45 1:46

Equations 1.41 and 1.42 describe the incident wave traveling in medium 1 in the positive direction of z (towards medium 2). Equations 1.43 and 1.44 are for reflected waves traveling in medium 1 in the negative z direction, away from medium 2. The incident wave is considered to be a forward moving wave and the reflected wave a backward moving wave. The intrinsic impedance and angular phase for these two waves depend on properties of medium 1 (1 , 1 ). The transmitted wave described by Equations 1.45 and 1.46 is a forward moving

16

Packaging and products for use in microwave ovens

wave traveling in medium 2 at positive z direction. The intrinsic impedance and angular phase in this wave is dependent on medium 2 (2 , 2 ). If medium 2 is a good conducting material ( ˆ 1), the corresponding 2 is approximately 0 (see Equation 1.14). Using Equations 1.39 and 1.40, the transmission coefficient  is then calculated to be zero and the reflection coefficient to be ÿ1. That is, the microwave is totally reflected at the interface. Microwave oven walls are made of metal sheets with large electric conductivities. Thus, in an enclosed microwave cavity, the microwaves are reflected back and forth between metal surfaces, forming standing wave patterns, which will be discussed in depth in a later section.

1.6.2

Oblique penetration

Polarization, defined by the direction of the electric field at a given point (Guru and Hiziroglu, 2004), of EM wave does not influence the form of the equations for plane waves traveling normal to the interface of two media. However, for waves traveling oblique to the interface, the expressions for transmission and reflection coefficients depend upon the manner in which the wave is polarized. Therefore discussions of wave equations for oblique penetration are made with respect to polarization of EM waves. An EM wave can either have parallel or perpendicular polarization relative to the plane of incidence. The plane of incidence is defined by two vectors: the propagation vector (in the direction of wave propagation) and the unit vector normal to the interface of the two media. For the simple case in Fig. 1.5, the x±z plane is the plane of incidence. In parallel polarization the direction of electric field is in the plane of incidence and the direction of magnetic field is perpendicular to the plane of incidence. In perpendicular polarization, on the other hand, the direction of electric field is perpendicular to the plane of incidence and magnetic field is in the plane of incidence. By applying continuity on the tangential component of both electric and magnetic fields for the two adjacent media, expressions for the reflection and transmission coefficients can be obtained in terms of intrinsic impedance of the two media. The equations for reflection and transmission coefficients for both parallel and perpendicular polarization are as follows (Sadiku, 2006): %k ˆ

2 cost ÿ 1 cosi 2 cost ‡ 1 cosi

1:47

k ˆ

22 cosi 2 cost ‡ 1 cosi

1:48

%? ˆ

2 cosi ÿ 1 cost 2 cosi ‡ 1 cost

1:49

Electromagnetic basis of microwave heating ? ˆ

22 cosi 2 cosi ‡ 1 cost

17 1:50

where subscripts k and ? denote parallel and perpendicular polarization, respectively. The relations between reflection angle r and incidence angle i and between transmission angle t and incidence angle i are described by Snell's law of reflection and refraction, respectively. Snell's laws are derived by considering the boundary condition at the interface. For example, at the interface shown in Fig. 1.5(a) at z ˆ 0, the tangential component of EM field follows a continuity equation (Guru and Hiziroglu, 2004): eÿ 1 x sini ‡ %? eÿ 1 x sinr ˆ ? eÿ 2 xsint 1 eÿ 2 x sini ‡ %k eÿ 1 x sinr ˆ ? eÿ 2 xsint 2

1:51 1:52

for perpendicular and parallel polarizations, respectively. In perpendicular polarization (Equation 1.51), both reflected and transmitted waves are proportional to the reflection and transmission coefficient, respectively. These coefficients will sum to one assuming a perfectly conserved EM wave. The expression can be obtained by setting x equal to zero in Equation 1.51. 1 ‡ %? ˆ ?

1:53

In parallel polarization (Equation 1.52), however, the transmitted wave is proportional to the product of transmission coefficient and the ratio of the intrinsic impedance at medium1 and intrinsic impedance at medium 2: 1 1 ‡ %k ˆ k 1:54 2 Equating Equation 1.51 with Equation 1.53 and Equation 1.52 with Equation 1.54 simultaneously for all values of x would give an equation of:

1 sini ˆ 1 sinr ˆ 2 sint

1:55

The relationship would result into three terms of equality. The first and second terms are the basis of Snell's law of reflection (Equation 1.56) which states that the incident angle (i ) is equal to the reflection angle (r ). Thus, it is convenient to assign both to 1 as they are in medium 1. Equating the third term of Equation 1.55 to either first or second term yields Snell's law of refraction (Equation 1.57) which states that the product of propagation constant of the first medium ( 1 ) and the sine of the angle in the first medium (1 ) is equal to the product of propagation constant of the second medium ( 2 ) and the sine of the transmission angle (t ). As t is for the second medium, we use symbol 2 instead. In summary: 1 ˆ i ˆ r

1:56

18

Packaging and products for use in microwave ovens  

1 2 ˆ sinÿ1 sin1 ) 1 sin1 ˆ 2 sin2

2

1:57

If interfacing media are dielectric±dielectric or free space±dielectric, the ratio of propagation constant would become (assuming non-magnetic media with r ˆ 1): r

1 j 1 "r1 1:58 ˆ ˆ

2 j 2 "r2 where "r1 and "r2 are the relative permittivity of the first and second medium, respectively. Snell's law of refraction can be written in a simplified form: r  "r1 1:59 2 ˆ sinÿ1 sin1 "r2 Snell's law is useful in understanding the unique microwave heating patterns within certain size spherical and cylindrical shaped foods. Detailed discussion of this subject can be found in Buffler (1993).

1.7

Standing waves

Consider a simple condition wherein a transverse EM wave (shown in Fig. 1.2) travels in the air in a direction normal to a good conducting surface, such as a metal wall, at z ˆ 0. As discussed earlier in Section 1.6, the wave will be completely reflected back. To satisfy the boundary condition that the tangential electric field intensity at the metal wall is zero, the reflected wave is 180ë out of phase with the incident wave at the reflection surface. The reflected wave and the incident wave, traveling with equal amplitude but in opposite directions, form a field pattern that appears to be stationary (referred to as a standing wave) with fixed locations of zero intensity, where the two waves are 180ë out of phase, and maximum intensity, where the two waves are in phase. The locations for the maximum and zero intensity are adjacent to each other and separated by 1/4 wavelength with a zero intensity location at the metal wall (see Fig. 1.6). The field intensity of the standing wave at the maximum is twice that of a single traveling wave.

1.6 Illustration of a standing wave oscillating with amplitude that changes with location in space. The right-hand minimum point is at the metal wall.

Electromagnetic basis of microwave heating

19

1.7 Illustration of a standing wave with a flexible string; the location of nodes (minimum amplitude) and anti-nodes (maximum amplitude) are fixed in space, depending on wavelength.

An intuitive way to describe a standing wave is to imagine a flexible string with one end attached to a fixed wall (Fig. 1.7). Waves can be introduced by swinging the other end of the string. When the first full wave encounters the fixed point, it is reflected back in the opposite direction. Reflection happens because the wave from the string cannot travel beyond the wall. The point of the attachment causes a momentum change, shifting the phase angle by 180ë. The first full wave now traveling backward encounters the second full wave traveling forward. The first and second waves interfere and form a standing wave pattern with node (minimum amplitude) and anti-node (maximum amplitude) at fixed locations. The standing waves in microwave cavities create cold and hot spots, which is one of the main reasons for uneven heating.

1.7.1

Voltage standing wave ratio

In a general case where a reflective surface is not a highly conductive material, only a portion of the incident wave is reflected. The amplitude of the reflected wave is less than that of the incident wave as quantified by the reflection coefficient (%) (refer to Equation 1.40). The standing wave formed by the

20

Packaging and products for use in microwave ovens

1.8 Voltage standing wave ratio: (a) incident wave in phase with partially reflected wave; (b) incident wave 180ë out of phase with partially reflected wave; (c) incident wave in phase with completely reflected wave; (d) incident wave 180ë out of phase with completely reflected wave.

incident and reflected waves has maximum and minimum amplitude at the locations of 0 and 180 phase difference (Fig 1.8a and 1.8b, respectively): Emax…standing† ˆ E0…incident† ‡ E0…reflected†

1:60

Emin…standing† ˆ E0…incident† ÿ E0…reflected†

1:61

Voltage standing wave ratio (VSWR) is a value used to quantify the maximum and minimum amplitudes of a standing wave. It is calculated as the ratio between the absolute value of the maximum and minimum amplitude of a standing wave: VSWR ˆ

jEmax j jEmin j

1:62

VSWR has a value between 1 and infinity. The VSWR value for the standing wave formed by an incident and completely reflected waves discussed earlier is equal to infinity (refer to Fig 1.8c and 1.8d). When there is no reflection, as in

Electromagnetic basis of microwave heating

21

the case where a wave travels from a waveguide into a matching load, no standing wave will be formed. Therefore, Emin ˆ Emax and VSWR is equal to one (VSWR ˆ 1).

1.8

Waveguide

A waveguide is a hollow metallic channel that has either a rectangular or a cylindrical cross-section. The main purpose of a waveguide is to direct electromagnetic wave from a microwave source (e.g., a magnetron) to a microwave applicator (e.g., an oven cavity). Although different shapes of waveguide are designed for different purposes, a rectangular shape waveguide (Fig. 1.9) is commonly used in industrial microwave heating and solely in domestic microwave ovens. When confined in a waveguide, an electromagnetic wave travels with certain patterns (modes) governed by the Maxwell equations under the boundary conditions defined by the conducting waveguide walls. TEM waves will not propagate in a waveguide. Propagation is either by transverse electric modes (TEzmn ) or transverse magnetic modes (TMzmn ). In TEzmn modes, the electric field is transverse to the direction of wave propagation along the waveguide (i.e., the z direction in Fig. 1.9), thus Ez ˆ 0. In TMzmn modes, the magnetic field component is transverse to the direction of wave propagation, and Hz ˆ 0. Each mode is characterized by a discrete field pattern quantified by integers, m and n (i.e., 0, 1, 2 . . .), which represent the number of half wave variations in field patterns along x and y direction, respectively (Sadiku, 2006). In TE modes both m and n cannot be zero at the same time; in TM modes m and n cannot be equal to zero which means the lowest value is 1. The type of modes, each having a discrete pattern inside the waveguide, depends on waveguide dimensions, the

1.9 Rectangular waveguide.

1.10 Field pattern of TEz10 (a) and TMz11 (b) (Guru and Hiziroglu, 2004).

Electromagnetic basis of microwave heating

23

medium inside, and the operating frequency of the electromagnetic wave (Guru and Hiziroglu, 2004). Figure 1.10 illustrates the electric field and magnetic field for TEz10 (a) mode and TMz11 (b) mode seen from different cross-sections of a waveguide. The solid lines show the direction of the electric field; the dashed lines show the direction of the magnetic field. The density of the lines indicates field intensity. Since the tangential electric field at a good conductive surface is zero, in the proximity of metal walls the electric field lines are always perpendicular to wall surfaces, accordingly the magnetic field lines are parallel to the wall surfaces. From the transverse cross-sectional view (top graph of Fig. 1.10a), the electric field pattern for the TEz10 mode has one half wave variation along the x axis, with zero field intensity along both vertical walls of the waveguide (in y direction). For the TMz11 mode, the magnetic field has one half wave variation in both x and y directions (top graph of Fig. 1.10b). Figure 1.11 illustrates threedimensional field patterns for TEz10 mode and TMz11 . The general equation of electromagnetic wave traveling inside a waveguide can be obtained by deriving the Maxwell's equations and applying the boundary conditions on four corners of the metal surface of the waveguide. The following are the wave equations for electric and magnetic fields in different directions (Ex, Ey, Ez, Hx, Hy, and Hz) for both TE and TM modes propagating along the z axis. For TEzmn mode: Ex ˆ Ey ˆ

j!NH0

…j z†2 ‡ !2 " ÿj!MH0

…j z†2 ‡ !2 "

cos…Mx†sin…Ny†eÿj z

1:63

sin…Mx†cos…Ny†eÿj z

1:64

Ez ˆ 0

1.11 Field pattern of TEz10 and TMz11 (Jefferies, 1994).

1:65

24

Packaging and products for use in microwave ovens Hx ˆ Hy ˆ

j MH0

…j z†2 ‡ !2 " j NH0

…j z†2 ‡ !2 "

sin…Mx†cos…Ny†eÿj z

1:66

cos…Mx†sin…Ny†eÿj z

1:67

Hz ˆ H0 cos…Mx†cos…Ny†eÿj z

1:68

For TMzmn mode: Ex ˆ Ey ˆ

ÿj ME0

…j z†2 ‡ !2 " ÿj NE0

…j z†2 ‡ !2 "

cos…Mx†sin…Ny†eÿj z

1:69

sin…Mx†cos…Ny†eÿj z

1:70

Ez ˆ E0 sin…Mx†sin…Ny†eÿj z Hx ˆ Hy ˆ

j!"NE0

…j z†2 ‡ !2 " ÿj!"ME0

…j z†2 ‡ !2 "

Hz ˆ 0

1:71

sin…Mx†cos…Ny†eÿj z

1:72

cos…Mx†sin…Ny†eÿj z

1:73 1:74

E0 and H0 is the maximum amplitude of electric field and magnetic field, respectively. M and N are the half wave representation of waves. For a rectangular waveguide (Fig. 1.9) M and N are equal to m 1:75 Mˆ a n 1:76 Nˆ b Cutoff frequency (fcmn) is the lowest frequency that allows propagation of EM wave. For electromagnetic waves to propagate along a waveguide, the operating frequency (fmn) should be greater than the cutoff frequency for a given mode. Consider the propagation constant of EM wave inside the waveguide ( mn ) which is a complex number (Equation 1.77). If the operating frequency is greater than the cutoff frequency (fmn > fcmn), mn will become an imaginary number ( mn ˆ mn ), indicating purely propagation of waves. The equation of the cutoff frequency (Equation 1.78) can be derived by equating mn to zero and using the expression ! ˆ 2f . r m2 n2 ‡ ÿ!2 " ˆ mn ‡ mn 1:77

mn ˆ a b

fcmn

Electromagnetic basis of microwave heating r m2 n2 1 ˆ p ‡ 2 " a b

25 1:78

However, if the operating frequency is less than the cutoff frequency, mn is a real number ( mn ˆ mn ), indicating purely attenuating waves. Under this condition, the EM wave will exponentially attenuate along the z direction (Harrington, 1961). It is possible that multiple modes may co-exist inside a waveguide. For a waveguide that has a dimension a ˆ 2b, the value of the cutoff frequency for given m and n integers are in the following increasing order; fc10 < fc01 < fc11. If the excitation frequency is between fc10 and fc01 (i.e., fc10 < fmn < fc01), only one mode will predominate, which is the TE mode. This is called single mode operation. However, if the excitation frequency is greater than fc11 (i.e., fc11 < fmn), both TE and TM modes may coexist. This is called a multimode operation. The field pattern and behavior of the wave is easier to characterize for a single mode compared to multimode. Most rectangular waveguide are designed to carry TEz10 mode. For example, in a domestic microwave oven operating at 2.45 GHz, a WR340 waveguide which has dimensions of a ˆ 86 mm and b ˆ 43 mm is commonly used (Guru and Hiziroglu, 2004). The cutoff frequencies of TEz10 and TEz01 modes are 1.74 and 3.49 GHz, respectively, hence a 2.45 GHz operating frequency is within the range and would propagate in the TEz10 mode.

1.9

Field patterns in single-mode and multimode cavities

During microwave heating, materials are enclosed in spaces surrounded by metal walls. Those specially designed spaces are commonly referred to as microwave cavities. A microwave cavity can be categorized as single mode or multimode. A single-mode cavity has dimensions which allow only one possible field pattern. This field pattern is created by the standing wave between the walls of the cavity. Figure 1.12 shows the example of a single mode cavity. It consists of a TEz10 waveguide, a small cavity (or resonator), and a coupling aperture to maximize the power coupled into the cavity. The size of the cavity is comparable to or slightly larger than that of the waveguide, and the excitation frequency from the source of microwave power is provided within a narrow frequency band to maintain the necessary coupling (Metaxas and Meredith, 1993). Inside the cavity shown in Fig. 1.12, the maximum electric field is at the center. The food material is loaded to a position that has a maximum electric field for optimum absorption of energy for microwave heating. This is a major advantage of a single mode cavity. A disadvantage of a single mode cavity is the relatively small zone in which food material can be effectively heated. This

26

Packaging and products for use in microwave ovens

1.12 TM010 cavity resonator (Schubert and Riegel, 2005).

design can be used for heating small samples in analytical laboratories, or for heating liquid or other pumpable materials in industrial applications. Multimode cavities are most commonly used in microwave heating applications. A typical domestic microwave oven is a multimode cavity. The size of a multimode cavity is much larger than that of a single mode for the same operating microwave frequency. Typically the dimensions of a multimode cavity are several times the free space wavelength of the microwave generated by the magnetron. In a multimode cavity, several different field patterns are possible over a narrow frequency range, with each field pattern representing a given mode. Calculation of cutoff frequency of modes inside a microwave cavity is different from that of the waveguide. This is because a waveguide is open ended while a microwave cavity is enclosed. The equation of cutoff frequency for microwave cavity is r m2 n2 p2 1 fcmnp ˆ p ‡ ‡ 1:79 2 " a b l where m, n, and p are integer numbers that represent the discrete pattern of the half wave variation of field with corresponding lengths of a, b, and l along the x, y, and z axes respectively (Fig. 1.13). Modes that exist in an empty microwave cavity are characterized by the discrete pattern of m, n, and p, representing the x, y, and z directions. Specifically, they are designated as TEmnp and TMmnp for transverse electric and transverse magnetic, respectively. In TM modes, the lowest possible value of p is zero (0). In TE modes the lowest possible value of p is one (1). Several TE and TM modes may co-exist for the same frequency bounded by its corresponding cutoff frequency. These modes are referred to as degenerate modes. But two

Electromagnetic basis of microwave heating

27

1.13 Rectangular cavity.

different modes (TE and TM) will only exist at a same frequency if their indices (m, n, and p) are non-zero or two sides of cavity (xy, xz, yz) are equal in length. Although different modes may exist for exactly the same frequency, their corresponding field pattern is not the same. The possible modes that may exist in a microwave cavity can be estimated using Equation 1.80: r m2 n2 p2 p 2fmnp " ˆ ‡ ‡ 1:80 a b l For an empty microwave cavity that has a cubical shape (a ˆ b ˆ l ˆ length), Equation 1.80 can be simplified to:   length 2 ˆ m2 ‡ n2 ‡ p2 1:81 4  Evaluating the left-hand side of Equation 1.80 using the corresponding operating frequency range (fmnp) and the dimension (a, b, and l) of microwave oven gives possible modes and their corresponding indices (m, n, p). This can be done by substituting a trial and error value of m, n and p to the right-hand side while considering the restriction for a TE and TM mode. A combination of m, n, and p that gives a value within the range of the left-hand side of Equation 1.80 is a valid index. Table 1.3 lists the possible modes and their corresponding indices for an empty non-cubical microwave oven operating in a frequency range of 2.425±2.475 GHz. Microwaves are introduced to the cavity via a waveguide. Plates I and II show the electric field patterns in an empty cavity when the excitation frequencies are at 2.4750 and 2.4518 GHz, respectively. When 2.4750 GHz is excited, the mode will be transverse magnetic, specifically TM350 (Plate I). On the other

28

Packaging and products for use in microwave ovens Table 1.3 Possible modes for an empty non-cubical microwave oven (Chan and Reader, 2000) Indices m

n

p

0 0 4 5 2 4 0 1 1 3

5 4 1 3 0 4 2 5 4 5

2 3 3 0 4 1 4 2 3 0

Modes

Frequency (GHz)

TE TE TE, TM TM TE TE, TM TE TE, TM TE, TM TM

2.4320 2.4343 2.4390 2.4464 2.4518 2.4578 2.4600 2.4674 2.4697 2.4750

hand, when 2.4518 GHz is excited, the mode will be transverse electric, specifically TE204 (Plate II). In reality, the above two and several other field patterns may simultaneously be excited in a multimode cavity, because a magnetron does not operate at a single frequency, rather over a certain frequency band width (Schubert and Riegel, 2005). An example of the microwave spectrum generated by a 2.45 GHz magnetron is shown in Figure 1.14. The microwave energy covers a frequency bandwidth of about 50 MHz. A 915 MHz magnetron may have a bandwidth of 15 MHz with operating frequency range of 900 to 915 MHz (Chan and Reader, 2000). When a load such as food is placed inside a microwave cavity, the resulting field distribution becomes even more complicated. It is not possible to use Equations 1.80 and 1.81 to accurately identify the modes inside a loaded cavity. This is because a presence of load can shift modes and can also split or merge degenerate modes (Chan and Reader, 2000). Plate III illustrates a computersimulated electric field distribution in a loaded microwave cavity excited at 2.4295 GHz. Changes in the field pattern, relative to the empty microwave cavity, depend on the complexity of the load. An arbitrary shaped load results in a field distribution that is more complex than a geometrically simple load. Similarly, field patterns in a cavity with multiple loads are more complex than with a single load. EM field distribution in a loaded cavity is totally different from the field distribution suggested by a certain mode or combination of modes in an empty cavity. There are, however, appropriate experimental methods to help determine field distributions in a loaded cavity. These methods primarily relate the proportionality of temperature distribution to electric field distribution. For example, Dibben and Metaxas (1996) and Pathak et al. (2003) used an infrared thermal camera to capture the temperature distribution inside a loaded cavity.

Electromagnetic basis of microwave heating

29

1.14 Frequency spectrum of 2.45 GHz magnetron (Chan and Reader, 2000).

Grellinger and Janney (1993) used fiber optic and infrared temperature sensors to compare temperature distribution within a loaded cavity. More recently, Pandit et al. (2007) and Chen et al. (2008) used chemical markers, resulting from Maillard reactions between amino acids and reducing sugars in low acid model foods (e.g., whey protein gels or mashed potato), to study heating patterns in microwave systems designed for high temperature processing of packaged foods. By far the most effective means to visualize the electromagnetic field patterns inside a microwave cavity is to numerically solve Maxwell equations for space and heated loads in the cavity using high power computer simulation. Among the numerical methods that can be applied to solve electromagnetic problems are finite element method (FEM), finite difference time domain (FDTD) method, and method of moment (MoM). Commercial software such as QuickwaveTM and AnsoftTM are available for this purpose. QuickwaveTM software works using FDTD while AnsoftTM uses FEM. The accuracy of numerical simulation for electromagnetic applications depends on mesh sizes used for cavity and the heated object. A smaller mesh or element normally provides more accurate results (refer to Celuch and Kopyt in Chapter 14 for proper mesh sizing discussion). However, the time it takes to simulate an EM problem increases sharply with reduction in mesh size (Chen et al., 2007). In this regard, it is always a balance between accuracy and computing power of computer that runs the software. The field patterns shown in Plates I±III were generated with

30

Packaging and products for use in microwave ovens

computer simulation. Chapter 14 provides more detailed discussion on FDTD and FEM.

1.10

Microwave heating of foods

1.10.1 Food dielectric properties Food materials are in general not good electric insulators nor good electric conductors, thus fall into the category of lossy dielectric materials. When exposed to an alternating electric field, foods can partially store electric energy as a capacitor and partially convert electric energy into heat, like a resistor. These characters are determined by the complex relative permittivity (relative to free space or air): " ˆ "0 ÿ j"00 ˆ j"jeÿj

1:82

where " ˆ the complex relative dielectric constant, "0 ˆ the relative dielectric constant, "00 ˆ the relative pdielectric loss factor,  ˆ dielectric loss angle (tan  ˆ "00 ="0 ), and j ˆ ÿ1. The relative dielectric constant ("0 ) is related to the material's ability to store electric energy (for vacuum or air "0 ˆ 1), while relative dielectric loss factor ("00 ) indicates dissipation of electric energy due to various mechanisms. As will be discussed later, the rate of microwave heating is directly proportional to the value of relative dielectric loss factor. Foods do not interact with the magnetic field component of electromagnetic waves ( ˆ 0 ). This is because although on a micro-scale each moving electron in a molecule interacts with the magnetic field, the extremely large number of electrons, each having its own random spin direction, provides no global effect in food molecules. But magnetic materials, such as ferrite sometimes used in susceptors and special packages, cause significant heating in strong magnetic fields (Buffler, 1993). Over the electromagnetic spectrum between 0.1 and 100 000 MHz, electric conduction and various polarization mechanisms (including dipole, electronic, atomic and Maxwell±Wagner) contribute to the overall value of relative dielectric loss factor of biomaterials including foods (Metaxas and Meredith, 1993; Kuang and Nelson, 1998). Figure 1.15 provides a brief summary of those mechanisms. The importance of the contribution by each mechanism varies in different frequency ranges and is influenced by temperature, electric conductivity, moisture content, and molecular size of polar molecules (Tang, 2005). In the microwave frequency range of practical importance to food applications (e.g., 2450 and 915 MHz in North America), dipole rotation and electric conductivity are the dominant loss mechanisms, as illustrated in Fig. 1.16 for water solutions. Thus, the value of the loss factor of high-moisture foods at microwave frequencies is the sum of two major components:

Electromagnetic basis of microwave heating "00 ˆ "00d ‡ "00 ˆ "00d ‡

 2 f "0

31 1:83

where subscript `d' stands for the contribution due to dipole rotation of polar molecules, in particular free water molecules in food, and `' stands for the contribution due to electric conduction; f represents angular frequency of the microwaves, and "0 is the permittivity of free space.

1.15 Contributions of various mechanisms of the loss factor ("00 ) of foods as a function of frequency (Tang, 2005).

1.16 Contribution of electric conductivity and relaxation of free water molecules to overall loss factor of 0.5 N aqueous sodium chloride (adapted from Roebuck and Goldblith, 1972).

32

Packaging and products for use in microwave ovens

Typical values of dielectric properties of water, ice, and several selected foods at 915 and 2450 MHz are provided in Table 1.4. It is clear from this table that both relative dielectric constant and loss factors of foods are largely influenced by moisture and salt contents, as well as by structure. For instance, the relative dielectric constant of cooked ham for 2450 MHz ("0 ˆ 72) at room temperature is very close to the value of distilled water, while the relative dielectric loss factor is twice that of the free water ("00 ˆ 23 vs. 10.3). At 2450 MHz, Red Delicious apples with 87.5% moisture content have a relative dielectric constant of 54.5, significantly smaller than that of water, but a relative dielectric loss factor of 11.2, slightly larger than that of free water. Upon removal of moisture content in drying, both relative dielectric constant and loss factors of Red Delicious apples sharply decrease (Table 1.4). Table 1.4 The dielectric properties and penetration depth of selected foods (Tang, 2005) Foods

Temp (ëC)

915 MHz

2450 MHz

"0

"00

Air

1.0

0

Water distilled/deionized 20 0.5% salt 23 Ice ÿ12

79.5 77.2 ±

3.8 20.8 ±

122.4 22.2 ±

78.2 75.8 3.2

10.3 16.8 15.6 10.9 0.003 11,615

Corn oil

dp (mm)

"0

"00

1.0

0

dp (mm)

25

2.6

0.18

467

2.5

0.14

220

Fresh fruit and vegetables apples 22 potato 25 asparagus 21

60 65 74

9.5 20 21

42.6 21.3 21.5

57 54 71

12 16 16

12.3 9.0 10.3

Dehydrated apple* Red Delicious with %moisture (wet basis) 87.5 22 30.3 9.2

56.0 14.4 2.2

8.0 6.0 0.2

48.9 33.7 387

54.5 10.7 2.2

11.2 5.5 0.1

12.9 11.9 289.0

High protein products yoghurt (pre-mixed) 22 25 cooked ham** 50 25 cooked beef*** 50

71 61 50 76 72

21 96 140 36 49

21.2 5.1 3.7 13.0 9.5

68 60 53 72 68

18 42 55 23 25

9.0 3.8 2.8 9.9 8.9

*From Feng et al. (2002). ** From Mudgett (1986). *** From Bircan and Barringer (2002).

Electromagnetic basis of microwave heating

33

Most water molecules in ice at ÿ12 ëC are locked in rigid ice structure and are less mobile. Corn oil contains long chain fatty acids. Thus, both ice and oil at 25 ëC have much smaller dielectric constant and loss factors compared to that of water at 20 ëC. The value of the relative dielectric loss factor influences conversion of electromagnetic energy into thermal energy, while both relative dielectric constant and loss factor affect heating uniformity in microwave heating applications.

1.10.2 Microwave heating As discussed in Section 1.5, a plane EM wave loses its power when traveling in a lossy material. This is because part of the microwave power is converted into thermal energy within this material. Local conversion of the electric component of microwaves into thermal energy in foods can be calculated by (Goldblith, 1967): Pv ˆ 2 f "0 "00 E2

1:84 3

where Pv ˆ the power conversion per unit volume (W/m ), f ˆ frequency (GHz), "00 ˆ relative dielectric loss factor, "0 ˆ permittivity for free space, and E ˆ electric field intensity (V/m) in food. Equation 1.84 suggests that the converted thermal energy for microwave heating in foods is proportional to the value of the loss factor and the square of the electric field within the food. Electric field intensity is a parameter depending upon microwave field distribution within foods in a microwave cavity. That is, for a given location in foods with a fixed electric field intensity, larger relative loss factor causes more rapid heating. The increase in temperature (
T), without consideration of heat transfer, is calculated from:
T 1:85 ˆ 2 f "0 "00 E2
t where Cp (J kgÿ1 ëCÿ1) is the specific heat,  (kg mÿ3) is the density, E (V mÿ1) is the electric field intensity, f (Hz) is the frequency,
t (s) is the time increment and
T (ëC) is the temperature rise. Values of specific heat and density of different foods, and heat transfer calculations from generated heat can be found elsewhere (Singh and Heldman, 2001). Cp

1.10.3 Microwave power penetration in foods For food materials, the attenuation constant () and phase propagation constant ( ) in the propagation constant for Equations 1.13a and 1.13b are expressed as:

34

Packaging and products for use in microwave ovens v 2s 3 u  00 2 u " u0 "0 "0 4  ˆ 2 f t ÿ 15 1‡ 2 "0 v 2s 3 u  00 2 u 0 " u0 "0 " 4 ‡ 15 1‡ ˆ 2 f t 2 "0

1:86

1:87

Microwave power penetration depth in foods is then written from Equations 1.35 and 1.86 as: dp ˆ

1 ˆ 2

1 v 2s 3 u  00 2 u " u 2 f t20 "0 "0 4 1 ‡ ÿ 15 "0

1:88

Using Equation 1.26b, the above expression can be written in terms of the speed of light (c ˆ 3  108 m/s), microwave frequency, f , and food dielectric properties, ("0 , "00 ): c v dp ˆ 1:89 3 u 2s  00 2 u " u 2 f t2"0 4 1 ‡ ÿ 15 "0 Microwave power penetration depths for selected foods were calculated with the above equations and included in Table 1.4 to demonstrate the influence of food composition and microwave frequency. Those values vary from 2.8 mm for 2450 MHz in cooked ham to 467 mm for 915 MHz in corn oil. Thus, the shallow power penetration depth of 2450 MHz in salty foods often causes severe nonuniform heating when using domestic microwave ovens. Microwave at 915 MHz is used in industrial microwave heating systems and has three times the wavelength of 2450 MHz microwave in air. Microwave at 915 MHz generally penetrates deeper into foods than microwave at 2450 MHz, thus may provide more uniform heating or can be used to process relatively larger size foods. Microwave penetrates very well in ice at ÿ12 ëC because of the extremely low value of relative dielectric loss factor ("00 ˆ 0:003); both 2450 and 915 MHz are used in the food industry for tempering frozen foods (bring product from deep freezing to sub-freezing temperatures). Change of microwave power in foods along the depth of transmission can be estimated using Equation 1.22: Pave …z† ˆ Pave …0†eÿ2z ˆ Pave …0†eÿz=dp

1:90

But, Equation 1.22 was derived for plane waves in large bodies without considering reflection within the materials at the opposite interface with the air.

Electromagnetic basis of microwave heating

35

Ayappa et al. (1991) have shown that the above relationship only applies to foods when their general dimension L satisfies the following condition: L > 5:4dp ÿ 0:8 mm

1:91

Otherwise, complex Maxwell equations should be used along with two or three dimensional computer simulation models to predict more realistic heating patterns.

1.10.4 Wavelength in foods Based on Equations 1.13b, 1.87 and 1.26b, the wavelength of microwave in foods can be calculated from: ˆ

2 ˆ

2 0  v 2s 3ˆv 2s 3 1:92 u u  00 2  00 2 u u 0 0 " " u0 "0 " 4 u" 2 f t 1‡ ‡ 15 t 4 1 ‡ ‡ 15 2 "0 2 "0

That is, the wavelength is inversely proportional to the square root of relative dielectric constant of foods. As shown in Table 1.4, the values for "0 in foods are much greater than 1. Thus, the wavelength of microwave is sharply reduced when it enters foods. For example, using the values in Table 1.4, one can calculate the wavelength at 2450 MHz to be 13.8 mm in water, 16.6 mm in potato and 15.0 mm in ham; and the wavelength at 915 MHz to be 36.7 mm in water, 40.2 mm in potato and 35.0 mm in ham. Those are about 1/9 to 1/7 of the wavelength for 2450 MHz (122 mm) and for 915 MHz (328 mm) in air. Therefore, in spite of the fact that the dimensions of most food packages are smaller than the wavelength of microwaves in air, standing wave patterns may form within foods, partially contributing to uneven heating.

1.11

Conclusions

While microwave heating has brought much convenience to daily lives of modern society, the physical phenomena involved in this heating method are complicated, much more than other traditional heating methods. This provides significant challenges for technical people in the food industry charged with responsibilities to develop microwaveable foods and prepare appropriate cooking instructions for general consumers. Equal challenges are faced by engineers and scientists working on new industrial microwave heating applications. This chapter attempts to provide basic principles that describe how microwave propagate in air and cavities, and interact with foods without going into too much detail of practical implication in specific applications. These gaps are filled by other chapters.

36

1.12

Packaging and products for use in microwave ovens

References

Ayappa, K.G., H.T. Davis, G. Crapiste, E.A. Davis, J. Gordon, 1991. Microwave heating, an evaluation of power formulations. Chemical Engineering Science 46(4): 1005±1016. Bircan, C., S.A. Barringer, 2002. Determination of protein denaturation of muscle foods using the dielectric properties. J. Food Sci. 67(1): 202±205. Buffler, C.R., 1993. Microwave Cooking and Processing, Van Nostrand Reinhold, New York. Chan, T.V., H.C. Reader, 2000. Understanding Microwave Heating Cavities. Artech House, Boston. Chen, H., J. Tang, L. Liu, 2007. Coupled simulation of an electromagnetic heating process using the finite difference time domain method. J. Microwave Powers and Electromagnetic Energy 41(3): 50±56. Chen, H., J. Tang, F. Liu, 2008. Simulation model for moving food packages in microwave heating processes using conformal FDTD method. J. Food Engineering 88: 294±305. Decareau, R.V., 1985. Microwaves in the Food Processing Industry, Academic Press, Inc., New York. Dibben, D.C., A.C. Metaxas, 1996. Frequency domain vs time domain finite element methods for calculation of the fields in multimode cavities. Proceedings, 7th Biennial IEEE Conference on Electromagnetic Field Computation, Okayama, Japan, 322, 1996. Feng, H., J. Tang, R.P. Cavalieri, 2002. Dielectric properties of dehydrated apples as affected by moisture and temperature. Transactions of the ASAE 45: 129±135. Goldblith, S.A., 1967. Basic principles of microwaves and recent developments. Adv. Food Res. 15: 277±301. Grellinger, D.J., M.A. Janney, 1993. Temperature measurement in a 2.45 GHz microwave furnace, Ceramic Transactions Microwaves: theory and application in materials processing, American Ceramic Society, Westerville, Vol. 36, pp. 529±538. Guru, B.S., H.R. Hiziroglu, 2004. Electromagnetic Field Theory Fundamentals, Cambridge University Press, Cambridge. Harrington, R.F., 1961. Time-harmonic Electromagnetic Fields, McGraw-Hill, New York. Ingle, J.D.J., S. R. Crouch, 1988. Spectrochemical Analysis, Prentice Hall, Englewood Cliffs, NJ. Jefferies, D., 1994. Waveguide and Cavity Resonator. Department of Electronics and Electrical Engineering, University of Surrey. Kuang, W., S.O. Nelson, 1998. Low-frequency dielectric properties of biological tissues: a review with some new insights. Transactions of the ASAE 41(1): 173±184. Metaxas, A.C., 1996. Foundations of Electroheat ± A Unified Approach. John Wiley & Sons, New York. Metaxas, A.C., R.J. Meredith, 1993. Industrial Microwave Heating. Peter Peregrinus Ltd, London. NPL, National Physical Laboratory, National Measurement Institute, UK. http:// www.npl.co.uk Mudgett, R.E., 1986. Microwave properties and heating characteristics of foods. Food Technology 40(6): 84±93. Pandit, R.B., J. Tang, F. Liu, G. Mikhaylenko, 2007. A computer vision method to locate cold spots in foods in microwave sterilization processes. Pattern Recognition 40(12): 3667±3676.

Electromagnetic basis of microwave heating

37

Pathak, S., F. Liu, J. Tang, 2003. Finite difference time domain (FDTD) characterization of a single mode applicator. J. Microwave Powers and Electromagnetic Energy 38(1): 37±48. Pozar, D.M., 1998. Microwave Engineering, 2nd edn, John Wiley & Sons, Hoboken, NJ. Roebuck, B. D., S.A. Goldblith, 1972. Dielectric properties of carbohydrate-water mixtures at microwave frequencies. J. Food Science 37: 199±204. Sadiku, M.N.O., 2006. Elements of Electromagnetism, Oxford University Press, Oxford. Schubert, H., M. Riegel, 2005. The Microwave Processing of Foods, CRC Press, Woodhead Publishing Limited, Cambridge. Singh, R.P., D.R. Heldman, 2001. Introduction to Food Engineering, 3rd edn, Academic Press, New York. Sullivan, D.B., 1983. Speed of light from direct frequency and wavelength measurements. Bibliographic note from 17th Conference Generale des Poids et Mesures. Tang, J., 2005. Dielectric properties of foods. In Microwave Processing of Foods. H. Schubert and M. Regier (eds), CRC Press, Woodhead Publishing Limited, Cambridge, pp. 22±40.

Plate I Electric field pattern for M350.

Plate II Electric field pattern for TE204.

Plate III Electric field pattern for a loaded microwave cavity at 2.4295 GHz (Chan and Reader, 2000).

2

Influence of food geometry and dielectric properties on heating performance È P P L I N G - R A A H O L T , SIK ± Swedish Institute for B WA Food and Biotechnology, Sweden and T O H L S S O N , formerly at SIK ± Swedish Institute for Food and Biotechnology, Sweden

Abstract: The chapter overviews food related phenomena which influence microwave heating performance and heating uniformity. Special focus is put on the effects of food geometry, size, placement of components, as well as dielectric properties on microwave heating characteristics. Methodology and applications of controlled microwave heating are exemplified, and modelling based tools for improving heating uniformity are presented. Sources of further information and advice are given. Key words: microwave heating, microwave heating performance, microwave heating characteristics, microwaveable food products, microwave heating uniformity, microwave heating distribution, dielectric properties, loss factor, loss tangent, microwave heating phenomena, edge overheating, corner overheating, centre overheating, food geometry, in-depth heating, concentration effects, run-away heating.

2.1

Introduction

During microwave heating, several interacting variables related to food, packaging and the microwave oven itself will influence how the food will be heated. Multi-component foods often require tailor-made product development, aiming at avoiding uneven heating, which might otherwise cause problems with both sensory and microbiological qualities. In this chapter an overview is given of the food-related phenomena which influence microwave heating performance, with a special focus on how food geometry and dielectric properties of foods affect the microwave heating characteristics. As food parameters, both geometry and size of different components, as well as recipe formulation and relative placement of different components in, for example, a tray, could be regarded. Examples are given for some selected scenarios. Owing to the limited space, this overview cannot be complete; instead some important information is given regarding the effects of food geometry and dielectric properties on microwave heat distribution. This chapter provides a starting point; the interested reader can find more information in the references.

Influence of food geometry and dielectric properties

39

Sections 2.2 and 2.3 describe how food geometry and dielectric properties among several other parameters could influence microwave heating performance by contributing to different microwave heating phenomena. Section 2.3 focuses on factors which influence microwave heating performance, and the related problem of non-uniform heating is described, exemplified and discussed. In Section 2.4, some remarks on methodology and applications of controlled microwave heating are given. Section 2.5 presents modelling-based tools for improving heating uniformity, where parameters such as food geometry might be one of the variables in the modelling and optimisation. References are also given to previous works. Finally a section on future trends is given, followed by sources of further information and advice (Sections 2.6 and 2.7).

2.2

Microwave heating distribution and uniformity

Electromagnetic waves with frequencies in the range from 300 MHz to 300 GHz are defined as microwaves, with the corresponding wavelengths between 1 m and 1 mm. There are several distinct frequency bands which have been allocated for industrial, scientific and medical (ISM) use. For food applications, the frequency is however often limited to the ISM band of 24501  50 MHz. In North and South America, another recognised ISM frequency is used industrially, namely 915  13 MHz. In European countries, the latter frequency band is not generally available. However, in the UK the frequency 896  10 MHz is generally available. Another frequency, 5.8 GHz has also been available for some time, with applications mainly for heating of materials in some specific cases (on the one hand, materials which do not couple well to lower microwave frequencies; on the other hand, materials of low volume such as fibres and thin sheets, but also lower quantities of, for example, powder and granulates). This latter frequency is, however, not so commonly used. Microwave heating of foods has sometimes been connected with uneven heating, due to so-called `hot and cold spots' which may be present in the food product after heating. The microwave heating profile in foods is determined by the thermo-physical properties of the food item (dielectric properties, but also thermal properties) as well as of the distribution of the absorbed microwave power in the food. The latter is, in turn, determined by several factors: the electric field inside the microwave cavity or applicator, the dielectric properties (complex permittivity) of the food item but also by the microwave frequency. Computational modelling-based design of the oven cavity (e.g. size and shape of the cavity or applicator) as well as the waveguide system, gives tremendous possibilities to control the electromagnetic field pattern. Heating uniformity is, however, also to a great extent influenced by size, geometry, position and composition of food as well as package during heating. This will be described 1. With the exception of countries where 2375  50 MHz is used.

40

Packaging and products for use in microwave ovens

further in Section 2.2.1. More information on the general principles for microwave heating can be found in the literature. Several authors have described the subject, e.g. Bengtsson and Risman (1971), Ohlsson (1983), Walker (1987), Buffler (1993), and Ohlsson and Bengtsson (2001).

2.2.1

Factors which influence the microwave heating uniformity

The microwave heating performance of foods is influenced by several factors, which interact in a complex way with each other. Among such factors which may affect the heating uniformity are, for example: the design of the oven cavity, the waveguide or applicator system, as well as food parameters like the geometry and size2 of the food item and the food packaging, the relative placement of food components, as well as the distance between neighbouring components. Furthermore, another significant variable which will affect the heating performance is the permittivity of the food, commonly called the dielectric properties.

2.2.2

Dielectric and thermal properties

The macroscopic interaction between an electromagnetic field and a material is expressed by the permittivity " and the permeability  of the material. The permittivity describes the electrical properties, while the permeability describes the magnetic properties of the material. However, since foods are non-magnetic, the magnetic part of the power contribution will not give rise to heating. The permittivity designates how a material will interact with microwaves by expressing to what extent and how the material will absorb microwave energy and convert it into heat, how strong the reflection and transmission phenomena will be, as well as how much the microwave wavelength will be reduced in the material. The permittivity is a complex quantity. Thus, it consists of both a real part (the real permittivity "0 ) and an imaginary part (the dielectric loss factor "00 ). Basically, the permittivity describes the ability of a material to absorb, transmit and reflect electromagnetic energy. Several measurement techniques are available for determining the permittivity of materials. The choice of technique will be based on the different advantages and limitations of available methodologies. A relatively large amount of data are available on basic food components, especially at 2450 MHz. However, much less data are available for ready made recipe foods and formulated foods. Few predictive models are available by which dielectric properties can be calculated from proximate analysis, and these models have limited applicability (Mudgett, 1986). Predictive equations for 2. Size relative to the used frequency.

Influence of food geometry and dielectric properties

41

dielectric properties of foods have been developed by several authors, where the influence of food composition, moisture content and temperature is often included. The absorbed microwave power is related to the permittivity and to the electric field by the following equation: Pv ˆ 2 f "0 "00 jE2 j

2:1

where Pv is the power which is absorbed in a given volume of the food material (W/m3), f is the frequency in Hz, E is electrical field strength in V/m inside the food, "0 is the permittivity in free space (8:854  10ÿ12 F/m) and "00 is the relative dielectric loss factor. This equation gives an understanding of the influence of the dielectric loss factor and the field strength on power absorption. Furthermore, it illustrates the advantages of using very high frequencies for heating, e.g. when comparing microwave and high frequency dielectric heating at 27 MHz. At the higher frequency, considerably lower field strength is required for a given energy input. The dominating variable, the electric field strength, is unfortunately variable and very difficult to estimate or measure, when heating in a microwave oven. Modelling tools are however here valuable in order to predict the electromagnetic fields. The dielectric properties of foods of normal salt content are dependent on the water content in the following way: the dielectric constant, "0 , increases almost linearly with water content, while the loss factor, "00 , only shows a moderate increase, except for higher salt content. Illustrations of dielectric properties of several common foods of different water content can by found in Ohlsson and Bengtsson (2001). Frozen foods show much lower dielectric properties than thawed foods. Pure ice has very low dielectric properties; most of the water in frozen foods is present as ice crystals inside the food. However, approximately 10% of the water remains unfrozen as a freeze-concentrated strong salt and sugar solution in the food. This explains why frozen foods absorb microwave energy to any significant extent. There is an abrupt increase in the dielectric loss in the melting region. This partly explains the tendency towards so-called run-away heating in microwave thawing of foods, when already thawed parts of higher loss factor absorb most of the available microwave energy. Very even temperature profiles can be maintained as long as the temperature remains below about ÿ2 ëC and thawing is only partial, that is tempering instead of complete thawing. Under those circumstances, the thermal conductivity of the food is still high, which tends to level out temperature differences. The complex permittivity, or as commonly said the dielectric properties, of a food material varies with the composition of the food, but also with the temperature and frequency. Since water is generally a major constituent in most foods, its permittivity will play a major role in determining the dielectric

42

Packaging and products for use in microwave ovens

properties of the food. For more detailed information on dielectric properties for different kinds of food, as a function of temperature at selected frequencies, the reader is referred to Bengtsson and Risman (1971). Knowledge of the dielectric properties of foods is useful when developing foods and constructing ovens, as well as when selecting packaging material. Today, oven construction, packaging design and product development of microwaveable foods are to a large extent made based upon microwave simulations which predict the heating patterns for a given scenario. For a multi-component ready meal, the various components will have different dielectric and thermo-physical properties. This will affect the heating performance. This is further discussed in Section 2.3. Changes in recipe formulation will affect the dielectric properties. However, as concluded by WaÈppling-Raaholt (2000), RyynaÈnen et al. (2004) and RyynaÈnen (2002), the factors which are most significant in controlling the temperature profile of a ready meal are the geometry and placement of the food components, and the design of the tray. RyynaÈnen et al. (2004) further concluded that when it comes to the possibility of affecting the temperature development by changing salt content of foods (two types of salt were studied), measurements showed that such chemical modifications had either no or only minor effects on temperature distribution, in spite of the fact that the dielectric properties varied considerably. It is thus difficult to use recipe modifications based upon changes in salt content as a means to influence the heating performance in a desired direction. It should also be noted that even if salt content is an important factor for modifying the dielectric properties, the salt variations which would be required in order to control the heating performance in a specific direction, e.g. when it comes to penetration depths, would very seldom be possible to perform in practice, without influencing the corresponding sensory properties in an undesired direction. Furthermore, the geometry and design of the food package are variables which affect the heating performance. However, the effect of the packaging material will generally be small as long as ordinary trays are regarded, owing to the relatively low permittivity of the material as well as its thin walls. Nevertheless, a packaging material which includes susceptor materials will affect the heating results. So will the distance between and position of neighbouring products if several items are heated at a time, as is the case, for example, for a multi-component ready made meal. The extent to which microwave heating will occur `from above' and `below', respectively, will depend on the microwave oven mode properties. These are in turn related to the cavity volume modes and trapped surface waves (Risman, 1994). Last but not least, not only electromagnetic field pattern and heat conduction but also water transport within the food will affect the overall microwave heating distribution. This can intuitively be understood by the fact that the water content is indeed affecting the dielectric properties, which in turn are related to the microwave heating performance.

Influence of food geometry and dielectric properties

43

The influence of geometry parameters on the microwave heating distribution was described by Ohlsson and Risman (1978) for spheres and cylinders. For multi-component ready meals, such or similar geometries are relatively common. Further parameters of importance to heating performance are the size and placement of each food component as well as the distance between neighbouring components. More on this will be discussed in the next section.

2.3

Heating phenomena which influence heating performance and uniformity

The absorption of microwave energy in foods is to a large extent dependent on both the electromagnetic fields and the microwave penetration pattern in the particular food material. The field distribution is in turn strongly influenced both by the type of cavity, the microwave applicator or waveguide system, as well as by the type, shape and distribution of the food inside. In this section selective heating effects are described, related to the composition and shape of the food material itself. For simplicity, we consider the microwave field to be evenly distributed and of a given field strength at the food surface.

2.3.1

In-depth heating

In a rectangular slab of food of even thickness, the power level will gradually decrease inwards to an insignificant level if the slab thickness is large in comparison to the calculated penetration depth. We have here assumed, for simplicity, that the microwave field is evenly distributed and of a given field strength at the food surface. For a thinner slab, the remaining power level from microwaves which are impinging on the two opposite surfaces will overlap. This may result in more rapid heating of the central parts than of the surface regions, taking into consideration that the surface will be cooled both by heat transfer to the surrounding air space and by evaporative cooling. For a slab, waves which are transmitted through the material will to a specific extent be reflected (within the slab) towards the opposite surface of the slab. This phenomenon generates internal standing waves. The height of a rectangular slab will affect the heating distribution, in the vertical cross-section of the slab. For layered materials of different dielectric properties, the microwaves will also be reflected and refracted at the interface between these materials, for example between meat and an outer layer of fat. Depending on the thickness and dielectric properties of the layers, standing wave patterns may be developed. The result can, for example, be that the fat layer will be overheated, in spite of its lower dielectric loss factor. A contributing factor will then be the much lower specific heat of the fat material. For inhomogeneous3 food or if different food 3. In composition.

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materials are heated side by side, temperature differences will result from the combined differences in dielectric and thermal properties, when uniform microwave field strength is anticipated.

2.3.2

Concentration effects

A slab with sharp corners and edges which is microwave heated will show field and energy concentrations there, which cause selective heating, especially at the corners. Briefly described, a sharp edge or corner will act as an antenna and attract more energy than surrounding areas. Considering microwave heating as electromagnetic waves which may be reflected, absorbed or refracted, it can be seen that part of the energy is reflected at the food surface, and part of the energy is refracted. Part of the refracted energy will be absorbed, as understood from elementary electromagnetics. Most of the remaining energy will be reflected back at the other food surface and so on. Depending on the food geometry, the result can be focusing of energy to certain areas, which may be part of the explanation for so-called concentration heating effects. For cylindrical or spherical geometries, such concentration effects can cause concentration of energy to the centre of the food, depending, however, on both the food diameter and the dielectric properties. This centre overheating effect occurs for diameters of approximately one to three times the penetration depth in the material. For cylinders, concentration effects occur when the electrical field is parallel to the cylinder axis. The effect will be stronger for foods with high permittivity values. At 2450 MHz centre heating usually happens at diameters between 25 and 55 mm, while the values are correspondingly larger (about 2.5 times larger) for 915 MHz. Microwave heating performance is thus affected by several possible heating phenomena. Among these are edge overheating, run-away heating in frozen foods and standing wave patterns in food loads. Edge overheating is a result from electric fields of strong amplitude, which field vectors are parallel to an edge of a food item.

2.3.3

The run-away heating phenomenon

Pure ice has much lower dielectric properties than thawed foods. Most of the water in frozen foods is found as ice crystals within the food item. The reason for the fact that frozen foods absorb microwave energy at all is that approximately one-tenth of the water remains unfrozen as a strong salt solution inside the food (Ohlsson and Bengtsson, 2001). Since the regions which are thawed in the very beginning of a microwave thawing process will have much higher loss factors "00 , as compared with still frozen regions, they will heat very rapidly. This phenomenon is called thermal runaway heating (Buffler, 1993). Particularly in

Influence of food geometry and dielectric properties

45

foods of high salt content, (e.g. salty ham, the dielectric data of which are given by Bengtsson and Risman, 1971), the surface may at higher temperatures act as a shield during microwave heating. This is because the penetration depth will be lower for salty foods. Run-away heating may thus occur for high-salt foods, especially in the surface regions.

2.3.4

Edge and corner overheating

The so-called edge (or corner) overheating effect is often noted especially when frozen foods are heated or thawed. Edges and corners have a tendency to heat or thaw first, which intuitively could be understood by the fact that the amplitudes of the electromagnetic fields are concentrated at such areas of the food, due to scattering phenomena (see Plate IV and Fig. 2.1). At the boundary between the food load and the surrounding air one of the boundary conditions in the solution of the electromagnetic problem leads to the continuity condition of the parallel component of the electric field. Edge overheating is strongly influenced by the polarisation and incident angle of the incident field, the angle and curvature of the edges, the permittivity of the heated food materials, and the presence of other scatterers close to the edge (Sundberg, 1998a). For food loads heated at 2450 MHz, both loss mechanisms due to ionic conduction (as e.g. in salty foods) as well as dielectric relaxation are present. The effective loss factor "00effective , where both types of loss are included, is then often used (Metaxas, 1996).4 The following relationship then describes the relative effective loss factor:  ‡ "00 2:2 "00effective ˆ !"0 where  is the electrical conductivity in S/m, ! is the angular frequency in radians/second, "0 is the absolute permittivity of free space and "00 is the loss factor. The time-average value of the dissipated power density pdiss (W/m3) in typical food products is proportional to the square of the electric field (equation 2.2): 1 1 2:3 pdiss ˆ RefE
J g ˆ !"0 "00effective jEj2 2 2 where J* is the complex conjugate of the electric current density (A/m2), "00effective is the relative effective loss factor of the food material, and jEj is the amplitude (peak value) of the electric field intensity (V/m). An assumption behind equation 2.2 is that the relative complex permeability  of the food material is assumed to be 1, i.e. the food is magnetically close to vacuum. In other words, we assume that foods do not contain metal. 4. For applications related to microwave heating of foods, the loss factor refers to two types of losses into heat: the dipole relaxation and the ionic conductivity. At other frequencies, however, other mechanisms may be more dominant (Hasted, 1973).

46

Packaging and products for use in microwave ovens

2.1 The phenomenon behind edge overheating. The electromagnetic fields are concentrated at the corners of the food, due to scattering phenomena.

At the food edges, microwaves approach the food from two directions. Furthermore, parallel to a surface at the boundary the electric fields have two polarisations. The resulting concentration of the energy distribution to the sharp edges is explained by the continuity condition at the boundaries of the parallel electric fields. This heating phenomenon is one of the dominating ones, related to heating uniformity problems in rectangularly shaped foods. For corners, the corresponding will analogously be the case for electric fields of three polarisations. This results in an even more pronounced heating at the corners. By optimising the food product design with modern tools (WaÈppling-Raaholt and Ohlsson, 2000), it is often possible to avoid corner and edge over-heating. In several cases, more than 15% of the microwave energy which is absorbed by the food item is lost by the edge overheating phenomenon (Risman, 1992). The edge overheating effect is investigated for high-permittivity dielectrics in the work by Sundberg (1998a). Furthermore, resonances between food items in the near vicinity of each other are illustrated in Plate V.

2.3.5

Centre overheating

For foods which are spherically or cylindrically shaped, i.e. foods with convex surfaces, refraction and reflection phenomena will result in concentration of the

Influence of food geometry and dielectric properties

47

microwave power distribution to the geometrical centre for certain diameters (Ohlsson and Risman, 1978). This phenomenon is called centre overheating. It is influenced by different factors, mainly the geometries, sizes and complex permittivity values of foods. The phenomenon of centre overheating is exemplified in Plate VI.

2.3.6

Standing wave patterns in microwave heated foods

Several different types of standing wave phenomena are occurring in foods during microwave heating (RyynaÈnen et al., 2004). Standing waves may appear for the following cases: · between plane upper and lower surfaces; · within certain thick loads (this latter phenomenon will be due to internal resonances, i.e. standing waves);5 · at larger surfaces; and finally · at edges of larger surfaces (which in turn is partly a result of the edge overheating effect, partly of surface wave phenomena). Internal `hot and cold spots' in the food item, i.e. the standing wave patterns of absorbed and reflected electromagnetic waves, can by modelling be quantified in simplified scenarios, as described by RyynaÈnen et al. (2004). This was performed by using an extension of the transverse resonance method (Harrington, 1961), in order to include the behaviour of all transverse electric (TE) and transverse magnetic (TM) waveguide modes propagating in the vertical direction. Other kinds of phenomena also occur during microwave heating of foods. Examples of such phenomena are those which are related to different penetration depths6 for different kinds of food materials. This is described for multicomponent foods in the following section.

2.3.7

Effects of geometry and dielectric properties

Let us assume that microwave ovens are designed to give as even field distribution as possible in the loaded oven and to support TM microwave modes around the food sample in order to minimise corner and edge overheating. Then food composition, geometry and positioning as well as packaging will constitute the main remaining significant factors that determine heating performance and resulting food quality. In general, for slab-shaped foods, product thickness should be even, and preferably limited to less than 2.5 times its microwave penetration depth at the 5. It should be noted that external resonance phenomena, like the exploding egg effect, is not a standing wave phenomenon. 6. For a definition of the penetration depth in this context, the reader is referred to Risman (1991).

48

Packaging and products for use in microwave ovens

specified frequency. Rounded edges and corners will limit preferential tendencies to corner and edge overheating. The hot area is usually found diagonally from the edge or corner some 7±8 mm into the food (Ohlsson, 1993). So-called `hot and cold spots' may also be present. These are shown as temperature variations over large, flat surfaces of food, and are normally larger than the indepth temperature variation. Therefore such `spots' may often have a larger influence on the overall heating results. When heating food components of different dielectric and thermal properties together, such as in ready made meals on a tray or compartmented plate, the geometry and size, as well as the relative arrangement of the components must be selected in order to optimise the heating uniformity. Advantages may often be taken of the tendencies to focus the electromagnetic fields to the centres of rounded (cylindrical or semispherical) foods. This is particularly true for thick food samples of limited penetration depth. To even out temperature distribution, food components with high dielectric loss, e.g. meat stew, may be partially shielded by food components of lower loss (e.g. mashed potato). Material with low dielectric loss is also less susceptible to corner and edge overheating. One reason is that the low loss factor reduces each contribution to field concentrations at corners as well as edges. The formation of variable standing wave patterns inside the food can be kept to a minimum, by adjusting the thickness of material with low dielectric loss (Ohlsson and Thorsell, 1985; RyynaÈnen and Ohlsson, 1996). In layered materials, standing wave patterns may develop as a result of microwave reflection at the component interfaces (Cheng, 1984). This might be taken advantage of, in terms of `controlling' the energy distribution and heating effects by the choice of layer materials and thickness of the layers. RyynaÈnen et al. (2004) described the situation when a hamburger is heated, sandwiched between two pieces of bun. A standing wave pattern will develop between the microwave oven top and bottom walls, but also between the oven shelf and the bread as well as the meat. However, since the food or dish must have a `natural' appearance for consumer acceptability, the extent to which food geometry and positioning can be modified is sometimes fairly limited. Furthermore, for multi-component ready meals the difference in dielectric and thermo-physical properties of the components will influence the heating result, as will microwave reflections owing to the boundaries between different components (Mudgett, 1986). The latter phenomenon is caused by the fact that each component will differ in microwave penetration depth dp , because of the different relative permittivities between the components. The microwave reflections at the interfaces between air and food material will depend on permittivity for each component, frequency, as well as on the microwave oven mode properties. Several different selective heating phenomena such as edge overheating, centre overheating and run-away heating will also play a role. These types of phenomena were described earlier.

Influence of food geometry and dielectric properties

2.3.8

49

Effect of food composition and formulation

Another means of influencing heating performance is by modifying the food composition or formulation, which in turn will change the dielectric properties. Microwave absorption will tend to be reduced, and the microwave penetration depth in the food will be raised by lowering the water content and/or mixing with material of low permittivity. Increasing the ionic content, such as by adding salt, will increase dielectric loss and reduce penetration depth without affecting the wavelength in the food. However, the sensory demands for natural taste, flavour and texture will put rather narrow limits on what changes in dielectric or thermal properties can be achieved. To compensate for lacking flavour development, the addition of flavour substances (natural flavours, spices, etc.) may be required, for example microencapsulated flavours with controlled release above a certain temperature during re-heating. For foods in which warm swelling starches are being used, the temperature reached during microwave heating may not everywhere be sufficient for such starches to swell, resulting in a raw taste and undesirable texture. As noted by Katt (1991), a combination of warm swelling and cold swelling, modified starches is sometimes presented as the answer to this problem. White bread is not very suitable for reheating by microwaves, since a soggy and tough texture will easily develop (Hoseney and Rogers, 1989). Patented additive ingredients are available which may at least partly prevent such texture changes.

2.3.9

Surface browning and crisping

Another field of interest is surface browning and crisping of microwaveable foods. One solution to obtain surface browning (for unpacked products) would be to combine microwave heating with convection or radiation, by using a microwave combination oven. Another solution would be to convert part of the microwave energy into conductive or radiant heating by using a special browning element, which absorbs microwave energy. For packaged foods, susceptor materials can be used to absorb part of the impinging microwave energy and convert it into heat, with the aim of achieving browning and crisping. There are also ingredient susceptors available.7 Some of those, for example, consist of a dry powder or highly concentrated solution of a component or additive that will strongly enhance surface absorption of microwaves. The food surface can alternatively be coated with ingredients which enhance Maillard reactions, such as sugars and amino acids, or other chemical 7. A microwave packaging which acts as a susceptor captures the microwave energy and transforms it into heat energy in order to contribute to browning and crisping of foods during microwave processing.

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Packaging and products for use in microwave ovens

browning agents in combination with moisture absorbing agents. These ingredients are used to contribute to surface browning at a moderate surface temperature. In order to maintain surface crispiness, conventional precooking or baking prior to packaging in combination with strong moisture absorbers (fibres, hydrocolloids, etc.) and moisture barriers (edible coatings) near the food surface have been suggested as alternatives to the use of metal susceptor films.

2.4

Some remarks on methodology and applications of controlled microwave heating performance

Many new microwave products have been developed over the years. In several cases good results have been achieved. However, some food products do not perform well from a food quality point of view in microwave cooking, reheating or thawing. Quality variations related to heating uniformity are differences in temperature and moisture distribution in microwave heated foods compared with those that are conventionally cooked. Higher moisture levels in the surface areas of microwave heated foods may result in less development of desirable `cooked food' flavours and to variations in product appearance, which in turn may lower sensory quality. Ingredients which are particularly designed for modifying microwave heating characteristics are sometimes suggested to partly overcome and solve the occurring problems. Among the suggestions of such ingredients are flavours and salts. Other examples are starches and sweeteners (Grimwood, 1989; Katt, 1991). Furthermore, Miller and Hoseney (1997) suggest emulsifiers and several approaches to increasing the water content as other means to improve microwave heating characteristics. Water and salt content are two major factors in affecting the dielectric properties of a material. However, as described in Section 2.2.1, it is often difficult to use modification in the recipe as the sole means of controlling the overall microwave heating distribution. Today's methods for achieving a more uniform microwave heating distribution involve knowledge of the influence which food geometry and dielectric properties may have on the heating performance. Such methods may often assist in avoiding previous problems with non-uniform heating patterns (WaÈpplingRaaholt et al., 1999, 2001; WaÈppling-Raaholt, 2000). Methodology based upon numerical modelling of microwave heating of foods gives a strong tool for development of optimal product and packaging for use in microwave ovens. However, it is recommended to combine such methods with practical validation. It is possible to use numerical modelling as a means to influence the heating distribution favourably, e.g. in order to find the optimal geometry of a specific food product so that it can be heated as uniformly as possible. For example, for microwave heating of frozen foods, the change in permittivity during the tempering and thawing process may result in run-away heating (see Section 2.3). In many cases the heating performance can be controlled towards the desired heating uniformity. At the same time the heating times can often be significantly

Influence of food geometry and dielectric properties

51

reduced. It should be pointed out that, for a successful result, electromagnetic modelling and mathematical optimisation methods should be used as tools in combination with knowledge of microwave engineering and food science. Analogously, the method for optimising heating uniformity can also be used as an aid e.g. in oven design (WaÈppling-Raaholt and Risman, 2000). Heating uniformity in microwave heated foods of different geometries has been studied experimentally using temperature measurements and infrared thermography as well as numerical modelling of the electromagnetic fields. In a study of heating uniformity of prepared meals, as influenced by geometry and size of food parameters, as well as by placement of food components, results by WaÈppling-Raaholt et al. (2001) show that improvement of uneven heating is possible by modifications in the design of the meal (with respect to geometry and size of food components, combined with an appropriate placement of these relative to each other). Methods for evaluating temperature distribution and heating uniformity have been developed, e.g. for the IEC standard works (IEC publication 60705, 1999). Such measurements must always be related to the performance in heating of actual food products (Ohlsson, 1981). From a microbiological perspective also, uniform heating is of course important. Particularly in the UK, concern about insufficient inactivation of pathogenic bacteria in microwave heated foods has been a subject of much publicity. The risk that sufficiently high temperatures are not reached everywhere in the foods during microwave processing was discussed, especially in the early 1990s (e.g. Walker et al., 1991). Cole et al. (1991) evaluated survival of Listeria monocytogenes during microwave heating. After reaching a temperature of 70 ëC and maintaining it for at least 2 minutes throughout a food product, there is a substantial reduction in the numbers of L. monocytogenes (Walker et al., 1991). Such risks with microwave heating do not, however, differ from those of traditional heating. For both types of heating methods it is required that foods are cooked throughout to the desired temperatures in order to inactivate foodpoisoning bacteria that may be present in the food (Ohlsson, 1991). Among others, George et al. (1995) reported efforts towards solving the problem by improving the manufacturer's reheating instructions. The paper describes an investigation into the reheating of lasagne meals, a multi-component product which by that time was known to be difficult to heat uniformly in a microwave oven. When necessary, reheating instructions on the product label were further developed to allow a minimum of 70 ëC for 2 minutes to be achieved in the samples of commercially available lasagne. The new instructions incorporated longer heating times, rest periods, a 90ë turn and retention of a pierced film lid throughout reheating. Much of the discussion on safety and quality of foods is characterised by limited understanding of the qualitative and quantitative importance of factors related to heating uniformity. Since the early 1990s, improved heating uniformity of ovens, improved cooking instructions and novel methods for

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Packaging and products for use in microwave ovens

designing food products which give a much-improved level of uniformity after microwave heating have resulted in solutions to many of the previous concerns. Today, methods are available which can serve as valuable tools in design of microwaveable foods, with the aim to improve uniformity in heating patterns (WaÈppling-Raaholt et al., 1999, 2001; WaÈppling-Raaholt, 2000). More on this can be found in Section 2.5.

2.4.1

Some examples from industrial microwave heating applications

The heating performance of industrial applications are, as for all microwave heating applications, influenced by the food parameters, e.g. the geometry and size of the food components, as well as by the dielectric properties. In the following, selected examples are given of industrial microwave heating applications to exemplify the fact that food geometry and dielectric properties influence microwave heating performance. For a more complete picture of industrial microwave heating applications the reader is referred to Ohlsson and Bengtsson (2001). In multi-applicator tunnel ovens, the dominating causes of non-uniform heating are load diffraction phenomena in combination with the applicator heating pattern (Sundberg et al., 1995). Such load diffraction phenomena are directly dependent on food geometry as well as permittivity of the food material. Possible industrial applications of such ovens include drying of wood (Antti, 1997), drying of various foods (Funebo and Ohlsson, 1997), as well as pasteurisation and sterilisation of foods (Sundberg et al., 1996). Since in the latter application the packaged ready meals on the conveyor belt are moving under (or above) the applicator, its instantaneous overall microwave efficiency will often vary significantly, which sometimes results in an even more pronounced heating non-uniformity. On the other hand, irregular fields in the feed direction will be evened out by the continuous movement of the food on the conveyor, similar to the function of the rotating turntable in a household microwave oven. In addition, the non-linear behaviour of magnetron sources complicates the overall efficiency problem. If circulators are used, this problem will be reduced. Sundberg (1998b) studied the analysis and design of industrial microwave tunnel ovens, and suggested a quantification of heating uniformity in multi-applicator tunnel ovens (Sundberg et al., 1998). More details on modelling-based tools are found in Section 2.5. An industrial unit operating under `steady state conditions', may give better matching of the load and larger power efficiency. In general, industrial microwave applications often show a more even field and temperature distribution (Ohlsson and Bengtsson, 2001). For industrial applications, single mode applicators will often allow for the use of very high field strengths, if designed to give a uniform field inside the food material. For a specific food and a specific

Influence of food geometry and dielectric properties

53

application, such applicators have to be carefully tailored since the introduction of the food material into the applicator affects the electromagnetic field distribution considerably. Another example where food geometry is a significant parameter in influencing the heating performance is the tubular TM020 applicator, which was designed for continuous microwave processing of pumpable liquid or semiliquid foods, as described by Risman and Ohlsson (1975). By selecting a suitable tube thickness, it was possible to control the heating profile towards a compensation of the centre heating by the higher centre velocity of the food stream due to the flow profile (Ohlsson, 1993). Inspired by a patent by Risman (1997), Isaksson et al. (2002a) used numerical modelling to design an applicator for continuous microwave heating of pumpable foods, with the aim of making the design permit larger work load radii with as small an axial field variation as possible also at 2450 MHz. This was by superposition of two single modes, and by selecting the geometrical radius of the tube in a way which contributed to the favourable heating distribution over the cross-sectional area of the tube. This is because the heating profile over this cross-sectional area during pumping is determined by the superposed microwave mode behaviour. This relation could be mathematically described by Bessel functions which respectively correspond to each of the modes. These Bessel functions are in turn functions of the geometrical tube radius parameter. For a successful heating result, the design of the feed system as well as of the circular cavities is important. A proper design is important, in order to get the desired heating pattern associated with each specific mode, especially for microwave heating applications of high loss loads.

2.5

Modelling-based tools for improving microwave heating uniformity

Knowledge of heating phenomena can be used for product development of food products as well as packaging. Modelling-based tools give enhanced possibilities of relating the influence of food geometry and dielectric properties to the resulting electromagnetic distribution and heating profile. Numerical modelling of microwave processes could be used as a tool for improving heating uniformity. This also gives a means of controlling the heating performance in a desired direction. Among available variables in the numerical model are the geometrical parameters of the food components, as well as the permittivity of the food material. In this section, focus will be on tools for improving the microwave heating uniformity by controlling parameters related to the food and packaging. It should be mentioned, however, that the method could also be generalised to oven design.

54

2.5.1

Packaging and products for use in microwave ovens

Background to modelling

Modelling plays an important role as a tool to give an increased knowledge and understanding of microwave heating of foods. This knowledge may be used to optimise the process with respect to certain dimensions of quality, such as improved heating performance and increased heating uniformity, e.g. by modifying the geometry, placement and size of food components. Increased heating uniformity in turn also improves the quality from a microbiological as well as a sensory and nutritional point of view. Several textbooks (e.g. Kok and Boon, 1992) describe the mechanisms behind the general behaviour in an empty cavity. However, for the case of microwave heating of foods, the situation generally becomes much more complex. For all but the simplest product geometries and cavity configurations, an analytical or exact solution of Maxwell's equations is unfortunately extremely difficult or impossible. A good alternative is to use numerical modelling. A survey of computational methods for electromagnetics and microwaves is given by Booton (1992). Among such methods are the finite difference time domain approach, first described by Yee (1966), the finite element method (e.g. Silvester and Ferrari, 1983), and the moment method (Harrington, 1968). Hybrid methods, where the finite difference time domain scheme and the finite element method are combined for Maxwell's equations have also been described (Rylander and Bondeson, 2000). Numerical modelling of microwave processes involves solving for the electromagnetic fields, described by Maxwell's equations (Maxwell, 1892), coupled to the heat transfer problem. SIK has a long tradition within modelling of microwave heating, with work already starting in the 1970s (Ohlsson and Bengtsson, 1971; Ohlsson and Risman, 1978). Numerical modelling of electromagnetic fields in ovens and foods during heating has become a valuable tool when designing microwave heating units as well as microwaveable food products and packages. For microwave processing of foods, the electromagnetic problem can be solved numerically by several methods. The most common ones are: the finite difference time domain (FDTD) method (Yee, 1966; Taflove, 1980; Lau and Sheppard, 1986, Gwarek, 1988; Sundberg et al., 1996), the finite element method (FEM) (Dibben and Metaxas, 1994), and the method of moments (MM) (Yamashita, 1990). Furthermore, hybrid methods such as the stable FEM-FDTD method (Rylander and Bondeson, 2000) should be mentioned. Several commercial software packages are available, which have offered increased opportunities to use modelling as a tool to find the optimal solutions for microwave processing, with respect to design of food products and packages, but also for oven design. By coupling electromagnetic models to heat transfer models, it is possible to predict the temperature distribution within microwave processed foods. As described by WaÈppling-Raaholt (2000), Fu and Metaxas (1994) included

Influence of food geometry and dielectric properties

55

coupling of the electromagnetic and thermal processes by using the method of lines (Fu and Metaxas, 1993). Ma et al. (1995) suggested a combined electromagnetic and thermal FDTD model, where, however, the two algorithms had time steps of very different order of magnitude. The use of a timescaled form of the heat transfer equation was suggested by Torres and Jecko (1997) in order to overcome this difficulty. In both papers, temperature-dependent thermal properties were included in the model, though only to a limited extent due to the complexity of the numerical model. However, the thermal properties of the microwave heated dielectrics were held constant by these and other authors, and microwave-only heating was modelled (i.e. no convective boundary conditions were included). Zhang and Datta (2000) also studied a microwave-only heating process, by using a finite element (FE) frequency domain software for the microwave part, and a separate FE software for the heat conduction part. Variations of dielectric properties and weak convection were taken into account. However, they assumed constant thermal properties and did not include any surface evaporation. WaÈppling-Raaholt (2000) and WaÈppling-Raaholt et al. (2002) modelled and validated combined microwave and forced air heating of foods in a microwave combination oven, using the FDTD method, taking into account the temperature dependence of the thermo-physical properties, convective heat transfer at the boundaries and evaporation in the product. Further developments are modelling of microwave defrosting of foods in three dimensions (WaÈppling-Raaholt and Janestad, 2003), taking into account the strong enthalpy and temperature dependence of dielectric and thermal properties. To summarise, numerical modelling today gives a valuable and cost-effective tool for design of food products, packages, as well as microwave ovens.

2.5.2

Modelling as a tool in product development

Modelling of microwave processes may thus serve as a tool to learn more about a process, and for improving the heating uniformity by finding the optimal settings of relevant food and package parameters. In many practical situations it can also be used to reduce the number of experiments needed to find the best design of a food product. Product development of microwaveable foods, which in many food companies and institutions was previously empirically based, has to a large extent been replaced by numerical modelling, computer simulations and optimisation, which offer both products with improved microwave heating performance, but also a faster innovation cycle from product idea to market.

2.5.3

Theoretical background for today's microwave modelling tools

Today's knowledge in coupled electromagnetic and heat transfer modelling (WaÈppling-Raaholt et al., 2001; WaÈppling-Raaholt and Janestad, 2003) can, in

56

Packaging and products for use in microwave ovens

combination with knowledge and experience in food science give enhanced opportunities to improve design of microwaveable food products. This was demonstrated by WaÈppling-Raaholt et al. (1999, 2001) and WaÈppling-Raaholt (2000). Since then, the developed modelling together with tailor-made methodology for optimisation has been used in a large number of applications. Plate VII illustrates the predicted power distribution as a result of numerical modelling of microwave heating of a compact ready meal. For rectangular cavities, the simulated electromagnetic fields are often expressed in terms of field components in the x, y and z directions. The values of these field components in the x, y and z directions, respectively, are given by the projection of the electric field vector in each of these directions. In Plate VII, the Ey and Ez field components illustrate the simulated electric field distributions in the horizontal y direction8 and vertical z direction, respectively, for a horizontal cross-section of the load. In the upper part of the figure, the simulated power distribution in the food load is shown for the same horizontal cross-section. The simulations describe microwave heating of a non-rotating load. As can be seen in the figure, edge overheating, especially at two of the corners, is present during microwave heating of the load. This is explained by noting the strong electric field components in the horizontal direction, Ey, parallel to the edges of the load. Analogously, several other heating phenomena can often be understood by studying the behaviour of corresponding simulated electromagnetic field patterns. For analysis of industrial microwave ovens, Sundberg (1998b) suggested using the concept of cost functions in order to classify the heating performance of a specific oven design. A similar approach could of course be used for household microwave ovens, for example. The cost functions serve as a measure of how close the field generated by the oven comes to the requested field distribution, by assigning a figure of merit to the electromagnetic field distribution within the oven. Sundberg introduced two different cost functions. The first one will give as uniform heating as possible in the load (equation 2.4), by suppressing the difference between the coldest and hottest part of the food. The other one will minimise the horizontal component of the electric field, which in turn contributes to decrease overheating of the edges of closely positioned food packages, e.g. food loads transported on a conveyor belt (equation 2.5): f1 …a; b; c; X † ˆ maxjEj2 ÿ minjEj2 P f2 …a; b; c; X † ˆ

P jEx j2 ‡ jEy j2 P jEz j2

8. In this example, the y direction is in the oven depth direction.

2:4 2:5

Influence of food geometry and dielectric properties

57

where the sums are performed for all points which are included in the data set (Sundberg et al., 1998, page 43). `Simulated annealing' is further suggested by Sundberg (Press et al., 1992), as a suitable method for optimisation. The method is motivated by the fact that the strong field variation inside the cavity and within the food load gives rise to many local minima. A patent by Risman (1997) describes a technique for exciting pure TM0n0 and TM1n0 modes. In the same patent on the one hand a method to superimpose these modes to enable larger work load radii is presented, on the other hand a principle for enlarging the cavity length. The same concept for achieving uniform heating by combining selected modes was used by Isaksson et al. (2002a) for a continuous microwave heating process of meat. For microwave frequencies of 915 MHz, the penetration depth dp is considerably higher (approximately 2.5 times larger) than at 2450 MHz, assuming that the permittivity is similar at both frequencies. This has been industrially used, for example in applications with continuous tubular microwave heating as a means to overcome the limited penetration depth at the frequency 2450 MHz (Nykvist and Decareau, 1976; Isaksson et al., 2002b). On the other hand, at lower frequencies the temperature dependence of the complex permittivity becomes stronger (Ohlsson et al., 1974). This has to be considered in electromagnetic modelling because it results in more time-consuming 3D simulations than otherwise. Isaksson et al. (2002a) developed and suggested a simple and fast tool, based on a semi-analytical method for solving the eigenmode problem and for estimating the heat profile, in order to get a quick view of the behaviour of the process. The system of equations for the electromagnetic axial fields is given by Jin (1993). Under the assumption that the axial field is uniform, and that there is no azimuthal variation of " and , the modes become TE and TM. For TM modes, this leads to the radial solution to Bessel's differential equation   1d " dEz "m2 ÿ 2 2 Ez ‡ "Ez ˆ 0 r 2 2:6 r dr kt dr kt r where ! is the angular frequency (rad/s) and kt is the transverse wavenumber. The advantages of this approach are several, especially in the estimation of the heat profile for scenarios with markedly strong temperature dependence on the dielectric properties. WaÈppling-Raaholt et al. (1999, 2001) and WaÈppling-Raaholt (2000) suggest a statistical criterion for a quantitative measure of heating uniformity: the standard deviation of the dissipated power distribution normalised by the mean value, for a representative plane of the food load. Practical examples of improving the heating uniformity for real food products are given in WaÈpplingRaaholt et al. (1999, 2001) and WaÈppling-Raaholt (2000). As described in WaÈppling-Raaholt et al. (1999) an error norm to control the grid computational accuracy was defined, as given in (2.7).

58

Packaging and products for use in microwave ovens s X  2 P
x …i; j; k† ÿ P0:9
x …i; j; k† Error ˆ

…i;j;k†2M

X

jP
x …i; j; k†j

"

2:7

…i;j;k†2M

where M is a set of points in the food load, epsilon is a given error parameter, P
x …i; j; k† and P0:9
x …i; j; k† denote the power density at a point ……i ‡ 12†
x, …j ‡ 12†
y, …k ‡ 12†
z† for grids with cell sides
x and 0:9
x, respectively. A corresponding error norm to control the convergence of iterations was defined, as given in (2.8): s X  2 Pn‡1 …i; j; k† ÿ Pn …i; j; k† Error ˆ

…i;j;k†2M

X

jPn‡1 …i; j; k†j

"

2:8

…i;j;k†2M

Today's methods (WaÈppling-Raaholt et al., 1999, 2001; WaÈppling-Raaholt, 2000) provide the opportunity to design microwaveable food products with improved microwave heating characteristics. This is demonstrated for three types of ready-meals: meat loaf (WaÈppling-Raaholt et al., 1999), lasagne and a multi-component ready meal (WaÈppling-Raaholt et al., 2001), and illustrated in Plates VIII and IX. Among industrial applications designed to give uniform heating is a continuous microwave process of liver paste. The equipment design of 2002, discussed below, is based upon simulation results in order to achieve optimal heating performance. Based on a technique for achieving uniform heating by combining selected modes (Risman, 1997), Isaksson et al. (2002a) use the same concept for a microwave process of meat emulsion. The meat product is transported in the axial direction of a circularly cylindrical tube geometry and uniformly heated during pumping. In the process, two single-mode circularly cylindrical cavities are involved, each carrying a different mode (TM010 and TM120 mode). This combination of modes allows for uniform heating if designed properly. Isaksson analysed the heating by a simplified one-dimensional analysis, extended by introducing temperature-dependent dielectric properties. The validity of the one-dimensional results was evaluated by full-geometry finite difference time domain simulations (Quickwave-3D), which showed good agreement. This approach also allows for analysis at lower frequencies, where

2.2 A schematic drawing of the heating principle for continuous microwave processing of pumpable foods at 2450 MHz.

Influence of food geometry and dielectric properties

59

the dielectric properties show stronger temperature dependence. The validity of the model-based analysis was demonstrated by microwave processing of liver paste at 2450 MHz. Figure 2.2 shows the principle of the experimental plant for continuous microwave heating of pumpable foods.

2.6

Future trends

Household microwave ovens have become increasingly common in many countries, with a saturation level in the homes in the UK and northern Europe exceeding 80%, while in Australia, the United States and Japan the saturation level has been for several years well over 100% (Ohlsson and Bengtsson, 2001). In a few countries, such as Australia and the United States, almost all households have one or more microwave ovens. Nevertheless, the market for household microwave ovens is expected to grow worldwide. Furthermore, improvements in oven components, such as solid state components, will lower size, oven weight and production cost. The number of combination ovens, combining microwave heating with convection or radiative heating, is expected to grow continually, at least in Europe. Furthermore, the ongoing international standardization of performance and testing methods will lead to improved heating performance. Today, microwave ovens and microwaveable foods contribute to an important segment of the food market in Japan, the United States and increasingly in Western Europe. The microwaveable food segment does not only comprise prepared foods, such as entreÂe and side dishes, but also products especially made for microwave heating, the most striking example being the microwave popcorn bag, which was developed by Pillsbury in the late 1970s. The preparation or cooking instruction for more or less all packed food products are affected by the presence of microwave ovens in the households, even for such products which are not traditionally associated with microwave heating. The food packaging industry has also to a great extent been influenced by the growing number of microwave ovens and microwaveable foods. Requirements of microwave compatibility have considerably changed the way in which the food industry selects food packaging. For prepared foods, microwavetransparent plastic and paperboard packaging has grown at the expense of aluminium packaging. A vast number of packaging designs, specific to microwave heating, have been developed, e.g. the so-called susceptor package, in which an extremely thin metalised film on a polyethylene terephthalate (PET) film is heated by the microwaves to temperatures sufficient to crisp or brown pizza or pie crusts, or alternatively to pop popcorn. The differences between microwave and conventional heating are for some products shown by differences in development of food flavour and aroma and of food texture and appearance. In order to overcome this, modified recipes and tailor-made `microwave-adapted' food ingredients have been developed by

60

Packaging and products for use in microwave ovens

industry, in order to overcome at least partly some of the quality problems of microwave-heated foods. The fast development of foods, packaging and ingredients for microwave heating has resulted in an increased general knowledge about microwave heating in the industry (Buffler and Stanford, 1995). Even if much of this knowledge is still empirical, a clear trend towards more scientifically based R&D has, however, been seen in the past decade. There is a steady interest in industrial applications with a number of suppliers of industrial microwave equipment, particularly in Europe. Interesting additions to the already well-established application areas are given, by innovative novel applications which are more recently developed by the suppliers. This results in an increase in the R&D efforts into drying and pasteurisation applications within research programs at universities, institutes and large food industry R&D centres. The increasing knowledge of electromagnetic field distribution during microwave heating and interactions between factors which influence the heating performance, are expected to gradually improve microwave oven performance. Modelling-based product development in combination with packaging development (including different materials, shielding, susceptors, geometry, etc.) has increased rapidly in the food industry since the start of the century. Industrial microwave processing has been considered very promising for decades, but practical application has previously developed slowly. There are several reasons for expecting an increasing growth in the future: · Today's microwave heating units have a reliability which is comparable to that of alternative processing equipment, which makes microwave heating with its special advantages more attractive. · There is a trend in the food industry towards continuous processing lines and on-line process control. Thus, there will be an accelerating need for microwave heating as a unit operation for very rapid and in-depth heating. The advent of more sophisticated applicators, giving more uniform power distribution and improved process control will be a contributing factor; both for the tubular heating of pumpable liquids, and for the continuous heating of food packages on conveyor belts. · Tempering, pasteurisation, drying and snacks production will probably also in the future be the dominating applications, but with a steadily increasing number of applications. · The generally recognised ISM frequency of 915 MHz will be important for industrial processing because of its advantages in penetration depth and generator power and efficiency. However, properly designed 2450 MHz systems will also in the future be a strong alternative for many applications. · Further developed modelling tools will be invaluable tools for modern product design of microwaveable foods. By combining today's optimisation tools with knowledge of microwave engineering and food science, unique

Influence of food geometry and dielectric properties

61

possibilities for optimising and developing microwave food products are generated. These tools will also enable modelling of combination processes, where microwaves are combined with other heating techniques. The tools will reduce the time from product development to market for food products within the microwaveable segment, with increased possibilities to meet the increased requirements from consumers and respond to market needs.

2.7

Sources of further information and advice

SIK has long experience within microwave processing of foods, with projects already starting in the late 1950s. Today the work includes a large range of applications including tempering, thawing, heating and microwave assisted drying. For many years, one of SIK's primary areas of focus within microwave engineering has been the improvement of food quality (for example heating uniformity and texture) during microwave processing. Much of this work has been published previously. Parts of the present research will be submitted as papers to scientific journals, and presented continuously on SIK's web site: www.sik.se. An introduction to the subject of microwave processing of foods is found in Bengtsson and Ohlsson (1974). For further information on dielectric properties and their consequences for heating uniformity, the reader is referred to Ohlsson and Bengtsson (2001). The subject of the principles for microwave heating is described by several authors, e.g. Bengtsson and Risman (1971), Ohlsson and Risman (1978), Ohlsson (1983), Walker (1987), Buffler and Stanford (1995), Buffler (1993) and Ohlsson and Bengtsson (2001). For a review of the fundamental aspects on electromagnetics and numerical modelling, see e.g. Dibben (2001).

2.8

Bibliography

Antti, L. `Microwave drying of wood components in a continuous conveyor system', Technical Report 95-09638, NUTEK, the Swedish National Board for Industrial and Technical Development, 1997. Bengtsson, N.E. and Ohlsson, T. `Microwave heating in the food industry', Proceedings of the IEEE 62:1, pp. 44±55, 1974. Bengtsson, N. and Risman, P.O. `Dielectric properties of foods at 3 GHz as determined by a cavity perturbation technique. II. Measurements on food materials', J. Microwave Power, 6(2), pp. 107±123, 1971. Booton, R.C. Computational Methods for Electromagnetics and Microwaves, John Wiley and Sons Inc., New York, 1992. Buffler, C.R. `Microwave cooking and processing', in Engineering Fundamentals for the Food Scientist, AVI, van Nostrand Reinhold, New York, 1993. Buffler C.R. and Stanford, M. `The effects of dielectric and thermal properties on the microwave heating of foods', Microwave World, 12(4): pp. 15±23, 1991, and 16(1), pp. 5±10, 1995.

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Cheng, D.K. Field and Wave Electromagnetics, Addison Wesley, Reading, MA, 1984. Cole, P.J., Holyoak, C.D. and Cole, M.B. `Thermal inactivation of Listeria monocytogenes during a process simulating temperatures achieved during microwave heating', J. Appl. Bacteriology, 70, pp. 489±494, 1991. Dibben, D. `Electromagnetics: Fundamental aspects and numerical modelling', Chapter 1 in Handbook of Microwave Technology for Food Applications, edited by Datta, A.K. and Anantheswaran, R.C., Marcel Dekker, New York, 2001. Dibben, D.C. and Metaxas, A.C. `Time domain finite element analysis of multimode microwave applicators loaded with low and high loss materials', in Proc. Int. Conf. Microwave and High Frequency Heating, 17±21 September, St John's College, Cambridge, UK, A3.1±A3.4, 1994. Fu, W.B. and Metaxas, A.C. `MAXEMOL-A numerical scheme for the solution of Maxwell's equations using the Method of Lines', in Proceedings of Microwave and High Frequency Heating, GoÈteborg, Sweden, paper A5, 1993. Fu, W.B. and Metaxas, A.C. `Numerical prediction of three-dimensional temperature distributions inside a microwave oven using the method of lines', in Dig. 2nd Int. Conf. Computation in Electromagnetics, Nottingham, pp. 255±258, 1994. Funebo, T. and Ohlsson, T. `Microwave-assisted dehydration of fruits and vegetables using applicators', in Proc. of the 6th Int. Conf. on Microwave and High Frequency Heating, Fermo, Italy, pp. 229±232, 1997. George, R.M., Evans, D.G., Hooper, G.I., Campbell, G.M. and Dobie, P.A.P. Assessment and Improvement of the Manufacturers' Reheating Instructions for Microwaveable Lasagne Based upon the Voluntary UK New Microwave Labelling Scheme, MAFF Publications, London, 1995. Grimwood, N. `The convenience culture ± producing the quality in microwave foods', I. Eur Food Drink Rev, 3 (Autumn), pp. 11±12, 1989. Gwarek, W.K. `Analysis of arbitrarily shaped two-dimensional microwave circuits by finite-difference time-domain method', IEEE Trans. Microwave Theory Tech., 35(4), pp. 738±744, 1988. Harrington, R.F. Time-harmonic Electromagnetic Fields, McGraw-Hill, New York, pp. 158±163, 1961. Harrington, R.F. Field Computation by Moment Methods (reprint edition), R.E. Krieger, Malabar, FL, 1987; original edition, 1968. Hasted, J.B. Aqueous Dielectrics, Chapman and Hall, London, 1973. IEC Publication 60705, Household Microwave Ovens ± Methods for Measuring Performance, article 8, International Standard, 3rd Ed., Geneva, Switzerland, 1999. Hoseney, R.C. and Rogers, D.E. Problems and solutions in the microwave reheating of bread. Contribution No 90-94-A. Kansas Agric. Exp. Station, Manhattan, KS 66506, 1989. Isaksson, S., Bondeson, A. and Ohlsson, T. `Computer-aided design of a continuous tubular microwave process, using the TM0n0 and TM1n0 modes'. Paper II in `Tubular Microwave Heating', Thesis for the Degree of Licentiate of Engineering, Chalmers University of Technology, 2002a. Isaksson, S., Bondeson, A. and Ohlsson, T. `Tubular microwave heating of meat with temperature-dependent dielectric properties'. Paper III in `Tubular Microwave Heating', Thesis for the Degree of Licentiate of Engineering, Chalmers University of Technology, 2002b. Jin, J. The Finite Element Method in Electromagnetics, Wiley, New York, 1993. Katt, J.L. `The effects on starches and sugars on microwave cooking', Microwave World, 12(2), pp. 19±23, 1991.

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Kok, L.P. and Boon, M.E. Microwave Cookbook for Microscopists. Art and Science of Visualization, Coulomb Press, Leyden, 1992. Lau, R.W.M. and Sheppard, R.J. `The modelling of biological systems in three dimensions using the time-domain finite-difference method: I. The implementation of the model', The Institute of Physics, Phys. Med. Biol., 31, pp. 1247±1256, 1986. Ma, L., Paul D.-L., Pothecary N., Railton, C., Bows, J., Barratt, L., Mullin, J. and Simons, D. `Experimental validation of a combined electromagnetic and thermal FDTD model of a microwave heating process', IEEE Trans MTT, 43(11), pp. 2565±2572, 1995. Maxwell, J.C. A Treatise on Electricity and Magnetism, Vol. 1-2, unabridged republication of the last third revised edition 1892. Dover Publication, New York, 1954. Metaxas, A.C. Foundations of Electroheat ± A Unified Approach, John Wiley and Sons, Chichester, 1996. Miller, R.A. and Hoseney, R.C. `Method to measure microwave-induced toughness of bread', J. Food Sci., 62(6), pp. 1202±1204, 1997. Mudgett, R.E. `Electrical properties of foods', Chapter 7 in Engineering Properties of Foods, Rao, M.A. and Rizvi, S.S.V. (eds), Marcel Dekker, New York, pp. 32±90, 1986. Nykvist, W.E. and Decareau, R.V. `Microwave meat roasting', J. Microwave Power, 11(1), pp. 3±24, 1976. Ohlsson, T. `Methods for measuring temperature distribution in microwave ovens', Microwave World, 2(2), pp. 14±17, 1981. Ohlsson, T. `Fundamentals of microwave cooking', Microwave World, 2(4), pp. 4±9, 1983. Ohlsson, T. `More uniformity in heat from microwave ovens', Food Technology International ± Europe 1991, London 1991, pp. 77±78, 80±81. SIK publication 552, 1991. Ohlsson, T. `In-flow microwave heating of pumpable foods', Paper presented at International Congress on Food and Engineering, Chiba, Japan, May 23±27, 1993. Ê stroÈm, A., `Sensory and nutritional quality in microwave cooking', Ohlsson, T. and A Journal Microwave Power, 17(4), pp. 320±321, 1982. Ohlsson, T. and Bengtsson, N.E. `Microwave heating profiles in foods. A comparison between heating experiments and computer simulation. A research note', Microwave Energy Applications Newletter, 4(6), pp. 3±8. SIK publication 232, 1971. Ohlsson, T. and Bengtsson, N. `Microwave technology and foods', Advances in Food and Nutrition Research, 43, pp. 65±140, 2001. Ohlsson, T. and Risman, P.O. `Temperature distribution of microwave heating ± spheres and cylinders', Journal of Microwave Power, 13(4), pp. 303-310. SIK publication 320, 1978. Ohlsson, T. and Thorsell, U. `WiederwaÈrmen gekuÈhlter Lebensmittel und Speisen mittels Mikrowellen', ErnaÈhrungs-Umschau, 32(4), pp. 104±108, 1985. Ohlsson, T., Bengtsson, N.E. and Risman, P.O. `The frequency and temperature dependence of dielectric food data as determined by a cavity perturbation technique', J. Microwave Power, 9(2), pp. 129±145, 1974. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, New York, 1992. Risman, P.O. `Terminology and notation of microwave power and electromagnetic energy', J. Microwave Power and Electromagnetic Energy, 26(4), pp. 243±250, 1991.

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Risman, P.O. `Metal in the microwave oven', J. Microwave Power and Electromagnetic Energy, 13(1), pp. 28±35, 1992. Risman, P.O. `Confined modes between a lossy slab load and a metal plane as determined by a waveguide trough model', J. Microwave Power and Electromagnetic Energy, 29(3), pp. 161±170, 1994. Risman, P.O. `Tubular Microwave Applicator', US Patent No. 5,834,744, 1997. Risman, P.O. `A microwave oven model: examples of microwave heating computations', Microwave World, 19(1), pp. 20±23, 1998. Risman, P.O. and Ohlsson, T. `Theory for and experiments with a TM02n applicator', J. Microwave Power, 10(3), pp. 271±280, SIK Publication 286, 1975. Rylander, T. and Bondeson, A. `Stable FEM-FDTD hybrid method for Maxwell's equations', Comput. Phys. Comm., 25, pp. 75±82, March, 2000. RyynaÈnen, S. `Microwave heating uniformity of multi-component prepared foods', thesis for the degree of Doctor of Philosophy, EKT Series 1260, Helsinki, 2002. RyynaÈnen, S. and Ohlsson, T., `Microwave heating uniformity of ready meals as affected by placement, composition and geometry', J. Food Eng., 29, pp. 13±21, 1996. RyynaÈnen, S., Risman, P.O. and Ohlsson, T. `Hamburger composition and microwave heating uniformity', J. Food Sci., 69(7), M187±M196, 2004. Silvester P.P. and Ferrari, R.L. Finite Elements for Electrical Engineers, Cambridge University Press, New York, 1983. Sundberg, M. `An investigation of the edge overheating effect for high-permittivity dielectrics', Paper F in: Sundberg, M. `Analysis of Industrial Microwave Ovens', Ph.D. thesis, Department of Microwave Technology, Chalmers University of Technology, 1998a. Sundberg, M. `Analysis of Industrial Microwave Ovens', Ph.D. thesis, Department of Microwave Technology, Chalmers University of Technology, 1998b. Sundberg, M., Risman, P.O. and Kildal, P.-S., `Quantification of heating uniformity in multi-applicator tunnel ovens', in Proc. of the 5th Int AMPERE Conference on Microwave and High Frequency Heating, Cambridge, UK, Sept., 1995. Sundberg, M., Risman, P.O., Kildal, P.-S. and Ohlsson, T. `Analysis and design of industrial microwave ovens using the finite difference time domain method', J. Microwave Power and Electromagnetic Energy, 31(3), pp. 142±157, 1996. Sundberg, M., Kildal, P.-S. and Ohlsson, T. `Moment method analysis of a microwave tunnel oven', J. Microwave Power and Electromagnetic Energy, 33(1), pp. 36±48, 1998. Taflove, A. `Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems', IEEE Transactions on Electromagnetic Compatibility, EMC-22(2), pp. 191±202, 1980. Torres, F. and Jecko, B. `Complete FDTD analysis of microwave heating processes in frequency-dependent and temperature-dependent media', IEEE Transactions on Microwave Theory and Techniques, 45(1), pp. 108±117, 1997. Walker, J. `The secret of a microwave oven's rapid cooking is disclosed', Scientific American, 2, pp. 98±102, 1987. Walker, S.J., Bows, J., Richardson, P. and Banks, J.G. Listeria Survival in Chilled Retail Products: Effects of Recommended Microwave Cooking, MAFF, Food Safety Directorate, Ministry of Agriculture, Fisheries and Food. Microwave Science Series No. 1, 1991. WaÈppling-Raaholt, B. `Finite difference time domain analysis of heating of foods in household microwave ovens ± improving the heating uniformity of microwave heated foods', Thesis for the Degree of Licentiate of Eng., Chalmers University of Technology, 2000.

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WaÈppling-Raaholt, B. and Janestad, H. `Modelling of microwave defrosting of foods using a coupled electromagnetic and heat transfer approach', SIK internal technical report, 2003. WaÈppling-Raaholt, B. and Ohlsson, T. `Improving the heating uniformity of microwave processing', Chapter 15 in The Microwave Processing of Foods, Woodhead, Cambridge, 2003. WaÈppling-Raaholt, B. and Ohlsson, T. `Tools for improving the heating uniformity of foods heated in a microwave oven', Microwave World, 21(1), pp. 24±28, 2000. WaÈppling-Raaholt, B. and Risman, P.O. `FDTD simulation of a microwave heating process: effects of oven parameters on heating uniformity', 3rd Int. Conf on Predictive Modelling, Leuven, September, 2000. WaÈppling-Raaholt, B., Galt, S. and Ohlsson, T. `FDTD simulation of a microwave heating process: effects of food parameters', in Proceedings of the 7th International Conference on Microwave and High Frequency Heating, Valencia, Spain, 1999. WaÈppling-Raaholt, B., Ohlsson, T., and Risman, P.O., `Microwave heating of ready meals ± FDTD simulation tools for improving the heating uniformity', in Proceedings of the 8th International Conference on Microwave and High Frequency Heating, Bayreuth, Germany, 2001. WaÈppling-Raaholt, B., Scheerlinck, N., Galt, S., Ohlsson, T. and NicolaõÈ, B. `A combined electromagnetic and heat transfer model for heating of foods in microwave combination ovens', J. Microwave Power and Electromagnetic Energy, 37(2), pp. 97±111, 2002. Yamashita, E. Analysis Methods for Electromagnetic Wave Problems, Artech House, Boston, 1990. Yee, K.S. `Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media', IEEE Trans. Antennas Propagat., AP-14(4), pp. 302± 307, 1966. Zhang, H. and Datta, A.K. `Coupled electromagnetic and thermal modeling of microwave oven heating of foods', J. Microwave Power and Electromagnetic Energy, 35(2), pp. 71-85, 2000.

Plate IV The upper part of the figure illustrates microwave heating of one rectangular food block (50 mm  60 mm  60 mm) with rounded corners and top edges. From left to right: heating patterns in lower plane (5 mm from the lower surface of the block), middle plane (at 30 mm height), and upper planes (10 mm and 5 mm respectively, as measured from the top surface). The corners and vertical edges are overheated. So are the horizontal edges in the x direction at the upper surface, as well as at the lower surface. The lower part of the figure indicates the strong electric field components in parallel with the edges, and at the corners. The contours of the load are marked with a dotted black line. The electric field components Ex and Ey in the lower plane and Ez in the upper plane (5 mm from the upper surface) are shown.

Plate V The dissipated power in food loads located close to each other, heated in a model microwave oven with a sinusoidal waveform excitation, and rectangular TE01 excitation field (WÌppling-Raaholt and Janestad, 2003). Resonances between cylindrically shaped food items in the near vicinity of each other are illustrated in the uppermost figures. Lower figure: the corresponding situation for several rectangular blocks (9 blocks close to each other; the leftmost figure shows the result for the middle horizontal plane, while the second figure from the left shows dissipated power 5 mm from the upper surface of the same blocks). The two right-most figures illustrate that the heating pattern in nine blocks will show similarities to the corresponding result for one block, having the same volume as the nine.

Plate VI Centre overheating in cylindrically shaped meatloaf, placed with the circular bottom area at the turntable in a microwave oven. The load has thawed during heating (relative permittivity 52 ÿ j20 at 20 ëC). The radius of the cylinder was set to 20 mm, and the height of the cylinder was selected to be much larger than the radius, so that the heating in the centre of the cylinder at half its height would not be affected too much by heating effects at the edges. The upper figure shows the dissipated power in the cylinder at the middle horizontal plane (total height of cylinder ˆ 160 mm). The next two figures illustrate the electric field pattern in the oven cavity and in the load, with the cylinder placed in the middle, for the y and the z electric field components, in the middle horizontal plane. The cylindrical load is marked with a dotted black line.

Plate VII The predicted power distribution as a result of numerical modelling of microwave heating of a compact ready meal (the top part of the figure). In this example, the meal is a rectangularly shaped load with rounded corners. The top figure illustrates the result for the horizontal cross-section located 5 mm below the upper surface of the load. At that plane, overheating occurs at the corners and at the left edge. The electric field components in the y and z direction in the cavity and load are illustrated in the lower part of the figure. Model oven as in WÌppling-Raaholt and Janestad, 2003, with a sinusoidal waveform excitation, and rectangular TE01 excitation field.

Plate VIII Microwave power distribution in meatloaf, as a compact ready meal, before (left) and after (the two figures to the right) optimization. After optimization, the geometry and dimensions of the package were changed. In the optimized cases, the overheated and underheated areas are less pronounced.

Plate IX Dissipated power in lasagne and in a multi-component ready meal, before and after optimization. The multi-component meal consists of a meat patty, mashed potatoes and carrots. In both cases, the same volume of the meal is maintained after optimization. Geometries, dimensions and placement of the individual components were changed. The optimized meals have a more levelled out heating distribution.

Plate X Relative power densities at 2450 MHz in a 90ë (left) and 60ë (right) wedge, " ˆ 52 ÿ j20. Results obtained by free space modelling, with the electric field parallel to the tip and impinging from the left.

3

Advanced topics in microwave heating uniformity P R I S M A N , Microtrans AB, Sweden

Abstract: Food heating evenness depends on oven/cavity factors which cannot be modified by the microwave food developer. However, there are many distinguishable factors which depend on the load dielectric properties and its geometry. After an introduction to cavity volume mode and underheating trapped modes, twelve such factors are described and quantified. Key words: cavity, mode, surface wave, standing wave, permittivity, diffraction, edge, proximity, overheating, coldspot.

3.1

Introduction

Dielectric properties are expressed by two quantities, the real (relative) permittivity "0 (sometimes called `dielectric constant', even if it varies) and the loss factor "00 (Risman, 1991). It is very convenient for many computations to 0 00 bring these together p 00to the complex permittivity " ˆ " ÿ j" , where j is the complex unit ÿ1. " may include a contribution by conductivity; see Chapter 6, Section 6.4. Detailed studies of the dielectric properties of foods began in the 1960s, when industrial microwave heating and microwave ovens became increasingly common. It was generally thought that improved knowledge of these properties would quite immediately assist in improving the engineering designs of microwave ovens, as well as the development of microwave snacks and meals in the food industry. But this did not happen. The main reason was a poor understanding in the food industry of the many kinds of interactions between microwave fields and dielectric bodies ± the food loads. There was also a rather weak development of microwave oven characteristics ± the so-called multimode concept dominated, particularly in the United States. Today, most microwave-food interactions are understood, but literature descriptions are scarce and scattered. The separation into distinguishable phenomena which are discussed here has turned out to be very fruitful in the research and development in some industries. Several of the phenomena have been qualitatively and quantitatively dealt with before only at microwave conferences and symposia. Knowledge of them assists in development of ready meals and in the understanding of causes of problems that may then occur. With This chapter is ß Per Olov Risman and printed with his permission.

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numerical modelling being increasingly used in industry, knowledge of the individual phenomena will also assist in achieving improved results for microwave food heating and processing. Those described in the literature are still, with only very few exceptions, for example by Sundberg (1998), based on approaches of overall heating evenness, without particular considerations of food item tolerances and microwave oven property variables. Characterisation of microwave ovens is outside the scope of this chapter, but a knowledge of some properties is necessary in order to understand how the dielectric properties influence the heating results. Cavity volume mode basics are addressed in Sections 3.3 and 3.4, and their influence on horizontal heating patterns in Section 3.11.2. A more comprehensive treatment is given by Risman (2003), including a measurement method for determination of cavity volume mode characteristics. The strength of underheating trapped modes can be measured by heating experiments described in Section 3.6. Only these two kinds of modes are geometrically bound by the cavity, making it possible to even out patchy heating patterns by load movement such as rotation. Twelve load-dependent phenomena are also dealt with, some of which are partially interrelated. They are: · · · · · · · · · · · ·

the penetration depth (Section 3.2); internal vertical standing waves in large loads (Section 3.5); simultaneous heating of loads with different permittivities (Section 3.7); influences by different "00 , with the same "0 ± and the "00 increase runaway effect (Section 3.8); the edge overheating effect (Sections 3.9 and 3.11.3); heating of small isolated round objects (Section 3.10.2); the exploding egg effect (Section 3.10.3); the cold rim effect (Section 3.10.4); particular heating effects in uneven top surfaces (Section 3.11.4); the hot corner effect (Section 3.11.6); the burnt stripe runaway effect (Section 3.11.7); the multiple load item proximity effect (Section 3.11.8);

All these phenomena are bound to the load itself and are therefore not evened out much by load movement. However, the strength of some of them also depends on the cavity mode characteristics. The very significant variability between microwave ovens thus remains a problem for the food industry.

3.2

The microwave penetration depth

The only important microwave interaction property directly related to the dielectric properties that began to play an early role in industry was the penetration depth (depth of power penetration), usually labelled dp . It is defined as the depth below the surface of a

68 1. 2. 3. 4. 5. 6.

Packaging and products for use in microwave ovens large, flat and infinitely thick load item irradiated from straight above (incidence angle i ˆ 0, TEM) by i a plane microwave, at which 1/e (about 37%) of the power density at the surface remains. Owing to the exponential decay of the power density, this depth is also that below which 1/e of the total power is deposited.

There is a quite complicated formula given in most textbooks, but a much simpler and still exact expression for dp is p dp ˆ ÿ0 =…4
Im "† 3:1 where 0 is the free space wavelength of the microwaves and " is the complex "0 ÿ j"00 . The expression can easily be evaluated with a calculator accepting complex numbers. If "00 ="0 is less than about 1, an approximate formula p0 3:2 dp  0
" =…2
"00 † can be used. This indicates that dp is less sensitive to deviations in "0 than to deviations in "00 . Actually, the complete definition of dp above indicates what may vary in real practical situations. When items 1 to 3 above are not fulfilled: · additional phenomena may occur near the edges of a flat food surface (see Sections 3.9, 3.10.4 and 3.11.6); · additional phenomena may occur in thin loads (see Section 3.6); · it is unclear what happens inside rounded food items (see Section 3.10). All conditions 1 to 4 above may change the power deposition pattern, making the `dp concept' less useful in many practical situations.

3.3

Cavity modes

3.3.1

Geometric optics conditions

Some volume mode concepts must now be introduced. A starting point is then the angle of incidence in geometric optics; see Fig. 3.1. The relationship between the incident and transmitting angles is the well-known Snell's law (law of refraction): p 3:3 sin i ˆ j"j
sin t The fact that the wave is no longer transmitted perpendicularly into the dielectric results in a shorter penetration depth as calculated straight inwards from the surface. One can show that j"j in equations 3.3 and 3.2 is replaced by …j"j ÿ sin2 i †1=2 . Since " is high for most food substances, the difference may

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3.1 Incident (i ) and transmitted (t ) angles of a plane wave incident on a large dielectric. S is the direction of irradiation and the electric field (E) is drawn for TM polarisation.

become significant with low " values. As an example for a typical compact frozen food item, " ˆ 4 ÿ j1 gives dp ˆ 39:2 mm, which is reduced to 34.2 mm for striking incidence (i ˆ 90ë). Another characteristic is the wave polarisation. A transverse electric (TE) polarised incident wave has its electric (E) field parallel to the surface (and thus its magnetic (H) field at an angle to the surface). The opposite applies to transverse magnetic (TM) polarised waves. i ˆ 0 gives TEM polarisation.

3.3.2

Waveguide and cavity modes

It is found that microwave fields in closed metal tubes or cavities assume characteristic and discrete single or multiple (added) patterns. These can be of many kinds, examples being the single pattern in a coaxial line and the multiple interference pattern in large metal cavities. Theoretically, there is only one solution to the wave equation in each such case, but this solution can almost always be separated into dependent, partially dependent or independent simpler modes, which are each of the possible configurations of the fields in a given domain in space. In microwave heating applications, separation of the overall field pattern into modes is a very important tool for both understanding of mechanisms and for system synthesis. The understanding of volume mode interaction with large loads is greatly simplified by a partial analogy to plane wave (geometric optics) radiation. The use of image sets of plane waves to represent waveguide modes is generally called the electromagnetic ray concept. Figure 3.2 shows two TM-polarised waves with the same (i ) incidence angles towards a dielectric at the bottom of a two-dimensional waveguide. The vertical (z-directed) wavelength g is an important parameter and the figure can be used to deduce the following important relationship:

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3.2 A metal trough with two TM-polarised rays.

g ˆ 0 =cos i

3:4

The simultaneous plane waves combine into a vector field, shown in Fig. 3.3. If there is a reflection at the dielectric boundary, there will be both a downwards and upwards propagating wave, creating a standing wave. The wave positions in Fig. 3.3 correspond to the standing wave pattern. The heating pattern of a single mode will be patchy, with heating minima where the vertical electric field dominates. This is discussed further in Section 3.11.2. The link between the horizontal indices (the number of standing halfwave variations) m and n of a cavity or waveguide having the corresponding

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3.3 Vector E fields.

dimensions a and b in the other directions x and y ± and sini is sin2 i ˆ …12 0 †2
‰…m=a†2 ‡ …n=b†2 Š

3:5

This equation has a limited number of integer solution pairs (m; n) in each given interval of sini , as determined by the dimensions a, b and the operating frequency interval. As a consequence, all possible combinations of (m; n) for given values of a and b are represented by a finite set of sini values. The distance between the cold spots will theoretically be half a horizontal cavity mode pattern wavelength; this equals a/m or b/n and is thus always somewhat larger than the half wavelength in free space 0 . However, the heating evenness can be improved by the presence of several cavity modes, and/or rotation of the food load.

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3.4

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Wave reflections at an external flat surface

When the direction of i 6ˆ 0, phenomena in accordance with Fresnel's laws in optics occur also with microwaves. With a dielectric load, TM-polarised incidence (TM modes) is of particular interest, since there is a condition of minimal reflection at the Brewster angle iB . It can be shown that: iB  arctan

p j"j

sin2 i 

j"j j" ‡ 1j

3:6

where index B is for this pseudo-Brewster condition for lossy dielectrics. It is of importance in microwave cavity studies and design that the mode wavelength g in the z direction of Brewster modes can become much larger than the free space wavelength 0 . The following applies: p 3:7 g;B =0  j"B j ‡ 1 The quotient g;B =0 becomes quite high for " values typical of many load substances with a high water content, an example being g;B =0 ˆ 6 for j"B j ˆ 35. The sini interval of interest is thus rather narrow and close to the `cut-off' limit sini ˆ 1 which corresponds to striking incidence angle i ˆ 90ë and g ! 1. It can be shown that the pseudo-Brewster mode reflection at the surface remains almost insignificant also for quite large "00 ="0 values. Fresnel's laws can be used to obtain the results shown in Fig. 3.4: · The reflected power remains low for all "0 values for foods if i is 70 or more, with TM-polarised incidence. · Perpendicular (i ˆ 0; TEM) irradiation gives a high reflection for high "0 values. · TE-polarised irradiation is still worse than TEM incidence. Microwave oven cavity modes corresponding to TM-polarised incidence are thus more favourable. Microwaves are then absorbed with fewer reflections, which results in the performance becoming less sensitive to load item geometry and location variations. There are other advantages as well, which are discussed in the next section.

3.5

Internal vertical standing waves in large flat loads

It is often stated in the microwave oven literature that an important reason for uneven heating of food items is `internal total reflection'. But Brewster-type modes are not reflected much at flat horizontal interfaces, either when entering the top surface or when leaving the bottom surface of the load item. Neither are any waves totally internally reflected. The waves leaving the bottom surface do not disappear but are instead reflected by the cavity bottom. When they return

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3.4 Power transmission into an infinitely thick dielectric with the incidence angle and polarisation as parameters.

through the load, a simple standing wave pattern is created. A second basic influence by "0 ispthen  manifested: the waves inside the dielectric are slowed down by a factor "0 , resulting in the wavelength in the direction of propagation being reduced by the same factor. Figure 3.5 shows the solution obtained by calculations using the standard analytical so-called transverse resonance matrix method, for a 20 mm thick unidirectionally irradiated slab above a metal plane. The dp of the material is 7.1 mm for all i . Two items are seen: there is a tendency for a maximum of the standing wave at the surface facing the incoming irradiation, and the location of the heating minima depend on the distance to the cavity metal bottom. The first item is due to the so-called magnetic wall effect, but occurs only if the retroreflected wave escapes into free space. However, efficient microwave heating also requires the cavity ceiling to reflect microwaves back downwards, creating vertical standing waves. This also applies for Brewster modes, since the load does not cover the whole cavity bottom area. The second item is due to the escaping energy from the slab has to return, according to the energy principle. Figure 3.6 shows what happens under realistic microwave oven conditions: the standing waves become much stronger, with almost no heating at all in the lowest minimum. The load is the same, and with horizontal dimensions 140  140 mm2 but now in the small microwave oven of Fig. 3.9. The

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3.5 Theoretical power density pattern in a 20 mm thick slab under perpendicular plane wave incidence.

3.6 The numerically modelled vertical heating pattern in the centre of a 140  140  20 mm3 load with " ˆ 52 ÿ j20, in the microwave oven in Fig. 3.9.

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QuickwaveTM software (QWED, 1997) was used, with a resolution (cell height) of 0.5 mm. The power density in the vertical direction at the load centre is shown. The differences to the simpler analytical scenario result are mainly due to a realistic cavity mode pattern with retroreflected waves back down to the top of the load. Actually, patterns like that in Fig. 3.6 occur in most well-performing microwave ovens. The distance between maxima in the figure is about 8 mm, p which corresponds well to 12 0 =j "0 j  8:2 mm. The standing wave has stronger maxima and practically zero power density in the lowest minimum. This may result in unfavourable phenomena, such as power loss by stronger and earlier evaporation from the top surface, and a need for overall power reduction for allowing sufficient temperature evening out by heat conduction. A very uneven microwave heating pattern in the vertical direction should always be assumed in slab-shaped loads, with half an internal wavelength between the maxima. One might think that internal total reflection would be significant if the food slab does not have parallel surfaces. This is not correct in practice, for two reasons: the cavity modes in `good' microwave ovens are typically TMpolarised, which reduces food surface reflections in general, and coupling phenomena of the trapped surface wave type at/under the load are different from those in geometric optics.

3.6

Underheating modes

There is a shelf in all microwave ovens. Apart from the practical need for a flat surface to support the load, and the cleaning aspects, it is highly desirable that the microwaves reach the whole bottom surface of the load and thus also give heating from below ± underheating. The shelf is commonly of a microwavetransparent material such as borosilicate glass. Creation of sufficient underheating is one of the essential targets in microwave oven development and does by no means occur by itself. Strong underheating can actually be obtained in the bottom centre of slab-shaped loads having a diameter in excess of 20 cm, and there are some microwave oven models which typically provide about half the heating power from below for such loads on a recessed shelf. However, microwave oven performance test reports in consumer magazines also indirectly indicate that the underheating is insufficient for such and similar loads in many other models. The performance of seemingly similar microwave ovens may thus vary considerably. The geometry of the space below the load does not allow normal cavity volume modes, since the vertical height of the region below the food is less than half the free space wavelength. The particular trapped mode between the underside of the load and the cavity bottom is typically stabilised by the thick glass shelf and is characterised by having no vertical magnetic field. It is called a longitudinal section magnetic (LSM) mode. Such modes were first investigated

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3.7 Trapped surface wave properties, 2450 MHz (from Risman, 1994).

and reported by Pincherle (1944). Their fields have pattern similarities to Brewster and other TM-type cavity modes with very long vertical wavelength, and can therefore be excited by such modes. Additionally, the favourable Brewster modes are typically of the so-called hybrid type, lacking the horizontal electric field in one direction, which is then the cavity depth (y) dimension (see Fig. 3.9). A description of these LSM modes and their properties is given by Risman (1994). Figure 3.7 is from that work, and shows the horizontal absorption distance (that over which 1/e of the inwards-going energy density at the load periphery of a thick load has been absorbed by the load) as function of the distance between its underside and the cavity bottom (without a shelf), with the load permittivity and a characteristic length b as parameters, at 2450 MHz. The parameter b is half the horizontal standing wavelength in the y direction (see Fig. 3.9), and the LSM mode propagation is in the x directions. The coupling of the cavity volume mode to the LSM mode is favourable when b equals the whole cavity depth dimension, which requires the mode index n of also the cavity volume mode in that direction to be 1. It is commonly stated in the microwave literature that defrosting is problematic because an already thawed part absorbs more microwaves than a

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still frozen part. This phenomenon is sometimes called a runaway effect, but it can actually be overcome with LSM modes. The two crosses in Fig. 3.7 are for 20 mm airspace between the load underside and the cavity bottom, and for b (the cavity depth; y direction) about 300 mm. It is seen that the absorption distance is twice as long (120 mm) for the defrosted load (" ˆ 52 ÿ j20) as for the same load but now frozen (60 mm, for " ˆ 4 ÿ j2). This can be used to accomplish stronger power absorption of the LSM mode in the frozen food item. Full power defrosting is now recommended in the user manuals for some household microwave oven models in the market. The LSM mode properties are then employed. Packaged food items defrosted at full power may allow the selfregulating effect to work better than if evening-out by heat conduction is promoted, as is the case with slow defrosting. It may sometimes be difficult to separate the actions of cavity volume modes and underheating modes in heating experiments with typical food loads. There are two common methods for experimental investigations. The first is useful with geometries similar to ready meals, and employs the heating pattern in the `IEC batter load' (IEC, 2006), as evidenced by partial solidification by microwave heating and subsequent pouring-off of the remaining unsolidified batter. A typical action of underheating modes is then the occurence of solidified regions in central areas of the container bottom, with no corresponding solidified regions straight above. In contrast to this, cavity volume modes heating a raised batter load will give `hot spots' in the same inner horizontal positions in the top and bottom of the load, since the same modes are acting from both sides. The second method employs a thin metal sheet at half the height of a load of, for example, mashed potatoes. A significant temperature rise in the lower part indicates the presence of underheating modes. This is shown in the numerical modelling using the QuickwaveTM software (QWED, 1997) images in Fig. 3.8, with a scenario of a special microwave vending machine with microwave feed from above (SchoÈnning and Risman, 2007) having a 20 mm high load separated into two by a thin horizontal metal plane at half height. The shorter horizontal absorption distance in the low-" load is seen, and also that there is an LSM mode

3.8 The under-heating power deposition pattern in the central long side vertical cross-section of 160  110  20 mm3 loads with a horizontal thin metal sheet at half the load height. Top image: " ˆ 4 ÿ j1; bottom image: " ˆ 52 ÿ j20.

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resonance with the high-" load. It is also to be noted that volume mode heating of 10 mm high loads directly on a metal plane has a low efficiency (see Chapter 15, Section 15.2.2); this will increase when the metal sheet is removed. The phenomenon just described is used with so-called crisp plates in some microwave oven models, for example by Whirlpool. Crisp plates are thin-wall aluminium frying pans with a thin ferrite rubber coating on the underside. This absorbs the magnetic fields of the LSM wave, so a combination of frying (by the hot metal) and microwave cooking (by the volume modes from above) is obtained. There have been, and still are, recommendations by some food manufacturers on raising food items to be defrosted in household microwave ovens. Either the outer packaging or special so-called defrost racks are then to be used as support. It can be deduced from Fig. 3.7 that any LSM mode action will now essentially vanish owing to the too great absorption distance. But if there is no LSM wave excitation in the first place, cavity volume modes may now persist around the whole raised food item, perhaps resulting in some heating of the underside also. Raising of the load may thus not improve the defrosting performance in ovens with significant LSM mode action. It may, however, help in ovens with weak or no LSM mode action. It may finally be noted that the common statement in some microwave oven literature that a load height above the cavity floor of about 14 0 provides `good impedance matching' is incorrect. The only situation where this may help some is for defrosting (see the example in Fig. 3.5, and with the oven in Fig. 3.9, which has essentially no LSM waves).

3.9 The small microwave oven scenario (Risman, 1998) with the two symmetrical loads.

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79

Simultaneous heating of loads with different permittivities

It is often stated in the literature that a frozen item next to a thawed item in a microwave oven is heated less. This is then explained by the larger penetration depth in the frozen item. However, this is not true with typical, reasonably wellperforming microwave ovens. One must of course observe that the defrosting requires much energy and that the temperature changes slowly during the phase transition. What actually happens can be explained by the behaviour of TM-type modes such as Brewster modes, as described in Section 3.4. Additionally, the wave energy passing through the frozen load is reflected back into it, extending its `effective height'. If they exist, the under-heating modes (see Section 3.6) typically contribute by providing a stronger power absorption in lower permittivity loads. Numerical modelling was used to obtain some illustrative results, using a representative microwave oven. A scenario with such a simple oven was presented by Risman (1998); data are given in Fig. 3.9. The cavity is smaller than in typical ovens, but the scenario was carefully designed to represent several aspects of wellperforming household microwave ovens. However, the underheating mode is weak. There is a rotating turntable, so proper modelling for determinations of heating evenness has to be done with several positions of the turntable. Since the present objective is to describe heating mechanisms rather than to quantify overall performance, no rotation was used in the modelling described here. The symmetry of the scenario allows direct comparisons of coupling efficiency and heating patterns of loads with different geometries and dielectric properties. A first layout is shown in Fig. 3.10, with the modelling results in Fig. 3.11. A vertical standing wave pattern is seen in the two loads with higher ". A tendency of edge overheating (see Section 3.9) is seen in the high-" load but not in the others. The oven design, in combination with the low permittivity of the frozen load and its penetration depth being comparable to its height, results in a heating maximum in its bottom region. There is also heating from below in the load with intermediate permittivity. This result is due to the same type of standing wave phenomenon as shown in Fig. 3.6, and not any underheating mode. Much the same is seen in Fig. 3.12. The heating maximum in the bottom of the low permittivity part remains. It is caused by wave transmission through it, from above, and creation of a simple standing wave.

3.8

Influences by different "00 , with the same "0

As mentioned in Section 3.4, the wave reflection and thus the relative total absorption of the impinging power flux density, does not change much with the loss factor "00 . However, dp changes. This is illustrated in Fig. 3.13, which also

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3.10 Top view of the small microwave oven, with the load configurations of Figs 3.11 and 3.12.

3.11 The modelled heating pattern in central vertical y-directed cross-sections of two loads with diameter 70 mm and height 20 mm, in the oven scenario in Figs 3.9 and 3.10.

3.12 The modelled heating pattern in the central vertical y-directed crosssections of a square load with sides 140 mm and 20 mm height, with an included central circular load with diameter 70 mm; see Fig. 3.10. The square load in the top image has " ˆ 4 ÿ j2 and the circular has " ˆ 52 ÿ j20. The two permittivities are swapped in the bottom image.

shows a consequence of the equal total power absorption in the two cases: the power density in the surface region becomes proportional to "00 . Of course, this applies fully only under the idealised conditions of the definition of dp . However, it should be noted that it is normally undesirable to have, for example, a salty sauce layer on a piece of meat: the sauce will be overheated, and also to

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3.13 Comparative theoretical power dissipation in two large thick loads in the same heating cavity, with only different "00 .

some extent shield the underlying meat so that it gets less microwave power flux than if the sauce were less salty. A food item such as cooked ham with a high salt content (see Chapter 6, Fig. 6.5) has an increasing "00 with temperature. This will result in an already hotter part to receive more microwave power. This dynamic phenomenon is a wellknown runaway effect. There is, however, at least one other, completely different, runaway effect (see Section 3.11.7), so this one can be called the "00 increase runaway effect.

3.9

The edge overheating effect

The edge overheating phenomenon is in many practical cases the most problematic kind of uneven heating. It has been, and is still, one of the major problems in achieving even heating of food items in microwave ovens as well as in industrial processes. It is a non-resonant diffraction phenomenon caused by the electric field component parallel to the edge of the item. This is TMpolarised incidence with the wedge axis as reference, and is called TMz here, to avoid confusion. High permittivity items create a more significant issue. However, the effect disappears for TEz-polarised incidence, which corresponds to TM-type cavity volume modes (for horizontal edges). If these have a very long vertical wavelength, the edge overheating effect is also reduced on all horizontal edges, since a vertical electric field is then dominant. This makes it

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possible to largely avoid edge overheating by particular designs of microwave ovens and industrial systems. It is indeed remarkable that this important phenomenon in microwave heating has not received the attention by academia it deserves, in comparison with cavity mode theory. A possible reason may be that analytical methods alone cannot be used to derive descriptive equations. The effect is caused by diffraction which has to be non-resonant because a wedge has no dimensional scale, as opposed to other simple geometries such as spheres and circular cylinders. The phenomenon is concentrated on quite a small region; see Plate X. The strength of the phenomenon can be deduced by a first order theory, which has also been confirmed by numerical modelling and experiments (Risman, 2008). It turns out that the statements in many textbooks that the effect results from simple addition of wave energy irradiating the edge from two directions (from the side and from above, instead of one direction) is in error: for "0 > 40 and wedge angle 90ë, the maximum power density in the tip is typically four times higher than some distance away from the tip, and six times higher for wedge angle 60ë. For "0 about 15 the factor is about 2 for wedge angles between 30ë and 60ë. The effect has almost disappeared for "0 ˆ 4. The size of the overheated zone also varies with "0 ; the length 12 mm for the 60ë wedge in Plate X becomes 34 mm for " ˆ 16 ÿ j4. The first order equation for the electric field maximum E" inside the edge tip is E" 2 0:50
…90 ÿ † p ‡ p  Ei 1 ‡ j"j 90 ‡ 0:50
arcsin…1= j"j†

3:8

where Ei is the incident field and the wedge angle is 2. The first term is a wave potential term which also gives the field just inside a large flat load, and the second term a diffraction source term. The factor 0.50 is a so-called canonical constant that cannot be derived theoretically, and has been determined by numerical modelling (Risman, 2008). It should finally be noted that the direction of incidence has a very small and only second order influence on the effect, as long as it is within the `free' (180 ÿ 2) angle. Impinging waves which do not hit the edge tip first will also create surface waves. The wave potential term will then change, and with that the edge overheating effect. There is some additional information on edge overheating in Section 3.11.3.

3.10

Heating of isolated rounded objects

3.10.1 Introduction It is often said that microwaves heat `from the inside out'. As has been shown earlier, that is generally not true, since the penetration depth dp is shorter than

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the typical thickness of the food load. However, particular phenomena may be caused by the curvature of the load and by its overall size in relation to the free space wavelength of the microwaves. Its permittivity is of course also a basic variable, by determining the characteristic dimensions and strength of internal standing wave phenomena. The first investigation of spheres and circular food cylinders by analytic calculations and experiments in 2450 MHz microwave ovens was made by Ohlsson and Risman (1978). They showed that very significant heating maxima occur in the centre regions of spherical objects with diameters from 20 to 75 mm, and circularly cylindrical objects with about 20 to 60 mm. However, no qualitative explanations were given. The centre heating which may occur is often explained in the literature to be a result of quasi-optical refraction and internal total reflection, as would be the case for high permittivity "0 (the square root of which is the index of refraction) if the wavelength were much shorter than the curvature of the object. It is, however, obvious that the strength of the actual phenomena, as well as the small size of the hot spot in spherical objects, are such that that explanation is not correct. Instead, the effects are caused by diffraction and resonant phenomena, when the external fields vary so quickly in time that their free space wavelength 0 becomes comparable to the dimensions of the sphere. The resonant phenomena are of two basic kinds: internal and external (Gastine et al., 1967). Most of the diffraction field energy bound to the sphere is then inside and outside the object, respectively. The theory for what happens when an electromagnetic plane wave hits a dielectric sphere that is small in relation to 0 was published a century ago (Mie, 1908). Mie studied scattering of light, which is that part of the diffraction that concerns the propagating modes or plane waves emanating from the scattering object. The scatterers were small lossless particles such as air molecules. He set up the equations in exact analytical functions, and showed that rather distinct internal resonance patterns may be set up. However, he could only make some very approximate manual calculations, since the complete trigonometric equation system is quite complicated. The first-order approximation for the scattering by very small bodies in relation to the wavelength 0 of light by air molecules had, however, been earlier proven to be inversely proportional to 40 by Lord Rayleigh, thus explaining the blue sky. For the calculations of the diffraction shown in the following figures, the complete analytical function solution procedures in the classic book by Stratton (1941) have been used. The QuickwaveTM (1997) software has been used for the numerical modelling.

3.10.2 Small spheres In free space, the spherical TE101 mode (see Fig. 3.14, where indices are also defined) has the smallest radius at which an internal resonance occurs. The next

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3.14 The magnetic field lines of the internal spherical TE101 resonance pattern of a free dielectric lossless sphere with " ˆ 14 (from Gastine et al., 1967). The first index (m) refers to the azimuthal variation, the second (n) to the equatorial and the third (p) to the radial.

internal resonant mode is TM101, for a radius that is about 1.4 times larger than that for the TE101 mode. The TE101 mode pattern will thus be very dominant for small spheres. Its resulting electric field, and by that the heating pattern, has the shape of a torus. Figure 3.14 shows the magnetic field and the associated electric field is maximal in the loop centre, i.e. around the equator in the figure. Using the first order of the exact analytical solution, the resonant radius aR for this mode becomes, for large "0 , aR 

3:1
0 p j"j

2


3:9

At 2450 MHz and for "0 ˆ 52, this gives aR  8:1 mm, i.e. a diameter of about 16 mm. For "0 ˆ 52=4 ˆ 13, the resonant radius doubles, to about 16 mm. The next question is how significant the phenomenon may be. This can be assessed by Figs 3.15 and 3.16, which illustrate the analytical equation calculation results for spheres with three different complex permittivities as function of their radii, at 2450 MHz. It is seen in Fig. 3.15 that the relative averaged power density in the sphere is indeed quite sensitive to its radius for high-" materials, with a dominating effect

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3.15 Relative absorbed power density (1/r3) in free spheres under plane wave irradiation, as function of the radii and with " as parameter, at 2450 MHz. Analytical calculations.

3.16 Relative absorbed power flux density (1/r2) in free spheres under plane wave irradiation, as function of the radii and with " as parameter, at 2450 MHz. Analytical calculations.

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3.17 The averaged relative power density in free spheres with " ˆ 52 ÿ j20, under plane wave irradiation, as function of their radii. Computed by modelling.

of the TE101 mode. However, the `antenna function' (i.e. the ability to efficiently absorb the impinging wave flux), illustrated in Fig. 3.16, is not so extreme. Additionally, another absorption mechanism that is obviously not an internal resonance effect is also seen in that figure. It is dealt with in Section 3.10.3. The maximum relative heating intensity for different diameters as determined by numerical modelling for spheres with " ˆ 52 ÿ j20, is given in Fig. 3.17. When the radius reaches about 10 mm, the TE101 heating pattern begins to be taken over by that of the TM101 mode; the heating pattern maxima as seen in the right image in Fig. 3.18 then move towards the axis. The first interesting phenomenon in addition to the resonance effect is the drastic reduction in power density when the diameter of the sphere is reduced. The slope is maximal between 6 and 7.5 mm radius, but almost as steep up to the resonant radius which is about 8.1 mm in this case, according to equation 3.9. The absorption becomes proportional to r6 in the steepest interval, which is even for small more than the Rayleigh scattering which is proportional to ÿ4 0 scatterers. The power density reduction with size is thus so strong that there will be a significant heating unevenness when several small, separated and only slightly differently sized objects such as carrot dices are heated simultaneously. The second interesting phenomenon is that the power density in successively smaller spheres approaches a constant value, as seen in Fig. 3.15. This occurs for radii smaller than about a third of the resonant one, i.e. about 2.5 mm for

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3.18 The 2450 MHz heating pattern in an isolated 7.5 mm radius, " ˆ 52 ÿ j20, sphere irradiated by plane (TEM) wave. The S vector of irradiation direction is indicated, as is the wave polarisation ( E ˆ electric field). Obtained by modelling.

" ˆ 52 ÿ j20. Figure 3.15 indicates how small this quasistatic power density is in relation to that at TE101 resonance; it is a function of both "0 and "00 , since the quality factor (Q value) depends on both. The electric field in the small sphere becomes constant and the "0 dependence if "00 is not large follows the classical equation for the induced electrostatic field in a dielectric sphere: dP=dV / "00
‰3=…"0 ‡ 2†Š2

(very small sphere)

3:10

3.10.3 The exploding egg effect This well-known phenomenon is manifested for example by a chicken egg in its basic shape, raw or boiled and deshelled, shattering violently in any microwave oven within about half a minute. There are many explanations offered in the literature, such as a successive pressure build-up inside the shell, together with some kind of quasi-optical focusing of microwaves to its centre. These are wrong. Instead, an external diffraction resonance phenomenon occurs, resulting in a quite small but intense hot spot at the centre. In the case of the chicken egg, it seems as the proteins inhibit normal boiling at temperatures above 100 ëC, so a sudden release of steam occurs when the inhibition is no longer capable of withstanding the formation of a microscopic steam bubble. The pressure of the generated longitudinal sound wave then causes an avalanche effect of vapour bubble formation, within less than a millisecond. The hot spot temperature may exceed 135 ëC at the time of shattering (Rothla and Risman, 1994). Since most of the wave energy causing the hot spot is in this case on the outside and bound to the surface, the phenomenon as such is rather insensitive to

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the dielectric properties of the round object. Instead, its diameter, or rather circumference, must be in a certain interval for the phenomenon to become strong. This can be seen in Fig. 3.16: there is a maximum of the absorbed power flux density for about 20 mm radius for " ˆ 52 ÿ j20 as well as 16 ÿ j8. As said before, this cannot be traced in Fig. 3.15. This is consistent with the fact that only a small volume in relation to the whole is heated strongly. It is also seen in Fig. 3.16 that there is a weak tendency at about twice the radius (40 mm) for all loads. That these radii correspond to about one and two wavelengths in circumference is not coincidental. Actually, the external field pattern is that of a standing so-called Zennek wave (Risman, 1994), which has a number of radially directed electric field maxima: two as seen in the explanatory Fig. 3.19 and then obviously four for the 40 mm radius sphere. The field pattern illustrated schematically in Fig. 3.19 is of the spherical TM1 mode type (only an azimuthal variation; see Fig. 3.14 for co-ordinate definitions). The chain of events begins with conditions for creating a standing TM1 surface wave at the object. Since the pattern then becomes externally resonant and thus in time phase, the resulting pattern inside the object will propagate inwards with the same time phase everywhere, setting up a series of concentric ring-shaped standing waves. At the centre, a characteristic magnetic field pattern is then created, amplified by the converging wave energy. This induces strong currents which cause heating just at the centre. It may again be noted that the phenomenon is not related to some geometric optics focusing effect. It is not difficult to calculate that such a focusing effect, with the wavelength being much shorter than the diameter, cannot result in the strong and concentrated centre heating that actually occurs. An illustration of the effect ± again using the microwave oven model in Fig. 3.9 ± is shown in Plate XI. It shows the instantaneous vertically directed electric

3.19 A schematic illustration of the instantaneous external resonant electric field pattern, and the internal power-generating magnetic field at the centre of a spherical load item, with the exploding egg phenomenon.

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3.20 The heating pattern of the load in Plate XI, in the same plane (right) and in the equatorial plane (left). The radius of the volume in which the power density is larger than half the maximal is about 3.2 mm, corresponding to about 4% of the overall volume. The average power density in most of the load volume is about 7% of that at the centre.

field in the vertical central constant y plane, with a 40 mm diameter load with " ˆ 52 ÿ j20 (corresponding to dp ˆ 7:1 mm). The field at the sphere has the same direction at the opposite top and bottom sides and is thus of the spherical TM1 type. It is seen that the required fields of the surface wave resonance are in this case directly related to the cavity mode pattern, which is obviously of the TMz type with horizontal index 3 in the plane of the figure. As also shown in Plate XI, there is no need for the excitation fields to completely surround the spherical object. The heating pattern in the same load plane as in Plate XI is shown in the right image of Fig. 3.20 (underside to the right). The left image (in the equatorial plane) clearly shows the ring-shaped standing wave pattern inside the sphere. The same phenomenon occurs also in ellipsoidal and long circularly cylindrical objects, such as potatoes, small cups of coffee, etc. However, in such objects, the strong central overheating pattern becomes elongated. The hot zone may also be somewhat displaced from the axis. Another consequence of the limited requirements on the external fields is that the phenomenon is not very sensitive to the load dimensions. This was verified by Ohlsson and Risman (1978) and can be verified more easily now by numerical modelling. The following are then found: · For " ˆ 30 ÿ j12 (dp ˆ 9:1 mm), the radius of the hot spot (as defined in the caption to Fig. 3.20) is about 5 mm, for all sphere radii between about 12 and 27 mm, at 2450 MHz. For smaller radii, the TE101 resonant pattern successively becomes significant. · For " ˆ 16 ÿ j4 (dp  20 mm), the radius of the hot spot is about 6.8 mm and the average power density in a 20 mm radius item is now about 15% of that in the centre. · At 27 mm radius at " ˆ 52 ÿ j20, the intensity at the centre is about half of

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that for 20 mm radius. This reduction is due to a combination of less favourable item curvature and the penetration depth effect. · The hot spot intensity is largest around 20 mm radius, for all "0 values in principle. It may finally be noted that as the effect becomes reduced by increasing curvature radius and thus increasing radial distance to the centre, conditions for quite even heating throughout in food items such as baked potatoes occur. Were it not for the exploding egg effect, fast microwave baking of large potatoes would not work!

3.10.4 The cold rim effect External surface wave interference patterns do of course also occur for geometries other than spheres. The example now given, the common shape of a short circular cylinder (`puck'), can only be studied by experiments and numerical (non-analytical) modelling. A qualitative and quantitative description of the diffraction phenomena is given by Risman (2007) for thin (3±10 mm) flat circular high-" lossy objects with radii 3±50 mm, under 2450 MHz irradiation with different polarisations. It is found that a peripheral cold rim of variable width occurs, with an inner circular ring-shaped or single hot area. The resulting heating pattern changes somewhat for lower permittivities, the inner hot ring then being replaced by centre heating with a wider cold rim. A suitable term for the phenomenon is therefore the cold rim effect. Qualitatively, the cold rim is caused by two phenomena. The first occurs where the electric field component is parallel with the rim. The electric coupling slows down the propagation, resulting in creation of magnetic field components parallel to the axis, at essentially the same time phase (due to the high "0 ), over the rim region. Since this is curved, a depletion of the coupled horizontal electric field occurs at the rim, as the induced currents will follow the shortest paths. The second phenomenon occurs where the electric field is perpendicular to the rim. Owing to the propagation slow-down, this external field will remain perpendicular around the rim surface in this region, and thus become weakened by approximately a factor "0 inside the object. The phenomenon is the same as with TEz-polarised diffraction at a small dielectric cylinder. A very weak heating at the rim will result. For small puck-shaped objects with medium high "0 , the cold rim effect can also be explained by the creation of a field pattern similar to that of the spherical TM101 mode. The field pattern is then similar to that of the TE101 mode shown in Fig. 3.14, but with the electric and magnetic fields interchanged; it must also be noted that the radially directed electric field is discontinuous at the surface. Such

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an external field is actually similar to that of the spherical TM1 mode shown in Fig. 3.19, indicating the generality of that type of diffraction effect. Examples of the cold rim effect are shown in Plate XII. The maximum heating area in the 11 o'clock direction of the high-" load is not edge overheating, since there is a small cold rim at the periphery. Actually, there is no overheating anywhere at the periphery. The top region heating patterns in two similar loads is shown in Fig. 3.21, the only difference to the loads in Plate XII being that the load height is now 20 mm. In the high-permittivity load (lower image) there is now a hot ring almost all around, inside a narrow cold ring zone. In the low permittivity load, the hot zone is patchy and closer to the centre. The cold rim effect may be quite sensitive to the load diameter. An example of this is shown in Fig. 3.22, which is the same scenario as in the previous figures, but now with load radii 25 mm and 20 mm, and 10 mm heights. The cold rims are wider in the radius 20 mm loads, and the microwaves couple less efficiently to them.

3.21 The horizontal heating pattern in the top region of two symmetrically located loads. All conditions and data are the same as those in Plate XII, except that the loads are now 20 mm high.

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3.22 The cold rim effect for 20 and 25 mm radius loads, both with 10 mm height and in the oven of Fig. 3.9. The upper loads have " ˆ 16 ÿ j4 and the lower " ˆ 52 ÿ j20. The heating pattern is shown in the top region, and the amplitude scale is the same for the two modelling runs.

The cold rim effect may be significant for radii from 50 to 12 mm or less, for thin loads; thickness up to more than 20 mm for the larger radii and less than about half of the radius when this is small.

3.11

Combination effects

We have already seen the combination of underheating and cavity volume modes ± which can of course be very advantageous. Some of the described effects can be said to have electric fields as their primary source, but others are instead primarily caused by the magnetic field. How do these act on the different microwave coupling phenomena to the load, and influence the power deposition patterns? Some basic considerations are given in Section 3.11.1, followed by descriptions of some such combination effects.

3.11.1 Some remarks on power absorption mechanisms The common equation given in the literature for the time average of the power density dP/dV in a lossy dielectric is dP=dV ˆ  f "0 "00 jEj2

3:11

where "0 is the electric constant, f the frequency and E the internal electric field

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strength in the volume unit. The problem with this equation is that it may be very difficult to relate the internal field strength to the measurable field external to the load. It can therefore not be used in practical situations. The basic expression for the power density is dP=dV ˆ ÿ 12 Re‰r
…E  H †Š

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where H is the vectorial magnetic field, r the del operator and  the vectorial cross-product. This indicates that both E and H are needed for power to be expended. This is in analogy to direct current power formulas: the power is U
I (voltage times current), but can also be expressed as R
I 2 or U 2 =R, where R is the resistance. Which of the E and H fields dominate in determining the heating pattern? This basic question has different answers under different conditions. A hint is given by the boundary conditions at interfaces between different dielectric media: the H field is continuous, but the perpendicular E field component is reduced by a factor ". Additionally, the fact that the parallel E field component is continuous across the interface is typically accompanied by a standing wave minimum of this external electric field at the surface of a high permittivity load.

3.11.2 Horizontal heating patterns by cavity volume modes in large flat loads Since "0 is quite high, up to 70, for water and non-frozen non-dry food substances at 2450 MHz, the pattern of the magnetic (H) field will determine the heating pattern of such large flat load surfaces by cavity volume modes. The vertically directed electric (E) field will be substantially weakened just inside the load, and there is an H field minimum of the standing wave pattern of the cavity mode where this E field is maximum. There will thus be a cold spot at the position of maximum vertical external E field. The same reasoning is applicable to susceptors, which are thin metal films, characterised by a film resistance in ohms per square. They will not be heated at all by a perpendicular electric field but instead by the parallel component (or, equivalently, by the parallel magnetic field inducing a current). Therefore, using susceptor films or fax papers for `cavity field mapping' as described in some literature, will not work unless used in different positions and sheet directions for confirming what are the mode types, including their polarisations and vertical wavelengths. Can there be any direct heating of low permittivity loads by the vertical E field? Obviously, the induced current by the H field will be weakened for low "0 . It turns out that equal heating intensities by the E and H fields in the cavity TM mode case requires the equivalent of sin2 i ˆ "0 =3

(equal heating by TM mode E and H fields)

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This condition will not provide an even overall heating; it will be even only along some linear paths. However, the direct heating by the perpendicular E field may be still stronger in thin low-" loads, which is then typically advantageous.

3.11.3 The edge overheating effect As stated in Section 3.9, the edge overheating effect is caused by a direct action of an electric field parallel to the edge tip. If the cavity volume mode has a low vertical impedance, the dominating fields will be a strong vertical electric field and a strong magnetic field in at least one horizontal direction, since the energy of the electric fields has to be equal to that of the magnetic when there is wave propagation. As a consequence, the horizontal electric fields are weak, and one of them may even be zero if the cavity mode is of the so-called rectangular hybrid type. The edge overheating effect will then become very weak. The heating intensity caused by a cavity mode in the main surface regions of large flat loads will be proportional to the loss factor "00 . This applies also to the edge overheating effect, so the runaway effect mentioned in Section 3.8 may also occur here. The power deposition in a rounded edge region will be different from the sharp edge case. The spreading-out of the heating pattern will, however, not be large. The reason is that another phenomenon will begin to play a role: the strong coupling of TMz-polarised diffraction (the axis is reference) in a long isolated dielectric cylinder. Figure 3.23 shows two comparative heating patterns obtained by numerical modelling under conditions of free space irradiation.

3.23 Edge overheating in a sharp and 12 mm radius, respectively. The intensity and geometric scales in the images are the same, but the amplitude at the tip is slightly more than twice as large in the sharp tip.

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3.11.4 Particular heating effects in uneven top surfaces The small sphere TE101 diffraction resonance described in Section 3.10.2 has two symmetry planes and can exist also in a small hemisphere. Small parts protruding over the mean surface may thus considerably modify the microwave coupling. This explains why it is typically difficult to obtain reproducible laboratory microwave heating results with heating of a semi-solid food item such as mashed potatoes with a `rugged' top surface by imperfect spreading. It is better to use a smooth poured viscous surface such as the IEC batter (IEC, 2006). The rugged surface effect can also be intentionally used to improve the overall evenness of heating over the top surface in ready meals. The examples shown in Figs 3.24 and 3.25 are with " ˆ 52 ÿ j20 throughout, and provide very significant small hot spots in the small spherical segments, which will not occur without them. This results in an improved heating of the top surface, and also a deeper wave penetration downwards, by some millimetres.

3.24 Example of a rugged top surface of a ready meal model. The rounded items are spherical segments with about 16 mm width and 3 mm height, on a 30  150  150 mm3 solid load.

3.25 The heating pattern in the central cross-section of the load in Fig. 3.24, and in a load with a flat top as comparison, in the vertical plane shown in Fig. 3.10 of the small microwave oven.

3.11.5 Combination of the cold rim and exploding egg effects As seen in Plate XII, there is a `hot ring' inside the edge of a puck-shaped load, and there is strong centre heating in a spherical object, as seen in for example Fig. 3.20. An example of a favourable combination effect of the two coupling mechanisms is offered by commercially available microwave egg cookers; see Fig. 3.26. Even if there are tendencies to centre overheating, this is sufficiently weak to allow quick denaturation without splutter. Even if the top edges have a small wedge angle, the cold rim effect for this curved top periphery essentially eliminates the edge overheating.

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3.26 A commercially available microwave oven egg cooker. The spherical segment-shaped `holes' are 78 mm in diameter and 30 mm high; a normal chicken egg fills up to about 23 mm.

3.11.6 The hot corner effect A rather typical heating pattern in a slab-shaped load in household microwave ovens ± particularly models designed according to the so-called multimode principle with a ceiling stirrer or a rotating shelf ± is shown in Fig. 3.27. There is edge overheating and also hot corners, and a central cold region. Clearly, most

3.27 IR camera temperature pattern measurements on a 20  15 cm2 simulated flat food load in a multimode microwave oven.

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of the unevenness pattern follows the rotating load rather than being controlled by cavity volume modes. The strength of the particular heating pattern, in relation to that primarily caused by the periodicity and combination of the cavity mode field patterns, does however vary between ovens. The reason for this variability is that the wave type builds up over a large part of the load surface, as opposed to, for example, the exploding egg effect. The electromagnetic ray concept describes each cavity volume mode as a vectorial sum of typically four plane waves with the same angle of incidence and four symmetrical side angles. This may be used to explain the possibility of creation of surface waves of the Zennek type (Risman, 1994) propagating along the top surface of slab-shaped loads. They are characterised by the main electric field component being dominantly vertically directed out from the slab surface. The main feature of such waves is manifested when they encounter the `end' of the slab, where they are reflected back, creating a standing wave. It is to be noted that this standing wave follows the slab end rather than the cavity volume mode pattern, and will therefore be maintained for rotating loads and for varying load surface sizes. Figure 3.28 shows a plane wave free space scenario and Fig. 3.29 the numerical modelling result. Free space was chosen to obtain a better separation from other phenomena, and a TM-polarised impinging wave was used for obtaining reasonably good conditions for establishing a surface wave. It has most of its energy in the space above the slab and will encounter a region with higher impedance ± the cavity space ± at the slab `end' rim. This will result in a maximum of its standing electric field there, but this is essentially perpendicular to the slab surface and will thus not heat this rim much; see the left image in Fig. 3.29 at x ˆ 0. Since the electric field of the impinging wave is perpendicular to

3.28 A plane wave free space modelling scenario. The load has " ˆ 52 ÿ j20.

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3.29 The heating pattern in the top region of the load in Fig. 3.28, obtained by numerical modelling. The wave impinges from the left. The amplitude scale level is three times lower in the right image.

the left rim (xmax), this will not be heated much either. However, the horizontal component of the electric field will induce currents in the y ˆ 0 and ymax rims ± the edge overheating effect. Surface waves propagating in the y directions will also be created at these rims. The first interesting phenomenon is that the surface wave propagating in the ÿx direction will cause this edge overheating to be patchy, by a standing wave phenomenon as seen in the right image of Fig. 3.29. The maximum of this standing wave is always strongest some distance away from the `end' rim (x ˆ 0 in this case), and is thus primarily not determined by any cavity volume mode pattern. The second interesting phenomenon is that the y-directed magnetic field vector accompanying the surface waves will rotate at the rims and together with the impinging magnetic field will induce maximum heating typically some distance inwards from the rims. This distance is in the order of 20 mm from the rims for high-" loads and is strongest near the x ˆ 0 rim in the figure, as a consequence of the chosen excitation. As is clearly seen in the left image in Fig. 3.29, these magnetic fields will interfere constructively at some distance 45ë inwards from the corner. The corner edges will not be heated much, so there will be an often rather distinctive hot spot some distance inwards. This distance depends on the load permittivity and thickness ± and of course also on the microwave frequency. For 20 and 30 mm thick rectangular loads with " ˆ 52 ÿ j20 the x and y directions are about 20 mm. They increase to about 26 mm for " ˆ 32 ÿ j12. The combination of the surface-wave induced standing edge-overheating wave near the corner tip and the constructive interference of the reflected magnetic fields from two adjacent straight rims causing an inner hot spot is the hot corner effect. It has, to the knowledge of the author, not been explained

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before, but attempts to tie the standing wave along the rim to cavity mode fields or even so-called circular wave functions have been published in some literature. Interestingly, the strength of the hot corner effect increases some if the corner is rounded with radius 20 mm, but its position relative to the straight rims does not change. This effect is related to the exploding egg effect, by a radially directed electric field at the rounding. How can the hot corner effect be minimised? A first possibility is to avoid a flat top surface, but this must then be so uneven that there is an almost discontinuous edge. Another possibility is by rounding the corners of the food container, but the rounding must then be with a significantly larger radius than 20 mm. Replacing the single corner tip by two tips at some distance from each other (polygonal container shape) is another possibility. Paradoxically, a 20 mm radius may actually be worse than no rounding at all; the removed tip part would not be heated much at all by the microwaves. It would therefore improve temperature evening out by heat conduction. It should finally be pointed out that there is a relationship between the hot corner effect and the cold rim effect: if the rim is curved, the heating maximum will be some distance inwards from it. The necessary curvature requires the overall size of a load item subjected to the cold rim effect not to be large, whereas the hot corner effect can occur in larger load items. A general conclusion is therefore that food containers with large radii roundings are advantageous.

3.11.7 The burnt stripe runaway effect The cold rim effect (see Section 3.10.4) is strong for thin semi-dry loads with radii less than about 35 mm (at 2450 MHz), which thus get a centre heating that cannot be modified much by the design of the microwave heating system. But a particular amplification of the heating in a typical narrow zone across the diameter in load items such as potato chips may also occur. An example is shown in Fig. 3.30. If there was only drying-out by the microwave energy, this would be faster in the central region. Since the permittivity then decreases and by that the absorption capability of these dryer parts, a negative feedback would then occur and even out the drying. But as is seen in Fig. 3.30 the burnt stripe effect is indeed a runaway phenomenon, where an already dried-out region absorbs additional power so burn marks are created. It is concluded that liquid water transport is necessary for the effect to occur. What happens is illustrated in the numerical modelling scenario in Plate XIII. This shows a circular 24 mm diameter thin potato chip at 100 ëC (permittivity " ˆ 50 ÿ j16), having an elliptical inclusion with axes 18 and 4 mm, representing a partially depleted region (permittivity " ˆ 8 ÿ j1:6). It is irradiated from the left with a free space TM-polarised 2450 MHz wave with incidence

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3.30 A selection of four raw potato chips with diameter about 30 mm and thickness 4 mm, after partial drying in a microwave system providing dominant TM-polarised modes with no load movement. Note that the orientations are changed in the photo. Courtesy of SIK, Sweden.

angle i ˆ 82ë; the magnetic source field is thus y-directed and the main current x-directed; the dominating electric field is z-directed. The following phenomena can be distinguished: · There is a heating (and thus current) concentration in the high-" part close to the low-" area. One can explain this as being due to the current following the shortest path and thus `avoiding' the low-" area. The boundary is concave and not convex as is the case with the cold rim effect, so conditions are now reversed, but obey the same principle. · There is a significant heating in the centre region of the low-" area. This is due to direct action by the strong external z-directed electric field, as discussed in Section 3.11.2. The phenomenon is amplified by the fact that the load is thin. It is to be noted that the heating intensity in the centre is more than a third of the maximum in the non-depleted area, in spite of "00 being ten times lower and the penetration depth dp being more than three times larger than in the non-dried region. This power density will indeed cause overheating, in consideration of the now limited amount of remaining water for evaporative cooling. · There is a significant heating intensity minimum just inside the low-" area boundary. This is a result of the z-directed electric field being almost shortcircuited there, by the close high-" area. One can also explain the minimum

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as a so-called magnetic wall effect. The minimum intensity is less than half of that in the centre of the low-" area. These sharp heating gradients result in the boundary between the outer relatively moist and the inner dry regions becoming relatively constant, while the inner region continues to dry out. The resulting narrow burnt regions are clearly seen in Fig. 3.30. Can this effect of uneven heating be avoided? Load rotation or TM-polarised field variations will not help much; the inner overheated region will then instead become symmetrically circular. The use of other microwave polarisations will result in edge overheating as well as a risk of lower microwave system efficiency. There are no easy solutions.

3.11.8 The multiple load item proximity effect When experimenting with positioning of food items such as small potatoes, carrots, onions and meatballs in ready meal containers, it is not uncommon to experience such strong heating in the small contacting regions of such items that they dry out or even burn. The causes of the phenomenon and some quantitative factors are now discussed. A simplification is made by using spherical items with 16 mm diameter and exposing them to a plane wave. This will reduce the variabilities of phenomena caused by coincidental amplifications or weakenings by the overall positioning resulting from the variable cavity mode fields. The chosen diameter will provide a compromise between large and small surface areas being close. Figure 3.31 shows three examples, with 4, 1 and 0 mm distance between spheres with " ˆ 52 ÿ j20. The amplitude settings are for about equal power density greytone in the regions away from that with close contact. In the 4 mm distance case, there is no coupling effect at all, and the maximum power density level can be set to 1. The maximum level goes up to 1.4 in the 1 mm case, and to 11 in the contacting case. There are thus two effects: a general increase of the power density with closer contact as stated in Fig. 3.31, and a drastic increase of the power density in the contacting spot. The heating in the close contact area must be caused by a concentration of the displacement current, due to the requirement on its continuity in the region. The wave impedance of free space is about 377 per square and is reduced by a p factor " in a dielectric. If we now assume an effective capacitor surface area of the dielectric body of, for example, 4  4 mm, the current-carrying capacitance will become almost eight times smaller in the airspace than in the bodies with " ˆ 52 ÿ j20. Thus, a distance in air of only 0.5 mm has the same capacitance as 4 mm inside the load. With the 0.5 mm airspace between the dielectric surfaces there will then very roughly be a comparable heating effect in the body in general and locally by the additional capacitive coupling.

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3.31 The numerically modelled heating pattern in the vertical central crosssection of 16 mm diameter spheres with " ˆ 52 ÿ j20, irradiated from above with the electric field in the plane of the paper, in free space: top: 4 mm distance, set amplitude = 1; middle: 1 mm distance, set amplitude 1.2; bottom: contacting, set amplitude 1.6.

If the permittivity of the spheres is instead 16 ÿ j4, the coupling phenomena would occur for larger distances between the items. Figure 3.32 shows the same three examples as in Fig. 3.31, but with the spheres having " ˆ 16 ÿ j4. There is now coupling also for 4 mm distance. It is about as strong as for the 1 mm distance in the " ˆ 52 ÿ j20 case. The maximum power density level goes up to 1.4 for the 4 mm distance, to 3.7 in the 1 mm case and to about 20 in the contacting case. With permittivity 4 ÿ j2, the coupling becomes significant for slightly less than about 12 mm distance, i.e. three times larger than with " ˆ 16 ÿ j4. The capacitance concept with unchanged capacitor area of the dielectric body would result in only about a doubling of the distance from the same effect. But a larger part of the lower-" bodies participates in the effect as indicated by the size of the affected regions. One may therefore conclude that the effective coupling distances are approximately inversely proportional to the permittivity, at least for typical small objects of spherical shape. As mentioned in the beginning of this section, the heating of small regions may become very strong. They will then dry out and by that reduce the capacitance and by that the effect ± a negative feedback may occur. Even if burns or Maillard reaction discolouring occur, fires very rarely, if at all, start by the close contact effect. For that to happen, arcs between quite sharp edges or points of food substances containing parts with high fat or sugar content are needed; see Chapter 6, Section 6.9.3.

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3.32 The numerically modelled heating pattern in the vertical central crosssection of 16 mm diameter spheres with " ˆ 16 ÿ j4, irradiated from above with the electric field in the plane of the paper, in free space: top: 4 mm distance, amplitude = 1; middle: 1 mm distance, amplitude 1.2; bottom: contacting, amplitude 1.6.

It is stated in some literature that this and other phenomena are caused by an internal total reflection effect related to the internal standing waves and resonant patterns dealt with in Sections 3.5, 3.10.2 and 3.10.3. However, the wavelength of the microwaves is comparable to the characteristic sizes of food items and these are furthermore so curved that geometric optics concepts are not applicable anyway; the fields as such have instead to be studied, as is done here and in previous sections. The quasi-static capacitance concept provides sufficient coupling data for most practical purposes.

3.12

Summary and conclusions

The heating result ± both the heating patterns and the microwave coupling efficiency ± depends on a multitude of separable parameters. There are two such important parameters which depend on the design of the oven cavity or applicator and its feed structure: volume mode polarisations with their vertical wavelengths, and the presence and strength of underheating trapped surface wave modes. These mode types behave differently as functions of the load permittivity. Twelve distinct phenomena which depend on the load permittivity and geometry have been described ± see the list in Section 3.1. Some of these are interrelated, and all are to a varying extent dependent on the load permittivity. Modern, efficient software for numerical microwave modelling has been

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commercially available for about ten years and this chapter provides many illustrations of its use. Analytical calculations are possible for only some few simple load geometries, so modelling is an indispensable tool not only for simulating actual heating experiments but also towards qualitative understanding and practically oriented quantifications of the various phenomena described in this chapter. Separation of the phenomena additionally provides possibilities to construct new and efficient goal functions for automated optimisation computations.

3.13

Acknowledgement

Thanks to Per Floberg, formerly at SIK ± the Swedish Institute for Food and Biotechnology ± for valuable discussions and recommendations.

3.14

References

Gastine M et al. (1967) 'Electromagnetic resonances of free dielectric spheres', IEEE Trans MTT-15(12), 694±700. IEC (2006) Household Microwave Ovens ± Methods for Measuring Performance. Consolidated edition 3.2, IEC, Geneva. Mie G (1908) Ann Physik 25, 377. Ohlsson T and Risman P O (1978) `Temperature distribution of microwave heating ± spheres and cylinders', J Microwave Power 13(4), 303±309. Pincherle, L (1944) `Electromagnetic waves in metal tubes filled longitudinally with two dielectrics', Physical Review 66(5), 118±130. QWED Sp. z o.o. (1997) QuickWaveTM software for electromagnetic design, www.qwed.eu. Risman, P O (1991) `Terminology and notation of microwave power and electromagnetic energy', J Microwave Power & Electromagnetic Energy 26(4), 243±250. Risman P O (1994) `Confined modes between a lossy slab load and a metal plane as determined by a waveguide trough model', J Microwave Power & Electromagnetic Energy 29(3), 161±170. Risman P O (1998) `A microwave oven model ± examples of microwave heating computations', Microwave World (IMPI) 19(1), 20±23. Risman P O (2003) `Understanding microwave heating in cavities in use today', AMPERE conference, Loughborough, UK. Risman P O (2007) `Puddles and droplets ± an investigation of their influences on microwave system performance', IMPI symposium, Vancouver, Canada. Risman P O (2008) `Diffraction phenomena inside dielectric wedges ± qualitative theory and verification by modelling and experiment', MIKON 2008 conference paper A7/ 1, Wroclaw, Poland. Rothla M and Risman P O (1994) `Splutter of foods during microwave heating', IMPI Symposium Digest, 26±29. SchoÈnning U and Risman P O (2007) `A microwave system for direct frozen-to-hot vending applications', IMPI symposium, Boston, MA. Stratton J A (1941) Electromagnetic Theory, McGraw-Hill Book Co., London. Sundberg M (1998) `Analysis of industrial microwave ovens', PhD thesis No. 332, Chalmers University of Technology, GoÈteborg, Sweden.

Plate IX Dissipated power in lasagne and in a multi-component ready meal, before and after optimization. The multi-component meal consists of a meat patty, mashed potatoes and carrots. In both cases, the same volume of the meal is maintained after optimization. Geometries, dimensions and placement of the individual components were changed. The optimized meals have a more levelled out heating distribution.

Plate X Relative power densities at 2450 MHz in a 90ë (left) and 60ë (right) wedge, " ˆ 52 ÿ j20. Results obtained by free space modelling, with the electric field parallel to the tip and impinging from the left.

Plate XI The instantaneous vertically directed electric field in the central vertical cross section of the model microwave oven in Fig. 3.9, with a 20 mm radius load with " ˆ 52 ÿ j20. Magenta is maximum upwards-directed field and dark blue is maximum downwards-directed. Green is zero.

Plate XII Modelling of a diameter 24 mm thin high-" load with a central inclusion of a low-" load, under TM-polarised incidence i ˆ 82, from the left). (See text for further information.)

Plate XIII (a) The horizontal power density pattern in the top regions of two symmetrically located radius 35 mm, height 10 mm loads, in the oven of Fig. 3.9. The `upper' load has " ˆ 16 ÿ j4 and the lower load " ˆ 52 ÿ j20. (b) The power density pattern in the vertical cross-sections of the loads in (a). The left load has " ˆ 52 ÿ j20; the right " ˆ 16 ÿ j4. A standing wave pattern is seen in the left image. (c) The colour scale in modelling: blue ˆ0; magenta ˆ maximal.

4

Microwave ovens N C O O P E R , Formative Solutions LLC, USA

Abstract: This chapter begins with a brief history of the microwave oven since its invention in 1946. The chapter will review the many design variations of microwave ovens that can have an impact on product or package design, uniform heating and product testing. The chapter will briefly discuss the test requirements and federal regulations relating to microwave oven safety. Key words: microwave oven construction, mode stirrer, speed oven, microwave leakage.

4.1

Introduction

The microwave oven is now over 40 years old. It is present in virtually every home in the United States and has established itself as an appliance we can scarcely do without. We will explore the history of the microwave oven and examine construction features, especially those features that impact product or packaging design. We will look at niche products such as combination ovens and speed ovens. Finally, we will look at some of the test requirements and regulations that make the microwave oven such a safe appliance.

4.2

History of the microwave oven

Microwave technology, developed for radar during World War II, was put to peaceful uses immediately after the end of the war. Dr Percy Spencer is credited with inventing the microwave oven (see Fig. 4.1) while employed by Raytheon Co. of Woburn, MA. In the manufacture of radar systems in those days, open air operation of magnetrons at `exhaust stations' (sometimes referred to as aging racks) was common practice. At the exhaust station, a worker would mount a tube in a fixture and connect a vacuum line between the magnetron tube and a high vacuum pump. After a predetermined level of vacuum had been achieved, the tube would be baked out at high temperature for at least one hour to further degas the tube. Finally, the cathode would be slowly energized and voltage applied to the anode until full power was achieved (Osepchuk, 2008). Dr Spencer observed that a candy bar in his shirt pocket had melted when he was in the vicinity of these magnetrons.

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4.1 World's first microwave oven patent.

Raytheon Corporation was a pioneer in the development and marketing of early microwave ovens. The first Raytheon microwave oven was introduced to a select audience of food editors, home economists, restaurateurs, and airline operators in October 1946 in New York City (Hammack, 2005). This oven was huge, standing over 1.7 m tall, weighing over 340 kg and costing about $5000 (about $54,000 in 2008 dollars). While this oven was physically large, it was limited to sandwich heating due to its small cavity dimensions. A production oven with a larger, more useful cavity was introduced in early 1947, called the RadarRange. But it was still very large, measuring over 1.5 m tall, 0.6 m wide and 0.6 m deep. The weight had been trimmed down to a mere 300 kg and the cost pared down to the $2000 range. Like the very first Raytheon ovens, the magnetron was water cooled and required a plumbed water connection. It was aggressively marketed to restaurants, railroads, and cruise ship companies, but sales were disappointing. In 1952, Raytheon licensed its oven technology to Tappan. Three years later, Tappan introduced the first home microwave oven. It was a built-in wall unit, about the size of a dishwasher. The magnetron was air cooled, so a plumbed water connection was not needed. However, the cost of $1200±1300 was still an impediment to sales. By the mid-1950s other manufacturers had also taken an interest in the microwave oven. Manufacturers such as General Electric (GE), Bruder Corpora-

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tion (later to become a part of Litton Industries) and Philips Company of the Netherlands were soon selling commercial microwave ovens. The competition between companies, directed by feedback from users, pushed the engineers to design ovens with more power and more features but in a smaller size. The early 1960s saw demonstrations of the first conveyorized microwave oven for foodservice by Philips Company. A working model was exhibited at numerous venues across Europe in 1961±62. The oven was capable of continuously heating 150±200 pre-plated meals per hour from ÿ25 ëC to 80 ëC. Although a technical success, efforts to market the equipment in Europe and the United States were not successful. In 1961, Sharp Corporation developed Japan's first microwave oven, the Model R-20. By 1962, the first Japanese-built microwave oven, the Sharp Model R-10 was on the market. Panasonic was also selling commercial microwave ovens in Japan. Throughout the 1960s manufacturers tweaked and fine-tuned the technology in order to develop the one microwave oven with the broadest appeal. To address the lack of browning, resistance heating elements were added to the top of the oven (Tappan). Microwave ovens were sometimes combined with conventional ovens in a `kitchen center' approach. GE produced one model that operated at 915 MHz to address the problem of limited microwave penetration at 2450 MHz (Osepchuk, 1984). Behind the scenes, magnetron manufacturers were feverishly designing smaller, more efficient and more reliable magnetrons. Sales of commercial microwave ovens climbed in a slow but steady rate until 1966, when Litton Industries introduced the Model 500, a compact countertop microwave oven with 1 kW of power, operating on standard 110 V and priced under $1000. In the same year Sharp Corporation introduced the Model R-600, the first Japanese-built microwave oven with a turntable. By 1970, total sales of microwave ovens in the United States had reached approximately 40 000 units at prices from $300 to $400 (Hammack, 2005). Development of combination ovens began in the late 1960s. Hot air convection combined with microwave achieved the quality available from a conventional oven with the speed of a microwave oven. However, it was not until the mid-1970s that this type of oven was available for sale. They gained some popularity in foodservice and in the galleys of passenger trains. The first marketing efforts for this type of oven began in England with the Hirst Corporation Articair oven (Andrews, 1989). Litton soon followed in the United States with their Jet-Wave oven. The 1970s were the hey-day of the consumer microwave oven. By 1971, prices of Japanese-manufactured ovens were as low as $200. By 1978 about 10± 12% of US households had microwave ovens. Sales grew steadily through the decade, hitting the 6 million mark in 1983. Today, annual sales are about 13 million ovens. This equates to a market penetration of over 90% (Anonymous, 2007).

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Manufacturers introduced many new features in an effort to attract the consumer. The first humidity sensor was invented by P.O. Risman of Sweden (US Patent 3939618) and was initially used in Husqvarna ovens. Amana brought microwave ovens into the digital age with the introduction of the TouchmaticTM RadarangeTM. The TouchmaticTM replaced the rotary knobs with a digital touchpad. The consumer could, for the first time, program defrosting, cooking, and reheating with the help of the built-in microprocessor. It was an instant hit, and soon every manufacturer was marketing a touchpad/microprocessor equipped oven. By the mid-1970s, microwave ovens were becoming a common fixture in American kitchens, with sales of microwave ovens exceeding sales of gas ranges for the first time. Food manufacturers began to take notice of the increased sales and began marketing food specifically for this technology. Also, third party manufacturers were marketing accessories for the microwave oven, such as a pressure cooker (US Patent 2622187), popcorn popper (US Patent 4158760), wind-up turntable (US Patent 4254319), the microwave griddle (US Patent 3591751), and microwave steamer (US Patent 4317017). The microwave griddle transforms microwave energy into thermal energy which then browns the food in contact with the griddle. Microwave griddles can be made from steel rods (US Patent 3591751) and lossy dielectrics, such as ceramic (US Patent 3662141). While technically not a griddle, ferrite-loaded rubber and plastic have been used as a thermal heating surface on microwave cookware (US Patent 3302632). All of these thermal heating devices act as an additional load to the microwave oven, thus robbing the food of microwave energy and, in most cases, prolonging the cook time. It was believed in the 1970s that the microwave oven would eventually become the primary cooking appliance in the home. Virtually every manufacturer produced well-made, hardback cookbooks which shipped with their ovens. Food companies and independent writers also produced cookbooks. Eventually oven prices fell to the point where (in the mid-1980s) it was no longer economical to include a book with each oven. Prices of microwave ovens continued to fall through the 1980s±1990s. Nevertheless, the list of available features continued to grow, leading to those commonly found today. Sensor assisted cooking and specialized, preprogrammed buttons (such as Popcorn and Defrost) are now available on many models. Sensor cooking uses built-in humidity sensors to measure moisture released from the food while cooking. Special cooking algorithms automatically adjust the microwave power and cook time to achieve optimum results.

4.3

Oven design and construction

A microwave oven is, in its most simplistic form, a rectangular metal box with a hole or holes through which microwave energy is delivered into the cavity.

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4.2 Components of a typical microwave oven.

Figure 4.2 shows the major parts of a microwave oven. The oven cavity must of course have a door so that food can be introduced into and removed from the oven. The door is one of the most highly engineered parts of the oven. Generally, in consumer ovens, it has a viewing window which allows visible light to pass through but restricts the passage of microwave energy. When the door is closed, microwave energy must not leak out at unsafe levels. Microwave ovens are limited to 1 MW/cm2 of microwave leakage when new and no more than 5 MW/cm2 over the life of the oven. Leakage is measured at a distance of 5 cm from any surface of the oven including the viewing screen, vents, and around the door seal. To insure that manufacturers build robust products, consumer microwave ovens must meet the above standards after the door has been opened and closed 100 000 times before the oven is approved for production. Commercial ovens must test their doors for 200 000 cycles (Anonymous, 1973). These tests are conducted with the ovens generating full microwave power every time the door closes and in the case of combination ovens, the ovens must also be at operating temperature. The door cycling test not only tests the integrity of the hinges and latches but also the durability of the safety interlock switches. By law, every microwave oven sold in the United States must have two interlock switches and one interlock monitor switch. All three switches must function in order for the oven to operate when the door is closed. They must also interrupt microwave generation upon the slightest opening of the door. Microwave leakage levels cannot exceed the levels stated above even when opening the door slightly. There are basically two ways to seal in microwave energy with a door: a contact seal or a choke seal. The contact seal, as the name implies, depends on metal-to-metal contact between the door face and the oven face. To keep microwave energy inside the oven, the contact area must extend around the

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entire face of the oven. When the oven is clean, leakage levels near zero are possible. However, food spills, grease spatter and such make this type of seal impractical in most microwave ovens. Choke seals utilize a quarter wave slot or choke around the perimeter of the door. The geometric dimension of the choke creates a high impedance path to the microwave energy trying to leak out (Reich, 1953). When microwave energy encounters the choke it is simply reflected back into the cavity (Harvey, 1963). Virtually every oven sold today utilizes a microwave choke. It is usually covered or filled with a dielectric material to prevent contamination by foodstuffs. Choke designs have been improved to the point that microwave leakage is typically below the resolution of common microwave leakage meters. Chokes are also more forgiving than contact type seals, allowing larger amounts of relative movement between the door and oven face without an appreciable increase in microwave leakage. Microwave energy is delivered into the oven cavity via a waveguide. The waveguide is basically a metal tube of rectangular cross-section. The size of the waveguide is dictated by the frequency of the magnetron, which in most cases is 2.45 GHz. Microwave fields of this frequency will easily propagate or travel down a rectangular waveguide that is approximately 75  40 mm2. The waveguide is welded or bolted firmly to the oven cavity to prevent microwave leakage. The waveguide can deliver energy into the cavity through a single large hole, a series of slots, or a combination of the two. Depending on the anticipated use of the oven, the waveguide may deliver energy from the top, sides or bottom of the oven. When developing food products or packaging for use in a particular oven design (for example in a food service application), one must know where the energy enters the cavity. For example, trying to heat a product in a metal pan or cookie sheet would be very inefficient, if not impossible, in an oven with microwave feed only from the bottom (see Fig. 4.3). In some ovens it is difficult to determine where energy is entering the cavity. The oven may have a glass floor or a plastic cover over the mode stirrer, either of which can obscure visibility of the waveguide entrance. When in doubt, contact the manufacturer or, in the case of an older oven, a qualified service agent should be able to help. When developing a consumer food product or package, one has no control over the oven that the consumer uses. The microwave energy can enter the cavity from any direction and your product and package must be able to handle the variety of ovens in consumer kitchens. Fortunately, the majority of household ovens are built with the microwave entering the cavity from the top or side. Generally, bottom-fed microwaves are seen infrequently, usually on commercial or older (> 10 years) ovens. The source of microwave energy for all consumer microwave ovens is the cavity magnetron. It is a vacuum tube device, and although it does not look like it, it is a close relative to the vacuum tube used in early radios and televisions. It

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4.3 Effect of cookware material and waveguide window location on microwave heating.

emits microwaves at 2450 MHz with a wavelength in free space of 12.24 cm. Magnetrons were invented in the early 1920s, but the cavity magnetron, a device capable of producing significant power, was not invented until the late 1930s. They were originally developed as a source of microwaves for use in radar systems. The first magnetrons were large, expensive, inefficient (12±20% efficient), and water cooled (Redhead, 2001). By comparison, a modern magnetron weighs about 900 g, costs about $12.00 (in quantity), is up to 75% efficient and can be water or air cooled. The heart of the magnetron is a resonant cavity where high voltage DC is converted to microwave energy at 2.45 GHz. (The early history of the cavity magnetron can be found in Osepchuk, 1984.) Detailed descriptions of magnetron construction and operation can be found in Harvey (1963), Metaxas and Meredith (1993) and Meredith (1998). The microwave energy radiates omnidirectionally from an antenna on the top of the magnetron. The antenna resides inside the waveguide, which directs the microwave energy to the oven cavity. Only four to five other pieces of hardware are required for the magnetron to function. A high-voltage transformer is necessary to produce high voltage (about 2200 V). A filament transformer (or a filament winding integral to the highvoltage transformer) provides a low voltage (about 3.3 V) and a high current potential to the filament inside the magnetron. The magnetron filament is similar to the filament inside an incandescent light. The hot filament is also the cathode of the magnetron and emits electrons by thermionic emission. The high-voltage

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diode half wave rectifies the high-voltage AC line leading to the magnetron. The high-voltage capacitor, in conjunction with the diode, form a half wave doubler circuit which boosts the voltage at the magnetron to almost 4000 V DC. This can be a potentially lethal voltage (a charge may remain in the capacitor for some time after the mains power has been switched off) and is the reason why service of microwave ovens is left to qualified personnel. The filament in the magnetron takes a finite amount of time to warm up before it emits electrons. This `filament warm-up time' takes from 2±3 seconds in small magnetrons and up to 5 seconds in larger industrial tubes. Most consumer ovens use transformers that have the filament winding and highvoltage winding wrapped around the same core. In these ovens, line voltage is applied to the filament and high-voltage windings simultaneously. This type of power supply will always produce a few seconds delay between the time the start button is pressed and when the magnetron actually starts emitting microwaves. This type of power supply is called a `cold-start' power supply (see Fig. 4.4) because the filament is cold when the magnetron is energized. Designers of ovens with this system must take into account this delay when calculating actual magnetron on/off times as discussed below. A variation of the preceding power supply uses separate filament and highvoltage transformers and is called a `hot-start' power supply. In this system, the filament transformer is energized even when the oven is idling. With the filament remaining hot, application of the high voltage results in almost instantaneous generation of microwaves. This type of power supply is useful for critical commercial/industrial processes or where rapid cycling of microwave power is anticipated. The half wave doubler power supply described above has been standard in microwave ovens for decades. The transformer is large and heavy, weighing from 4.5 to 7 kg in a consumer oven to over 11 kg in a commercial/industrial oven. In this type of oven microwave power is varied by cycling the power to the high-voltage transformer on and off, resulting in a pulsing of power to the food. For 100% power, the magnetron is turned on 100% of the time. For 50% power, full power is turned on for a preset amount of time (usually between 15 to 30 seconds) then turned off for an equal time. Defrost is simply 30% on time and 70% off. The inverter power supply is a relative newcomer, initially sold in the United States by Sharp in the mid-1990s. Panasonic has the broadest line of oven models with inverter supplies, although LG has announced similar ovens. Inverter supplies use switching (or switched-mode) power supply techniques to reduce the size and weight of the magnetron power supply. Inverter power supplies operate by first converting the 50/60 Hz alternating current (AC) line frequency to direct current (DC). Next, the DC power is fed through a power oscillator to convert it to back to AC at 20 000 Hz or higher. This high frequency allows the use of transformers that are less than one-tenth the size and weight of a normal

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4.4 Typical hot start and cold start power supply wiring.

microwave oven high-voltage transformer. Manufacturers also claim higher power supply efficiency and larger cavity size (for a given oven footprint) due to the smaller inverter power supply. Output power is controlled using duty cycle control at the higher frequency and this allows the user to turn down the microwave power in a manner similar to a lamp dimmer turning down the intensity of a light bulb. Thus, it is claimed that inverter microwaves provide more even cooking and faster defrosting. When developing products or packaging for use in microwave ovens, an inverter microwave should be in your stable of test ovens.

4.4

Heating uniformity

Most common residential and commercial microwave ovens are considered multi-mode applicators. A multi-mode applicator is a closed metal box with

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some means of coupling power from the magnetron. The dimensions of the box must be several wavelengths long in at least two dimensions. This enclosed box can support many resonant modes over a limited frequency range (e.g., the 50 kHz bandwidth of the typical magnetron). The multi-mode applicator is tolerant of a large range of heating loads, but heating uniformity can be a problem. In general, the larger the box (or cavity), the more uniform the heating. The modes allowed inside a cavity of dimensions a, b, and d can be calculated from 2  2  2  2  l m n !lmn ‡ ‡ ˆ 4:1 c a b d where l, m, and n are integers corresponding to the number of half periods of field along principal coordinate axes. !lmn is the angular resonant frequency of the l, m, and n mode and c is the velocity of light (Harvey, 1963). Equation 4.1 is valid only for an empty cavity. Since we are in the business of cooking food, the cavity is never empty. As a result, Equation 4.1 is useful only from a purely theoretical standpoint. Besides, those developing products or packaging for a microwave oven seldom, if ever, have influence over the dimensions of the cavity.

4.4.1

Mode stirrers

The microwave field inside a resonant cavity, as discussed in Chapter 1 (Section 1.9), is completely stationary. While it is possible to cook in such a cavity, results will be less than optimum and defrosting frozen items will be particularly difficult. Depending on the size of the cavity (and the corresponding number of modes) the presence of hot and cold spots that do not move makes heating uniformity almost impossible to achieve. For this reason oven manufacturers install mode stirrers and/or turntables to generate relative motion between the E-field and the load. Some newer microwave ovens, which allow the consumer to switch off the turntable when cooking large rectangular items, have both. Without a mode stirrer or movement of the food, heating will generally be very uneven. Mode stirrers may take many forms. They are usually hidden from view in the roof or under the floor of the oven, covered by a piece of microwave transparent plastic. They are made from metal, usually aluminum, of sufficient thickness to be nearly perfect reflectors. They can be rotated by a small electric motor or driven by the fan that cools the magnetron and circulates air through the oven cavity. Some examples of mode stirrers are shown in Fig. 4.5.

4.4.2

Influence of metal on heating uniformity

It is a common misconception that one should not put metal of any kind in a microwave oven. However, most people do not question the fact that many

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4.5 Various designs of mode stirrers.

microwave ovens are equipped from the manufacturer with metal racks and combination convection/microwave ovens come with metal turntables. A metal rack is essentially microwave transparent owing to the limited number of wire supports and the relatively wide spacing between wires. So, placing glass, ceramic or plastic cookware on a metal rack allows microwave penetration into the product from all sides. If metal cookware is used, there is no penetration from the bottom or sides, since the metal reflects 100% of the microwave energy. Risman at SIK (Sweden) examined the effect of packaging materials on oven efficiency and heating uniformity (Risman, 1992). The study evaluated round and rectangular food containers fabricated from dual ovenable crystalline polyethylene terephthalate (CPET) and aluminum. Four microwave ovens were used with the following configurations: · · · ·

Oven 1 ± power fed from below, through a microwave transparent shelf. Oven 2 ± large cavity oven fed from the top and with a large mode stirrer. Oven 3 ± side feed oven with rotating metal turntable. Oven 4 ± large cavity commercial oven with feed from top and bottom. Power supply was modified to reduce the output power by one-half.

A sugar and water solution (450 g sugar/1000 g water) was selected as the test medium because of dielectric properties typical of many foods. To measure thawing efficiency, the solution was frozen. Prior to any experiments, baseline power tests were conducted on each oven per IEC 705. The results of all tests are shown in Fig. 4.6. It should not be a surprise that Oven 1 had the largest drop in delivered microwave power. The bottom-fed microwave `illuminated' the

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4.6 Influence of cookware material on delivered power to (a) thawed product and (b) frozen product (Risman, 1992).

bottom of the metal pan and a good portion of the microwave energy was simply reflected back to the magnetron. Oven 3 was the least affected by the aluminum tray. That oven was originally designed with a metal turntable and the presence of an aluminum tray had little effect on oven performance. Ovens 2 and 4 exhibit heating and thawing efficiency somewhere in between. Their relatively large cavities enabled them to deliver reasonable performance to the aluminum trays. A more recent study of metal cooking containers was conducted by the Fraunhofer Institute for Process Engineering and Packaging (Pfeiffer, 2007). The goal of this study was to examine the safety and performance of microwave food heating in rigid steel and aluminum containers.

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Four different microwave ovens were used and, like the SIK study, the ovens had different power levels (700, 800, 900, and 1000 W) and different cavity sizes. But, unlike the SIK study, all the ovens were similar in construction (standard household type with the microwave feed in the right-hand wall of the oven cavity and the product rotated on a glass turntable, similar to the oven in the lower left-hand corner of Fig. 4.3). Five metal containers were tested: · · · ·

Round steel bowl (99 mm dia  35 mm height) with 200 g filling. Round steel bowl (127 mm dia  30 mm height) with 250 g filling. Square steel container (125 mm  125 mm  25 mm) with 300 g filling. Rectangular aluminum container (160 mm  99 mm  35 mm) with 400 g filling. · Round steel container (153 mm dia  36 mm height) with 425 g filling. Plastic containers of similar size and shape were also used in the experiments for comparison. The plastic containers were all made from CPET and they were filled with the same quantity of filling as their metal counterparts. Four different fillings, in a liquid or semi-liquid state, were poured into each container, filling the containers from wall to wall. The fillings used were tap water, chili con carne, egg batter, and an infant meal (pasta, small meat balls, and vegetables in a sauce). The following experiments were performed: · Measurement of heating efficiency using containers filled with tap water. · Visualization of heating patterns using partially solidified egg batter. · Measurement of heating performance and temperature distribution in containers filled with chili con carne and the infant meal. The results of the Fraunhofer experiments were:

· Heating efficiency: as might be expected, heating efficiency in a metal container is lower than the heating efficiency in a similar sized plastic container. Quite obviously, this is due to the fact that microwave energy can enter the product only from the top surface, whereas microwave energy can enter a plastic tray from all sides. Depending on the size and shape of the metal tray, heating times were two to three times longer than the equivalent plastic tray. Larger metal containers exhibited shorter heating times and better heating efficiency when compared with smaller metal containers, likely due to the larger surface area exposed to microwave. · Heating patterns: hot spots and cold spots were observed in all experiments with egg batter, chili con carne, and the infant meal. However, product heated in the metal containers exhibited less temperature variation and better heating uniformity than product heated in plastic containers. For example, chili con carne heated in metal containers exhibited a variation of 20±40 ëC between

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hot and cold spots. The same product heated in a plastic container exhibited a 40±60 ëC difference. The longer heating times in metal containers yielded more even temperatures within the product at least partially due to internal thermal conductivity. It was also noted that product heated in a metal container exhibited the highest temperatures near the center and the lowest temperatures near the walls and bottom edge, while product heated in a plastic container exhibited the highest temperatures near the walls and bottom edge, but the center remained cooler (see also Chapters 2 and 3). Throughout these experiments certain guidelines were observed for the safe use of metal containers in a microwave oven: · Remove any metal lids from the container prior to placing in the microwave oven. · Use only full containers. · Heat only one metal container at a time. · Place the metal container in the center of the turntable/oven. Maintain an air gap of at least 2.5 cm between the metal container and the oven walls. Approximately 1000 tests were performed using the guidelines above. During these experiments not a single spark or potentially dangerous situation was observed (Pfeiffer, 2007). Arcing A high-energy electrical field exists inside microwave ovens when cooking. Any place where a metal±air±metal gap less than approximately 1±2 mm exists, there will be a large electrical potential between the two pieces of metal. Pfeiffer (2007) intentionally offset metal containers on the turntable to induce arcing between the container and oven walls. A 2 mm gap or greater was found to be sufficient to eliminate arcing in their ovens. Just like the spark plug in a car, when the voltage potential is high enough and the gap between the metal is just right, an arc (or sparking) will occur due to a dielectric breakdown or ionization of the air. Unlike a spark plug, which only arcs for a few milliseconds, the arcing in a microwave oven can be continuous because of the continuous flow of energy from the magnetron. You can repeat the above experiment with a similar sized piece of flat foil placed in the center the microwave. With the microwave running, nothing happens. However, if the flat piece of foil is placed off-center on the turntable, the foil can arc to the walls of the oven. The effect of gaps between metal edges can be observed when a loosely crumpled ball of foil is heated in a microwave oven. Arcs will occur violently between gaps in the foil. The arcs will start and stop or erupt at different locations on the foil ball as it rotates on the turntable or as the mode stirrer turns.

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It is usually a good idea to include a small cup of water in the oven cavity to provide a load for the magnetron. While technically not arcing, another source of extreme heat inside the oven is at the sharp point of a piece of metal. A thin sliver of foil or a needle placed in an oven will produce a concentration of energy at the sharp point, such that the point can become white hot. Dinnerware or fine china with gold or other metallic decorations must never be placed in a microwave oven. These decorations typically contain a volume fraction of metal sufficient to be electrically conductive, suspended in an organic paint system. When exposed to high levels of microwave power, high current densities flow in the metallic decoration, resulting in strong heating, burning and, depending on the size and shape of the design, an almost instantaneous vaporization of the metallic decoration. Product packaging should be designed to minimize the risk of arcing. If arcing occurs near paper or plastic packaging, there is a real risk of fire. There have been cases where a `twist tie' from a loaf of bread started arcing, made the plastic bag catch fire, and subsequently melted the plastic liner of the microwave oven. The twist tie (particularly when near Ü to Ý wavelength long) can act as a microwave antenna. These are real dangers and, as a result, oven manufacturers take the conservative (and safe) approach and continue to warn consumers never to place metal in a microwave. This stance is unlikely to change, because the risk of fire or oven damage due to the actions of an uninformed consumer is simply too great for the manufacturers to bear. But ± as a designer ± you must also keep in mind that there are consumers that will not knowingly put metal in their microwave oven, no matter how well designed the package may be or what the package instructions may say. As a result, the product will never perform to their expectations. From a cooking standpoint, arcing reduces efficiency because the arc consumes microwave power that is intended for the food product. Microwave arcing produces broadband radio frequency (RF) noise. The door choke is designed to stop microwaves at 2450 MHz but not the lower frequency RF emissions. As a result, you may notice static on nearby TVs and radios. Also, in a lab environment, you may notice temporary instability or interference in some nearby test equipment, particularly digital volt meters and thermocouple meters. This instability, of course, will stop when the arcing stops.

4.4.3

Other influences on non-uniform heating

As we have stated before, microwave heating in a multi-mode cavity is not uniform (see Chapters 2 and 3). Properly designed packaging and/or package directions can increase the effective heating uniformity. Mode stirrers and turntables also increase uniformity. However, there are other factors that conspire against ideal heating results.

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It is important that the operator of the oven knows where the microwave feeds into the oven for optimum heating (refer to Fig. 4.3). For instance, if the microwave feed is from the top of the oven, then a food product in a metal or foil tray will get fairly uniform microwave illumination across the top surface of the product. However, that same package, heated in an oven with side or bottom feed, will get very little heating. When heated in a typical multi-mode microwave oven, a product in a microwave transparent package (paper, ceramic, glass, etc.) will get the most microwave illumination if the package is at least a quarter wavelength (3.0 cm) from the metal floor or walls. A package resting directly on a metal turntable or the metal floor of the oven will receive illumination only from the top and sides. Most residential and commercial microwave ovens have a glass shelf or turntable that is already  14  above the metal floor (cavity wall) of the oven. As mentioned before, metal racks present in some microwave ovens are virtually transparent to microwaves and also allow illumination from all sides. Non-uniform heating within the cavity is one of the greatest challenges that the product and packaging developer will have to deal with. Also, every microwave oven model from every manufacturer will have a different field distribution inside the cavity. Table 4.1 illustrates the variations of absorbed power at various locations within a single oven cavity. For this test a 5-year-old oven with a cavity size of 0.034 m3 and a rated output of 1000 W was used. The 500 g water load was carefully measured into a polycarbonate beaker measuring approximately 85 mm diameter by 135 mm tall. Water was heated in the beaker for 60 seconds at various locations in the oven cavity and with different amounts of aluminum foil shielding. Microwave power was calculated using the formula: Microwave power (W) ˆ …Cp  W 
T†=t

4:2

where Cp is the heat capacity of water (4.189 J/kg ëC, between 25 and 85 ëC), W Table 4.1 Effect of aluminum shielding on delivered microwave power Location of beaker

MW power % of Unshielded Unshielded (W) baseline area (cm2) (%)

Center of turntable: baseline At perimeter of turntable Center of turntable, elevated 30 mm At perimeter of turntable, elevated 30 mm Center of turntable, 37% shielded with foil Center of turntable, 70% shielded with foil At perimeter of turntable, 70% shielded with foil

727 660 631

100.0 90.8 86.8

644.4 644.4 644.4

100 100 100

642

88.3

644.4

100

636

87.5

406.9

63.1

555

76.3

195.8

30.4

527

72.4

195.8

30.4

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is the weight of water (g),
T is the temperature rise of the water (ëC) and t is the length of time the microwave is energized (seconds). Referring to Table 4.1, it is interesting to note that ± for this oven and load ± the point of maximum heating is with the load positioned in the center of the oven, directly on the turntable. Placing the beaker near the periphery of the turntable or elevated above the turntable reduced the power delivered to the load by about 10%. It is also interesting to note that shielding almost 70% of the container with aluminum foil resulted in a reduction of absorbed power of only 24%. Another source of heating variability is fluctuation in the incoming line voltage. With the exception of the inverter type power supplies, microwave ovens typically use ferro-resonant transformers. This transformer is designed to provide a stable output voltage regardless of variations in the input (i.e., line regulation). However, there are limits to its ability to regulate as can be seen in Fig. 4.7. The residential ovens in Fig. 4.7(a) all exhibit different power output versus line voltage curves. Looking at the curve of Oven 2, a variation of only 6% in line voltage resulted in a 18% variation in microwave power (Buffler, 1993)! A prototype commercial oven (Fig. 4.7b) exhibited severe degradation in performance below 200 V with the output power dropping precipitously below 150 V. This oven's performance may not be typical, but one should be aware that this level of performance can exist. Brown-outs and overloading of kitchen circuits can cause such conditions. Such conditions are infrequent and are usually confined to industrial environments, trade shows or during restaurant start-up. A common mistake is thinking that 240 V AC power is available when, in actuality, you only have 208 V power. Most commercial and industrial microwave ovens have an additional winding or `tap' which allows use of the oven on either 208 or 240 V. This `tap' is on the high-voltage transformer and should be changed only by qualified service personnel. Most consumer microwave ovens run on 110±120 V AC power and usually do not have an additional `tap'. A low input power condition in a home would most likely be related to a grid-based brown-out condition and the consumer would most likely observe slightly dimmer light bulbs during such occurrences.

4.4.4

Aging of microwave ovens

As microwave ovens get older, the permanent magnets in the magnetrons get weaker. All magnets get weaker with time and exposure to heat, causing the output power of the magnetron to decrease and the turn-on time to increase (the turn-on time is the time between the application of voltage to the transformer and the actual output of microwave energy by the magnetron). This time can easily double over a 10 year period. The change in turn-on time, of course, is not a factor in a hot-start circuit.

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4.7 Effect of line voltage variation on delivery microwave power: (a) consumer ovens (Buffler, 1993); (b) commercial oven (with kind permission of Springer Science and Business Media).

However, weak magnetron magnets will cause a reduction in microwave output, regardless of the power supply used. A measurable loss in power is usually not noticeable for the first few years. After 5 years, studies have measured a 5% power loss, typically increasing to a 30% loss after 10 years. Ovens approaching the end of their useful life (13±15 years) have about half their original power (Decareau, 1985).

4.5

Combination ovens

The term combination oven has traditionally been used to describe an oven that combines two or more food heating technologies such as microwave, conventional heat, steam, infrared, convection, radio frequency, or induction

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4.8 Microwave oven with grilling (infrared) element.

heating. Our discussion here will be limited to ovens that combine microwave with other heating technologies inside the same cavity. The simplest form of a combination oven is a microwave oven with an infrared heating element (often referred to as a radiant element or grill) mounted near the ceiling (Fig. 4.8). An oven with a infrared element was built by Raytheon as early as 1947. Early experimenters quickly realized that microwave-heated foods did not have the color, flavor, or texture of conventionally cooked foods (US Patent 2716694, August 30, 1955). An infrared element is an easy and fairly inexpensive piece to add to a microwave oven and yields reasonably favorable results. Infrared is a form of electromagnetic energy having wavelengths in the range 750±10 000 nm, i.e., longer than visible light and shorter than microwaves. The infrared spectrum present in any oven is dependent on the temperature of the actual heating element in the oven. This temperature will vary with line voltage and between manufacturers. This source of variability can prove challenging when developing products or package instructions.

4.5.1

Speed ovens

Speed ovens combine the speed of a microwave oven with the flavor, color, and texture development of a traditional thermal oven. Generally, microwaves are combined with hot air convection or impingement. An important distinction between speed ovens and combination ovens is the electrical power requirements. A counter top (and many built-in) combination ovens run on standard 120 V service (in the United States and Canada). Per the National Electric Code, standard wall outlets are limited to 15 A maximum. That is only 1800 W total

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(i.e., power similar to a typical blow dryer) which is not enough power to simultaneously run the magnetron(s) and heating elements. To overcome this limitation, these ovens will alternate between running the magnetron and the heating element. The result is an oven that can produce a higher-quality product but is only marginally faster than a conventional oven. A true speed oven operates on 208±240 V. These circuits can provide up to 50 A (12 000 W). This is more than enough power to operate the magnetrons and heaters simultaneously. Some residential and commercial ovens take advantage of the extra available power by utilizing multiple magnetrons. Demonstration ovens with three and four magnetrons combined with air impingement have been built. These are currently among the fastest cooking ovens on the planet. Just like conventional microwave ovens, speed ovens can apply the same technology differently. The SuperJetÕ Oven from Fujimak (Tokyo, Japan) features hot air impingement from the top and bottom and dual microwave feeds from each side of the cavity. The product rotates on a turntable to provide even exposure to the air jets and also stir the microwave. The TornadoTM Oven, also known as the SubwayÕ Oven, from TurbochefÕ Technologies (Atlanta, GA) has air impingement only from the top and dual microwave feeds from the bottom. The product is placed on a stationary rectangular metal rack. An infrared heating element is located under the metal rack to provide toasting, if desired. The oven does not have a turntable or mode stirrer. As one might expect, heating uniformity is less than ideal, especially on frozen items. The combination of air impingement, short cook time and a sufficient dwell time after cooking will help mitigate hot and cold spots in the product. Speed ovens have also found their way into vending machines. A small speed oven based on air impingement and microwaves (Fig. 4.9) resides inside a vending machine built and marketed under the name Hot ChoiceÕ by KRh Thermal Systems of Irvine, CA. The machines are fully automated and require no labor to cook, only to replenish stock and remove money. The customer may choose from five different menu items and then the technology (US Patent 5147994) cooks the selected food from frozen. Products for the vending machine are stored frozen in pressed paperboard trays with a decorative paperboard outer sleeve. When a customer selects a menu item, the package moves from its location in the freezer and is positioned in front of the oven door. The oven door opens automatically and the paperboard tray is pushed out of the outer sleeve and into the oven for about 60 seconds. The paperboard survives the hot oven environment because it is inside for such a short duration. At the end of the cook cycle, the tray slides out of the oven and back into the outer sleeve. The outer sleeve provides a place for product advertising and nutritional information, as well as providing a cool handling surface for the consumer. The entire package is then delivered out of the front of the vending machine to the waiting customer. The total time from product selection to product delivery is about 90 seconds!

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4.9 Hot ChoiceÕ vending machine oven and product tray.

4.6

Microwave oven safety

Up until the early 1970s there were no Federal microwave emission standards for microwave ovens. In fact, in Percy Spencer's first patent US (Fig. 4.1), the illustration on the cover shows food being heated by microwave on an open conveyor. There are not even any oven walls in the illustration. Manufacturers knew, however, that excessive microwave exposure would raise concern and had been working on improved door seals and conveyor choke systems since the 1950s. As part of the Health Service Act of 1971, HHS standard, CFR21, Part 1030 was passed into law. Part 1030, `Performance Standards for Microwave and Radio Frequency Emitting Products' was applicable to all microwave ovens manufactured after October 6, 1971. Microwave ovens have proven themselves to be very safe appliances in the kitchen. This is due to strict microwave leakage limitations set by HHS 1030.10 and rigorous testing by the manufacturers. Since there are subtle differences between oven models, the best advice is to adhere to all safety warnings and cautions printed in the manufacturer's Owner's Manual. The following precautions are quoted directly from HHS 1030.10 and are applicable to all microwave ovens manufactured for sale only in the United States. Please refer to CSA Standards and appropriate EU Standards for regulatory requirements in Canada and the European Union, respectively. PRECAUTIONS TO AVOID POSSIBLE EXPOSURE TO EXCESSIVE MICROWAVE ENERGY (a) Do not attempt to operate this oven with the door open since open-door operation can result in harmful exposure to microwave energy. It is important not to defeat or tamper with the safety interlocks.

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Packaging and products for use in microwave ovens (b) Do not place any object between the oven front face and the door or allow soil or cleaner residue to accumulate on sealing surfaces. (c) Do not operate the oven if it is damaged. It is particularly important that the oven door closes properly and that there is no damage to the: (1) door (bent), (2) hinges and latches (broken or loosened), (3) door seals and sealing surfaces. (d) The oven should not be adjusted or repaired by anyone except properly qualified service personnel.

In addition to the Federal Standards, third party Safety Testing Labs require manufacturers to meet the strict requirements of UL 923 in order to place a UL sticker on a microwave oven sold in the USA. Some of the tests involved in passing UL 923 include but are not limited to the following: · Microwave Radiation Emission Test ± This test must be conducted prior to any other tests in UL 923. The test dictates that microwave radiation existing in the proximity of the external appliance surface shall not exceed 1 mW/cm2 at any point 5 cm or more away from the external surface of the appliance. · Temperature Test ± This is a series of tests designed to determine the applicability of materials (wire insulation, plastic insulators, etc.) to actual temperatures experienced during oven operation, as well as insuring that external oven surfaces do not exceed safe values. · Door Assembly Test ± This series of tests are designed to simulate the forces expected during intended usage. This includes slamming the door closed, slinging it open, impacting the microwave seal area with a steel ball and overloading the hinges. · Interlock System Endurance Test ± This is the test of the reliability of the Interlock/Monitor circuit. The test requires the opening and closing of the door 100 000 times for residential products and 200 000 times for commercial products. · Abnormal Operation Test ± A series of tests are conducted in abnormal conditions and the oven is checked for emission of flames, risk of electrical shock and excessive emission of microwave energy. Some of the tests include operating the oven in a no-load condition, stalling motors and fans and shorting out the high-voltage diode and capacitor. This is just a sample of the 27 UL tests an oven model has to pass before it can be purchased by consumers. Combination ovens, since they operate at elevated temperature, are subject to an additional battery of tests outlined in UL 858. In addition, every oven sold in the United States and Canada must pass a Dielectric Voltage Withstand Test (Hi-Pot Test) to insure that the product is electrically safe before it is shipped to consumers. The Hi-Pot test subjects the appliance wiring to an elevated voltage (usually no less than 1000 V) for a predetermined amount of time (usually 60 seconds) between the live components (wiring and anything attached to the wiring) and the exposed

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metal surfaces of the appliance. The sensitive electronics in the Hi-Pot meter are able to measure the leakage current between the appliance wiring and chassis ground. Excessive leakage current is indicative of insufficient clearance between live components and the appliance chassis, pinholes/cracks in electrical insulation or manufacturing defects. The result of this arduous testing is an appliance that is quick cooking, relatively efficient, reliable, and, above all, safe to use.

4.7

Sources of further information and advice

· US Food and Drug Administration, Center for Devices and Radiological Health, Microwave Oven Radiation, http://www.fda.gov/cdrh/consumer/ microwave.html · Microwave Ovens and Food Safety, USDA Food Safety and Inspection Service, http://www.fsis.usda.gov/Fact_Sheets/Microwave_Ovens_and_ Food_Safety/index.asp · Hot food vending machine manufacturer, KRh Thermal Systems, www.hotchoice.com · American speed oven manufacturer, www.turbochef.com · Japanese speed oven manufacturer, www.fujimak.biz · History of the Sharp microwave oven, http://www.sharp-world.com/ corporate/info/his/chronology/p4.html · History of Raytheon Co, http://www.raytheon.com/about/history/leadership/ index.html

4.8

Bibliography

Andrews G (1989), `Commercial catering in combination ovens', Microwave World, Vol. 10, No. 3, 11±15. Anonymous (1973), Code of Federal Regulations, Title 21, Vol. 8, Subchapter J ± Radiological Health, Part 1000±1005, 1010 and 1030.10. Anonymous (2007), `30th Annual portrait of the U.S. appliance industry', Appliance Magazine, Vol. 64, No. 9. Buffler C R (1993), Microwave Cooking and Processing: Engineering Fundamentals for the Food Scientist, New York, Chapman & Hall. Chan T V C T and Reader H C (2000), Understanding Microwave Heating Cavities, Boston, MA, Artech House Publishers. Collin R E (2001), Foundations for Microwave Engineering, Hoboken, NJ, IEEE Press Series on Electromagnetic Wave Theory. Decareau R V (1985), Microwaves in the Food Processing Industry, Orlando, FL, Academic Press, Inc. Decareau R V (1992), Microwave Foods: New Product Developments, Trumbull, CT, Food & Nutrition Press. Hammack W (2005), `The greatest discovery since fire', Invention & Technology Magazine, Vol. 20, Issue 4. Harvey A F (1963), Microwave Engineering, London, Academic Press.

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Meredith R (1998), Engineers Handbook of Industrial Microwave Heating, London, Institution of Electrical Engineers. Metaxas R and Meredith R (1993), Industrial Microwave Heating, London, Peter Peregrinus Ltd. Osepchuk J M (1984), `A history of microwave heating applications', IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-32, No. 9, Sept. Osepchuk J M (2008), Personal correspondence. Pfeiffer T (2007), Microwaveability of Steel and Aluminum Food Packaging, Fraunhofer Institute for Process Engineering and Packaging, Freising, Germany, Sept 27. Redhead P A (2001), `The invention of the cavity magnetron and its introduction into Canada and the U.S.A.', Physics in Canada, Vol. 57, No. 6, Nov/Dec. Reich H J (1953), Microwave Theory and Techniques, Cambridge, MA, Boston Technical Publishers, Inc. Risman P O (1992), `Metal in the microwave oven', Microwave World, IMPI, Vol. 13, No. 1, Summer.

5

Measurements of dielectric properties of foods and associated materials P R I S M A N , Microtrans AB, Sweden

Abstract: A series of methods is described, from commercially available which are easy to handle and have accuracy but may have representativity problems, to special purpose that have high accuracy and are suitable for inhomogeneous materials under test (MUTs). It is concluded that no single method fulfils all practical criteria, but that there is at least one available method fulfilling each particular criterion. So the choice is also a compromise. Key words: dielectric, measurement, food, cavity, applicator, retromodelling.

5.1

Introduction

To measure is to gather information, but in order to know how a measurement project is most efficiently laid out, one must know how the resulting data are to be used. Examples of use are: · quantifying permittivity changes by differences in composition, for example added sugar and salt; · providing data for calculation of the power penetration depth dp and other microwave effects on food geometries ± see Chapter 3; · assessing the suitability of packaging, container and susceptor materials for their purposes; · development and optimisations of microwave ovens and industrial microwave systems; · numerical modelling of heating evenness, performance, robustness, efficiency, etc. Other factors of vital importance for a measurement project layout are related to practical problems and cost issues: · the preparation of the material under test ± MUT ± which may be difficult to shape or be available only as film, or be partially non-homogeneous; · the range of microwave data, for example very high or quite low lossiness; · the level of accuracy that is needed. This chapter is ß Per Olov Risman and printed with his permission.

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p It is to be noted that "0 occurs only as "0 in equations for internal wavelength and penetration depths. This means that the allowed inaccuracy in "0 may in most cases be allowed to be twice as large as that in "00 . This chapter does not deal with the mode and propagation equations or the analytical equation sets or matrices needed for extraction of the permittivity data. No recommendations on the choice based on commercial availability versus internal manufacturing of the measurement devices are given. The focus is instead on what methods exist, their accuracies, practical advantages and disadvantages in use. For algorithms, the reader is referred to the references and to the websites of the vendors of commercially available measurement devices and software packages.

5.2

Historical developments and chapter outline

The first methods had to depend on absolute and analytical methods, i.e. those where only geometric data and the frequency must be known, and solving of exact analytical equations provides the end result. Developments were along two lines: the filled waveguide method and the cavity perturbation method, both described in Section 5.3. Basically, these suffer from sample preparation problems, and the filled waveguide method is also quite cumbersome in use with solid or frozen MUTs. Based on the availability of data produced by the absolute methods, it became possible to employ calibration methods. The first significant use of such a method for food measurements was around 1970, at SIK in Sweden. Its first advantage is in sample preparation: lossy samples can be 5 mm in diameter instead of 2 mm, which is necessary for cavity perturbation systems. Its second advantage is that the sample ends do not need to touch the measurement cavity or protrude out of it; this causes errors with most perturbation methods. Additionally, the property of fieldless ends of the MUT may be used. This calibration method is dealt with in Section 5.4. The resolution of the measurements is better with resonant cavity methods than with non-resonant methods. As microwave measurement instruments and components improved over the years, an infinite MUT method using a contacting open-ended coaxial line was developed and later made commercially available by Hewlett-Packard (now Agilent), among others. The company presently dominates the market for commercially available microwave dielectric measurement systems, with their open coaxial probe and associated software. The method is analytical, resulting in very quick calculations for obtaining final results. Also, another infinite sample method, but for very large MUTs and based on trapped surface waves, is analytical. The two principles are described in Section 5.5. Since about 1997, numerical software has made it possible in principle to allow arbitrary shapes of the MUT, by retromodelling techniques. The great gain

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in sample preparation may, however, be offset by the need for access to modelling software, computations being either manual trial and error or automated but time-consuming. However, it may also be possible to use modelling to provide the relationships between resonant frequency and transmission loss versus complex permittivity for given MUT shapes, and then use the results to create software that quickly provides the permittivity by interpolation among the modelling results. Some methods are described in Section 5.6. Measurements on flat as well as low-loss MUTs such as packaging materials, and also susceptors, require special considerations and are dealt with in Section 5.7. It should finally be mentioned that there is a quite significant special literature on electromagnetic measurements on materials in general. An important work is the book by Nyfors and Vainikainen (1989). There has also been a series of international conferences on electromagnetic wave interaction with water and moist substances (ISEMA), which had its most recent (7th) conference in Finland in May 2009; information can be found on the internet (ISEMA, 2005).

5.3

Absolute and analytical methods

5.3.1

The filled waveguide or coaxial line non-resonant method

This method was the first to be used (Roberts and von Hippel, 1941). The measurement system consists of: · a microwave generator, which has to be impedance matched as a load, so that no standing waves other than those caused by the reflection from the sample occur in the `feeding part' of the system; · an impedance matched transition to the MUT holder section which is in this case just a rectangular waveguide or a coaxial line; · a means for holding the MUT in place, including tight microwave-transparent seals for liquids; · behind the MUT, either a shorting wall (reflection method) or a second matched transition and detector for measuring the transmitted signal (transmission method). Figure 5.1 is a schematic drawing of a waveguide with the filling MUT at the end, as a resonant system (see Section 5.3.2). In the non-resonant mode, there is instead an impedance matched transition to a coaxial line which is then connected to a network analyser. Both the amplitude and phase of the reflected signal are needed for determination of the complex ". For very lossy MUTs, the reflected signal may be used for determination of "0 and the transmitted signal for "00 , providing what is the probably the best accuracy of any method for such MUTs.

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5.1 Schematic drawing of a waveguide with the filling MUT at the end, as a resonant system; after von Hippel, 1954.

A coaxial system can be used over a fairly large frequency range, but a short MUT is then typically necessary. Reasons are that there may be resulting ambiguities or reduced resolution if the MUT is about half a wavelength long of its internal wavelength, and/or that the damping may be excessive in lossy MUTs and then severely reduce the resolution in "0 . Waveguide systems can be used only over a limited frequency range, but may offer very high resolution with liquids if a number of precautions are applied (Kaatze, 1989). The most problematic issue for these methods is the need for the sample to touch the cell walls. This is particularly problematic for high-permittivity MUTs. Other problems are the need for precision machining of solid samples, or cleaning and means for reduction of evaporation of liquids. It is also imperative that the end surfaces of the MUT are parallel and flat. Reasons for using the method are that it is absolute and can provide accurate results for a large range of both "0 and "00 . The calculations for obtaining the permittivity of the MUT are fairly straightforward. Handling and preparation of the MUT are major obstacles for general use, so the methods are mainly used in materials research laboratories.

5.3.2

End-filled waveguide and coaxial line resonant methods

By closing the input end of a waveguide with the MUT filling the cross-section in the other end, the system can be made resonant; see Fig. 5.1. If the MUT is much longer than its penetration depth dp in the longitudinal direction, the "00 evaluation becomes inaccurate, but if the whole sample `participates' in the measurement, the resonant frequency will depend on its "0 , and the quality factor (Q value) on its "00 . The advantage with this method over that in Section 5.3.1 is that the requirements on generator and detection accuracy become less stringent, as does the calibration of the system, in particular for measurements on low-loss MUTs. However, the sample preparation issues remain. A version of the method is the so-called re-entrant cavity. The geometry is shown in Fig. 5.2 and is basically that of a coaxial line cavity with a part of the centre conductor replaced by the MUT. The advantage is that the resonant frequency can be tuned over a range of perhaps 3:1 and then also include frequencies lower than those corresponding to the geometric size of the cavity.

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5.2 A resonant re-entrant measurement applicator; after von Hippel (1954).

The resonant frequency varies with the MUT height and permittivity. However, there are many more failed than successful measurement projects with this kind of system, owing to problems with galvanic contact imperfections of the moving plunger and dimensional accuracy problems. The method is in many cases less absolute for high-"0 MUTs than anticipated, owing to the existence of disturbing microwave modes.

5.3.3

Resonance perturbation methods

As the name implies, there is no longer a need for the MUT to fill the whole cross-section of the waveguide resonator. It is instead so small and of such a shape that it only perturbs the resonance of the empty cavity. Approximate but accurate analytical functions can then be used for determinations, using only geometries and measurements of frequency and system damping or Q value. By far the earliest and most common such method employs the circular TM010 cavity resonance, illustrated in Fig. 5.3. The first-order (perturbation) factors provide a linear relationship between the relative change in resonant frequency (fLoad/fEmpty) and ("0 ÿ 1) of the centred MUT, and with a linear dependence of its diameter as well. But these simple relationships apply only if the circular cross-section MUT is in direct contact with the cavity ceiling and floor. In typical use, there is instead at least one MUT insertion hole. The corrections which can be calculated with analytical function approaches, however, do only cover the case when the MUT fills the hole. There are exact analytical solutions for the larger-than-perturbation case, using Bessel function equation iterative solutions. These, combined with solutions taking the changes of the cavity wall current distribution into consideration, provide highly accurate solutions that can be calculated without any numerical modelling (Hedvall and HaÈgglund, 1963) except that the cavity feed loops and their resistive losses are not considered.

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5.3 The electric and magnetic fields of the TM010 resonance (a), and a cavity with MUT (b); after von Hippel, 1954.

The only important practical limitations of the TM010 resonator analytical method are that measurements are made at only one resonant frequency, and that samples have to be quite thin for high-"0 MUTs. A maximum of 2 mm in diameter is necessary for lossy materials at 2450 MHz, since the Q value will otherwise be too low, or the attenuation in transmission mode will be too high, reducing the resolution and allowing otherwise weak non-modal field components to `contaminate' the main mode. Perturbation systems are not limited to circular cavity modes with circular cross-section MUTs. However, no examples are given here, since perturbation techniques have now been largely replaced by other methods allowing larger samples.

5.4

A calibration method

There are of course cases where the theoretical perturbation solutions to the approximate analytical functions become too uncertain. This is then mainly dictated by practical contraints of MUT shape or preparation technique. Older methods had then to rely on permittivity data of, for example, a number of calibration liquids, for creating nomograms or semi-empirical equations for obtaining the permittivity of the MUT. An example of this kind is given in the next section. But there is also another kind of method, which needs just one calibration liquid. This is then for eliminating dimensional uncertainties of the MUT `holder', typically when relatively thin capillary tubes are used with perturbation methods. An example of that kind is given in Section 5.6.2, in that case with water as reference substance in a retro-modelling technique.

Measurements of dielectric properties and associated materials

5.4.1

135

The circular TM012 cavity

Such a system was developed at SIK in Sweden more than 35 years ago (Risman and Bengtsson, 1971), with the objectives of allowing larger sample diameters than with the TM010 method, avoiding inaccuracy problems related to the MUT insertion hole in that cavity, and handling of the problems with food MUT expansion upon freezing. Later on, it was found that the cavity mode insensitivity to objects in the null field region allowed the use of metal capping of the MUT tubes, which in turn resulted in the possibility of measuring pressurised MUTs at sterilisation temperatures up to 140 ëC (Ohlsson and Bengtsson, 1975). The cavity is outlined in Fig. 5.4 and the intensity of its axially directed electric field pattern in the axis plane is shown in Fig. 5.5. Owing to the field pattern, the cavity is made as three separable parts in the axial direction, with thin low loss dielectric sheets between them. The gaps act as mode filters and as MUT tube holders. The upper cavity part has a simple bayonet fitting and is removed for MUT tube insertion. There are also axial slots in the cavity walls, acting as suppressers of unwanted transverse electric (TE) modes (transverse magnetic, TM, modes have only axial wall currents) and by that extending the dynamic range of the system. Systems are in use today in some laboratories, also using numerical retromodelling for measurements in food drying projects. This allows an extension of the dynamic range of the system with low loss materials. MUTs then hang down from the top mica disc, being directly fixed by a short horizontal metal wire on top of it. A further advantage of the system is also employed: since the displacement current follows the MUT and is strongest at the middle of it, it must not be absolutely axial and straight; measurements on MUTs which become slightly bent by the drying is thus possible, without any corrections.

5.4 The circular TM012 measurement cavity (after Risman and Bengtsson, 1971).

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5.5 The envelope of the amplitude of the axial electric field in the resonant TM010 cavity with MUT, obtained by modelling.

5.5

Infinite MUT methods

5.5.1

The contacting open-ended coaxial line method

As mentioned in the introduction, this method is analytical, i.e. equations can be set up and quickly provide the complex permittivity of the MUT from the measurements. The measurement system needs to be calibrated to eliminate the losses in cables, etc. The accuracy is improved by also using a reference MUT such as pure water in the original set-up. The sensor head is not complicated to manufacture. Since the method is also non-resonant, a single system can be used over a very large frequency interval. This method is now the most popular for measurements on foods (AET Japan (2008); Agilent, 2006, 2008; Nelson, 2003). However, the principle has a number of limitations. Some of these may not be sufficiently observed by users. The main limitation is that the volume of the MUT being measured is typically very small and also thin, often comparable with the small inhomogeneities of typical food materials and those caused by pressing the sensor head hard against the MUT. Figure 5.6 shows a typical sensor head region with 4 mm diameter aperture. There is a 0.2 mm borosilicate glass coating at the end which prevents the centre conductor from directly contacting the MUT. This increases the effectively sensed MUT volume somewhat. It is to be noted that many commercially available sensors are smaller than that in Fig. 5.6. The figure also shows the effective MUT volume, obtained by numerical modelling (QWED, 1997). If this volume is defined by the power decay distance (dd ± about 37% remaining power density), it becomes about 0.23 mm3.

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5.6 Modelling of a typical but comparatively large coaxial line end MUTcontacting sensor (top) and the power density in a contacting MUT with " ˆ 52 ÿ j20 (bottom). The gridding is 0.1 mm and the centre conductor is seen. The dashed curve is where this is 1/e of the maximal at the contacting surface. This axial power decay distance (37%) is about 0.35 mm.

The amplitude and phase of the sensor reflection factor can be `measured' by modelling. An air bubble with dimensions 0.1 mm cube (i.e. 0.001 mm3, about 0.5% of the effective volume defined as above) at the centre of the sensor surface changes the reflection factor considerably: the change indicates that there will be an error in " of at least 20% due to the small airbubble for " ˆ 52 ÿ j20, and at least 10% for " ˆ 16 ÿ j4. In spite of these potentially severe requirements on MUT homogeneity, systems typically give quite good results with MUTs which can be distorted to a close fit to the sensor head.

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Owing to the small effective volume of the MUT, measurements on low-loss materials become inaccurate, since a certain absolute loss is needed for detection and the system is non-resonant. The loss factor sensitivity deteriorates for high-"0 materials, and the MUT must, as just pointed out, be homogeneous and representative at the sensor contacting region. The instructions by the manufacturer in these respects are important; see for example those from Agilent (2006, 2008).

5.5.2

The trapped surface wave method

This method can be regarded as the opposite of the open-ended coaxial line method, since the effective volume of the MUT is now very large ± perhaps larger than with any other method. The method is non-resonant but a waveguide is used, limiting the usable frequency range to within a factor of about 2. An outline of a system for 2450 MHz is shown in Fig. 5.7, from Risman (1994), where the theory is also described. The MUT is typically a non-homogeneous substance or a mixture that can be poured into the compartment above the plastic plate which is sealed to the vertical metal walls. The height of the MUT (a liquid in Fig. 5.7) must be large in comparison with its microwave penetration depth dp . The procedure begins by obtaining system impedance matching to the microwave generator by the screw below the input antenna. The real part of the wavenumber along the waveguide (defined as the z direction; corresponding to the wavelength) is then measured by a small fixed straight probe through the bottom of the waveguide, protruding about 2 mm. The shorting plunger is moved while the signal is measured, and the plunger positions in relation to that of the probe are recorded. The distance between positions giving maximum and minimum signals gives the quarter wavelength 1 4 g of the system. If the absorption by the MUT is very strong, there will not be much signal variation when the plunger is far away from the probe, since the standing wave will then be strong only near the plunger. One can then use only

5.7 Layout of the measurement applicator for the trapped surface wave method (after Risman, 1994).

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5.8 Measured loop signal with moving plunger, with water as MUT (Risman, 1994).

the maximum signal and the distance between the probe and shorting wall of the plunger for determining 14 g . The imaginary part of the wavenumber (corresponding to the absorption distance da in the z direction) is then measured by a small loop in the shorting plunger, for a series of plunger positions as far away from the input end as possible but not so far away that the damping by the absorption in the MUT is excessive and too near the instrumentation noise limit. The damping rate gives the power absorption distance da directly, by plotting a number of points as shown in Fig. 5.8. The method is suitable for measurements on non-homogeneous materials with quite large particulates (see Chapter 6). An advantage is that the mode field corresponds well with the under-heating modes in microwave ovens and industrial systems (Risman, 1994), so that data become representative for these practical applications; the absorption distance addressed in Chapter 3, Section 3.6 is directly measured. Since this is larger for high-"0 materials, the resolution becomes lower for those than for low-"0 materials. Owing to the requirement of the MUT being very high in relation to its dp , the method requires large MUT volumes for very low-"00 materials, and the resolution then also deteriorates, unless the MUT is very long.

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5.6

Retro-modelling techniques

5.6.1

Introduction

With the revolutionary developments in commercially available numerical modelling software, as well as in speed and storage capacities of personal computers, it became possible towards the end of the 1990s to model dielectric measurement applicators, not only accurately but also freed from the bounds of analytical function solutions. One can now choose what system properties to analyse or emphasise, what data to extract and how to perform the extraction. The only costly systems parts are a network analyser and the modelling software. The range of permittivity data for which a good resolution is desired is now the basis for choice of MUT dimensions and measurement applicator, unless the MUT cannot be shaped, as is the case for some plastic film materials and, of course, susceptors. Non-homogeneities can be allowed if the overall MUT dimensions are much larger than these. But there may be internal resonant and anti-resonant phenomena in MUTs of certain dimensions (see Chapter 3, Section 3.10), which may cause drastic changes, or very small changes, when " varies. However, tests for these possibly non-advantageous phenomena can be made beforehand, by modelling with permittivity data in the expected range. Actually, internal MUT resonant phenomena have historically been and are still used for accurate " determinations of some high "0 and low "00 materials such as ceramics, by measuring the resonant frequency and the Q value of the measurement set-up. With access to numerical modelling, such determinations may be easier to make and also be more accurate, since the influences of cavity or waveguide losses can be more accurately accounted for. The principle of extraction of " data by modelling is to change " in the geometric model of the measurement set-up until there is an agreement with the measured data. These can be the amplitude and phase of the reflection factor over a small frequency interval (see page 147), the behaviour of the amplitude of the reflection factor over a larger frequency interval (see Section 5.6.3) or a resonant frequency and its Q value or transmission at resonance (see pages 141± 2). The changes of " in the model can be made by trial and error (which may be time-consuming unless small variations are sought for), by some automated optimisation (goal function) algorithm (which requires access to special software and programming work) ± or by choices of MUT geometry and measurement applicator so that simple curves and equations can be used (as with calibration methods such as in Section 5.4). Four examples are given in the following: · a highly accurate dual resonant frequency method for determination of " of liquids; · a degenerate resonance method for large MUTs of highly variable ";

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· a commercially available single frequency method using ceramic inserts in the measurement cavity, which allows larger sample diameters than the airfilled TM010 cavity; · a circular TE011 resonant cavity method for determination of " of dielectric films.

5.6.2

A dual resonant frequency method

General The details of the system and accurate relaxation data obtained for liquid water from ÿ20 to ‡100 ëC are described by Risman and WaÈppling-Raaholt (2007). The measurement applicator was originally developed for measurement on plastic materials in the two common mobile phone frequency bands about 900 and 2000 MHz, and is shown in a modified version for thin MUT tubes in Fig. 5.9. It allows the use of two different frequencies with the same MUT. This property

5.9 The dual resonant frequency measurement applicator.

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facilitates practical use and in essence eliminates the only disadvantage with single frequency resonant measurement systems: that dispersive (relaxation) properties and relative influences of ionic conductivity are in principle not obtainable. The cavity is rotationally symmetrical, which facilitates manufacturing. Since axially elongated dielectric MUTs couple best to an axial electric field, the basic cylindrical TM010 mode is suitable for the lowest frequency. However, since the lower usable frequency is around 900 MHz, such a circularly cylindrical applicator will have a diameter of about 200 mm. Therefore, a reentrant-like design was developed, having an inwards-going conical section from the top of the circular wall, with an axially centred hole for sample insertion. Both the inductance and the capacitance of this distributed system then become larger than for the simple TM010 resonator. This allows a resonator diameter of only 80 mm for a resonant frequency about 940 MHz in empty condition. The active load height is then 15 mm and the basic insertion hole diameter is 10.2 mm for low permittivity loads. The next item was to modify the cavity so that a higher frequency mode can also be used. This was accomplished by introducing a metal tube starting from the cavity bottom some radial distance away from the sample, and extending about halfway towards the cavity ceiling; the cavity inner height is about 70 mm. The function of this system cannot be deduced by analytical functions ± so design, analysis and optimisation was made by microwave modelling; the commercial QWED software (1997) was used for this and throughout the work. What happens is that a TM011 mode is excited outside the inner metal tube, and then transforms into the TM010 mode type inside and at the load. The resulting empty cavity resonance frequency becomes about 2300 MHz. Another major advantage with the system is that the resonance frequency changes with sample permittivity become similar in MHz for both resonances: about 40 MHz for a sample of 3.3 mm diameter and "0 ˆ 80. The retro-modelling The FDTD software has a Fourier package allowing the use of a chosen bandwidth input waveform of a chosen duration for extracting the transmission data (only amplitude as a function of frequency is used here). However, circuits with sharp features in the frequency domain, such as the measurement cavity, require considerably longer simulation times than broadband structures devoid of internal resonances. The software company has developed semi-automated algorithms according to Prony's method (QWED, 1997). The first step is of course to put all actual dimensions into the editor for the simulator. This so-called scenario is the complete input data set including material properties, frequency input type and bandwidth, and also contains test data for the metal(s) conductivity. Typical cell sizes are 1 mm3 in the outer regions and about 0.2 mm3 at the sample, the diameter of which is modelled to

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within 0.05 mm. The number of cells in the whole scenario is about 2 million. The first simulator run is with an empty cavity in a narrow band around the resonant frequency; one run for each resonance. The coupling loops are rectangular with about 3  4 mm2 loop size of diameter 0.4 mm wire; the software actually provides the quasi-static field solution in the `loop cells'. Consecutive fine adjustments of the conductivity and loop size are then made, until the coupling factor and Q values coincide with those measured. This procedure entails the only major difficulty: that of obtaining correctly balanced surface conductivities of the various parts of the cavity (walls and the coupling loops, in this case). Adapting a single conductivity for agreement in transmission loss between the model and the real empty cavity is easy, but the surface current distribution changes with the complex permittivity of the MUT, modifying the overall surface current losses and through that changing the equivalent no-load transmission loss that is used here for determination of the sample loss factor. The quotient between these measured empty and modelled empty cavity transmission losses becomes less than 1 dB. It can be shown that this value becomes quite constant when the overall transmission quotient with a lossy sample exceeds about 6 dB. The next steps are measurements and modelling with an empty glass vial. Its outer dimensions are known, but the inner dimensions need to be finally known with high accuracy, and are still only approximately known. Using these data and test values of the complex permittivity of the glass, new simulations are made until there is again agreement with the measured values. The resonant frequency of the applicator is temperature dependent, which is of course taken into account by all resulting measurement data being differences between empty and filled vials. There is typically no need to consider the empty cavity data variation with temperature in the modelling; a constant empty frequency is used there. The following step is calibration (determination) of the inner diameter of the vial, using pure water at a carefully controlled temperature at about ‡20 ëC. The best available literature data at the actually measured resonance frequencies with the water load are then used for changing the vial inner dimension in the scenario, until a good agreement is obtained. It should be noted that this calibration is not necessary in principle, but it is preferred since it gives very accurate inner dimensions of the vial, and the accuracy of the following `difference measurements' increases considerably. Finite differences time domain (FDTD) modelling must be done with frequency-independent dielectric data of the sample, since the method mimics nature by allowing the use of any type of excitation signal such as delta pulse, step, gaussian pulse ± and sinusoidal continuous. An equivalent conductivity  rather than the loss factor "00 must thus be used in the computations, since "00 is frequency dependent; see equation [6.6] in Chapter 6. The real permittivity "0 is also frequency dependent by the relaxation properties of water (see Section 6.5 in Chapter 6), but since the actual and modelled resonant frequencies of the

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measurement applicator deviate by less than 4 MHz and water at 20 ëC is used for calibration, "0 can be linearly corrected in the computations. In the final steps, the sensitivity factors of resonant frequency variation
f =
"0 and resonant transmission attenuation
T=
 are modelled, around the specific values obtained by the measurements. All retromodelling for obtaining the unknown permittivities of the following water samples with changed temperatures, or MUTs, is done analogously, with empty cavity measurements at each temperature as reference. It is of course too tedious to try to find the exact data match between measured and modelled data. However, the
f =
"0 function is linear over small intervals (but becomes "00 -dependent for large tan (ˆ "00 ="0 ) of the MUT), and the
T=
 function can be simplified as was done by Risman and Bengtsson (1971), but now using more precise approximations where the 20 dB for an "00 quotient of 2 is replaced by a modelled factor (typically between 9 and 19 dB). Sources of error; accuracy In high-accuracy work, one has to consider and control many sources of error. However, the difference principle and the use of accurate and proven retromodelling eliminate most of the first-order errors. What remain are three kinds of error sources: in temperature, influences by the axial insertion holes ± and the inaccuracies of literature data between about ‡20 and ‡30 ëC. These are discussed in Risman and WaÈppling-Raaholt (2007). The uncertainty of most "0 values of water are within 0:5 units, and of the "00 within 2%. This is an accuracy improvement with a factor about 2 over the previously available best literature data, and corresponds to temperature errors of about 0.5 K.

5.6.3

A degenerate resonance method for large MUTs

The cavity is circularly cylindrical with diameter and height about 150 mm; see Fig. 5.10 (Risman, 1999; WaÈppling-Raaholt and Risman, 2003). There is a fixed `chimney' with 41 mm inner diameter at the top, for sample insertion and removal; it also acts as a wavetrap so that it does not need to be closed in use. The feed is by a type N coaxial connector fixed by screws to a metal standoff of about 11 mm length. The 50 line connects to an inner vertical off-centre antenna which is 5 mm in diameter and protrudes 12 mm into the cavity. This choice of antenna system facilitates modelling, by avoiding very small cells and allowing a symmetry plane so that only half the applicator with sample, etc. needs to be modelled. In addition, the measurement applicator can be used at high temperatures, if needed, by air-cooling of the coaxial connector and cable, or by using a rigid coaxial line. Since the MUTs can be quite large, the applicator with MUT can also be thermally insulated, for determinations of the complex " as function of enthalpy during very slow heating or cooling.

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5.10 The measurement cavity for large MUTs, with MUT flask, pliers and network analyser.

Only the amplitude of the reflected signal is measured. The result for three resonant frequencies is used to fine-tune the empty cavity dimensions by adapting the modelling scenario so that the resonant frequencies become the same as those measured. Since these three major resonances are TM012 (at about 2470 MHz), TM110 (at about 2410 MHz) and TM111 (at about 2590 MHz), all important dimensions including any ellipticity of the applicator can be brought into the scenario. In this step, another important parameter is also set by retromodelling: the conductivities of the cavity and antenna. In a following step, a sample container support of polytetrafluoroethene (PTFE) is introduced, since experiments have indicated that locating the sample about 20 mm up is favourable for the discrimination and resolution of the method; see the part on which the flask is standing, in Fig. 5.11. Since the exact dimensions of the support are known, only its dielectric properties need to be found for equal measurement and modelling results. Thereafter, the same procedure is carried out with an empty sample container or flask; see Fig. 5.11. Finally, the container is filled to a predetermined height with a well-known substance such as water at a controlled temperature (also shown in Fig. 5.11); retro-modelling of this provides an extra check of the inner dimensions. When there is a lossy sample, the three TM fields become degenerate and the behaviour of the reflection factor as a function of frequency becomes highly variable, depending on the dielectric properties and geometry of the sample. In effect, a kind of `reflection factor bridge circuit' is created and may provide an excellent resolution; see Fig. 5.12. As an example, it becomes possible to detect a temperature change of 1 K or less in water. Obtaining permittivity data from result curves such as that in Fig. 5.12 is made by using the frequency and reflection factor maxima and minima.

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5.11 A scenario image of the PTFE support and the capped glass container with MUT to half height. Because of the symmetry of the system, only half the applicator needs to be included in the model. The container outer diameter is about 30 mm.

Typically, the curve is more smooth for high-loss MUTs and a few test runs with the modelling software provide "0 data within about 10%, after which "00 values are tested. Simple interpolations using a number of pre-run modelling result curves for complex " data within the expected interval of the MUTs normally quite quickly gives final results with acceptable accuracy. It is in principle also possible to use computerised optimisation algorithms, with data for some frequency points in the experimental curve as goal function and with the complex " as the only variable.

5.6.4

A circular TE011 resonant method for determination of " of films

Introduction and a comparative example Three factors are important when choosing the measurement system for MUTs with both low "0 and "00 :

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5.12 Typical reflection factor for a high-loss MUT in the container of Fig. 5.11. Minima represent resonant frequencies.

1. 2.

3.

Resonant systems provide a better resolution than non-resonant systems, since the waves are then transmitted back and forth many times through the MUT. The filling factor should be as high as reasonable, i.e. the volume of the MUT in relation to that of the resonant volume where it is placed should not be very small. However, this is not applicable to susceptors, for obvious reasons. Systems which are open or openable without need for galvanic contact are preferred, since the system Q values tend to be high and are therefore sensitive to variable quality of the contact.

A way of combining items 2 and 3 is by using a resonator which has an external evanescent field at the surface contacting the MUT; see Fig. 5.13. The resonator consists of a circular waveguide containing a copper beryllium helix soldered to the prolonged centre conductor of a 6 mm semi-rigid cable. A helix is used as the main resonance frequency determining element and allows the small overall size: the sensor has a diameter of 10 mm and a length of 20 mm. The MUT is brought into contact with the open-ended circular high-"0 ceramic waveguide, having an evanescent mode which prevents microwave radiation without MUT. When the MUT is brought into contact, the resonant frequency and the Q value change, owing to evanescent leakage.

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5.13 Small resonant contacting sensor (Sokoll et al., 2005).

The system works similarly to the coaxial end probe principle described in Section 5.5.1, but it is much more sensitive owing to the resonance. However, it suffers from a need to have good and flat MUT contact, and a very homogeneous MUT. Using several layers of a MUT film causes errors if these are not very tightly packed and homogeneous. General properties of TE011 resonators Circular TE01p waveguide resonators are quite special, by the lack of electric fields everywhere at the curved and end surfaces. It is directed only in the circumferential direction and can be said to be toroidal, being zero also at the axis. The `enclosing' magnetic field is also toroidal and perpendicular to the electric field. It is thus maximal and axial at the circular wall, and also maximal and axial at the axis. There are no other modes which can provide higher Q values than TE01p waveguide resonators. An additional and very important advantage for measurement purposes is that the currents at the circular wall are only circumferential. The mode will thus not be disturbed by circumferential slots. There is, however, a disadvantage with the TE01 mode: it is degenerate with the TM11 mode. This means that special precautions must be taken to avoid disturbances. One such precaution is to use circumferential slots, which will partially cut off the axially directed wall currents of the TM11 mode. Another possible way is to introduce a dielectric body in the cavity; see Section 5.6.5. For sensitive cases such as with measurement cavities, the microwave feed must be designed to not excite the TM11 mode at all.

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A system for 2450 MHz measurements on low-loss films A system is shown in Fig. 5.14, which consists of a standard 43  86 mm2 waveguide, fed by a suitable matched transition to a coaxial line and then by the network analyser (not shown). The waveguide end is connected to a circular TE011 resonant cavity. This is split into a tubular body plus two flat lids with 2 mm air gaps. These are maintained by external supports (not shown). The MUT is a circular flat with diameter 150 mm in this case, and rests on a grid of some thin filaments of, for example, PTFE (not shown). Both the upper cavity part and the lid can be easily removed for insertion and removal of the MUT. Since the electric field is parallel to it, the coupling becomes maximal. Furthermore, the coupling is zero both at the centre and at the cavity periphery, so the diameter of the MUT is not sensitive. The field configuration additionally allows the use of multi-layered MUTs, without a need for tight packing. An example of the system performance, obtained by numerical modelling, is given in Table 5.1. The conductivity  of the cavity metal was chosen to 5  107 m, approximating that of non-polished aluminium. The system was

5.14 A 2450 MHz circular TE011 applicator for measurements on low-loss flat MUTs. Dimensions in mm.

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fres (MHz)

ÿ (refl. factor)

Qu

Empty

2443.1

0.78

6090

2 mm thick; " ˆ 2 ÿ j0:00073 (dp ˆ 375 mm)

2404.5

0.52

5630

overcoupled both empty and with the MUT. The overcoupling is manifested by the polar reflection factor circle in the Smith diagram, as measured by a vector network analyser encircling the polar centre. The coupling is, however reduced for thicker and/or more lossy MUTs, resulting in the whole circle now being outside the polar centre. The Qu value is the unloaded quality factor, but only the loaded factor can be measured. The relationship is: Qu ˆ 2QL =…1 ÿ ÿ†

5:1 0

where ÿ is the reflection factor, it is seen that the sensitivity to " is high, by the almost 40 MHz frequency difference. The resolution in "00 is typically best if the reflection factor ÿ rather than the Q value is used.

5.6.5

A commercially available resonant applicator system for food MUTs

A schematic illustration is given in Fig. 5.15. Owing to the dielectric resonator, mode degeneracy is avoided and quite effective algorithms for determination of

5.15 Illustration of TM01 mode dielectric resonator measurements of powders and liquids at 2.45 GHz (Givot et al., 2008).

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the complex " can be constructed for transmission mode designs (Givot et al., 2008; QWED, 1997). Other advantages are that about 6 mm MUT diameter can be allowed for food materials, and that a superior resolution in "00 compared with the filled waveguide technique can be obtained for low-loss materials. However, reasonable homogeneous MUTs and precise centring of them are required, and the temperature dependence of the dielectric properties of the dielectric (ceramic) resonator has to be considered.

5.7

Summary and conclusions

This chapter has shown that measurements of dielectric properties require decisions in advance on several matters: · · · · · ·

What range of permittivity data are of interest? What accuracy is needed? What temperature range is considered? Is the MUT non-homogeneous and if so to what extent? Is the MUT easily shaped and put into a small tube of glass or similar? Does the MUT shrink (drying) or expand (freezing) or change in any other way during normal processing? · Is a commercially available system preferred or is internal manufacturing an option? · How important is easy and quick evaluation of data into permittivity data? There is fortunately at least one available method which can fulfil at least some of the criteria above, but other criteria have then to be discarded. So to measure is also to compromise. With the ongoing computerisation of algorithms and instrumentation, the user of today and tomorrow is expected to prefer commercially available systems allowing quick evaluation of data. But as has been indirectly pointed out in this chapter, the resolution of, or number of digits in, a computed result may say very little about its actual accuracy, representativity and reliability. The experimenter must therefore always be aware of the weaknesses of the chosen method, and may then perhaps come to the conclusion that an internally manufactured system may be the best solution. What accuracy ± and not fictitious resolution ± is needed may therefore be the most important of the matters to consider in the list above.

5.8

Acknowledgement

Thanks to Per Floberg, formerly at SIK ± the Swedish Institute for Food and Biotechnology ± for valuable discussions and recommendations.

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References

AET Japan (2008) `Microwave Dielectric Measurement System', www.aetjapan.com Agilent (2006) `Basics of measuring the dielectric properties of materials', Application Note, www.agilent.com Agilent (2008) `85070E Dielectric probe kit, 200 MHz to 50 GHz', Technical Overview, www.agilent.com Givot B L et al. (2008) `Measurement of powders and liquids employing dielectric resonator technique', XVII International Conference on Microwaves, Radar and Wireless Communication (MIKON 2008), Poland, pp. 411±414. Hedvall P and HaÈgglund J (1963) `Cavity method for measuring dielectric constants at microwave frequencies', Ericsson Technics 19(1), pp. 89±96. von Hippel A, ed. (1954) Dielectric materials and applications, MIT Press, Cambridge, MA. ISEMA (2005) Sixth Conference on Electromagnetic Wave Interaction with Water and Moist Substances, www.uni-weimar.de/mfpa/indx3/isema_2005/isema2005.html, or Internet search on `ISEMA water'. Kaatze U (1989) `Complex permittivity of water as a function of frequency and temperature', J. Chem. Eng. Data 34, pp. 371±374. Nelson S O (2003) `Frequency- and temperature-dependent permittivities of fresh fruits and vegetables from 0.0l to 1.8 GHz', Transactions of the ASAE 46(2), pp. 567± 574. Nyfors E and Vainikainen P (1989) Industrial microwave sensors, Artech House, Boston, MA. Ohlsson T and Bengtsson N E (1975) `Dielectric food data for microwave sterilization processing', Journal of Microwave Power 10(1), pp. 93±108. QWED Sp. z o.o. (1997) www.qwed.eu Risman P O (1994) `Confined modes between a lossy slab load and a metal plane as determined by a waveguide trough model', J. Microwave Power and Electromagnetic Energy (JMPEE) 29(3), pp. 161±170. Risman P O (1999) Public Seminar at QuickWave modelling course, GoÈteborg, Sweden (November). Risman P O and Bengtsson N (1971) `Dielectric properties of foods at 3 GHz as determined by a cavity perturbation technique. I. Measuring technique', Journal of Microwave Power 6(2), pp. 101±106. Risman P O and WaÈppling-Raaholt B (2007) `Retro-modelling of a dual resonant applicator and accurate dielectric properties of liquid water from ÿ20 ëC to ‡100 ëC', Meas. Sci. Technol. 18, pp. 959±966. Roberts S and von Hippel A (1941) `A new method for measuring dielectric constant and loss in the range of centimeter waves', MIT Electr. Engineering Dept., Massachusetts Inst. of Technology (March). Sokoll T et al. (2005) `A compact network analyzer for resonant microwave sensors', ISEMA Conference Proceedings (Weimar, Germany, May±June), paper 5.5. WaÈppling-Raaholt B and Risman P O (2003) `Permittivity of inhomogeneous food items by retro-modelling with a degenerate mode cavity', AMPERE Conference, Loughborough, UK (September).

6

Microwave dielectric properties of foods and some other substances P R I S M A N , Microtrans AB, Sweden

Abstract: Without the dipolar properties of water at microwave frequencies, there would be no life on earth, and certainly no microwave food heating. The microwave oven frequency of 2450 MHz was chosen rather arbitrarily 60 years ago and is indeed optimal for the purpose. But even a quite small ionic content causes a comparable absorption of microwaves to that of water. With the increased use of microwave modelling, accurate dielectric and thermal data for foods are becoming more important. The binding of water in various components is accounted for in mixture formulae, including semifrozen foods. The limits of use for dielectric data for homogenised samples (MUTs) for computations of the `effective' microwave permittivity are also dealt with. Finally, microwave data for some food container materials are given. Key words: dipole, relaxation, ionic conduction, enthalpy, microwave, dielectric data.

6.1

Introduction

There are three major differences between material properties at microwave frequencies and in the visible spectrum: · Many materials, such as plastics, glasses, ceramics, as well as pure fats, starches and proteins, are essentially transparent to microwaves and thus do not absorb them ± but their optical properties vary greatly. · Metals are highly reflective of microwaves and absorb them only very slightly, if the metal layer thickness exceeds some tens of micrometres (m) ± but are much less reflective in the optical region. · Polar liquids such as water and alcohols, as well as dissolved ions, absorb microwaves to a variable extent ± but these substances are optically transparent. This fortunate combination of microwave properties makes it possible to put food in plastic or glass containers, and then put this load in a metal cavity which does not leak microwaves and where heating of only the food then takes place. Most of this chapter deals with microwave properties of materials containing polar liquids. Microwave transparent materials are briefly dealt with, as are metals. Very thin metal films may absorb microwaves and are used in the This chapter is ß Per Olov Risman and printed with his permission.

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microwave food area. They are then called susceptors, which are dealt with in more detail in Chapters 9 and 15.

6.2

Absorption mechanisms in water

Water is indeed an extraordinary substance, certainly quite complicated and peculiar in relation to its simple chemical formula: H2O. But the small molecules stick together in very complicated fashions in liquid water, and are locked in a crystal pattern in ice. Water's absorption of energy is very different across the electromagnetic spectrum and one of the most fascinating aspects of this is its almost perfect transparency just and only in the narrow spectrum of visible light. For the slightly longer infrared wavelengths the absorption is by flexing of the highly electrically polarised molecule, and for still longer wavelengths the phenomenon of concern here comes into action: dipole relaxation. This is the completely dominating absorption mechanism in pure liquid water in the microwave range of interest here, from 100 MHz to 10 GHz (3 metres to 30 millimetres wavelength in free space). Pure ice is practically transparent to microwaves. The reason is that the molecules are now locked individually in the ice crystal lattice. However, significant absorption by ice appears at very low frequencies up to some tens of kHz; see Smyth (1955) where general explanations are also provided. As an example for ice at ÿ1 ëC, the static permittivity "s is about 91.5, and "1 is 3.15 (see Section 6.3.1 for explanations). The Debye relaxation frequency fD is about 6 kHz. As for liquid water, "s increases and fD decreases with decreasing temperature. The other dominating microwave heating mechanism in foods is due to ionic conductivity. This effect is basically frequency-independent, but its importance is higher at lower frequencies, owing to the heating by dipole relaxation in relative terms then being less effective. Contrary to statements in some literature, there is no significant microwave absorption in any other pure ingredient substance in foods, except in other polar substances such as higher alcohols. But mixtures behave very differently, even with small relative amounts of water. The properties depend on the overall composition, and also on which component is continuous, the dispersed phase and dispersed medium, different kinds of water binding to molecules and interfaces, etc. Prediction of dielectric properties based on composition is therefore in many cases problematic.

6.2.1

The dipole relaxation

The heating mechanism is caused by the molecules in a polar liquid having a tendency to stick to each other, owing to the uneven charge distribution of the molecule. The hydrogen areas have an excess positive charge and the oxygen areas

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6.1 Idealised attached water molecules and the action of an electric field.

an excess negative charge ± see Fig. 6.1. Quite large clusters are formed continually, in which each molecule binds to two to four others and other nonattached molecules move in between. The cluster pattern changes about every nanosecond, but the general lifetime of individual clusters is several times longer. The liquid water becomes more polarised with more clustered molecules and this is temperature dependent: the Brownian movement reduces the average cluster size with increasing temperature. The microwave field (‡ and ÿ and directed arrows in Fig. 6.1) will interact more strongly with clusters than with individual molecules, and then exert a turning force. Clusters and individual molecules between them attempt to align with the field and energy is then supplied to them. When the field direction changes (this occurs 4.9 billion times per second at 2450 MHz, i.e. about every 0.5 nanosecond), the clusters return the alignment energy to the field ± the system behaves like an electrical capacitor connected to an alternating voltage. If the microwave frequency is very high, the inertia of the clusters will, however, cause them not to have sufficient time for the turning. They remain unaffected and do not align with the field ± no energy transfer takes place. In a certain frequency interval, the clusters will statistically still be able to rotate but with some lag, which depends on their mass inertia. Not all the energy will be recovered when the field direction is reversed: a part of it will instead be permanently absorbed in the cluster structure, which will then heat up by a general net increase in the molecular movement. The phenomenon is called dipole relaxation. The so-called Brownian motion is a basic property of matter and has been known for more than 2000 years. It was Einstein (1905) who showed the direct connection to the temperature and atoms/molecules as such, in a famous paper. Later, Langevin formulated a stochastic differential equation describing Brownian motion in a potential (see e.g. Reif, 1965). This equation is now named after him. Collisions as such are fully elastic, i.e. no energy is consumed, so `friction' as stated in some literature to be the final heating mechanism is incorrect. In liquid water at room temperature, there are collisions about once every picosecond (a millionth of a millionth second). As stated earlier, water molecules are exchanged between the hydrogen-bonded clusters at about every 1000th collision. Microwaves at 2450 MHz change direction every 200 picoseconds. Hence, collisions occur about 200 times between every field reversal!

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The `geometric' effect of the energy of turning, i.e. the actual alignment of the molecule groups, can be calculated by the so-called Langevin equation (Reif, 1965), and one then finds that 1000 W in 100 g of water (corresponding to 2.3 K temperature rise per second) at room temperature causes a relative orientation alignment of only 0.003%. Hence, the energy that `a microwave' can add is almost insignificant in comparison with the inherent, internal and permanent energy of movement of the molecules. A very obvious conclusion is that microwaves just heat and do not cause any chemical changes of matter, in addition to what temperature as such does.

6.2.2

Ionic absorption

Ionic absorption results from many liquids (e.g. water) being able to dissolve salts, acids and bases which then become dissociated into charged ions. The ions are influenced by an electric field causing a net movement in its direction ± see Fig. 6.2, which very schematically shows a hydrated negative ion (e.g. the chloride ion in common salt) and a positive hydrated ion (e.g. sodium). The net movement increases the overall macroscopic energy of movement, which is the same as a temperature rise. This effect is frequency independent ± see Section 6.4.

6.2 The molecular effect of ions.

It is to be noted that water molecules `stick' to the charged ions and partially shield them from the external electric field. This effect is reduced with increasing temperature, since the shielding by adjacent water molecule groups diminishes with increasing temperature ± the ions become more `naked' and their absorption of the field energy increases.

6.3

Microwave dielectric data of water

The mechanism of dipole relaxation indicates a frequency dependence: the effect has a maximum at some frequency and diminishes for lower and higher frequencies. There is also a temperature dependence, by the increasing

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Brownian motion at higher temperatures, resulting in fewer molecules per cluster: the polarisation weakens at higher temperatures.

6.3.1

Static (zero frequency) permittivity data of water

The permittivity (also called `dielectric constant' even if it varies) is exceptionally high for pure liquid water. The common notation is "s. Actually, only one commercially available liquid (N-methylformamide) has a higher "s (about 180), and some other polar liquids have up to about half the value for water. The static permittivity may be measured by capacitive methods at kilohertz frequencies, but the use of two to more microwave frequencies eliminates the need for contacting metal electrodes and some other sources of error. A commonly accepted standard reference value at ‡20.0 ëC is "s ˆ 80:30  0:10. This increases to about 99 for supercooled water at ÿ20 ëC, and decreases to 55.3 at 100 ëC, as measured by a dual frequency microwave method (Risman and RaaholtWaÈppling, 2007). Extremely pure liquid water can exist below ÿ100 ëC. Interestingly, the permittivity should theoretically become infinite at about ÿ140 ëC, and the hydrogen-bonded clusters then be macroscopically large. The relaxation frequency (see Section 6.3.2) should then be zero. The dual frequency method of Risman and Raaholt-WaÈppling (2007), using about 1 and 2 GHz, was used to derive the following equation: "s …t† ˆ 1=…0:011 284 4 ‡ t
5:811 45Eÿ5 ‡ t3
9:8178Eÿ10

6:1

where t is the temperature in ëC. For temperatures ÿ20 < t < ‡5 ëC the inaccuracy is stated to be less than 0.7 units, and for t > ‡5 ëC less than 0.3 units, in both cases including the possible inaccuracy of 0.1 unit in the reference value. In comparison, an error of 0.3 units corresponds to a temperature deviation of 0.7 K.

6.3.2

Relaxation frequency and data of water

The time-harmonic frequency enforced by the microwave generator at which the molecular energy absorption capability by the relaxation effect is maximal is called the Debye relaxation frequency. The common notation is fD.1 For pure water at ‡20.0 ëC this is (16:8  0:6) GHz (Risman and Raaholt-WaÈppling, 2007), which is thus much higher than the microwave oven frequency 2.45 GHz. As a consequence, the actual microwave permittivity "0 at 2450 MHz is almost as high as "s.

1. It is also common to characterise the property by a `critical' wavelength c ˆ c=fc , where c is the speed of light, or by a `characteristic relaxation time', t ˆ 1=…2fD †. fD is chosen here, since it is the easiest to use in qualitative considerations.

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The relaxation mechanism follows a quite simple equation, called the Debye equation (e.g. Debye, 1945; von Hippel, 1954): "s ÿ "1 " ˆ "1 ‡ 6:2 f 1‡j fD where f is the enforced frequency, in GHz; " is the complex (relative) permittivity "0 ÿ j"00 ; "s is the static permittivity ( f ! 0); "1 is the (fictitious) permittivity for f ! 1. "1 is the remaining permittivity at very high frequencies, in consideration of action of the structures that cause dipole rotation. It can be derived accurately only by comparing results at several very high microwave frequencies. However, other phenomena such as additional weak relaxation mechanisms or distributed relaxation phenomena then also affect the measured data. An inexact value of "1 gives a very small possible error in the end result when the operating frequency is much below the relaxation frequency ± as is the case for 2450 MHz. Therefore, the data in equations 6.3 and 6.4, from Risman and Raaholt-WaÈppling (2007), are reliable below about 6 GHz: "1 …t† ˆ 5:00 

(no temperature dependence)

2:187 87 ‡ t
0:052 47 fD …t† ˆ exp 1 ‡ t
0:007 376 8

6:3

 (in GHz)

6:4

The inaccuracy of fD is within 2.5% for all temperatures except for the lowest, where it is 5%.

6.3.3

Water data at 915 and 2450 MHz

Equations 6.1 to 6.4 give the results in Table 6.1 (see also Fig. 6.3).

6.3.4

The penetration depth of liquid water

The penetration depth dp is a practically useful variable. It is discussed and defined in Chapter 3, Section 3.2 and the exact expression is dp ˆ

ÿ0 p 4
Im "

6:5

where 0 is the free space wavelength of the microwaves and " is the complex "0 ÿ j"00 . For water at 20 ëC, dp becomes 16.1 mm, which is comparable with the thickness of many food items and therefore a practically important value. At 100 ëC dp becomes 85 mm and in still unfrozen water at ÿ20 ëC it is only 4.0 mm. The first consequence of this is that the relative absorption capability of water decreases with increasing temperature. This provides a stabilising effect of

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Table 6.1 Dielectric data of water at 915 and 2450 MHz Temp. ëC ÿ20 ÿ15 ÿ10 ÿ5 0 10 20 30 40 50 60 70 80 90 100

915 MHz "0

915 MHz "00

2.45 GHz "0

2.45 GHz "00

93.73 92.91 91.44 89.66 87.75 83.85 80.07 76.48 73.07 69.82 66.71 63.72 60.83 58.03 55.31

21.36 16.65 13.13 10.49 8.49 5.77 4.09 3.01 2.27 1.76 1.40 1.126 0.921 0.763 0.638

71.33 77.44 80.88 82.44 82.75 81.34 78.72 5.71 72.60 69.53 66.52 63.58 60.73 57.96 55.26

42.74 36.74 30.87 25.69 21.36 14.96 10.76 7.96 6.05 4.70 3.73 3.01 2.46 2.04 1.71

Italic numbers represent `external' reference data.

heating of water-rich systems where this absorption mechanism dominates, by a hotter small part being heated less than if it were colder. The second consequence is related to defrosting of foods, and dealt with in Section 6.9.2.

6.4

Contributions by ions

As already mentioned in Section 6.2.2, the ionic conductivity is frequency independent. However, since the relaxation losses are frequency dependent, the quantitative relationship between the two loss mechanisms becomes frequency dependent, by the conductivity influence increasing with decreasing frequency. It is not possible to separate the two loss causes by measurements at a single frequency. Measurements at two frequencies separated by a factor of about two may, however, be sufficient for water-rich systems where there is no other polar constituent such as higher alcohols; see Chapter 5, Sections 5.5.1±2. The simplest procedure is to measure the conductivity at very low frequency with suitable equipment such as a precision plate capacitor (see for example von Hippel, 1954), and the complex permittivity at the frequency which is to be used for microwave heating. However, the conductivity measurements require water to be the continuous constituent of the material under test (MUT). The theoretical relation between the ionic contribution to the loss factor ("00 ) and the conductivity s is  6:6 "00 ˆ 2 f "0 where "0 is the electric constant ( 8:85  10ÿ12 S/ m). At 2450 GHz  becomes about 0.136 300"00 .

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The temperature dependence of the conductivity of common salt (NaCl) with a concentration c in per cent by weight of the water (not the overall mass for multi-component materials) can be approximated by an added contribution "00 to "00 , which at 2450 MHz becomes "00 ˆ …t ‡ 21†  c=4:0

…NaCl, t > ÿ21  C; 2450 MHz†

6:7

This correlates rather well with actual measurements on foods with added salt content less than some few per cent. In reality there is both a concentration and temperature non-linearity in …t†, so equation 6.6 only reflects the order of influences. A problem may be with an unknown ionic content without any added salt. It is then difficult to assess from which measured or estimated "00 value to apply the equation, so actual conductivity measurements may be needed. Equation 6.6 indicates that the "00 contribution vanishes at ÿ21 ëC. This is the NaCl±H2O eutectic temperature, at which the remainder of any concentrated NaCl solution solidifies when the temperature is lowered. Other salts give different contributions to "00 . This is because the number of ions is inversely proportional to the molecular weight, different ions have different sizes and therefore attract hydrogen-bonded water molecules differently, and temperature effects such as the eutectic temperature. There are conductivity tables for different salt solutions which can be used for such comparisons, but these typically do not cover the large temperature interval that may be needed for estimations from frozen to boiling temperatures. Again, resorting to low-frequency measurements of the conductivity in the actual food substance, with and without added salts often offers a simpler and better way to get the information needed.

6.5

Data of water and some other liquids at 2450 MHz

6.5.1

Pure water and alcohols

Figure 6.3 shows the dielectric data of water with and without salt, as well as data for some pure alcohols. The so-called `food map' axis system originally introduced by Bengtsson and Risman (1971; Buffler and Stanford, 1989) ± see Fig. 6.6 ± is used. It is convenient to include curves for equal penetration depth dp in the figure.

6.5.2

Sugar solutions

Sugar solutions have no electrical conductivity and they are not mixtures of particulates as dealt with in Section 6.8. Instead, the hydrogen bonding is changed, and the applicable relaxation data are different from those for pure water. Effects of both diminished water volume due to the added sugar and two

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6.3 The dielectric properties and penetration depths of water, a salt solution, a sugar solution and some alcohols, at 2450 MHz, as function of the temperature.

temperature effects occur. The first temperature effect is the same as in pure water. The second is due to the large sugar molecules partially hindering the establishment of free water type clusters at low temperatures, and this effect diminishes as clusters get smaller and more free at higher temperatures. The latter effect is also related to the near-saturation properties of concentrated solutions. Microwave dielectric data of sugar solutions are given by Kent (1987). Properties of concentrated solutions are of main interest since the data can be used for mixture calculations under equilibria with sugar crystals, and such

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Temperature (ëC)

"0

"00

60 60 70 (saturated) 70 80 (oversat.)

30 50 25 50 50

28.5 34.4 27  1 35  2 23  4

15.7 14.4 12  2 15  3 10  3

substances occur in many bakery products. A selection of data from Kent (1987) and measurements by the author are given in Table 6.2. The data with tolerances are the results by the author. There is 68% sucrose by weight in a saturated solution at 25 ëC, and 75% at 60 ëC. Oversaturation easily occurs when no crystals are in contact with the solution. The inverse Debye equations [6.8] are used with experimental data for assessing the relaxation properties of `unknown' substances such as the sugar solutions: f
…"0 ÿ "1 † "s ˆ "0 ‡ "00
…f =fD † 6:8 "00 with the same notation as for equation 6.2. If f ˆ fD one obtains "00 ˆ "0 ÿ "1 and if f ˆ 12 fD one obtains "00 ˆ 12 …"0 ÿ "1 †. These relations can be used with the data in Table 6.2 to assess the relaxation data. Assuming that "1  3 . . . 4 for the concentrated solutions, one finds that fD  5 GHz for the saturated solution at 25 ëC as well as for the oversaturated at 50 ëC. "s decreases with (over)saturation and increases with temperature. Crystallised sucrose has " ˆ 2:60. An example of a mixture of a saturated sucrose and sucrose crystals is given in Section 6.9.3. fD ˆ

6.6

Data of some food substances with high water content

The first comprehensive collection of food dielectric data was published by Bengtsson and Risman (1971) at SIK in Sweden, but von Hippel (1954) had already done some pioneering work in the beginning of the 1950s at the MIT Laboratory for Insulation Research. Figures 6.4, 6.5 and 6.6 are from the Bengtsson and Risman work, and give a good overall picture of the range and variations of data. They are at about 2.8 GHz, the reason being that most literature data suitable for calibration at the time were at 3 GHz and the accuracy of measurement method relied on the use of a series of calibration liquids with known data (Risman and Bengtsson, 1971). The same group at SIK also published a series of food dielectric data at sterilisation temperatures up to

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6.4 The permittivity "0 of some food substances at 2.8 GHz. From Bengtsson and Risman (1971).

6.5 The loss factor "00 of some food substances at 2.8 GHz. From Bengtsson and Risman (1971).

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6.6 The complex permittivity and power penetration depth in cooked cod as function of temperature, at about 2.8 GHz. From Bengtsson and Risman (1971).

‡140 ëC (Ohlsson and Bengtsson, 1975). A comprehensive and very useful collection of microwave dielectric properties of food materials is given in a bibliography by Kent (1987). Additional data are given by Buffler and Stanford (1989). As mentioned earlier, there are no generally reliable, simple relationships between the composition and dielectric data. However, accuracies sufficient for many purposes may be obtained for emulsified materials. An example is shown in Fig. 6.7, from Ohlsson et al. (1974). Mixture examples are given in Section 6.9. Data for frozen compact foods differ very much from those in the thawed condition. The reason is of course that most of the water is frozen. Pure ice has "0 about 3.15 and a dp of several metres. The complex permittivity " of cod is shown in a logarithmic scale in Fig. 6.6 and details of the properties for frozen cod are seen more clearly than in the previous figures. The loss factor "00 is

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165

6.7 Profiles for permittivity and loss factor for beef meat emulsions at 2.8 GHz and +20 ëC. From Ohlsson et al. (1974).

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surprisingly high in consideration of the low "0 and the data in equation 6.6 which suggest a rather low contribution to "00 from the ionic content. The reason is instead that the ionic content prevents some water from freezing, and that this unfrozen water as such has a high "0 and a very high "00 ± see Fig. 6.3. Actually, liquid water will have its strongest absorption capability when its relaxation frequency fD is about the same as the operating frequency 2450 MHz. At ÿ20 ëC fD is 3.8 GHz, and becomes 2.45 GHz at about ÿ28 ëC.

6.7

Data for some food substances with low water content

The impurity constituents may be very important. The presence of dispersing agents may also be very important. Some oils, such as olive oil, may contain higher alcohols or related polar substances. Many solid fats contain water and salt. Dissolved sugars also change the relaxation frequency; see Section 6.5.2. All these factors make it difficult to predict in particular the loss factor "00 . Table 6.3 contains some typical data, from mainly Bengtsson and Risman (1971) and internal work at SIK in Sweden. It is to be noted that more data are available in Kent (1987) and elsewhere, but generally with no specifications of impurities. The first item to be noted is that `commercial impurities' may play a very important role in "00 . The second item is that dp may be so large that the material will not be heated significantly when a layer of it is together with a normal food item in a microwave oven or process. The third item is that "00 in some cases increases with temperature. This may then be due to ionic influence, alone or in combination with the release of bound water (see below). As to the other solid non-dissolved constituents of foods, their permittivity in solid, dry, homogeneous (i.e. non-milled) state is usually in the order of 2.5 to 3. Some proteins may bind to water in complicated ways, resulting in additional relaxation frequencies influencing the permittivity data at 2450 MHz. Last but not least, some water will be bound to large molecules, or be partially locked at surfaces in crystal- or cell-like structures. An example of this Table 6.3 Dielectric data for some fats at ca 2450 MHz Material

Temperature (ëC)

"0

Corn oil Corn oil

‡20 ÿ10 ‡20 ‡60 ÿ10 ‡20 ‡60

2.50 2.57 2.63 2.66 2.43 2.50 2.62

Lard

"00 0.005 0.103 0.149 0.172 0.035 0.087 0.145

dp (mm)

Notes

6200 300 210 185 870 350 220

Highly purified Commercial Commercial Commercial

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167

is wood. Generally, such bound water absorbs microwaves quite weakly. When the temperature is increased, some of this bound water becomes free and may then be measured as a part of the water content of the MUT when, for example, the common drying temperature of ‡120 ëC is used for the determination. But this water may not be free in the material at lower temperatures and then have the dielectric properties described in Section 6.3. It is concluded that the dielectric properties of materials with low water content are sensitive to minor contaminations or additives, as well as any pretreatment. Taking actual measurements is the only reliable method to acquire data, in particular when data over a range of temperatures are needed.

6.8

Data for numerical modelling

With the increasing use of numerical microwave modelling of, in particular, defrosting of foods with simultaneous use of heat conduction modelling, there is a need for dielectric data as a function of enthalpy and temperature. However, most dielectric measurements are made under stationary, constant temperature conditions. This is very practical since no energy flow needs to be controlled. But the accuracy of data during the crucial phase change then suffers, as the temperature changes by perhaps only 3±4 K during most of the phase change. Other methods, employing controlled energy flow to the MUT, are needed. Measurement methods are described in Chapter 5. The dielectric data in Table 6.4 have been obtained from several measurement projects at SIK in Sweden, from Riedel (1957), and by various unpublished extrapolation and smoothing methods. For all but some few entries, the inaccuracy in "0 is less than 5%; for "00 the corresponding inaccuracy is less than 10%. The enthalpy data are believed to be accurate within 5%. The bread data in Table 6.5 are less accurate than the beef data, mainly due to compression errors in the sample preparation. This was from frozen bread at about ÿ10 ëC and the samples were directly put into glass vials which were subsequently tightly closed. An inaccuracy of 10% or less applies for almost all data except those for 50% evaporated water. The many decimals in the permittivity columns are due to smoothing for improving the accuracy when using the data for piecewise linear approximations.

6.9

Mixture formulas

If the size of the constituent particulates is very small, it is possible to consider the mixture to be a continuum with a single permittivity, for all practical purposes. This section deals with such cases. How large the non-homogeneities in a material consisting of packed particulates are when the formulas given here no longer apply is dealt with in the next section, 6.10.

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Table 6.4 Data for raw beef between ÿ20 ëC and 100 ëC. No density correction; nominal density is 1.15 g/cm3, water content 65%, with no salt added Temperature (ëC) ÿ40 ÿ30 ÿ20 ÿ15 ÿ10 ÿ5 ÿ3 ÿ2.2 ÿ1.6 ÿ1.3 ÿ1.1 ÿ1 10.0 20.0 35.0 50 (65) (80)

Specific enthalpy h (kcal/kg)

Enthalpy density dH/dV (J/cm3)

0.0 4.5 10.1 13.0 17.2 24.9 33.0 40.0 50.0 60.0 67.0 70.0 79.3 87.0 101 115 (130) (145)

0.0 21.7 48.6 62.6 83.0 120 159 193 241 289 323 337 382 419 486 554 626 698

Permittivity "

Approx. remaining ice, weight %

4.2 ÿ j0.24 4.4 ÿ j0.32 4.9 ÿ j0.47 5.5 ÿ j0.68 6.1 ÿ j1.12 12.3 ÿ j4.2 22.0 ÿ j8.2 30.0 ÿ j12.0 42.0 ÿ j15.5 46.0 ÿ j17.5 48.9 ÿ j17.8 49.2 ÿ j17.9 48.9 ÿ j17.0 48.2 ÿ j16.1 46.9 ÿ j15.2 45.5 ÿ j14.3 43.6 ÿ j14.1 41.7 ÿ j14.0

88 88 87 ± 82 73.3 63.0 ± ± ± ± 0 (0) (0) (0) (0)

Italic numbers ˆ null values.

Table 6.5 Data for white bread between ÿ20 ëC and 100 ëC. No density correction; nominal density is 0.25 g/cm3, water content 44%; Standard Nordic Bread recipe Temperature (ëC) ÿ20 ÿ10 ÿ5 ÿ3.5 ÿ2 ÿ1 0 10 20 40 60 80 100 104

Enthalpy density dH/dV (J/cm3)

Permittivity "

Approx. remaining ice, weight %

0.0 6.3 9.9 11.5 13.6 15.2 30.1 37 42.6 56.5 70.4 84.3 98.3 222

1.50 ÿ j0.15 1.70 ÿ j0.25 1.82 ÿ j0.35 1.90 ÿ j0.48 2.20 ÿ j0.72 2.39 ÿ j0.92 3.55 ÿ j1.88 3.89 ÿ j1.68 4.17 ÿ j1.55 4.57 ÿ j1.35 4.78 ÿ j1.30 4.73 ÿ j1.30 4.50 ÿ j1.35 2.00 ÿ j0.80

49 47.5 44 42.5 38 35.5 0 ± ± ± ± ± ± ±

Italic numbers ˆ null values.

Microwave dielectric properties of foods

6.9.1

169

Two mixture formulas

The literature on calculations of permittivity of mixtures is quite comprehensive, but typically directed towards choice of substances which do not interact at the molecular level. Simple geometric shapes of the inclusions are also preferred. A rather old but valuable review is given by Kraszewski (1977). Further reading on mixture theory and formulas are given there and in the book by Nyfors and Vainikainen (1989). Kraszewski recommends the following two formulas. Their usefulness depends on the shape of the inclusions and if the high- or low permittivity constituent is the continuous one. The following notation is used: · · · · ·

"i permittivity of the inclusion vi relative volume of the inclusion "c permittivity of the continuous phase vc relative volume of the continuous phase "m permittivity of the mixture

vi ‡ vc ˆ 1; all " may be complex. The Looyenga formula, which is based on the early Rayleigh mixture formula, and the BoÈttcher mixture formula for spherical inclusions is: 1=3 1=3 "1=3 m ˆ "c
…1 ÿ vi † ‡ "c
vi

6:9

The Kraszewski formula, which is based on a multi-layer concept with neglected internal reflections, is 1=2 1=2 "1=2 m ˆ "c
…1 ÿ vi † ‡ "c
vi

6.9.2

6:10

An example of frozen meat

Actual data from Table 6.4, for raw beef at ÿ10 ëC, are used for comparison and calculations. For the mixture, "m ˆ 6:1 ÿ j1:12 and the remaining ice weight is 82%. Pure supercooled water at ÿ10 ëC has "i ˆ 80:9 ÿ j30:9 according to Table 6.1. The solid material consists of ice and dry substance; if 82% of the water is frozen and the total water content is 65%, the total percentage of remaining water becomes 0:65  0:18 ˆ 11:7%. This is then the vi value. The remaining 88.3% is thus solids, of which 0:65  0:82 ˆ 53:3% of the total is ice. However, water expands when it freezes, so a correction may be made ± see the end of this section. The remaining 35% are proteins, etc. They are estimated to have " ˆ 2:5 ÿ j0 and ice has " ˆ 3:15 ÿ j0. In taking the average one may use mixture formulas, but a simple averaging is reasonable and gives " ˆ 2:8 ÿ j0. The NaCl equivalent is estimated to be 0.1 molar (0.58%) in the unfrozen meat. This would give an "00 contribution of 1.6. But the salt is now concentrated

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from 65% to 11.7% liquid water (the ice is pure), so the "00 contribution becomes about 8. Insertion in equation 6.9 requires the cube root of a complex number to be calculated. The first step is to calculate …j"j†1=3 ˆ a. The second step is to calculate  ˆ a tan…"00 ="0 †. Then =3 is used to calculate "1=3 as a
‰cos…=3†ÿ j
sin…d3†Š. In this case one obtains "1=3 ˆ 4:43 ÿ j0:667. "m then becomes 5:45 ÿ j0:73. Insertion in equation 6.10 is easier, and gives "m ˆ 6:48 ÿ j1:26. These values are to be compared with the experimentally determined value 6:1 ÿ j1:12. However, water expands by about 10% when it freezes. The 53.3% ice of the total should thus be increased by a factor 1.1 to 58.6%. The total relative volume then becomes 1.053, which means that the unfrozen water volume decreases from 11.7 to 11.1% of the total. The "m value from equation 6.10 then becomes 6:22 ÿ j1:17 ± in very good agreement with the experimentally determined value.

6.9.3

An example of saturated sugar solution and sugar crystals

Data from Section 6.5.2 are used: " ˆ 2:60 for the crystals, and " ˆ 27 ÿ j12 for a 70% solution at ‡25 ëC. It is supposed that there is 3% solution by weight among the crystals. One must now know the density of both the sugar crystals and the solution since microwave properties are by volume. The specific densities according to literature data are 1.58 g/cm3 and 1.32 g/cm3, respectively. The solution volume is thus 3.78% of the whole volume. Equation 6.9 then gives the mixture "m ˆ 3:1 ÿ j0:15. Its dp becomes about 230 mm. The mixture will thus be heated about as easily as warm commercial corn oil. The measured data in Table 6.2 and the data obtained by mixture theory may be used to help explain the rare but known phenomenon of sudden arcing followed by a fire in some bakery products having a partial covering of powdered sugar icing, particularly in the form of lines or circles of such icing. If the sugar has previously dissolved in a part of an icing line, it will become half p wave resonant at a length of about 60= "  12 mm, and thus be surrounded by a mixture with significantly lower "0 . The mixture part will then be exposed to a very strong electric field, and the sugar in it will decompose, creating free carbon, and begin to glow; the yellow arc phenomenon as described in Risman (1992). Surrounding fat in the thin baked layers will evaporate and then also catch fire.

6.9.4

Conclusions

Mixture formulas are valuable in particular for estimations of changes of dielectric properties with changes of composition. One can then choose the

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mixture formula that best suits a given set of data, without a need for dielectric measurements. Mixture formulas are also valuable for estimations of the dielectric properties of food substances in cases when data for only a similar substance are available. Finally, mixture formulas may be useful for calculations of dielectric properties of products during drying and thawing. The somewhat extreme case of calculating data for frozen meat by using water permittivity data and data on remaining unfrozen water in Section 6.9.2 illustrates the versatility of mixture formulas as well as the material physics. The actually measured value 6:1 ÿ j1:12 is close to, in particular, values obtained by the Kraszewski square root formula. The loss tangent tan  ˆ "00 ="0 values match almost perfectly, which indicates that there is indeed almost no direct ionic contribution to "00 . Apart from the representativity problems with the formulas, there are also uncertainties of the relative volumes of the constituents in cases such as in the examples here. Finally, the water content as measured by weighing before and after heating to a temperature above 100 ëC gives the total water mass, but some of that may be bound to molecular structures in the mixture and not participate in the water cluster relaxation phenomenon.

6.10

Large particulate foods and limitations of the mixture equations

It is reasonable to believe that inhomogeneities of characteristic sizes larger than a small but significant part of the wavelength of the microwaves can no longer be considered to be a continuum with a single permittivity. But how large should the non-homogeneities in a volume of packed particulates be for necessitating other methods of characterisation than those offered by the mixture formulas in Section 6.9? A first and quite obvious answer is that this occurs when the size of the individual particulates is comparable with the penetration depth in a minced and homogenised MUT of the particulates. The reason is that one can then no longer define the surface of the packed particulates from which to calculate dp . The second answer is related to the concept of the obvious need for field homogeneities, which is in turn a function of the particulate size in terms of their internal wavelength. In the simplest case ± that of packed spherical particulates ± the condition for homogeneous internal field is dealt with in Chapter 3, Section 3.10.2. It is concluded that the particulate diameter limit must be about a third of the spherical TE101 resonant diameter, i.e. about 5 mm for j"j  60 at 2450 MHz. It so happens that there is a common food substance consisting of spherical packed particulates: a heap of green peas on a plate. And the `effective permittivity' of just this type of food has been investigated (Risman, 2004), using retro-modelling in a degenerate mode measurement applicator; also see Chapter 5, Section 5.6.3. The MUT was in a circularly cylindrical beaker with about 40 mm

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diameter, and the height of it was varied, allowing extraction of two complex permittivities. The `outer permittivity' was for the layer contacting the container, assumed to have a thickness of half the sphere diameter. The `inner permittivity' was that of the reasonably tightly packed spheres inside the outer layer. Crushed compressed peas have "  63 ÿ j15:3 (dp  10:2 mm) at room temperature and 2450 MHz. The outer layer was defined to be 3 mm thick. The final result was · inner: " ˆ …30  0:4† ÿ j…4:8  0:4†; dp  22 mm · outer: " ˆ …1:8  0:1† ÿ j…1:2  0:1†; dp  23 mm Using the Kraszewski mixture formula with the theoretical reasonably dense hexagonal lattice packing of spheres filling 60% of the volume, one obtains " ˆ 27 ÿ j6. A denser packing will result in increases of both "0 and "00 . It is therefore obvious that the effective loss factor of the inner region obtained by modelling is lower than the theoretical value. This can, however, be explained by the outer structure (shell) of the pea, which constitutes the contact surfaces, having a lower water content than the average. Since the outer peas are more `isolated', the much lower " value for this region is expected. It is also interesting that "00 ="0 of the outer layer is quite high, but its dp is about the same as that of the inner layer. Obviously, this is caused by diffraction phenomena at the `rugged' outer surface. It is concluded that mixture theory begins to fail for MUTs such as a stack of green peas at 2450 MHz, but then mainly by the `rugged' external region having a very low equivalent "0 . The penetration depth dp of the surface layer seems to be the same as in the inner region, i.e. this has a good absorption capability in spite of its low filling factor. This is caused by diffraction and the phenomena are related to what is described in Chapter 3, Section 3.11.4, on uneven top surfaces.

6.11

Microwave transparency of food container materials, etc.

6.11.1 Basic effects by "0 Even a material that is transparent and does not absorb electromagnetic waves such as light and microwaves will to some extent reflect them. As shown in Chapter 3, Section 3.4, the transmission through a surface depends on the permittivity, the polarisation and the angle of incidence (or the normalised wavelength v). The condition of perpendicular incidence is suitable for assessing the reflection at flat microwave transparent material surfaces, and one obtains p 4
j"j i p 6:11 Ptransm =P  …1 ‡ j"j†2

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where Pi is the incident power flux density and Ptransm that transmitted into the material. As an example for ice with " ˆ 3:15, the relative transmitted power Ptransm/Pi through the surface becomes 92%. But since microwave heating systems are resonant and the microwaves are enclosed in a cavity or similar, the reflection is normally compensated for by repeated reflections and retroreflections. p The other effect of " is that the wavelength is shortened by ". But again, this is rarely of importance since food containers are typically thin-walled.

6.11.2 The loss factor "00 Microwave transparency is defined to exist for microwave applications in the IEC standard 60705 (2006), if "0 is less than 7 and "00 less than 0.015. The penetration depth can be calculated with the simplified formula: p dp  19:5
"0 ="00 …mm, at 2450 MHz† 6:12 and is thus 3.4 m in this case. The value is suitable in practice, and the following rules of thumb have been proven in industry over many decades: · If dp is less than 1 m, even of a thin wall container material, problems may occur. · dp should be at least 3 m for general usability in for example containers with semidry food products. · dp should be more than 10 m for critical applications such as when the whole cavity power is to pass through a thin protective layer or sheet. · If dp is more than 30 m, the material can be used also in the most critical applications with high power. · It must be observed that the dp limits apply at the temperatures of operation, but if these are not high and efficient radiation losses are expected, less stringent limits may apply.

6.11.3 Examples of some materials Properties of a selection of materials are given in Table 6.6.

6.12

References

Bengtsson N and Risman P O (1971) `Dielectric properties of foods at 3 GHz as determined by a cavity perturbation technique. II. Measurements on food materials', Journal of Microwave Power 2(6), pp. 107±124. Buffler C and Stanford M A (1989) `Effects of dielectric and thermal properties on the microwave heating of foods', Microwave World (IMPI) 12(4), pp. 15±23. Debye P (1945) Polar Molecules, reprint by Dover Publications, New York (original published in 1929 by the Chemical Catalog Company, Inc., USA).

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Table 6.6 Penetration depths for selected materials Material

Temperature (ëC)

dp (m)

Aluminium oxide ceramic Feldspar china Glass, borosilicate Glass, common Ice Melamine Micanite (mica)

20 20 50 20 ÿ12 20 20

30 5.8 8 0.33 12 0.2 28

Plexiglass Polycarbonate Polyethene Polyethene Polystyrene PTFE PVC PVC Quartz, pure Rubber, natural Steatite ceramic Steatite ceramic

30 25 25 80 80 20 20 100 25 20 25 80

2 1.6 40 18 28 90 2.1 0.51 165 4.3 2 1.8

Notes Used in magnetrons; "0  9 Microwave oven shelves; "0 ˆ 4:1 Window glass "0 ˆ 3:15 Not usable Used in microwave oven cavity feed openings Generally not usable

TeflonÕ Not usable Best of all materials

È ber die von der molekularkinetischen Theorie der WaÈrme geforderte Einstein A (1905) `U Bewegung von in ruhenden FluÈssigkeiten suspendierten Teilchen', Annalen der Physik 322(8), pp. 549±560. von Hippel A (ed) (1954) Dielectric Materials and Applications, MIT Press, Cambridge, MA. IEC (2006) Household Microwave Ovens ± Methods for Measuring Performance. Consolidated edition 3.2, IEC, Geneva. Kent M (1987) Electrical and Dielectric Properties of Food Materials, COST90Bis, Science and Technology Publishers, Essex, England. Kraszewski A (1977) 'Prediction of the dielectric properties of two-phase mixtures', Journal of Microwave Power 12(3), pp. 215±222. Nyfors E and Vainikainen P (1989) Industrial Microwave Sensors, Artech House, Norwood. Ohlsson T and Bengtsson N (1975) `Dielectric food data for microwave sterilization processing', Journal of Microwave Power 10(1), pp. 94±108. Ohlsson T et al. (1974) `Dielectric properties of model meat emulsions at 900 and 2800 MHz in relation to their composition', Journal of Food Science 39, pp. 1153±1156. Reif F (1965) Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York, section 15.5. Riedel L (1957) 'Enthalpie-Konzentrations-Diagramm fuÈr mageres Rindfleisch', KaÈltetechnik (Germany) 9(2), p. 38. Risman P (1992) `Metal in the microwave oven', Microwave World (IMPI), 13(1), pp. 28±33.

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Risman P O (2004) `Microwave modelling: a tool for dielectric measurements and material inhomogeneity studies', IMPI Symposium digest. Risman P O and Bengtsson N (1971) `Dielectric properties of foods at 3 GHz as determined by a cavity perturbation technique. I. Measuring technique', Journal of Microwave Power 2(6), pp. 101±6. Risman P O and Raaholt-WaÈppling B (2007) `Retro-modelling of a dual resonant applicator and accurate dielectric properties of liquid water from ÿ20 ëC to +100 ëC', Meas. Sci. Technol. 18, pp. 959±966. Smyth C P (1955) Dielectric Behaviour and Structure, McGraw-Hill Book Co, Inc., New York, pp. 171±174.

7

Flavors and colors for microwave foods S J R I S C H , Michigan State University, USA

Abstract: This chapter reviews the flavors and colors appropriate for microwave foods. It discusses the types of flavor additive available and the process of flavor formation during heating. It isolates the particular effects of microwave heating on the browning reaction in flavor formation and its implications for the choice and application of flavors for microwave foods. Key words: microwave foods, flavor, color, browning reaction.

7.1

Introduction

The flavor and color of a food product have significant impacts on consumer acceptability. Two of the challenges with microwave food products are that it is often difficult to achieve the desired flavor that matches products prepared in a conventional oven or by frying and to get the browning that the consumer expects. There are reactions that occur in those processes that do not occur when foods are heated in the microwave oven and this is part of what contributes to the lack of flavor and color development. In trying to solve the flavor issues, it is important to understand what flavors are as well as all of the attributes of a food product that lead to consumer liking. Solving the color problem involves an understanding of the reactions that produce color and finding ways to get those reactions to occur. The typical browning which occurs when foods are heated by conventional means produces not only the desired brown pigments but also produces a variety of desirable flavors. In the broad definition, the flavor of a product comprises the aroma components which are sensed by our olfactory system, the taste components which are sensed on the tongue and other sensory attributes including color, texture, pungency and temperature. All of these can be impacted by the difference encountered in microwave heating versus conventional heating.

7.2

What are flavors?

The aroma component is usually the part of flavor that is of most concern and can be the most challenging. Aromas come from low molecular weight organic compounds that can volatilize and be sensed in the nasal cavity. These

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compounds are not of one simple class of chemicals but rather are many different chemical types, including acids, esters, alcohols, ketones, pyrazines, thiazoles and terpenes as well as many others. The human body has a complex set of receptors that recognize both individual compounds as well as mixture of compounds to identify different flavors. Many flavor compounds occur naturally in foods. Character impact compounds are individual chemicals with a specific, recognizable aroma. Some examples are methyl anthranilate (concord grape), citral (lemon), cinnamic aldehyde (cinnamon), methyl salicylate (wintergreen) and diacetyl (butter). While these individual compounds have a characteristic odor, they do not make up the complete flavor of a product, whether naturally occurring such as in a concord grape or in a flavor added to a product. Many other compounds are also present which build the overall flavor profile. Considerable work has been done to identify the flavor compounds in different foods. There are over 170 compounds that have been identified that contribute to the flavor of a strawberry, while coffee and chocolate are much more complex with over 800 compounds identified. One good reference that has compiled the lists of flavor compounds naturally present in a wide variety of foods is VCF 2000 ± Volatile Compounds in Food Database (TNO Food and Nutrition Research and Boelens, 2000).

7.3

Natural versus artificial flavors

In the United States, there is a legal definition of natural and artificial flavors. The complete definitions are found in the Code of Federal Regulations (CFR) Title 21 101.22 (Code of Federal Regulations, 2008). Artificial flavors are defined in (a)(1) as follows: The term artificial flavor or artificial flavoring means any substance, the function of which is to impart flavor, which is not derived from a spice, fruit or fruit juice, vegetable or vegetable juice, edible yeast, herb, bark, bud, root, leaf or similar plant material, meat, fish, poultry, eggs, dairy products, or fermentation products thereof. Artificial flavor includes the substances listed in Sec. 172.515(b) and 182.60 of this chapter except where these are derived from natural sources.

Natural flavors are defined in (a)(3) of Title 21 101.22, as follows: The term natural flavor or natural flavoring means the essential oil, oleoresin, essence or extractive, protein hydrolysate, distillate, or any product of roasting, heating or enzymolysis, which contains the flavoring constituents derived from a spice, fruit or fruit juice, vegetable or vegetable juice, edible yeast, herb, bark, bud, root, leaf or similar plant material, meat, seafood, poultry, eggs, dairy products, or fermentation products thereof, whose significant function in food is flavoring rather than nutritional. Natural flavors include the natural essence or extractives obtained from plants listed

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The browning reaction will be discussed later and it is interesting to note that process flavors can be made using the browning reaction and are defined as natural since they are a product of roasting or heating. Spices are also defined in (a)(2) of Title 21 101.22 as follows: The term spice means any aromatic vegetable substance in the whole, broken, or ground form, except for those substances which have been traditionally regarded as foods, such as onions, garlic and celery; whose significant function in food is seasoning rather than nutritional; that is true to name; and from which no portion of any volatile oil or other flavoring principle has been removed.

The regulation goes on to list a number of individual spices. It should be noted that many materials that are considered artificial are identical to those in nature: it is simply how they were produced that determines whether they are natural or artificial. As an example, diacetyl is natural if it comes from milk or is produced by fermentation (as in wine and fermented dairy products) but is artificial if it is synthesized from other chemicals. All of the chemical properties are the same no matter where the individual chemical came from. The only time that a compound can never be natural is if it has never been found from any natural source. One compound, which gives a cotton candy type flavor, is ethyl maltol. This has never been found in nature so if a flavor contains this compound, it will be at least partially artificial. In other countries, there are different definitions as to what is natural and artificial. In some countries, there is the concept of nature identical. It states that if a compound exists in nature, then it does not matter where it comes from, it would not be considered artificial. The flavor could not be called natural but has simply been referred to as flavor. It is important that the regulations for each country be checked to understand what is allowed and how flavors added to products should be labeled.

7.4

Sources of flavors

Flavoring materials come from a variety of sources. One of the main sources is plants. The flavor materials can be present in any part of a plant including the flower, leaf, stem or bark. To be used in food products, the materials are generally extracted from the plant material to provide an isolate that is just the flavor. There are different techniques that can be used for isolation including solvent extraction (often ethanol), steam distillation and supercritical fluid extraction. Dairy products and meats and seafood can also be sources of flavoring materials. Dairy products provide a good source of base material that can be modified by enzymes to create much more concentrated flavors than are

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present in the natural dairy product. The enzymes break down the fats and proteins present to yield higher concentrations of the flavor compounds that represent the flavors of these dairy products. Some of the components of dairy flavors are short chain fatty acids including butyric acid that are unpleasant at high concentrations but help to contribute to the characteristic flavor of dairy products. Many flavors are produced by processing, primarily with the use of heat. The subject of browning will be covered in more detail later in this chapter but will be briefly addressed here. Flavors can be created by heating one or more reducing sugars with one or more amino acids for different times and at different temperatures. Very different flavors can be produced which can be added to foods as natural flavors. Flavors can also be produced using biotechnology. This is an area that has been explored for years to determine ways to get plants or microorganisms to produce higher quantities of flavoring materials than they do naturally. While there has been limited success by some companies to produce individual flavor compounds through this process, it has not achieved wide commercial success.

7.5

Flavor creation

While foods have their own inherent flavor, it is often desirable to add flavors that will either change or enhance the character of the product. In some cases, flavors are added to mask undesirable characteristics. It may be as simple as adding salt and pepper but is often much more complex. Not every chemical compound that has aroma can be used when creating flavors. As mentioned above, each country has its own regulations as to what can be used in a flavor. While definitions of types of flavors for the US are in the CFR, the individual chemicals that can be used in flavors are in the Flavor Extract and Manufacturers' Association Generally Recognized As Safe (FEMA GRAS) list. The first list was published in 1960 based on the flavoring materials in use at the time (Hall, 1960). The publication of the list was in response to the 1958 Food Additives Amendment to the Federal Food, Drug and Cosmetic Act ± Public Law 85-929,72 Stat. 1784 (1958). There was a provision in that law that exempted from food additive status those substances `generally recognized, among experts qualified by scientific training and experience to evaluate its safety, as having been adequately shown through scientific procedures . . . to be safe under the conditions of its intended use.' Since that time, the different classifications of compounds have been reviewed to confirm their safety and there is ongoing review. Some materials have been de-listed as data have become available, indicating that they are not safe to consume. Other materials have been added to the list. To get a chemical compound added to the list, information must be submitted with appropriate toxicology data to show that the material is safe for consumption at the intended

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usage level. In addition to the FEMA GRAS list, people creating flavors can also use natural extracts of plants and spices and flavoring materials produced through the use of enzymes or processing. It should be noted that there are compounds naturally occurring in foods that are not on the FEMA GRAS list so cannot be added individually to products but can be included if they are present in a natural extract. People who work in flavor creation develop materials that can be added to foods to bring out a certain characteristic or to modify the flavor. As an example, a beef flavor may be added to an entreÂe to give it a stronger, more desirable flavor or to give it the flavor of having been grilled. Developing flavors is an iterative process in which a flavor is created by combining a number of different chemicals that, based on the experience of the person and published reports, will give the desired flavor. The flavor is tried in the product and often has to be modified until the right characteristics are achieved. Creating flavors for microwave food products presents an additional challenge in that the food is heated prior to consumption and this impacts the flavor that has been added.

7.6

Microwave versus conventional heating

There are several major factors that impact the flavor quality of microwave food products. They primarily stem from the fact that in a conventional oven, the product is surrounded by hot air which heats the product from the outside and also dries the surface. In microwave heating, the entire product is heated at the same time but the heating may not be uniform (van Eijk, 1994). In drying the surface, it helps to reduce the rate at which volatile flavor molecules can move from inside the product to the surface and evaporate. It in a sense forms a crust that is more difficult for the flavor molecules to move through. In microwave heated products, the surface stays moist and cooler, which readily allows flavor compounds to be carried out of the food as steam is lost. The surface of the product will also get to a higher temperature in a conventional oven. This enhances the rate of the browning reaction on the surface as this reaction goes more rapidly under lower moisture and higher temperature conditions. The browning reaction provides not only the desirable brown color but also produces a large number of flavor compounds. In conventionally heated products, the added flavor is retained better and a large number of flavors are produced on the browned surface of the product. In products where browning is not expected, this is not an issue. If a product is simply to be reheated, the microwave does an excellent job as you are not relying on it to produce flavor. One additional factor that influences flavor development in products heated in the microwave is that they are in the oven for a much shorter period of time than those cooked in a conventional oven. The browning reaction takes time to develop and the product is not heated long enough for this reaction to proceed to the point where brown pigments and flavor compounds are produced.

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It should be noted that there are a wide variety of products where the time and temperature of heating do not create an issue for flavor development. Highmoisture products that are going to be reheated work very well. While some flavor will be lost during the heating process, it does not vary significantly from conventional reheating. Vegetables, with their own inherent flavor, can easily be steamed in the microwave oven.

7.7

Flavor forms

Most flavors are primarily oil soluble, although many have some solubility in water. Almost all flavor compounds are liquid at room temperature. Flavors that are added to foods can be in either the liquid or dry form. For liquid flavors, the mixture of flavor compounds is generally added to some liquid carrier. This aids in the solubility of the compounds so that the flavor is a uniform mixture and also helps in terms of mixing the flavor into a food as it creates a larger quantity that is easier to mix. For flavors that are referred to as oil soluble, the flavor compounds are incorporated into oil. One common type of oil that has been used is soybean oil, although any oil can be used. It is important to use oil that is stable to oxidation. If the oil starts to oxidize, it will negatively impact the flavor. Flavors that go into primarily water-based foods are referred to as water soluble. For these, the flavor compounds are added to a material that is either soluble or miscible in water such as ethanol or propylene glycol. The flavor compounds themselves are not converted into water-soluble materials. Dry flavoring materials can be produced in a number of different ways. The simplest method is plating. The flavor materials are blended with a dry carrier and coat the surface of the carrier. Some carriers are salt, sugar, maltodextrins and silicon dioxide. Any dry, particulate matter can be used as long as it is approved for use in foods. Flavors that are plated are dry but the process does not protect the flavoring material from volatilization when it is heated. Encapsulation can also be used to produce dry flavoring materials. The main advantages of encapsulation are protection from the atmosphere, which can cause deterioration, protection from volatilization and protection from other ingredients both in the flavor and in the food product. The primary process that is used in the flavor industry is spray drying. The typical carriers are maltodextrins, modified starches and gum acacia. Detailed information about spray drying and other encapsulation techniques can be found in an article by Dzieak (1988). The process produces a fine powder with the flavor molecules entrapped in the dry matrix. As long as the material stays in the dry state, it provides excellent protection for the flavors. Once it is exposed to any moisture, the water-soluble carriers start to dissolve and release the flavor. For this reason, this method of encapsulation does not provide any real benefits for most microwave food products as they are high in moisture and as soon as the flavors are added to the product during manufacture, they will release. One specific product where

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spray dried flavors can be advantageous is microwave popcorn. This will be discussed in more detail later in this chapter. There are many other encapsulation techniques that have found limited application in the food industry. These include coacervation, spray chilling, extrusion and molecular inclusion. These techniques tend to have very specific applications and are often for certain types of flavors. Extrusion is useful for mint and citrus oils as the process uses a fairly high temperature which can cause deterioration of more volatile flavors. Most of these have the same drawback as spray dried flavors and that is they release when exposed to moisture. Coacervation and variations of that technique which can use gelatin can provide somewhat better protection. The industry continues to research techniques that are cost effective and provide good protection not only during production of the food but also during microwave heating. Molecular inclusion is typically accomplished through the use of cyclodextins. These are molecules that consist of six, seven or eight glucose units that are connected together in a circle (alpha, beta and gamma cyclodextrin, respectively). In this type of encapsulation, you have a one on one complex of a cyclodextrin with a flavor molecule. There are some issues with this as some molecules will complex more easily than others and some will complex so well that it is difficult to get them to release. Reineccius et al. (2004) reported that while cyclodextrins could help retain flavors in heated foods, there were problems with the release of the flavors upon consumption. The use of cyclodextrins can be for targeted compounds that are problematic and are not well retained by other means of encapsulation. Another method that can be used to protect flavors is to put a secondary coating onto a dried particle. One effective coating is a high melt fat. This will protect a dried flavor from moisture so that the flavor does not release until the product gets to a high enough temperature to melt the fat and then release the flavor. The melt point of the fat can be altered by changing the level of saturation in the fat. A fully hardened vegetable oil will not melt until it reaches approximately 60 ëC. The only issue to be concerned with in these systems is that too much high-melt fat can cause a coating on the tongue that some people find objectionable. The fat solidifies at temperatures higher than body temperature and will solidify on the tongue and inside of the mouth when consumed, leaving a waxy coating. These products with a fat coating find application not only in the microwave food category but generally in any foods that are to be heated where there is a desire for further protection of the flavor.

7.8

Browning reaction

One of the other challenges with microwave food products that is associated with the overall flavor of a product is the color of that product. One of the primary reactions that occurs when foods are cooked is a browning reaction. A nicely browned bread crust or the browned surface on a steak is desirable to the

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consumer. Not only is the brown color appealing, but in addition to the color that is produced, there are also a number of flavor compounds produced that enhance the flavor of the product. This reaction is known as non-enzymatic or Maillard browning. One major challenge in heating products in a microwave oven is that this reaction does not occur to any great extent because of the low surface temperature and moistness of the surface, leaving products pale in color and lacking in flavor. The pale color can give the impression that the product is not fully cooked. The Maillard browning reaction is the most important and most challenging for microwave food products; however, there are other browning reactions that could have an impact on microwave products. There are other reactions that occur in foods which also result in browning of the product. These other reactions will be addressed briefly as they can be important for some products and have important considerations in product development. Two of these reactions are enzymatic browning and caramelization. In some cases, the reactions are desirable and yield both colors and flavors that enhance a product. In other cases, the reactions are undesirable and cause loss of quality of the product.

7.8.1

Enzymatic browning

The first of these is caused by enzymes (polyphenoloxidases) that are released when cellular disruption occurs in some varieties of fresh fruit, vegetables or other plant material. This disruption can be caused by cutting, freezing, bruising or disease. A typical example of enzymatic browning is the brown surface on cut apples. This renders the product undesirable and can cause a decrease in nutritional value. The actual mechanism of the reaction is not well understood; the reaction starts with the oxidation of phenols and proceeds through a number of stages to eventually produce brown pigments. In the processing of products for the microwave oven, this reaction needs to be taken into account to ensure that the ingredients do not develop the brown color prior to preparation. An example would be potatoes included in a soup or entreÂe. If the potatoes are not processed rapidly, they will develop the undesirable brown color. Enzymatic browning can easily be inhibited by heat inactivation of the enzymes. Blanching the product in steam or hot water will accomplish this. Another commercial treatment that is used is sulfur dioxide or sulfites which will also inhibit the enzymes. It should be noted that enzymatic browning is the desirable reaction occurring in the production of coffee, tea and cocoa. An extensive summary of enzymatic browning is included in the Wiley Encyclopedia of Food Science and Technology (Francis, 2000).

7.8.2

Caramelization

Caramelization is another reaction resulting in both flavor and brown pigments. This involves only sugars that initially melt when heated and then go through a

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further series of reactions. At temperatures ranging from 110 to 160 ëC, different sugars break down, resulting in the loss of water. The next stage is a condensation reaction between these individual sugar molecules. The reaction continues, to eventually form melanins that are brown in color. There are also compounds of lower molecular weight formed which contribute to the flavor of a product. As with enzymatic browning, the complete mechanism is not well understood. The one main microwave product where this reaction can play a role is in caramel corn. The caramel coating that is used on ready to eat caramel corn is a mixture of primarily sugars and butter. Both brown sugar and glucose can be used. The mixture is heated to drive off water and crack or break the sugars. The creation of flavors and brown pigments is produced both by caramelization and by the Maillard reaction in which protein reacts with the reducing sugars present. Any of the sugar mixture that is on kernels of corn will not get to a high enough temperature for the reaction to occur as the bag is filled with steam. The product may have some sugar coating but it will not be brown. The two to three minutes of popping time is not long enough for either type of browning reaction to occur on the corn itself. The other issue is that the package contains a microwave susceptor. When this heats to the typical temperatures of 180±200 ëC, any sugar in contact with the susceptor will burn. So the product ends up with a combination of some of the sugar burned on the susceptor and the rest not heated enough to cause browning and flavor formation. There have been a number of attempts at making a pop in the bag caramel corn. Some of these products were very good if the popcorn was removed from the microwave oven at exactly the right time. A term that is sometimes used for microwave products is the `doneness window'. This is the time between when the product is fully cooked and acceptable to a point where it is no longer acceptable to the consumer due to overcooking. With the variability of microwave ovens, a doneness window of only a few seconds is too close for the consumer, particularly when they cannot see the reaction occurring to know when to stop the heating of the product. Most of these products have suffered from too small a doneness window, resulting in either a product that was severely undercooked or burned. The products that have been successful use smaller amounts of sugar and high-intensity sweeteners to produce a sweet product. The products do not develop a heavy coating of caramel. This is a challenge that remains to determine how to get the sugars to brown and coat the corn without burning.

7.8.3

Maillard browning

The Maillard browning reaction is the most important and challenging for microwave products. The reaction came by its name from the French chemist Louis-Camille Maillard, who in 1912 observed the formation of pigments in reactions between sugars and amino acids when heated in solution even though

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the reaction was first recognized by an Englishman named Ling (1908). In 1953, J. E. Hodge published a paper entitled `Chemistry of browning reactions in model systems' (Hodge, 1953). In this paper, he laid out a complex series of reactions that is considered to be the Maillard reaction. It is referred to as the Hodge Scheme and is one of the most referenced works in food science. People have continued to study this important reaction and its impact on different food products. It has been the topic of books and symposia over the years. In 1988, a symposium entitled Thermal Generation of Aromas was held. The proceedings were published in 1994 (Parliment et al., 1994a). The book contains a general overview of flavors produced through heating and many specific studies on different systems and the flavors that are produced. When there was great interest in microwave products in the late 1980s and early 1990s, a symposium entitled Thermally Generated Flavors: Maillard, Microwave and Extrusion Processes was held in Washington, DC. The proceedings were published in 1994 (Parliment et al., 1994b). The contributors explored a wide variety of systems and reactions to better understand how flavors are produced through the use of heat. Whorton and Reineccius (1994) studied conventionally and microwave baked cakes to determine the flavor differences. While good texture can be developed in baked goods prepared in the microwave oven, the lack of browning results in lack of flavor formation that is typical of products baked conventionally. The types of compounds that were lacking were ones with nutty, brown and caramel-like aromas. There were also higher levels of green vegetable notes which are found in unbaked cake batter. Steinke et al. (1994) commented that the low temperature on the surface of food products and the high water activity minimizes flavor, color and texture development. In simple terms, the initial reaction is between a reducing sugar and either a free amino acid or the amino group of an amino acid in a peptide or protein. The first step of this reaction is reversible but once it goes beyond the initial step, it proceeds in a complex manner and cannot go back to the original sugar and amino acid. From this initial reaction, a continuing series of reactions occurs that create not only brown pigments but also a wide variety of flavor compounds. Once the reaction sequence starts, it follows a number of different pathways to create a wide variety of chemical compounds. Some of these are low molecular weight compounds which give flavor to the product while others have much higher molecular weights and give varying degrees of brown color. There are many factors which impact both the flavors that are formed and the amount of browning that occurs. These include the type of sugar or sugars, the amino acids involved, pH, temperature and water activity. One other important factor is that time is involved. Longer reaction time results in more color being produced and a continually changing flavor profile. As discussed earlier, there are two major issues that prevent microwave food products from browning. First is that the products are heated for a short period of

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time, so that the reaction does not have time to proceed beyond the initial stages. Second is that the surface of the product does not get to a temperature high enough for the reaction to proceed. Unlike cooking in a conventional oven, in a frying pan, on a grill or in a deep-fat fryer, there is nothing in the microwave oven that creates a high temperature surrounding the product. In the microwave, as moisture is lost, there is essentially evaporative cooling on the surface of the product.

7.8.4

Solutions

In development of microwave products, the lack of the browning reaction must be addressed from both a flavor and a color standpoint. The conditions are not conducive to the actual reaction taking place to give both flavor and color. The two challenges can be addressed in different manners. For color development, there are two main approaches. One has been to use packaging materials (microwave susceptors) that heat to temperatures high enough to create surface drying and browning. The susceptor does more to insure crispness on the surface than to get browning to occur in a completely uncooked product. Products such as French fries or fried fish that have been parfried and are already light brown will undergo some additional browning. Products that have not been cooked at all will develop some brown color where they are in direct contact with the susceptor but not to the extent that they would in conventional heating. The addition of a susceptor can solve only part of the problem and in some cases such as a product with an uneven surface or a crust on the top where it is difficult to design a package to have direct contact with that surface, browning agents have been developed. One particular product that was developed in the early 1990s was MailloseTM (from Red Arrow International, Manitowoc, WI) which is a sugar derivative from caramelization. This product provides a head start to the browning reaction as the Maillose will more readily react with the proteins present in the food product. It can be sprayed on the surface as a liquid, dusted on as a dry powder, or incorporated into the product. When heated, it will rapidly react with the proteins in the product to produce brown colors and flavors. The degree of browning can be controlled by the amount of the product that is used. Red Arrow now offers a range of browning agents that can be adapted to various needs. The use of a browning agent can help consumer perception but the flavors associated with the reaction also need to be incorporated in the product. Some people have tried using precursors such as adding individual sugars and specific amino acids to the formulation. This has not been very successful as the heating time in the microwave oven is too short for the reaction to proceed to the desired end products. The main effort has been to create flavors that replicate those produced in a browned food. The flavors produced by browning reactions have

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nutty, meaty, caramel, toasted, burnt, floral and plant aromas. Many of the compounds have ring structures. Some of the simple compounds are pyrazine, pyridine, furan, thiophene, pyrrole and thiazole. These basic ring structures can have many different groups attached to the ring to give the broad array of flavors. The flavors to be added to microwave food products can be produced in different ways. One is to mix individual compounds that have the toasted or other browned characteristic desired. More commonly, the flavors are produced as reaction or process flavors. The flavors can be made using only a sugar and amino acid or combinations of them. It takes experience to know what amino acids and sugars will give the desired results. While there are some publications that detail the results of heating simple model systems, most of the people who work in the area keep their information proprietary. Process flavors can also have a source of sulfur added which will help to produce some of the sulfurcontaining flavor compounds that have typical toasted or browned aromas. Fats can also be added. The breakdown products from fats such as free fatty acids will contribute flavor. They will also react with compounds that are formed as the Maillard reaction progresses. In addition to varying the amino acids and sugars, the flavor profile can be altered by changing the time and temperature of heating. Higher temperatures and longer times will yield more intense flavors. While the reactions can be carried out at atmospheric pressure, they can also be carried out in pressurized vessels to shorten the time needed and to produce stronger flavors. The flavors produced in this manner can be used as liquids or can be dried. It will depend on how they are to be incorporated into the finished product and what form will be easiest to use. If these flavors are mixed into the product, the flavor will be distributed throughout the product, whereas in conventional heating, the flavor is concentrated on the surface of the food. This can create a difference in perception. While there are many good flavors that can replicate the aroma of a fried, browned or grilled product, the overall perception by the consumer is not just of the flavor or color but of the entire product, which includes the texture. A combination of adding desired flavors to a product and finding a means to create brown color on the surface is essential to developing products for the microwave oven. These products need to replicate products that brown while being conventionally cooked.

7.9

Product categories and challenges

Different product categories have different flavor challenges when heated in a microwave oven. As mentioned earlier, some categories are very similar to conventionally heated products in that they are fully prepared and cooked and simply need to be reheated. Many of these foods are seasoned primarily with

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spices, which hold up well under reheating conditions. In high-moisture foods, there is no concern with burning of the spice. Most of the volatile components are trapped inside the cellular structure of the spice particles and tend to be less volatile. The foods do produce a good aroma while heating but retain a significant amount of flavor. For these products, the main challenge is to get a good seasoning blend to give the desired flavor profile. Flavors can be added in addition to spices. These flavors will enhance the flavor of the food and the spices added. The flavors need to survive during production and storage of the food. This is a challenge no matter how the finished product is to be cooked or reheated. In some ways, microwave heating can be gentler than cooking on a stovetop or in a conventional oven for soups, sauces and entreÂes as the cooking time is shorter and there is less time for the volatile flavor components to be lost. Chemically leavened breads and cakes have been tried for the microwave oven. With the rapid cooking time, there is no time for browning of the surface and significant lack of the fresh baked flavor. In addition, the flavors will steam distill out of the product during heating. This is an application where a flavor that has been spray dried or plated and then coated with a high-melt fat will be beneficial. The coating protects the flavor until the product reaches a high enough temperature to melt the fat and release that flavor. This is also an application where spices such as cinnamon or nutmeg would work better in flavoring the product than vanilla or lemon, which can be readily lost if not properly protected. Chocolate also works as it is a complex mixture of many different flavor compounds with no one compound having character impact. Many of the compounds in chocolate are less volatile and less likely to be lost. Cocoa can be used quite successfully to flavor baked products. Pieces of dried fruit could also be added to supplement the flavor of the product. The other issue with baked products in the microwave is getting the proper texture with a short cooking time. The product shape and size need to be such that it will evenly heat to be completely baked. Other dough products that can be made either from a pre-cooked crust or parbaked crust do not tend to have flavor issues for the crust itself but more for the product as a whole. One good example of this is pizza. Some of the early introductions into the market used a crust that had been fried to give it crispness and flavor. Most products today use a par-baked crust and a microwave susceptor package to help the browning and crisping of the crust. The susceptor, which is discussed in more detail, will heat in the microwave to temperatures often over 200 ëC and will aid in both crisping and browning to help the texture and flavor. With a microwave pizza, there are a number of factors which need to be addressed to yield the desired finished product. Much of this has to do with product formulation, using the right blend of spices for seasoning the sauce and packaging to help provide for uniform heating of the entire product. It is also possible to add a dough flavor either as an oil-soluble or encapsulated flavor to enhance the flavor of the crust. This is an excellent example of needing product

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formulation, processing and packaging to all work together to make the final product work. Simply adding good spices to the sauce and creating a good crust flavor will not give the consumer the experience they desire. Another dough-containing product is a pot pie. In this, a crust can be put either on top of the product or both under the product and on top. Again, this is more of a product formulation issue to get the right texture. Flavor can be added to enhance the flavor of the crust. The filling is typically a stew mixture where the flavors come from a combination of the sauce and the meat and vegetables that are added. A chicken flavor that is made through the reaction process may be added to a chicken product or a beef flavor may be added to a beef product to improve the flavor. Similar flavors can be used whether the final product is to be reconstituted in a microwave or conventional oven. Dough enrobed products fall into a similar category. Many of these handheld sandwiches are designed to be heated in the microwave oven. The filling has to have a good flavor but the challenge in the microwave is to have the crust at least slightly browned and crispy. In most cases, the packaging can play a major role in making these products deliver to the consumer. Any products that have been either fried or par-fried are not easy to reconstitute in the microwave oven. While the flavor of these products is from both the base product such as fish or potatoes, there is also the flavor that is developed during frying from both the oil and from surface browning. These flavors are retained during microwave heating; however, the surface of the product does not remain crisp and this lack of crispness impacts flavor perception. A soggy product does not come across with a good fried flavor due to the negative impact of the texture. There are ways to maintain or enhance crispness and create some additional browning through the use of packaging materials. A microwave susceptor similar to what is used for microwave pizzas can be used to help the surface of products to brown and crisp. One of the biggest challenges for flavors being used in a microwave product is popcorn. The two major issues are that the popcorn produces a tremendous amount of steam during the popping process and the product uses a susceptor in the face of the package which rests on the oven floor to provide additional heat to achieve good popping performance. If you calculate the amount of moisture lost by the popcorn during popping of a 100 g bag that has about 70 g of corn in it, the resulting volume of steam produced will fill the bag over six times. The steam being produced continually escapes from the vent at the end of the bag and carries with it the volatile flavor materials. This does produce what can be a wonderful aroma in the area in which the product is being popped. It can also result in the flavor being lost to the outside environment and nothing left in the product. Butter flavors will volatilize so that a good aroma is created but there is sufficient flavor that remains on the product to give it a good final flavor for the consumer. Encapsulated butter flavors will be retained during processing of the product and will help to better retain the flavor during popping. Encapsulation

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does add a cost and this has to be weighed against the possibility of adding a little extra flavor during production, knowing that a little more may be lost during popping. Cheese flavor is a particularly difficult flavor to produce with microwave popcorn. The components that give a good cheese flavor have a strong, unpleasant aroma in their concentrated form. When these volatilize during popping, it creates a strong aroma that is not pleasant to smell. The volatilization occurs to the extent that often little flavor is left on the product. Dried cheese powders have excellent flavor characteristics but will burn when combined in the product before popping. If the powder is sprinkled on after popping, it gives an excellent product but does not have the convenience that many consumers desire. There are cheese products on the market that deliver a mild, buttery cheese flavor. This is an area where companies continue to work to get a flavor that will survive in the microwave without giving off an unpleasant aroma. Other seasonings face similar challenges in that if the solids content is too high, the seasonings will scorch. It has been found that levels above about 1% will start to produce scorching that is noticeable on the finished product. Beverages can also be prepared to be heated in a microwave oven. Again, the flavor is inherent in the beverage and it is simply to be reheated so it is not exposed to intense heat that will drive off the flavors that are present. The larger challenge is to formulate beverages that have good flavor and that will retain their flavor during the shelf-life of the product. This is not a large category for microwave products although one large use of the microwave oven is often said to be to reheat coffee. Coffee is best when fresh brewed and any type of reheating does not produce a fresh cup of coffee. The microwave is simply a quick and convenient way to reheat it. For beverages such as tea, the microwave can be used to heat the water to brew a cup of tea. It is important to get the water hot enough so that it will extract the desirable flavors from the tea leaves.

7.10

Conclusions

There are many good flavored microwave products on the market. There are ongoing challenges to create better flavors in some products. The combination of lack of surface heating and browning makes it difficult to produce flavors similar to those produced when products are heated in an oven and are meant to be brown and crisp. For products that are simply seasoned and reheated, the microwave does not present significant challenges that are different from conventional heating. Microwave popcorn is an ongoing challenge to create a good flavor that will not all be volatilized during heating. Encapsulation can provide a benefit in protecting the flavor during processing and helping to retain it during the popping process. As work continues to better understand flavors, there will be new developments that will benefit microwave food products.

Flavors and colors for microwave foods

7.11

191

References

Code of Federal Regulations (2008). Title 21, Vol. 2, US Government Printing Office, Washington, DC. Dzieak, J. (1988). `Microencapsulation and encapsulated food ingredients', Food Technology 42(4), 136±147. Francis, F.J. (2000). Encyclopedia of Food Science and Technology, 2nd edn, John Wiley and Sons, Inc., New York, Vol. 1: 208. Hall, R.L. (1960). `Recent progress in the consideration of flavoring ingredients under the Food Additives Amendment', Food Technol. 14, 488±495. Hodge, J.E. (1953). `Chemistry of browning reactions in model systems', J. Ag. Food Chem. 1(15), 928±943. Parliment, T.H., McGorrin, R.J. and Ho, C-T. (1994a). Thermal Generation of Aromas, American Chemical Society, Washington, DC. Parliment, T.H., Morello, M.J. and McGorrin, R.J. (1994b). Thermally Generated Flavors: Maillard, Microwave and Extrusion Processes, American Chemical Society, Washington, DC. Reineccius, T.A., Reineccius, G.A. and Peppard, T.L. (2004). `Utilization of cyclodextrin for improved flavor retention in thermally processed foods', J. Food Sci., 69(1), pp. 58±62. Steinke, J.A., Frick, C.M., Gallagher, J.A. and Strassburger, K.J. (1994). In Thermally Generated Flavors: Maillard, Microwave and Extrusion Processes, ed. by Parliment, T.H, Morello, M.J. and McGorrin, R.J., American Chemical Society, Washington, DC, p. 519. TNO Nutrition and Food Research Institute and Boelens, M.H., eds. (2000). VCF 2000 ± Volatile Compounds in Food Database, BACIS, Huizen, The Netherlands. van Eijk, T. (1994). In Thermally Generated Flavors: Maillard, Microwave and Extrusion Processes, ed. by Parliment, T.H., Morello, M.J. and McGorrin, R.J., American Chemical Society, Washington, DC, pp. 395±404. Whorton, C. and Reineccius, G.A. (1994). In Thermally Generated Flavors: Maillard, Microwave and Extrusion Processes, ed. by Parliment, T.H, Morello, M.J. and McGorrin, R.J., American Chemical Society, Washignton, DC, p. 526.

8

Rigid passive microwave packaging forms A J G A L L O , Associated Packaging Technologies, USA

Abstract: While active packaging can provide dramatic results, not all products require this technology and perform well with designs or passive microwave packaging. Understanding the specific conditions of use for the product life cycle, including production, distribution, storage and reconstitution will allow designers to choose materials that facilitate design. Proper designs can improve product performance during microwave cooking. Key words: condition of use, geometry, elevation, steaming, distribution.

8.1

Introduction

Historically the primary purpose of packaging is to protect the product from the point of production, through the distribution cycle to the end customer use. As we move from antiquity and the ceramic jars through the Napoleonic era and the first cans to the modern time and active packaging, the demands on packaging continue to grow. Through this change containment and protection remained constant but now packages are called to aid in marketing the product, informing the consumer and improving quality all while being mindful to the environment. With the advent of microwave ovens improving product performance during cooking became increasingly challenging. One could argue that initially product quality decreased with reconstitution from the microwave. However, as the quest for convenient cooking drove the penetration rate of microwaves in the home higher and higher, packaging technology continues to keep pace with an increase in active packaging design specifically for microwave cooking. While active packaging can provide dramatic results not all products require this technology and perform well with designs or passive microwave packaging. With each product engineers need to ask what the specific demands are for this product/package system. Based on these requirements and demands the package can be tailored to the application.

8.2

Conditions of use

8.2.1

Conventional, microwave only or dual ovenable

In the food industry condition of use, or how the product will be re-heated or cooked, is a critical driver for material choice and design. Products such as

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candy may only need containment and protection through the life cycle. Recent advances to these packages include improved barriers, dispensing features and reclosing features. However, other products such as food require containment, cooking and serving. For the purposes of this chapter I will focus on foods, specifically those that require reheating or cooking. The different cooking methods have different stresses to the package and greatly affect the material choices. Conventional ovens work by heating a chamber which holds the product. The product in this chamber equilibrates to the temperature of the oven chamber through conductive heating, thereby re-heating or cooking the product. More generically conventional ovens have come to include a variety of cooking methods: convection ± where forced hot air helps heat the product; impingement ± where steam or moist air is induced in the chamber to heat without drying products; radiant ± electric heaters or gas flame to generate the heat. All these methods heat the products though conduction from the outside; meaning the center of the product is the last part to heat up. In essence the common use of the word conventional has come to mean anything but microwave cooking. The significance of conventional ovens is the severity of the heat which can range from 48 ëC for warming products to over 260 ëC for cooking raw whole muscle cuts. These elevated temperatures eliminate materials whose flashpoint or melt points are below the temperature conditions to which the product/package system will be exposed. Microwave ovens cook differently from conventional ovens. As explained in Chapter 1, microwave oven heat uses the dielectric properties of the food to reheat or cook the food. The food, placed in a chamber, is exposed to microwave radiation which excites the polarized molecules in the food. This excitation generates the heat to cook the product. Since the microwave energy targets polar molecules, the air within the oven chamber does not directly heat up (the air is warmed owing to the conduction of the heated product to the air, however this is negligible). Packaging materials can absorb, transmit or reflect the microwave energy. Certain materials, such as thick foils, reflect microwave energy, therefore effectively shielding the product from the microwave energy and, unless used in active packages (described further in Chapters 9 and 10), reduce the overall effectiveness of microwave cooking. Since the overall temperature of the oven is less severe than the conventional cooking process described above, the choice of materials is broadened. Some products are designed with both cooking methods in mind and thus dual ovenable product/package systems can go in a conventional oven or microwave oven. These systems tend to be more rigorous since they need to perform in the extremes. Dual ovenability reduces material options for the designer.

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8.2.2

197

Distribution: frozen/chilled/shelf stable

The conditions of use described above can be expanded to include the method of distribution. How a product is produced by brand owners, shipped to market and stored by the consumer prior to use are other factors in the material choice. The three most common methods are frozen, chilled and shelf stable. Based on the region of the world the product is designed for, one of these, or a hybrid of these systems, will be the dominant system. Certain materials perform better in frozen temperatures while others are better suited for ambient conditions. Frozen distribution covers a wide range of temperatures. Truck distribution ranges from ÿ17 ëC to ÿ12 ëC; however, initial freezing of the product can be as low as ÿ40 ëC in mechanical freezing to ÿ196 ëC for nitrogen freezing. Temperatures in retail freezers tend to increase owing to customer traffic and doors opening and closing. Storage temperatures in the end consumers' freezers vary widely, based on how the freezers are set. With the extreme low temperatures, material choices become more difficult. Embrittlement of the material at these low temperatures can create damage and loss of product. As the product moves through the distribution system and the product moves further from the production site, the producer has less control of the handling conditions. Potential damage increases as the distribution cycle and handling increases. As described by the Chilled Food Association, `Chilled foods, for reasons of safety or quality, are designed to be stored at refrigeration temperatures (at or below 8 ëC, targeting 5 ëC) throughout their entire life' (www.chilledfood.org/ MEDIA/POSITION+STATEMENTS/temperature.htm), while the stringent temperature requirements are needed to ensure safe, quality foods, package material options increase due to the relatively low temperature range when compared with frozen distribution. A modification of the true chilled distribution is shipping the product frozen but displaying on the retail shelf in the chilled environment. In cases such as these, the package must be designed for the more severe environment. Unlike the frozen or chilled distribution systems, shelf stable distribution can be less severe. Examples of products in the shelf stable distribution system would be retort cans and trays, modified atmosphere trays and dry goods. While the process to make these products can be fairly intense, as in the case of retort processing, the distribution requires no special temperature handling of the product in the distribution system.

8.3

Operations

8.3.1

Manual/semi-automated/automated

How the product is processed ± the operations the trays are exposed to during production ± is on par with the conditions of use in determining the design of the tray. The breadth of manufactures in the food industry range from completely

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manual to highly automated, from less than five meals per minute to more than five meals per second. As the production line becomes more complex with automation and line speeds increasing, package design and consistency become more critical to a successful operation. Denesting, the process of taking one tray out of a stack of trays and preparing to fill this tray, is the first step in the filling process. Critical dimensions for denesting are trim length, width and separation. Manual denesting is more flexile and can accept greater variation in these critical dimensions than semiautomated or fully automated denesting. Both the stack height and stack gap are important parts of semi- and full automated tray denesting. The sack height is the vertical distance from the bottom of one flange to the bottom of the next flange in the stack. The gap is the vertical distance between the top of the flange of the first tray to the bottom of the next tray (see Fig. 8.1). Note the terminology for trays with rolled flanges is slightly different but the concept is the same. Semi and fully automated denesters can have rotating screws, oscillating separating blades or vacuum cups to pull one tray out of a stack at a time. The consistency of the stack gap can be ensured through various tray design features including, but not limited to, full rings, lugs, sidewall interference, etc. Similarly, throughout the process the semi- and fully automated lines require more critical designs to ensure success. This is true for product filling, conveyor transfer points and carton feeding. Certain lines use the tray flange to push the

8.1 Stack view of two trays.

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tray through transfer point; other lines use belts along the side of the trays. Carton feeding is accomplished with pushing arms against the end of the tray and tray location (for filling) is managed with rails along the side of the tray. All aspects of the production line directly affect the design of the tray. These need to be taken into account during the design phase of the process.

8.3.2

Film sealed/flow wrapped/non-sealed

Trays may be exposed to film lid stocks based on the product and method of reconstitution. Although this is definitely part of the process, sealing deserves additional mention. Quality of the seal to the tray can define the package. With retort, pasteurized and modified atmosphere packages, poor seals will cause product failures and could end the brand. With some of the new film technologies that allow for steam cooking of the product, strong seals through distribution and cooking are required but once cooking is complete the consumer wants an easy peel. Similarly, chilled products need seals strong enough to contain the product through distribution but easy to peal upon reheating. To obtain these nuances tray materials need to be compatible with the sealants on the film. Less critical are applications where there is no film seal directly to the package. Over-wraps, where the film completely covers the tray and product and is sealed to itself is a good example of this. Another example is friction fit lids with tamper-evident bands securing the lid to the tray. While dimensional accuracy is important for these applications, chemical compatibility is not critical.

8.4

Application drives material choice/material choice drives design

Since the primary purpose of the package is protection and containment, conditions of use both through the distribution system as well as the reconstitution method drive the material choice at the design phase. Specifying high-density polyethylene, with a melting point of 120±130 ëC, for a tray which is destined for conventional oven reconstitution will result in product failure and most likely a complaint from the consumer. In the design process material properties must meet or exceed the conditions of use requirements through the life of the product. Alternatively, pressed paperboard trays, food grade paperboard with polyethylene terephthalate (PET) laminated or extrusion coated to the paperboard, which can withstand temperatures in excess of 204 ëC, would be sufficient for conventional oven reconstitution. Just as certain materials are better suited for one form of reconstitution than others so some materials are better suited for one distribution method over another. While aluminum does not break in extremely low temperature, non-

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modified polypropylene can fracture at the same low temperature. Conversely, the aluminum will shield microwave energy in microwave reconstitution but the polypropylene is transparent to the energy. There are trade-offs when choosing the material based on the overall condition. The material selection is important because the different materials have different forming technologies and capabilities. All materials have certain forming limitations; pressed paperboard is limited in the minimum bottom radius of the tray as well as the maximum steep sidewalls that can be formed with this material. The minimum radius and sidewall angle tend to be greater than those obtained with thermoform plastics, which can be formed with tighter radii and steeper sidewalls. However, pressed paperboard will not break in frozen temperatures so the seal flange can remain flat; polymers, which are susceptible to frozen damage, use return flanges (or turned down flanges) to help reduce the shock during frozen impact. Design of the tray will also be predicated on the product to be packaged. Although chicken with rice may or may not be put in a two compartment tray, packing a single serve portion of soups or stews in a compartmentalized tray would be ludicrous. It is intuitive that single compartment trays are easier to form than multi-compartment trays; what is not intuitive is that different materials have unique forming capabilities and requirements. If molded fiber can form sidewall angles at 10ë, you will need a certain amount of space to create a two compartment tray. If crystallized PET can form the same compartments using 7ë sidewall angle, the same product can pre packaged in a smaller overall footprint. This can be advantageous when designing to maximize pallet efficiencies. Packaging is not shielded from the ever-increasing importance of operational efficiencies in today's competitive marketplace. Based on the expected operation package designs can be adjusted to improve efficiencies. Common external footprints of two trays can be identical to help eliminate changes to the production line while the internal shape can be tailored to meet individual product requirements. Criticality of dimensions to ensure high process efficiency will affect design of the package. So understanding the product, the distribution system, the desired reconstitution method and the operational requirements is critical in determining the proper material. Tray designs will be based in part on the material and the product.

8.5

Product

8.5.1

Effect of product density

Product density can be viewed in two ways: the physical product and how the product is packaged in a rigid tray. Physical density refers to the actual weight to area ratio of the product, which cannot readily be altered. Commonly this refers

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8.2 Isometric view of a bowl.

to pieces of protein (meat, poultry and fish) that are packaged in whole muscle, breast or filets. The specific densities of these items will affect the manner in which microwave energy is absorbed. Similarly, package density is the weight of the product vs. the area of the package. Unlike product densities, package density can be altered based on the geometry of the design. A 178 mm diameter bowl can hold a 280 g entreÂe; see Fig. 8.2. Likewise a 156 mm  115 mm  38 mm rectangular tray as seen in Fig. 8.3 can hold the same 280 g entreÂe. In this example the package density changes from 0.003 g/mm2 to 0.004 g/mm2. As expected the distance to the product center of these two examples is also different; 23 mm from the top for the bowl and 19 mm from the top for the rectangle. These distances are important as they relate to the penetration depth of microwave energy. Later we will look at how these differences affect the cook of the product. Product profile is similar in that a thick, dense filet of beef will cook differently than the same weight of thinly sliced medallions of beef. Understanding these effects is important; however, changing them may be difficult. Certain identities force certain shapes. Consumers view lasagne as a thick, multi-layer, rectangular shape. It may be hard to convince them lasagne can be served in a round bowl. Conversely, stew is traditionally served in a bowl; however, it is not a stretch to plate stew in a rectangular tray.

8.3 Isometric view of a rectangular tray.

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8.5.2

Packaging and products for use in microwave ovens

Dielectric effect

Earlier in this book the concept of the dielectric constant was covered. In basic terms microwave energy heats polar molecules by exciting these polar molecules, which attempt to realign within the alternating electric field. This rotation heats the product. Different products have different dielectric constants. Additionally, dielectric constants of foods can change as a product is heated from a solid to a liquid. How quickly or slowly products heat up can be used in determining the placement in a rigid tray. For instance in a multi-component meal placing the component with a high dielectric constant near the edge of the tray and centering the component with the lower dielectric will result in the edge of the product becoming super-heated while the center may still be frozen. This can be magnified when combining products with a low dielectric constant and a large penetration depth. Microwave performance can be altered through using the product dielectric in conjunction with tray geometry and product placement.

8.5.3

Effect of reconstitution method

Although reconstitution methods were addressed in Section 8.2.1, since steaming is a method of reconstitution that is driven by the product we will cover it here. Certain food products perform better when steamed. Steaming can be accomplished through film selection and tray design. There are several film technologies that are designed to hold steam from the cooking process in a tightly sealed rigid tray. Patented technologies revolve around how these films meter the release of the steam from the package. Some of the methods such as self-venting, micro-perforations and overlapped seams can be tailored to specific products. The type of film and method of steaming can be critical in material selection and design. Certain films require stronger seal strength to the tray which may require special coatings or lamination to obtain the desired performance. Steam channels, small relieves in the seal flange of the tray, may be required to get the optimal steaming performance. This is important to know during the material selection and design stage. France and Baker exemplify the usefulness of package design on the improvement of cooking and steaming in their patent US20070090103 AL dated 26 April 2007. In this patent a rigid tray with holes is suspended over another solid tray. Sauce and protein can be placed in the lower tray and products which microwave better through steaming can be placed in the tray with holes. As the combined package is heated the steam from the sauce and protein rises through the holes of the second tray and steam cook the product in the elevated tray. This unique design takes advantage of the product and package design to improve the performance and provide a quality product using passive cooking techniques.

Rigid passive microwave packaging forms

8.6

Tray geometry

8.6.1

Rounds, ovals and rectangles

203

Through understanding the conditions of use, operation and product, the designer can choose the material that is best suited for the application. Once the material is chosen then design can be refined to optimize the cooking performance. As stated earlier, the same product can perform differently in different shaped packages. In the following example the same 280 gram product was platted in a round bowl, a rectangular tray and an oval tray; Figs 8.2, 8.3 and 8.4 respectively. Using a FISOCommander Microwave Workstation the frozen meals were individually cooked on high for five minutes. Four fiber optic thermocouples were placed on the products to record the heating profile of the product. In Fig. 8.5 we can see the results of microwaving in the bowl. Notice the center of the product took the longest to heat while the temperature at the edge was up to serving temperature (74 ëC) for over a minute and a half before the center came up to temperature. We can compare the microwave performance of the bowl and the rectangle by comparing Figs 8.5 and 8.6. By comparing the graphs we can see the product in the rectangle took 20 seconds longer to come to serving temperature than the product cooked in the bowl. Further evaluation shows that the product at the edge of the rectangular tray was up to serving temperature over 2.5 minutes before the center came to temperature. Once again the product in the center of the tray took the longest to come up to temperature. Again we can compare the microwave performance of the product heated in the bowl to the product heated in an oval tray, Figs 8.5 and 8.7. Here we see the product cooked in the oval tray came up to serving temperature 12 seconds faster than the product cooked in the bowl and the center took over 2 minutes longer to cook than the outer edge. These examples demonstrate the variation in cook time that can be attributed to geometry of the primary package. It is important to note that speed to cook is not the only criterion when evaluating performance. One should also look at the temperature extremes and how long products are exposed to these extremes. Altering heating instructions can aid in evening the temperature range. In the example above stirring the product halfway through the cycle will reduce the

8.4 Isometric view of an oval tray.

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8.5 Graph of bowl heat profile.

8.6 Graph of rectangular tray heat profile.

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8.7 Graph of an oval tray heat profile.

range (note it is near impossible to replace the thermocouples in the same location once the product has been stirred, therefore this graphic is not shown). While stirring may be an option for a mixed product it may not be suited for a multi-component meal.

8.6.2

Elevation

Finally, elevation of the tray can improve the overall performance in the microwave. Microwave cooking is a combination of heating by electrically exciting the polar molecules and conduction of heat from areas of the product that are warm to areas that are not. When you place the package directly in the floor of the oven heat from the warming product actually warms the floor of the microwave via conduction. Elevating the package can create an air insulator between the package and the floor of the microwave oven. So rather than warming the oven floor the heat stays within the package.

8.6.3

Two piece

The use of two trays was described as it specifically related to steaming; however, multiple trays can also be used to differentially heat components. Here multi-component meals can be shipped in separate trays so they can be cooked for different times. These separate trays can be individually designed to optimize each component. The individual trays can then be assembled in a carton.

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Alternatively a multi-compartment tray can be designed so that different compartments can be separated via perforations or scoring. With this concept a hot meal can be delivered with a chilled or frozen dessert.

8.7

Conclusions

The premise of this chapter is that design of the primary package will affect the performance during cooking and reconstitution. However, design will be based on the material of choice, which is based on the conditions of use. During the design phase care should be taken to fully understand the overall condition of use for the package/product system, including production, distribution, storage and reconstitution. Coupling this understanding with the knowledge of the product, unique packaging can be designed to optimize the microwave cooking of specific food products.

9

Susceptors in microwave packaging

M R P E R R Y , General Mills, USA and R R L E N T Z , California Tube Laboratory, USA

Abstract: Susceptors convert microwave energy to thermal energy and are used in microwave ovens to crispen and brown foods. Special attention is given to the temperature limiting feature of the conventional thin metal film on polyethylene terephthalate (PET) susceptor. The critical roles of water management and thermal insulation in susceptor use are examined. The measurement of susceptor characteristics is also treated with emphasis on surface impedance. Alternative susceptors, e.g. printed and ferrite, are reviewed. Key words: susceptors, surface impedance, thin metal film.

9.1

Introduction

Susceptors convert microwave energy into thermal energy to promote preferential heating of food through contact and are intended to make food rapidly cooked in a microwave oven resemble the same food conventionally cooked especially with regard to browning and crispness. Susceptors can be categorized into three groups distinguished by their primary heating mechanisms: · Resistive ± heats by resistive loss in an electrically conductive film. · Dielectric ± high dielectric loss. · Magnetic ± primarily magnetic loss with some dielectric loss in material with low electrical conductivity.

9.2

History

The ultimate susceptor configuration used in food preparation is a balance between performance, cost and the consumers' expectations for ease of preparation and delivering product organoleptic attributes. Susceptors can be incorporated into nearly any package geometry and style including pads, pouches, trays, bowls, and cups. During conventional heating of food products in ovens (baking) or on the stovetop (frying) heat is transferred from the hotter surrounding environment and then through several heat and mass transfer mechanisms proceeds from the hotter exterior surface towards cooler product interior. Since the exterior of the

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food is above the boiling point of water, the common experience is that foods prepared in this way tend to have a browned surface that is drier and crisper than the interior. The browning reactions also create flavors unique to the heating method. These have become the defining attributes for many foods. While an effective way to heat foods, microwave heating differs markedly from conventional heating. In the microwave oven the air in the cavity is replaced with outside air several times per minute to prevent excessive condensation on the cavity walls. Although the air is warmed by the oven electronics before entering the cavity, the food is hotter than its environment at least in the later stages of heating. Moreover, the interior of the food is hotter than its surface, thus driving moisture to the surface. The relatively wetter, cooler food surface creates major challenges to matching the texture, taste, and appearance of conventionally heated foods whose surface is dryer and hotter. Susceptors have been developed in an attempt to more closely match the conventionally heated product attributes when heated solely by microwave energy. The overarching concept behind these devices is to provide food contact surfaces that can exceed the boiling point of water when the product is being heated in the microwave oven. Under certain conditions, food products heated in a microwave field while in contact with a susceptor device can approximate some or all of the product surface characteristics experienced in conventional heating. The first commercially available susceptors were incorporated into heating utensils, commonly called microwave browning dishes or microwave browning grills, that appeared in the 1970s. Typically these utensils were made of durable materials, making them bulky and heavy but cleanable and reusable. Some of these relatively expensive utensils could accommodate foods as large as circular pizzas. To reach operating temperature, the utensil was first heated alone in a microwave oven for several minutes. Microwave heating was then interrupted to allow placement of the food on the utensil and microwave heating resumed. Utensils that require preheating compromise the primary benefit of microwave food heating ± reduced preparation time. These utensils were available in two basic configurations: either primarily transparent or reflective to incident microwave energy. Microwave transparent utensils were ceramic plates with an electrically conductive coating on a nonfood contact surface. The energy absorbed by the coating caused a temperature rise in the utensil. Some of the incident microwave energy passed through the utensil and, when the food product was placed on the utensil, heated the product. There was no temperature-limiting feature in the transparent utensil. Thus it was important that a material such as the ceramic be selected for its temperature resistance and thermal shock properties. The reflective utensil used a metal plate with a microwave absorbent coating on the non-food contact side of the plate. While similar to the transparent utensils in its use, the absorbent coating on the reflective utensil took advantage

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9.1 Susceptor construction.

of the Curie temperature of magnetic materials to create a device with true temperature-limiting capability. Late in the 1970s the first disposable and more cost-effective susceptors were introduced as part of the food packaging design. Oscar Seiferth and Larry Brastad created important patented technologies to make this major technology breakthrough (Seiferth, 1987; Brastad, 1981). The heart of this design is a thin film of polyethylene terephthalate (PET) with a very thin metal layer applied to the non-food contact side of the film and laminated to a paper based substrate (see Fig. 9.1). It will be referred to hereafter as either the susceptor or the PET susceptor. This cost-effective, temperature-limiting susceptor continues to be incorporated into packaging of food products intended for microwave heating. Further enhancements in heating performance for specific food applications continue to be applied to the susceptor. Examples include geometry of the package and food, use of reflective metal together with the susceptor to selectively limit the areas that incident energy impinges, use of metal patterns to improve heating uniformity and to control differential heating over the surface of the product. Patent art is a good place to start when looking for susceptor packaging applications. Many approaches and product-specific applications have been protected.

9.3

Reflection, transmission, and absorption of microwave power by a susceptor

In the following model of a susceptor only the very thin metal layer is retained. We ignore the plastic film, adhesive, and paperboard layers of a typical

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commercial susceptor. These items can be included in a more elaborate model but they do not significantly change the result since they are thin and have no electromagnetic properties, , "r, or r, comparable to the large conductivity of the metal layer. Surface impedance, a complex number, completely characterizes the microwave behavior of a PET susceptor. The surface impedance is composed of two parts: surface resistance and surface reactance. The type and amount of metal deposited determine the surface resistance and the surface reactance is a measure of how continuous the metal layer is over the coated surface. A uniform metal film coating the surface of the PET substrate would exhibit a surface resistance with zero reactance. PET susceptors, in fact, start with near zero reactance. The surface impedance of a metal film of uniform thickness is 1 d and the normalized surface impedance is   1 d Z~s ˆ Z0 Zs ˆ

9:1

9:2

where Z0 is the impedance of free space, 376.7 , and d is the thickness of the metal layer of conductivity  in ( m)ÿ1. Since Z0 ,  and d are all real numbers both Zs and Z~s are also real, hence the surface impedance is actually a surface resistance. Zs has units of ohms but is usually referred to having units of ohms per square. The terminology arises as follows. Consider a square sheet of conductivity 2 with sides of length h and a thickness d. Attach a perfectly conducting bar to one edge of the square sheet and a second bar to the opposite edge. The resistance of the sheet between the bars is Rsheet ˆ

(length) h 1 ˆ ˆ (conductivity)(cross-sectional area) 2 hd 2 d

9:3

The resistance depends only on the conductivity and the thickness of the sheet. It does not depend on the length of the sides of the square, hence the term `per square'. As discussed in Section 9.4, if the PET susceptor exceeds approximately 200 ëC during microwave heating the originally uniform metal film breaks up into islands of metal film separated by nonconducting gaps. The capacitance associated with these gaps results in a capacitive reactance in series with the film resistance. The surface impedance then becomes a complex number: the sum of a surface resistance Rs and a surface reactance Xs: Zs ˆ Rs ‡ jXs

9:4

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211

and the normalized surface impedance becomes: ~ s ‡ jX~s ˆ Rs ‡ j Xs Z~s ˆ R Z0 Z0

9:5

where j is the square root of minus one. Surface impedance measurement techniques are discussed in Section 9.5. The powers respectively absorbed, reflected, and transmitted by unit area of a susceptor sheet of infinite extent in air with a plane wave normally incident are given in Wait (1985, pp. 138±139, equations 4.104 through 4.113). Note that Wait uses R and T as electric field reflection and transmission coefficients. Power reflection and transmission coefficients are obtained by taking the square of the magnitudes of Wait's coefficients. In the present notation Wait's
becomes
ˆ

1 2Z~s

9:6

The fraction of the incident power that is reflected or the power reflection coefficient, R, is Rˆ

1

~ s ‡ 1†2 ‡ 4X~ 2 …2R s

9:7

The fraction of the incident power that is transmitted or the power transmission coefficient, T, is Tˆ

~ 2 ‡ X~ 2 † 4…R s s ~ s ‡ 1†2 ‡ 4X~ 2 …2R

9:8

s

From conservation of energy, the fraction of the incident power that is absorbed or the power absorption coefficient, A, is Aˆ

~s 4R

~ s ‡ 1†2 ‡ 4X~ 2 …2R s

9:9

The fractions of microwave power absorbed (A), reflected (R), and transmitted (T) must sum to unity. Figure 9.2, constructed using equations 9.7, 9.8, and 9.9 with zero reactance, illustrates the effect of changing surface resistance on the reflected, transmitted, and absorbed power fractions. In free space, susceptors with X~s ˆ 0 and less than 188 per square will reflect more than they transmit while susceptors with more than 188 per square transmit more than they reflect. Absorption increases as surface resistance increases from zero until a maximum is reached at about 188

per square and then decreases with further increases in surface resistance. When food is placed on a susceptor in a microwave oven the analysis is more difficult. Depending on the food, optimum values lie between 30 and 250 per square.

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9.2 Fraction of incident power absorbed, transmitted, and reflected by susceptor vs. surface resistance, Rs, with surface reactance Xs ˆ 0.

The power absorption, reflection, and transmission of an ideal resistive susceptor in free space is given by the Xs ˆ 0 curve on a tri-coordinate graph, Fig. 9.3, constructed from equations 9.7, 9.8, and 9.9. This is a measure of the true heating performance capability of a susceptor at the beginning of the heating cycle. Different metals used to coat the substrate all follow the same

9.3 Fraction of incident power absorbed, transmitted, and reflected by susceptor with surface resistance Rs and surface reactance Xs.

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relationship of absorption, reflection, and transmission to the surface impedance. Different metals vary in that each has a unique bulk conductivity and will have to be applied in a thickness chosen to achieve the desired surface impedance. In the manufacturing and converting processes, there may be some loss of conductivity versus that predicted from the bulk conductivity and the applied thickness of the coating due to effects such as oxidation and abrasion of the metal coating. Following the Xs equals zero curve in the direction of the arrow in Fig. 9.3 shows the effect of increasing Rs on the fraction of absorbed, reflected, and transmitted power. The nested curves with single arrowheads in Fig. 9.3 represent the effect of varying surface resistance with different but fixed levels of reactance. The arrows point in the direction of increasing Rs. The lines with double arrowheads in Fig. 9.3 show the effect of increasing reactance with different but fixed levels of Rs on the absorbed, reflected, and transmitted power fractions. The direction of the double arrowheads indicate increasing jXs j. Equation 9.9 and Fig. 9.3 show that for a fixed surface resistance, Rs, the power absorption coefficient, A, is always reduced by the introduction of a nonzero surface reactance, Xs. The temperature-limiting feature of PET susceptors utilizes this behavior.

9.4

Temperature limiting in PET susceptors

PET susceptors limit temperature by mechanically breaking the originally continuous aluminum thin film into small islands, thus reducing current flow and power absorption. The driving force behind the mechanical breakup is the biaxial orientation and heat set performed during film manufacture. During its manufacture PET is stretched in both machine direction and in cross-machine direction (biaxially oriented). The stretching process substantially straightens the molecular chains creating residual stresses in the PET film. The PET is then heated in a `heat set' process that raises the temperature of the PET film while it is supported in its stretched position. Stresses in the film are relieved up to the temperature at which it is heat set. When the temperature of an unrestrained PET film exceeds its heat set temperature, the remaining residual stresses in the film cause the PET film to shrink and shrivel as it returns towards its shape prior to biaxial orientation. Figure 9.4 shows the unrestrained shrinkage of a typical PET sample as a function of temperature. When the PET is used as a susceptor substrate adhesively bonded to a supporting structure, the shrinking of the film above the heat set temperature creates tensile forces in the plane of the film that are balanced by compressive forces in the paper resisting the shrinkage of the PET. As the temperature of the PET continues to rise above the heat set temperature, typically 225±235 ëC, during heating in the microwave oven the shrinkage forces in the PET film increase. Eventually the PET and the laminating adhesive soften to a point where the PET begins to stretch and thin itself,

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9.4 Shrinkage of unrestrained PET sample.

ultimately tearing itself apart. Above the heat set temperature the tensile forces in the PET film increase and the softening (over about 255 ëC), and melting point (about 265 ëC) of the film dictate the temperature at which the film thins and tears itself apart, introducing a large reactive component into the suseptor's surface impedance. These effects begin in small areas on the susceptor. The local temperature determines the break-up pattern seen on used susceptors. The overall average susceptor temperature typically reaches about 220 ëC. A PET film susceptor heated in a microwave oven develops a pattern of easily visible fractures while a similar susceptor conventionally heated, e.g., by hot air, develops pinholes. The fracture pattern results directly from the details of the electric current flow induced by the electric field incident on the susceptor. The cause of the pattern is especially apparent when the susceptor is heated with microwaves in a waveguide with known electric field orientation (polarization). Suppose that there is a circular void or pinhole in the metalization either due to a manufacturing defect or from PET shrinkage at high temperature. The surface current must now flow around the discontinuity. Current flowing around a hole or relatively high resistance region in a thin conductor concentrates at two opposite points on the circumference where the tangents to the circle are parallel

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to the incident electric field (Weeks, 1964, pp. 648±649; Bouwkamp, 1950). The higher currents flowing at these locations cause local heating preferentially shrinking and pulling apart the PET, further disrupting the thin metal layer. The two points on the circumference 90ë from these high current locations are current nulls and so stay cooler. The spot thus becomes elongated in the direction perpendicular to the electric field. For biaxially oriented, heat set, metalized films the microwave heating process thus has an intrinsic directional crack propagation mechanism. When heated conventionally by hot air there is no such directional growth mechanism. To illustrate the local heating mechanism, an infrared camera was used to produce the following two pictures of the heating patterns on PET susceptors mounted in a waveguide where the polarization of the electric field was known. The electric field strength was slowly increased to the point where the heating was detectable but well below the point where cracks develop. In the black and white figures, reproduced here from the original color photographs, the shaded areas are hotter than the solid black areas. Figure 9.5 shows the heating pattern near a 5 mm diameter hole in a susceptor mounted in a waveguide. The preferential heating of the two points on the perimeter of the hole where the tangents to the hole are parallel to the incident electric field is apparent. Figure 9.6 shows the heating pattern near a 6 mm long slit cut perpendicular to the direction of the electric field and thus perpendicular to the current flow. The ends of the slit are preferentially heated by the diverted current flow, thus feeding the crack propagation mechanism. In contrast, a slit cut parallel to the direction of the electric field and thus parallel to the current flow showed no preferential heating since the current flow was unimpeded.

9.5 Heating near 5 mm hole in PET/aluminum susceptor.

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9.6 Heating near 6 mm long slit in PET/aluminum susceptor.

Figure 9.7 shows an electron micrograph of a PET susceptor after microwave heating. The PET layer has been folded back to the left side of the figure exposing the adhesive layer shown on the right side. Notice the ridges formed by the PET on both sides of the melted track and the corresponding depressions and damage in the adhesive layer. The PET material that has pulled away from the hottest portions of the susceptor forms the ridges. The thin metal film was torn apart as the PET pulled apart, forming gaps in the originally continuous metal.

9.7 Electron micrograph of opened PET/aluminum susceptor after microwave heating.

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In other micrographs, not shown, the separation was even more extreme with only thin filaments of PET connecting the two ridges. The gaps impede current flow. If the susceptor were used with direct current or very low-frequency alternating current a single crack across the susceptor would halt all current flow exactly as a conventional fuse does when it burns out. The gaps appear as capacitors in series with the pieces of resistive sheet. At 2450 MHz the capacitive reactance is low compared with the reactance at mains frequencies of 50 or 60 Hz, so some current will continue to flow. In a strong microwave field current will thus continue to flow, forming new gaps in parallel with the original. The process continues until the capacitive reactance, the X~s term in the power absorption expression, equation 9.9, becomes large enough to reduce the absorbed power to the point where the PET comes into thermal balance with its surroundings at a temperature causing no further crack creation and propagation. Figure 9.8, adapted from Perry and Lentz (1996), shows the development of the surface resistance and reactance as temperature increases during microwave heating of a PET susceptor in a waveguide. As expected, the measured reactance becomes increasingly negative indicating an increasingly capacitive reactance as the susceptor heats. The reactance changes rapidly above 215 ëC in accordance with the increase in shrinkage above this temperature seen in Fig. 9.4. The surface resistance also changes, possibly because of oxidation of the aluminum. Figure 9.9 shows the fraction of the incident power this susceptor would reflect, absorb, and transmit in free space as a function of temperature using the surface impedance measured in a waveguide exposure system.

9.8 Surface resistance and reactance vs. temperature during microwave heating of a PET/aluminum susceptor.

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9.9 Fraction of incident power susceptor of Fig. 9.8 would reflect, absorb, and transmit during microwave heating in free space.

In the waveguide exposure system the gaps form perpendicular to the electric field polarization, i.e., parallel to the broad wall of the waveguide, breaking the metal film into strips. Rotating the susceptor by 90ë about an axis perpendicular to its face and re-exposing breaks the strips into islands. In a microwave oven the polarization is purposely randomized by rotation of the food or mode stirrer/ antenna, hence the susceptor ultimately breaks up into islands.

9.5

Measurement methods

The industry commonly uses optical density to monitor and report the amount of metal material applied to the PET. In fact, optical density provides only an indirect measurement of the surface resistance and does not measure reactance. Surface resistance measurements using two or four point probes at DC or low frequency are available. Direct surface resistance measurements are possible by these methods only if the resistive layer is exposed. Low-frequency eddy current measurement devices normally used to measure semiconductor wafer resistivity and surface resistance, for example the Semilab RT-110 wafer tester and the Lehighton LE188, work on continuous metal films even when the metal films are completely covered in the final packaging configuration. The eddy current and resistance measurement methods utilize DC or lowfrequency AC, below a few megahertz, and will not correctly predict microwave properties if the conductive film has been broken into strips or islands, for example after heating in a microwave oven or because of some manufacturing flaw.

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To understand the heating behavior of a susceptor both resistance and reactance are important. As shown in Section 9.3 absorption (i.e., the heating capability), transmission and reflection of microwave energy by the susceptor are derived from the surface impedance. Ramey and Lewis (1968) and Ramey et al. (1968) measured the microwave properties of continuous thin conducting films at microwave frequencies in a waveguide and related the transmission coefficient to the conductivity times thickness product. Microwave vector network analyzers allow direct measurement of surface impedance, Rs + jXs, at the 2450 MHz microwave oven operating frequency. Flaws in the conducting film, whether from processing or from exposure in a microwave oven, are correctly incorporated into the surface impedance value. The results are directly useful in microwave heating models. The susceptor sample is clamped between the flanges of two waveguide to coaxial line adapters that are in turn attached to the analyzer's measurement ports. A standard WR-284 rectangular waveguide, inside dimensions 7:21 cm  3:40 cm is both convenient and readily available. The network analyzer measures the scattering parameters that for a susceptor may be interpreted as a shunt impedance across the waveguide. The straightforward conversion of scattering parameters to surface impedance normalized to the waveguide impedance is given in Altman (1964, pp. 370±371). The impedance of WR-284 at 2450 MHz is 712 . The electric field in the waveguide is most intense between the centers of the broad walls and is oriented parallel to the narrow wall dimension. The susceptor is thus exposed to only one polarization. To reveal any elongated discontinuities in the metal, perhaps resulting from faulty manufacturing, surface impedance measurements should be made at several angular orientations by rotating the susceptor in the plane of the waveguide flange. A uniform metal coating would show no variation in Zs with rotation. A cut in the metal would cause a strong variation in Xs, and hence in Zs, with rotation. Vector network analyzers expose the susceptor to low-power microwaves, at most a few tens of milliwatts, which will not significantly raise the temperature of the susceptor. Using an external amplifier to boost the analyzer's microwave source to up to 200 W output allows susceptor characterization under dynamic, high-temperature conditions. Instead of sampling the various forward, reflected, and transmitted signals in a coaxial line as is done in low-power systems, the signal samples must be obtained using waveguide directional couplers. Signal levels must be attenuated to those acceptable to the network analyzer. Accurate measurements require that any harmonics or spurious signals generated by the power amplifier be filtered out of the signals going to the analyzer. In the high-power exposure system the sample is mounted as above. The temperature is recorded using a thermocouple, #30 awg or smaller, attached to the support structure (often paperboard), at the center of the sample. Typically the thermocouple is inserted into a small cut in the center of the support

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structure. The cut is made parallel to the electric field, i.e. parallel to the narrow wall dimension of the waveguide. A very small amount of silicone grease ensures good thermal contact. A small piece of high-temperature tape holds the thermocouple wire to the sample. The wire must be perpendicular to the electric field, i.e. parallel to the broad wall of the waveguide, as it is routed to the center of the sample from the middle of one of the narrow walls of the waveguide, otherwise the wire will itself cause local heating because of intense fields at its tip and heavy currents induced in the wire. A few trial runs will establish a power level giving a rate of temperature rise that allows the limiting temperature to be reached in about a minute. This enables the thermocouple to follow the temperature. Other temperature monitoring techniques, e.g. infrared or fiber optic thermometers, could be used. The data from the network analyzer and the thermocouple are recorded and presented in graphs like Fig. 9.8.

9.6

Manufacture

9.6.1

Manufacture: overview

Commercially available disposable susceptors are typically of the resistive type. The most common structure is built with four components: substrate, resistive coating, laminating adhesive, and supporting structure (Fig. 9.1). The metals deposited on the substrate form the electrically resistive layer that couples with the electrical field generated in the microwave oven. Current flow induced in the metal layer heats the metal layer by resistive losses. The metallized PET surface is adhesive laminated to the supporting structure, typically paper or paperboard although some polymer structures have been used in place of the paper or paperboard. The substrate is the food contact surface, carries the resistive layer, helps protect the integrity of the resistive layer, and reduces the tendency of food to stick to the susceptor after heating. The most commonly used substrate is biaxially oriented, heat-set PET. PET is available in thin gauges and is both temperature resistant and relatively economical. PET handles well in converting operations such as metallization and lamination. PET is acceptable for the microwave heating condition of use and is listed in the Code of Federal Regulations. PET is also used in paperboard structures with foods intended for heating in conventional ovens. Biaxially oriented heat-set polyethylene naphthalate (PEN) can also be metallized and used as a susceptor substrate. With its higher softening and melting point, a susceptor with a PEN substrate can operate at a higher temperature than a PET susceptor with the same surface resistance (see Perry and Lentz, 1996). PEN, however, is a more costly substrate. The resistive coating can be made from a number of materials and can be applied using multiple manufacturing methods. The most widely used coating is

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an aluminum layer deposited on the surface of the PET opposite the food contact surface. Aluminum has a relatively high vapor pressure that lends itself to high and cost-effective application rates. It can be uniformly applied resulting in uniform surface resistance. PET coated with aluminum in the working range of susceptors has a transparent grey tint. Held up to a light source, the light can be seen through the coated film. Identification of which side is coated is easily accomplished using a pencil eraser to rub the surface of the substrate. When the coated side is rubbed, aluminum is removed from the substrate leaving only the clear substrate. Following lamination to white paper, the susceptor film will appear grey. Other conductive metals such as copper, tin, lead, silver, gold, nickel may also be used. Safety concerns, cost, or manufacturing concerns such as control of the layer thickness and coating speeds, oxidation of the coating, and bonding to the substrate have limited their use. Metal oxides such as tin oxide can also be used with film substrates and were actually used in some reusable microwave heating utensils made of ceramics (Forker and Panzarino, 1976). Alloys can also be used to create the resistive coating. For example, nickel±chromium and various stainless steel alloys have been used to produce alloy coatings. Alloys present a challenge to make consistent susceptors since it is difficult to maintain the proportion of the alloy metals. When there is variation in the composition, the bulk conductivity of the applied coating is inconsistent. Given uniform thickness, the surface impedance is inconsistent and thus heating properties of the coating are also inconsistent. Deposition methods that can control alloy compositions are available but produce more costly susceptors.

9.6.2

Manufacture: applying the resistive active coating

Generally referred to as metalizing, several manufacturing techniques are available to apply the resistive coating to the substrate. The two most commonly used processes are evaporation deposition, also known as vapor deposition, and sputtering. The vapor deposition process is used almost exclusively to apply resistive coatings for commercially available susceptors. Evaporation deposition Of the coating methods, this is the fastest and most economical. Evaporation deposition is a batch manufacturing process. The coating is applied inside a vacuum chamber where unwind and rewind rollstands are used to facilitate coating large amounts of substrate each time the chamber is closed. A roll of substrate is loaded onto the unwind rollstand inside the vacuum chamber and threaded to a rewind rollstand. The chamber is closed and pumped down to the required vacuum level (usually less than the partial pressure of the metal at its molten temperature). The solid metal to be used for the resistive coating on the

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substrate is fed into heated boats inside the high vacuum chamber where it melts and vaporizes. The metal vapor condenses on the target substrate as it passes around a chilled drum above the boats containing the molten metal. This process is sometimes referred to as a liquid phase deposition because the solid metal is first converted to its liquid phase before vaporizing. In this method the heated boats are positioned horizontally and the target substrate is positioned above the boats for the most effective coating. Thinner substrates, such as the 12 m thick PET, are more economical to run in this process. The size of the vacuum chamber limits the useable roll diameter. For a given roll diameter, thinner films will yield more lineal feet of material. Evaporation deposition is limited to a single metal and is not used for alloys. The different elements making up an alloy have different vapor pressures and would not be applied in the same ratios as they are present in the alloy. Lower vapor pressure elements get concentrated in the boats and the higher vapor pressure elements are applied at higher levels than exist in the alloy. This effect is referred to as fractionation. As fractionation proceeds, the applied ratios of the elements comprising the alloy will continue changing. Since the different elements have different bulk conductivity, the net effect of using this process with alloys is non-uniform surface resistance over a batch. Aluminum is a good metal to use in evaporative processes due to its relatively high vapor pressure (boiling point: 2467 ëC), low cost, and abundant supply. The evaporation process with aluminum also lends itself to less resistive coatings such as less than 10 per square. These are coating levels used for improving the barrier properties of films and for decorative coatings with a shiny metallic appearance. Sputter deposition Also a high vacuum process, in sputter deposition high-energy particles, typically ions, are accelerated towards a solid coating material target and dislodge and eject molecules and atoms off of the target at high velocities. The ejected particles are deposited onto the substrate. Importantly, this process applies the same ratio of materials that is in the target with no fractionation caused by differences in vapor pressure. As a result, sputtering can effectively deposit alloys and other materials maintaining the same ratios of constituents as present in the target. The slower speed of this process is partially compensated by using multiple targets. Sputter deposition is used to create layers of coating materials in a single pass through the coater with each layer possibly composed of different metals. In addition, materials can be applied `reactively' to provide enhanced properties. For example, tin applied in an oxygen environment will form tin oxide. In general, sputtering will cost several times more than aluminum evaporation deposition.

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Electron beam High-energy electron beam guns shoot electrons onto the metal target and eject metal particles onto a passing substrate web. This method falls between the evaporation and sputter processes for cost and flexibility. It uses horizontal coating targets that can be selected from a wide range of metals and alloys. Chemical vapor deposition Gaseous chemicals are combined in a high-temperature environment and react to form compounds. The compounds, selected to be electrically conductive, coat the substrate. Many reaction products are possible. Very high temperatureresistant substrates are required in this process. In general, PET and PEN are not suitable substrates. The use of more temperature-resistant substrates and the continued need of a temperature-limiting feature that operates in a range to prevent scorching of food and packaging reduce the suitability of susceptors manufactured by this approach for use as disposable susceptors. The main benefit of this method is the ability to achieve a uniform coating on components with complex three-dimensional shapes.

9.6.3

Manufacture: applying the coated substrate to the supporting structure

A laminating adhesive bonds the resistive coating to the supporting structure. Under actual operating temperatures, the adhesive provides enough bond strength to keep the substrate intact and attached to the supporting structure during exposure to microwave energy. The adhesive allows the substrate to contract uniformly thereby enhancing uniform heating and avoiding scorching. The combination of a stable supporting sheet, a sufficiently strong adhesive and a contracting substrate limits the susceptor temperature during microwave heating (see Section 9.4). The adhesive is selected to prevent corroding the resistive layer and after curing to protect the resistive layer from oxidation which otherwise would increase the surface resistance above the intended value. The laminating adhesive is typically polyvinyl acetate (PVA) polymer or a copolymer of PVA. PVA has sufficient temperature resistance to keep the metallized PET bonded to the supporting structure to foster the temperaturelimiting mechanical breakup of the resistive coating on the PET substrate. The supporting structure is typically paper or paperboard. The paper is structurally rigid, heat resistant at the operating temperatures where PET shrinks, can provide some thermal insulation, and can be easily formed into desired configurations. Once the temperature-limiting mechanism of substrate shrinkage creates discontinuities, the paper supporting structure can also serve as a path for venting moisture from foods. In normal use the temperatures achieved

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with PET substrates adhesively laminated to paper are high enough to increase surface drying yet low enough so that paper may brown slightly but will not generate smoke. Selection of the correct grade of paper is important to performance.

9.6.4

Manufacture: susceptors in disposable packaging

Each food/package/susceptor combination needs to be designed to meet consumer expectations for the convenience, quality, and performance of the combination during heating and balanced with the retail cost to purchase the product. How the susceptor heats in the microwave field has a potentially big impact on the perception of the product offering. The absorption, reflection, and transmission of incident microwave energy by the susceptor can be adjusted by choosing the surface impedance created during manufacture to optimize perceived quality and performance. The manufacturing and converting processes may intentionally or unintentionally introduce electrical disruptions to the otherwise uniform metal coating. Sources of these disruptions include scratches in the metal surface, fracture of the coating due to stretching the substrate (including local strain created in the edges of folds and more general strain such as generated with web tension), etched patterns in the metal surface, creases, dimpling, cuts, and holes. These disruptions introduce reactance into the surface impedance of the susceptor, influencing the reflected, absorbed, and transmitted power fractions as shown in Fig. 9.3. Susceptor structures can be used as freestanding devices or can be incorporated into other packaging forms, such as pouches, trays, cartons, and single or double faced corrugated pads. Susceptors are incorporated into packaging components using several approaches. The metalized layer can be applied to PET as a uniform deposition. Stripes of susceptor can be created by metalizing with mask to coat the active material only in specific continuous lines in the metalizer. This approach provides an overall layer of PET with the active susceptor in only a specific area. The edges of the mask create a gradual transition from susceptor coating levels to none over a small distance. The overall PET in the package provides a large food contact surface that extends beyond the microwave active area. The transition areas at the edges of the mask typically have lower absorption and higher transmission owing to the thinner and thus higher surface resistance active coating. Susceptor stripes and patches can also be made by slitting or die cutting uniformly coated and laminated susceptors and applying these items in register to other packaging components. For example, patches have been applied to trays and cartons and pouches using windowing processes. The susceptor in this case has to extend beyond the food or have another layer of food contact material between the susceptor and the food product. In many microwave popcorn

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packages the metallized substrate is incorporated into the popping bag as a patch of the substrate adhesively applied to the desired spot on the wall of the bag whereby the wall acts as the supporting structure. More complex coating patterns are made using a moving mask during metallization to control where the metal strikes the PET or by uniformly coating the PET with the active coating followed in a subsequent converting operation by selectively removing metal in specific areas (de-metallization). The complex and expensive process using a moving mask has been used only rarely. Demetallization on the other hand has been used with both susceptor and reflective metal thicknesses. In de-metallization a patterned protective film (resist film) is applied to the metal coating after deposition in the areas that are desired to remain active. The coated structure is run through an etching acid solution and wash that removes the exposed metal while the metal deposition under the resist film remains intact.

9.7

Use and application

9.7.1

Use and application: oven considerations

Typically, susceptors are used for microwave heating of foods where a dry or crisp texture and in some cases a browned appearance is desired on the surface of the food. Susceptors perform best when the surfaces intended to be dried or crispened are in direct contact with the susceptor. For example, an interlocking arrangement of dividers made of susceptor board has been used to heat French fry pieces, each individual fry occupying a single cell thereby surrounded by susceptors. Susceptors must also reach temperatures well above the boiling point of water to deliver these characteristics. There have been some special cases where susceptors were employed to increase heating uniformity and/or modify the heating rate of certain foods, e.g. popcorn. In general, susceptor/food products intended to be heated in the microwave oven must be able to perform satisfactorily across oven cavity sizes and dimensions, the delivered heating power inside the oven cavity, spatial variation of field strength within the cavity, the dielectrics and thickness of turntables and floors, and the location of the susceptor/food product relative to all of the walls of the oven cavity (sides, top, bottom, door). The oven manufacturer establishes the dielectric properties of the floor or turntable together with the spacing of the floor or turntable from the metallic bottom of the oven cavity. Since the bottom wall of the oven cavity establishes a boundary condition for the propagating waves, it is a major consideration in designing susceptor/product packaging and in modeling food heating in the oven. Planar one-dimensional transmission line models of microwave heating can include food, susceptors, other packaging elements, and some microwave oven cavity features such as the shelf and metal floor. Both modeling and experiment

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indicate that the most effective range of surface resistance is 30±250 per square depending on the food. Clearly, such models do not account for all the electromagnetic effects that are apparent in microwave heating, e.g., polarization-dependent edge heating seen in soups and intense internal heating seen within rounded objects. However, planar layer models do offer insight into microwave propagation losses, interference effects and heat flow. Collin (1960, pp. 71±94), De Wagter (1984, 1985), Demir and Elsherbeni (2006), and Wait (1985, pp. 124±140) all present planar layer models. The packaging may be adjusted for optimum heating by adding appropriately positioned surface reactance using metal screens and patches (Ball et al., 1993; Otoshi, 1972; Chen, 1973; Weeks, 1964, p. 456; Habeger, 1997). Simple or complex microwave heating models give a good starting point for the design of the susceptor and product. But there is no substitute for making prototypes and verifying performance. A single representative oven is a good place to start in the initial design and development work with the product and package. As the development of the item progresses, an early assessment of performance in different ovens made by different manufacturers and with different power levels will provide valuable insight on the criticality of the food item design across the variations in oven performance. It is not unusual for food items to work very well in some specific ovens only to perform poorly in others. The heating instructions should be adjusted to get the best possible performance across oven variation. A design that delivers quality and performance across ovens is important to consumer satisfaction. Sometimes there are trade-offs intentionally made to optimize performance in certain size or power ovens at the expense of poorer performance in the others. The rationale for such a decision is sometimes dictated by assuring performance for the installed oven base used by the consumers most likely to use the food item. For instance, if the product will be used in convenience stores, the product should be designed for and tested in commercial ovens. Commercial ovens typically deliver more heating power than household ovens and during certain times of the day may be under nearly constant use. Product failure modes should also be investigated by experimenting with mistakes that consumers may reasonably make. Consumers may or may not follow preparation directions. The wrong power level or heating time may be keyed in or perhaps a pre-programmed heating key is incorrectly pressed. The product and package may not be properly assembled or placed in the best position in the oven. In addition, ovens that have not been used for about 45 minutes perform differently from recently used ovens. Recently used ovens have both a warmer thermal environment and a heated magnetron that can have a different power output from a cold magnetron. The earlier in the development cycle these tests are conducted, the more time will be available to properly assess and correct any risks and performance issues.

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227

Use and application: overview of design considerations

Three considerations for how effective a susceptor will be in enhancing surface heating to promote crispening and color changes in product are: (1) the energy absorbed by the susceptor, (2) the heat transfer environment around the susceptor, and (3) the management of moisture at the susceptor/food interface. Another requirement is to prevent runaway heating that can result in charring of the packaging and product. There needs to be a temperature-limiting feature inherent in the susceptor. Such a temperature-limiting system must be able to respond to the different heating rates resulting from non-uniform contact with food items, variation in the amount of power delivered to the product whether inherent in the design of microwave ovens or as a result of the product load, variation in the amount of heating time set by the consumers, and the spatial variation of power distribution inside an operating microwave oven. Since the magnitude of each of these effects can vary over small distances within an oven cavity, the temperature-limiting feature must be effective over these same distances. Ideally for best cooking performance, the temperature-limiting feature would be reversible. At a minimum, the susceptor must not exceed a predetermined temperature. A further requirement is maintaining a safe and wholesome food. At the elevated temperatures needed to crisp and brown products during the short heating cycle typical of microwave prepared products, the transfer of contaminants to the food is of primary concern. In most applications where susceptors are used in contact with food, the food rests on top of a `clean' surface that acts as a functional barrier separating the food from the other packaging components. The entire susceptor structure should be tested with the food item to demonstrate suitability for consumption.

9.7.3

Use and application: the heating dynamic

Susceptors absorb, reflect, and transmit the incident microwave energy as described in Section 9.3. The heat from the susceptor is then transferred to adjacent structures primarily via conduction. The product surface temperature provides the driving force to dry the surface of the food or cause other desirable effects. The actual temperature vs. time relationship that is achieved at the interface between the surface of the food and the contacting surface of the susceptor is determined by the microwave power absorbed by the susceptor, the power absorbed in the food, and all of the power losses from the susceptor. The susceptor heats the packaging components it rests upon which in turn heats the oven floor of the oven, the air, etc. Since microwave power is limited, it is important to utilize whatever power is converted into heat as efficiently as possible.

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Water management is a key consideration in the heating of foods on susceptors in microwave ovens. Ice and liquid water in contact with the susceptor create large heat sinks for the microwave energy absorbed and converted to heat by the susceptor, thus slowing the rise to crispening and browning temperatures. The enhancement of these attributes does not occur until the water is vaporized or drained away from the surface of the susceptor. As described above, the temperature-limiting feature of the metalized PET susceptor creates discontinuities in the metal film in response to high local temperatures. Thus in actual use, the susceptor has a beginning level of performance that is driven by its manufactured surface impedance. During exposure to microwave fields with a food item positioned on a susceptor, the local susceptor surface temperature is dictated by local incident microwave power absorbed combined with heat transfer on a local basis. Wherever the limiting temperature of the susceptor is reached discontinuities are generated. The reactance in that area will increase irreversibly, resulting in increased transmission and decreased absorption and reflection. This effect can be readily observed in the areas where the susceptor does not contact the product such as around the outside edge of the product. In these areas the susceptor temperature rises to the limiting value at which fractures irreversibly appear in the susceptor within the first few seconds of exposure to microwave power. Where a susceptor is used and water is a constituent of the food, liquid water is typically present at the susceptor/product interface. A power balance at the susceptor including these factors will help in understanding the operating temperature of the susceptor. Let: IA be the microwave power absorbed by the susceptor dQ be the net power into the susceptor dt m be the mass of the susceptor cp be the heat capacity of the susceptor dTs be the rate of temperature change of the susceptor dt dQsf be the rate of heat conduction to the product dt dQsm be the rate of heat conduction to the support materials under the dt susceptor dQv be the rate of heat loss due to the water vaporized by the susceptor dt dQ dQsf dQsm dQv dTs ÿ ÿ ˆ mcp ˆ IA ÿ dt dt dt dt dt or

9:10

Susceptors in microwave packaging dQsf dQsm dQv dTs IA ÿ dt ÿ dt ÿ dt ˆ dt mcp

229 9:11

From this balance, it can be seen that to increase the rate of temperature rise in the susceptor to achieve higher susceptor/product interface temperatures and to achieve a higher operating temperature the following methods can be used either individually or in combination: 1.

2. 3. 4. 5.

6.

Increase incident power at the susceptor (a) adjust product thickness and dielectrics (b) shield to create constructive interference (c) position above cavity bottom wall Increase the amount of incident power absorbed by the susceptor (a) adjust surface impedance (b) sustain absorption as susceptor temperature increases Increase heat transfer rate to the food surface by improved contact Slow down heat transfer from the food surface into the interior of the food (a) surface structure (b) multiple layers Reduce heat transfer to all support materials (a) reduced mass (b) reduce heat capacity of support materials (c) reduce heat transfer rate (add insulation) Reduce the amount of water at the susceptor/product interface (a) provide steam venting (b) drain excessive fluids away from interface (c) water barrier between interior of product and outer contact surface

Where large amounts of heat are needed to achieve surface drying, crispening, or color changes, some form of a thermal insulator may be used adjacent to the susceptor opposite to the product being heated. The insulator reduces the loss of heat to the surrounding structures and environment, making more of the converted energy available for transfer to the food. Patent literature describes many different means of delivering some form of insulation. The simplest and most cost-effective means is to provide an air gap between the floor of the microwave oven and the susceptor. This has been accomplished using susceptor trays with supporting structures such as legs. In other applications susceptors have been placed on the outside bottom surface on trays or cartons. The trays are placed in the microwave oven in an inverted position with the food item on the susceptor. The sidewall of the tray raises the susceptor and food off the oven floor or turntable thereby providing an insulating air gap between the floor/turntable and the food/susceptor. Single face and double face corrugated pads or wraps have been used as insulators. Corrugated pads or wraps can be placed directly on top of the floor or

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turntable in a microwave oven. A food product with a susceptor under it is then placed on top of the corrugated pad. Alternatively, the susceptor may be incorporated directly into or on the corrugated structure. A susceptor with its PET food contact surface facing out can be used as the face of a corrugated structure. The susceptor can also be incorporated into a single face corrugated structure as the medium, i.e. the fluted part of the structure, with the PET side facing the food. The susceptor makes food contact only on the raised sections of the flute. If the food item is pliable or flowable enough there could be contact between the susceptor and food item over the entire surface of the fluted susceptor. Insulation can also be created by folding, creasing, or dimpling susceptors or supporting structures underneath them. Again, the intention is to provide an insulating air gap between the susceptor and the floor. Susceptors have also been set on top of or incorporated into one of the layers of pillow pack and bubble wrap configurations. An interesting adaptation of this approach is to design the susceptor into a pillow or bubble configuration but in a flat state. Using the heat generated early in microwave heating, water vapor or other gases expand on heating within the flat structure to inflate the cells. This conserves space during distribution but provides insulation during heating. When used as a wrap encircling the food product, the inflation also enhances thermal contact with more of the food surface. Moisture control can be accomplished in many ways. The metallized PET food contact surface in susceptors will fracture on reaching the control temperature creating paths by which water (liquid and vapor) can migrate from the product/susceptor interface to the structure below. If the susceptor is resting directly on a water-impervious surface the moisture will be blocked at that point. Further, if the moisture-impervious surface is below the dew point temperature, liquid water will pool at this surface and effectively stop further drying of the food surface. As long as there is liquid water on a susceptor, that area of the susceptor cannot exceed 100 ëC. To maintain heating and allow moisture to migrate, a better performing susceptor will include a path for moisture to escape after penetrating the susceptor. Elevating the susceptor and providing an air gap will improve moisture loss. If the air gap is enclosed, moisture can condense and collect away from the susceptor. Creating vent paths such as holes in tray or carton walls allows the moisture to escape from underneath the susceptor into the oven cavity and is subsequently vented out of the oven. Single face and double face corrugated, creased, dimpled metalized PET susceptor structures provide a combination of benefits. They position the susceptor in a generally stronger and more uniform field, provide thermal insulation, and allow moisture to vent away from the food and susceptor. The bubble and pillow approaches by their nature will not allow moisture to permeate through the susceptor structure and so tend to accumulate moisture at the food/susceptor interface. However, this structure will allow moisture to vent

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through paths between the food and susceptor formed by the three-dimensional geometry of the bubbles and the air spaces between adjacent bubbles. With susceptor pouches and enclosed sleeves the moisture management approaches described above work well. Preparation directions to puncture or partially open package enclosures also are helpful. End and back seam pouches can be made to self-vent through the seals by controlling the seal strength at the operating temperatures achieved inside the pouch during microwave heating. Pressure-sensitive susceptor patches have been applied to pouches to heat a small region of a sealed pouch film during microwave preparation. The patch gets hot enough to weaken the film structure. The internal pressure created by heated air and water vapor inside the pouch is sufficient to rupture that weakened film thereby providing package vents. Similarly, susceptor structures have been incorporated into seal areas of packaging to heat the seal area on packages thereby weakening the seal. While it can be effective in certain applications, this approach is usually avoided because susceptors in the seal may cause overheating of the substrates. This is particularly true when the finished seal has more than one susceptor layer.

9.7.4

Use and application: geometry effects

The electric field at the susceptor can be modified through the use of reflecting structures such as continuous highly conductive foils. Positioning such a reflector in contact with the susceptor provides a boundary condition that makes the transverse electrical fields that create the electrical currents in susceptors go to near zero. In this condition the susceptor will not provide enough heat to be useful as a heating element. Moving the susceptor away from the reflector puts it into a position where electrical waves passing through the food and susceptor reflect back from the reflector and form standing waves. The maximum field strength at the susceptor is reached when the susceptor is positioned a quarter wavelength away from the reflector. This approach can be used to either intensify or reduce heating behavior. The electromagnetic waves entering the microwave oven cavity via the waveguide reflect off of the cavity walls. The waves also at least partially reflect when striking the floor or turntable, any cooking vessels (which includes packaging), and the products being heated in the cavity. As a result of the reflections from the cavity walls, the propagating waves that heat the product are striking from many directions. Thus the heating of products on susceptors is very complex. Limiting the number of incidence directions allows more effective control of heating by geometry, dielectrics, and susceptor components. For example, a reflector (shield) wrapped around the vertical walls of the susceptor/ product allows primarily the vertically propagating waves to heat the product. Electromagnetic and thermal modeling of the food and its packaging can provide valuable insights into optimizing heating performance. If modeling is

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not available, one can use trial and error testing or apply experimental design (Bowker and Lieberman, 1972; Brue and Launsby, 2003; WaÈppling-Raaholt et al., 2001). Designed experiments provide a systematic approach to evaluating the effect of many variables and linking those to the performance attributes of interest (referred to as responses). Many variables can be evaluated, such as the thicknesses of various components, the relative position of food and package layers, dielectric properties, the height above the oven floor, susceptor impedance, the use of reflectors and their position from the product, heating time, and power level. Responses can be attributes like browning, crispness, uniformity of heating, and internal temperature. Reflective metal grids and or islands have been used successfully to improve heating and attribute performance, e.g. Lafferty (2000), Lai and Zeng (2000a,b), Levin and Pesheck (1992), Mikulski et al. (1987), Zeng (2001), Zeng et al. (2001). These devices when used in conjunction with susceptors provide more consistent and sustained surface heating and more uniform product heating. They are used to control the heating rate to balance the development of interior temperature while giving time for the surface texture to develop. They have also aided in leveling performance across ovens.

9.7.5

Use and application: alternatives to the PET susceptor

While the dominant commercially available susceptor used today comprises a vapor deposited aluminum resistive coating on a PET substrate, there have been many attempts to make better performing, more affordable susceptors. Numerous printed or coated susceptors have been described, e.g. Prosise et al. (1994). These generally consist of an active component, a binder to hold the active materials, and a carrier to keep the materials uniformly suspended, thus aiding the coating process. The benefit of this type of susceptor is the great flexibility of patterns and possible shapes. Coatings can take the form of water-based, solvent-based, high-solids, or hotmelt systems. They can be coated, extruded, cast, powder-coated, or printed. Conductive particles can be added in forms such as powders, flakes, fibers, beads, and rods or as blends of these forms. Particle size and shape plus the concentration in the binder will affect the final impedance of the coating (Parker and Tighe, 1990). However, large conductive particles can cause arcing in the coating. Some applications use an inert filler to aid in achieving the electrical properties needed for heating. The active component can be an electrically conductive or semiconductive material or a dielectric material with a high loss factor. Similar to PET susceptors, printed susceptors using electrically conductive particles absorb, transmit, and reflect microwave energy as dictated by the surface impedance of the resulting coating. Typically the art has described graphite (e.g. Blackenbeckler et al., 2005) or metal flakes such as

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nickel, aluminum, silver, zinc, copper, brass, bronze, and stainless steel (e.g. Stone et al., 1989), dispersed in the binder to obtain the required electrical properties. To achieve the same range of surface impedance as aluminum vapor deposition film susceptors these structures must be relatively thick. The major factor limiting the use of printed/coated style susceptor is achieving a temperature-limiting mechanism to prevent runaway heating. The binder is used to attach the coating to the susceptor substrate as well as to hold the conductive particles together in close proximity to achieve the electrical properties. The thick layer of cured binder is relatively strong compared with PET and thus the temperature-limiting feature of conventional susceptors is inoperative with these thick structures. Patent art describes an approach in which temperature control with printed susceptors can be achieved by relying on thermal expansion of the binder and any inert material at elevated temperatures to increase the separation of the conductive particles. The increase in spacing potentially increases the resistance of the coating and creates a separation which stops tunneling currents between conductive particles (Pollart and Habeger, 1995). A coating of materials that couples with the magnetic field was used on a reusable microwave heating utensil. The coating was applied to a conductive aluminum plate. The large mass of the device required preheating in the microwave oven before heating the food. This device achieved temperature control through the Curie temperature of the magnetic particles. At the Curie temperature the material loses it magnetic properties and no longer heats. The magnetic properties are recovered when the temperature drops below the Curie temperature. This is a true reversible temperature-controlled microwave heating device. The device ends up being thick, has high thermal mass that heats slowly, and is relatively costly which limits its usefulness as a disposable packaging component. Another susceptor used ferrites applied to aluminum foil and was intended to be disposable (Turpin and Hoese, 1980). Instead of relying on the Curie temperature, this device controlled the amount of incident energy by partially shielding or reflecting microwave energy away from the coating and by adjusting the coating thickness to establish an energy balance and a corresponding steady state maximum temperature. A dielectric layer can be applied to a reflective substrate (Pesheck and Lentz, 1993a) to provide a steady state maximum operating temperature by selecting the dielectric and its thickness. It has also been noted that a dielectric that changes with temperature can be used to provide true temperature limiting. In addition to dielectric properties that are created by coatings or formulated compounds, controlling the placement of metal patches or plates in a parallel overlapping planar arrangement with layers of dielectric material in between the planes of metal can create artificial dielectrics (Pesheck and Lentz, 1993b). Dielectric-based susceptors may also use very lossy dielectric materials that absorb sufficient energy to reach browning and crispening temperatures while in

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contact with food products. An example is a salt-based chemical susceptor (Winters et al., 1981). This device relied on the energy absorbed in the susceptor to vaporize water in the specially formulated salt hydrate, thereby changing the hydrate state. The progression to more lossy salt hydrate states achieved temperatures sufficient for browning and crispening food products. The device exhibited a form of temperature limiting in that when all of the water was driven off, the microwave absorption dropped dramatically. The inventors state that temperature control is also possible by matching the absorption of microwave energy in the susceptor to the heat losses to the food and environment, thereby achieving a steady state operating temperature. A printed susceptor in contact with a conventional susceptor has been proposed as a means to maintain heating performance as the conventional susceptor reaches its limiting temperature (Watkins, 2006). This approach takes advantage of the fast heating and temperature limiting of conventional susceptors while using an underlying base of sustained low level heating from a printed susceptor.

9.8

Conclusions

Susceptors, like the browning dishes that preceded them, help crispen and brown foods heated in microwave ovens by converting microwave energy into heat to warm the food surface through thermal conduction. The overarching concept behind these devices is to provide food contact surfaces that exceed the boiling point of water during microwave heating. Susceptors are intended to make food rapidly cooked in a microwave oven resemble the same food conventionally cooked. Susceptors can be incorporated into nearly any package geometry and style including pads, pouches, trays, bowls, and cups. Microwave energy can be converted to heat through three electromagnetic loss mechanisms, resistive loss caused by finite electrical conductivity, dielectric loss, and magnetic loss. The commercially dominant thin metal film on PET susceptor uses resistive loss. In addition to low cost, PET susceptors also limit temperatures, by the mechanical breakup of the originally continuous aluminum thin film into small islands, thus reducing current flow and power absorption. The break-up pattern results directly from the high temperature shrinkage property of biaxially oriented heat set PET and details of the electric current flow induced by the electric field incident on the susceptor. If the susceptor exceeds approximately 200 ëC during microwave heating the originally uniform metal film breaks up into islands of metal film separated by non-conducting gaps. The capacitance associated with these gaps results in a capacitive reactance in series with the film resistance, thus reducing the current flow and the power absorbed. Surface impedance, a complex number, completely characterizes the micro-

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wave behavior of thin metal film susceptors. The power absorbed, reflected, and transmitted by unit area of a susceptor sheet of infinite extent in air with a plane wave normally incident is simply related to the surface resistance and reactance. Surface impedance can be directly incorporated into electromagnetic models of product heating. The most effective range of initial PET susceptor surface resistance is 30 to 250 per square depending on the food. The surface impedance of a finished susceptor can be measured by lowfrequency eddy current instruments or most reliably in waveguide by a microwave network analyzer. Susceptor impedance as temperature increases during heating is measured in waveguide using high-power microwave sources. Commercial susceptors have a plastic film substrate, a thin metal resistive coating, an adhesive, and a support structure. Biaxially oriented heat-set PET plastic film is used since it is available in thin gauges and is both temperature resistant and relatively economical. Other metalized biaxially oriented heat set films can give higher limiting temperatures but are more expensive. Of the coating methods evaporation deposition is the fastest and most economical. The coating is applied inside of a vacuum chamber where the PET film is exposed to vapor from molten aluminum. The metal vapor condenses on the film as the film passes around a chilled drum. The metalized PET surface is adhesively laminated to a paper or paperboard support structure. The PVA polymer adhesive provides enough bond strength to keep the substrate attached to the supporting structure up to the melting point of the substrate. The adhesive does not corrode the aluminum layer and protects it from oxidation. The paper is structurally rigid, heat resistant at the operating temperatures where PET shrinks, can provide some thermal insulation, and can be easily formed into desired configurations. Modeling gives a good starting point for product design but there is no substitute for making prototypes and verifying performance in a variety of ovens. Different ovens made by different manufacturers can give widely differing heating results. Since microwave power is limited, it is important to utilize whatever power is converted into heat as efficiently as possible by providing thermal insulation between the susceptor and the oven floor or turntable and draining away liquid water.

9.9

References

Altman J (1964), Microwave Circuits, Princeton, NJ, Van Nostrand. Ball M, Keefer R, LaCroix C and Lorenson C (1993), `Materials choices for active packaging', Microwave World, 14(1), 24±28. Blackenbeckler N, Chiu C and Kust P (2005), US Patent Application 2005/0142255. Bouwkamp C (1950), `On the diffraction of electromagnetic waves by small circular disks', Philips Research Reports, 5(6), 401±422. Bowker A and Lieberman G (1972), Engineering Statistics, 2nd edn, Englewood Cliffs,

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NJ, Prentice-Hall, Inc. Brastad W (1981), US Patent 4267420. Brue G and Launsby R (2003), Design for Six Sigma, New York, McGraw-Hill. Chen C (1973), `Transmission of microwave through perforated flat plates of finite thickness', IEEE Trans on Microwave Theory and Techniques, 21(1), 1±6. Collin R (1960), Field Theory of Guided Waves, New York, McGraw-Hill. Demir V and Elsherbeni A Z (2006), `A graphical user interface for the calculation of the reflection and transmission coefficients of a layered medium', IEEE Antennas and Propagation Magazine, 48(1), 113±119. De Wagter C (1984), `Computer simulation predicting temperature distributions generated by microwave absorption in multilayered media', Journal of Microwave Power, 19(2), 97±105. De Wagter C (1985), `Computer simulation for local temperature control during microwave induced hyperthermia', Journal of Microwave Power, 20(1), 31±42. Forker, Jr R and Panzarino J (1976), US Patent 3965323. Habeger C (1997), `Microwave interactive thin films', Microwave World, 18(1), 8-22. Lafferty T (2000), US Patent 6102281. Lai L and Zeng N (2000a), US Patent 6114679. Lai L and Zeng N (2000b), US Patent 6150646. Levin L and Pesheck P (1992), US Patent 5173580. Mikulski B et al. (1987), US Patent 4703148. Otoshi T (1972), `A study of microwave leakage through perforated flat plates', IEEE Transactions on Microwave Theory and Techniques, March, 235±236. Parker T and Tighe L (1990), `The evolution of conductive coatings', Tappi Journal, December, 86±92. Perry M and Lentz R (1996), US Patent 5571627. Pesheck P and Lentz R (1993a), US Patent 5182425. Pesheck P and Lentz R (1993b), US Patent 5254820. Pollart K and Habeger, Jr C (1995), US Patent 5410135. Prosise R et al. (1994), US Patent 5343024. Ramey R L and Lewis T S (1968), `Properties of thin metal films at microwave frequencies', Journal of Applied Physics, 39(3), 1747±1752. Ramey R L, Kitchen, Jr W J, Lloyd J M and Landes H S (1968), `Microwave transmission through thin metal and semiconducting films', Journal of Applied Physics, 39(8), 3883±3884. Seiferth O (1987), US Patent 4641005. Stone J et al. (1989), US Patent 4866232. Turpin C and Hoese T (1980), US Patent 4190757. Wait J (1985), Electromagnetic Wave Theory, New York, Harper & Row. WaÈppling-Raaholt B, Risman P O and Ohlsson T (2001), `Microwave heating of ready meals ± FDTD simulation tools for improving the heating uniformity', in Advances in Microwave and Radio Frequency Processing, 8th International Conference on Microwave and High-Frequency Heating, M. Willert-Porada ed., 243±255. Watkins J (2006), World Patent Application WO/2006/009779A. Weeks W (1964), Electromagnetic Theory for Engineering Applications, New York, Wiley, 648±649. Winters W, Chang H, Anderson G, Easter R and Sholl J (1981), US Patent 4283427. Zeng N (2001), US Patent 6251451. Zeng N et al. (2001), US Patent 6204492.

10

Shielding and field modification ± thick metal films

T H B O H R E R , Pac Advantage Consulting, LLC, USA

Abstract: Thick metal elements produce shielding and field modification when incorporated into microwave packages. Designs with materials that maintain conductivity and reflectivity at oven field intensities are used to create even heating, controlled differential heating and enhanced browning and crisping, offering food manufacturers the ability to create conventional oven food quality food in microwave cooking times. This chapter reviews the history behind the use of thick metal films, describes the package functions and designs possible from the use of thick metal elements and provides examples of the benefits resulting from their use. Key words: thick metal, shielding, field modification, foil, even heating, differential heating, browning, crisping, chemical etching, conductive, reflective, antenna, transmission.

10.1

Introduction

This chapter discusses the use of thick metal films in active microwave packaging. Section 10.2 frames the rationale for the use of thick metal films by highlighting the cooking problems that have and continue to motivate researchers to use these materials, and summarizing the evolution of the specific technologies evaluated and commercialized. The theory behind the use of thick metal films in microwave cooking is discussed in Section 10.3, which introduces and details the functionalities available from the use of these materials and why they can improve the quality and convenience of cooked foods in meaningful ways. The understanding of the basic principles involved leads to a discussion of desired design options for the different effects possible. Examples of packaging structures employing these designs are presented. The effective use of thick metal in microwave packaging requires the ability to accurately and economically pattern this material. Section 10.4 outlines approaches that have been proposed and/or introduced in the marketplace. Chemical etching, the primary approach utilized commercially, is given more detailed treatment. Section 10.5 focuses on attempts to use antenna structures to collect and transmit or transfer microwave power within a food/package system. Different approaches that have been proposed are reviewed.

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Commercial examples demonstrating the significant benefits of the use of thick metal films are highlighted in Section 10.6, which also describes the range of configurations possible using today's technologies. Finally, Section 10.7 wraps up the key points of the chapter, providing comments on the future use of thick metal films in microwave packaging.

10.2

History

10.2.1 Objectives of use As microwave food heating emerged as a viable food service and domestic alternative to conventional methods of cooking or heating foods (such as hot air ovens and frying utensils), an early objective was to find ways to use stamped foil trays, which were commonly used for retail frozen foods and for reheating foods in food service applications. Durable, heat resistant and relatively easy to form into complex shapes, including multiple compartments, these trays are manufactured from thick metal films. Unfortunately, the metal in these packages acts as a complete shield to incident microwave energy, and heating in traditional metal containers made with continuous thick conductive sheets is plagued by cold food near the walls, with particular problems at the container bottom, where energy can only reach the food after penetrating the food above it. This phenomenon is even worse in bottom corner areas and greater container depth exacerbates the effect; these difficulties have severely limited the use of foil trays or other metal containers as primary microwave compatible containers. This chapter will briefly mention approaches designed to overcome this limitation, but will focus on the use of patterns of thick metal films in conjunction with materials possessing meaningful levels of microwave transparency and/or absorption. The primary objectives for using patterns of thick metal films in packaging structures are to overcome two fundamental limitations of microwaving food items in largely transparent containers ± the tendency for many items to have overcooked edges and undercooked centers, and the difficulty of coping with the different component heating rates encountered when heating multi-component meals or foods. Overcoming the large temperature variability present when heating in conventional, passive microwave packages provides more benefits than convenience and consumer satisfaction; eliminating cold spots helps ensure that minimum temperatures for food safety can be met in a wide range of ovens and cooking conditions.

10.2.2 Introduction to shielding and field modification Thick, conductive metal films behave quite differently from the thin, resistive metal susceptor films described in Chapter 9 and form the basis for shielding and

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field modification packages and package components. These materials also have a role to play when difficult to brown and crisp products are encountered. Shielding and field modification approaches use similar principles; strictly speaking, a shielding component or indeed any object that interacts with the electromagnetic energy generated by the oven magnetron acts to modify the microwave field. The two approaches are treated somewhat separately here due to the different degrees of complexity associated with the design and production of effective packaging structures exploiting their effects. For this discussion, shields are considered to be structures which exclude by reflection all or a portion of the microwave energy that would otherwise impinge on a specific part of a food item, thus concentrating the available energy on those parts of the food that are not shielded (or shielded as much). Shields are those structures or packages that create macro or gross impacts on the energy distribution in the oven, and thus in the food. Field modification packages go a step further by affecting in a controlled and predictable fashion either local energy distribution (by intensifying, moderating, leveling or even accentuating small-scale energy distributions), or by transferring energy from the point of incidence to another point where this energy can be more advantageously used. Designers generally create shields by utilizing large contiguous areas or large-scale patterns of thick metal; they create field modification structures by employing more complex, smaller-scale patterns of thick metal to achieve heating objectives. When thick metal is used in conjunction with the resistive susceptors of Chapter 9, hybrid structures can be created that can achieve even more sophisticated effects, combining enhanced browning and crisping with controlled heating.

10.2.3 Early thick metal approaches Previous chapters describe the parameters that define heating rates of food items and components exposed to microwave energy and illustrate the significant differences that exist among the foods and ingredients of interest to food designers. This section uses selected US patents to provide a partial overview of early attempts to incorporate thick metal films to overcome heating challenges. Early users of food service microwave ovens quickly learned that reheating a multi-component food or meal in a microwave oven was an exercise in suboptimization and sought ways to overcome this challenge. In an early example of the search to apply conductive metal shielding, a patent issued in 1952 disclosed a means of heating a food package in a microwave oven and controlling the heating effect by an electrically conductive shield positioned in proximity to a portion of the food package and acting to prevent access of the high frequency waves to portions of the package and to cause the high frequency waves to reach and heat some portions of the package to a greater degree than other portions thereof.1

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10.1 Shielding appliance for cooking microwave sundae (from US Patent 2,600,566).

The approach employed a sturdy metal cup (item 6 in Fig. 10.1) to partially enclose a paperboard container (item 1) holding ice cream (item 3) topped with cake (item 4) and syrup (item 5); the cup shielded the ice cream from microwave energy, keeping it frozen, while allowing the syrup to heat, creating a frozen ice cream sundae topped with hot syrup. Another inventor described similar features in a patent issued in 1955,2 and a series of patents describing patterns of apertures and spatial deployment of conductive metal films issued over the next few decades, although few of these approaches ever saw commercial light beyond food service or in the form of permanent appliances. (A partial listing of early patents is included in an earlier publication.3) Inventors created shielding devices in the form of rigid apertured metal sleeves designed to slide over plated meals prior to microwave heating.4,5 While durable and reusable, these sleeves were bulky, expensive and inflexible in use. Each specific pattern of apertures only worked well with specific combinations and placements of foods, limiting food types, portion sizes and arrangements. The significant thickness and durable construction of these permanent devices made them largely free of problems with arcing, so long as they were kept away

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from the microwave oven walls and not placed in close proximity to other conductive packaging elements. Others recognized the potential advantage of using lightweight packages with foil elements and were granted a patent describing a food package made of dielectric material and partially overlaid with a single, continuous conductive sheet arranged to expose multiple food articles to different amounts of microwave radiation.6 In Fig. 10.2, area 40 is the foil sheet that is positioned on the paperboard blank, item 14. This patent acknowledged that package arcing and charring could result from certain conductive film configurations and described avoiding sharp points through the use of smooth, rounded corners. Fabrication, however, was simply described in the specification as laminating the two materials together, with no mention of specific means to prepare and adhere the conductive material to avoid defects that could cause arcing or charring. Developing safe, predictable and economical means to incorporate thick metal films became the primary impediment to the commercialization of disposable microwave packages incorporating shielding and field modification elements. Scientists at Raytheon, the company which introduced the first RadarangeÕ microwave ovens for commercial and home use, experimented with fringing heating (concept described below) to intensify heating using metal elements.7,8 Decades later, others would attempt to harness the fringing phenomenon in disposable packages.

10.2 Continuous foil sheet attached to folding carton blank for partial shielding (from US Patent 3,865,301).

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It was also known that microwave absorbing materials could be mounted on thick metal films and function effectively if of proper thickness.9 Absorbers exploiting both the magnetic and electrical components of the microwave field could be made this way and were proposed as packaging elements.10 Later, manufacturers of pressed aluminum containers would use this phenomenon to find ways to increase the acceptance of these containers for microwave use.11 None of these approaches would see meaningful use in disposable packages. While the primary focus of shielding technology using thick metal films was on rigid packages, significant effort was also expended on flexible packaging structures. A series of patents issued starting in 1979 to The Procter & Gamble Company described `microwave energy moderating bags'.12±16 Perforated foil sheets adhered between thermoplastic films provided partial shielding for bag contents, with meat roasts often the stated target food. These patents described both static and dynamic shielding capabilities; shrinkable films reduced foil aperture sizes as the films shrank due to exposure to elevated temperatures, providing greater shielding than pre-shrunk structures as cooking progressed. More recently, flexible packages have been proposed to protect popped kernels of popcorn from further heating.17,18 These designs attempted to overcome the tendency of popped kernels of microwave popcorn to continue to be exposed to significant direct microwave heating, which further dries and toughens the kernels, potentially leading to scorching and, in extreme cases, burning of the product. The first approaches use an expandable apertured shield to limit not only the amount of energy that penetrates the shield, but through proper aperture sizing, the depth to which a portion of the energy can propagate. (The penetration depth limiting phenomenon is described below as evanescent propagation.) This design permits continued power delivery to the susceptor for further popping while protecting popped kernels from excessive exposure to microwave energy and can be incorporated into bag structures. The second approach uses an expandable storage chamber made from a continuous shield material; popped kernels are displaced into the shield by the force of popping and are held there protected from further microwave energy exposure. The commercialization rate for patented structures is, in general, not high, and the packaging structures described in this section as well as the many other patents covering thick metal structures are no exception. Some were not commercialized due to functional failure, material availability or cost, safety or the lack of cost-effective converting equipment to produce reasonable packages. In some instances, the packaging technology described was well ahead of the requisite complementary food technology. These patents and the work they represent are significant manifestations of the intense desire on the part of package producers and users to manage electromagnetic radiation exposure in the microwave oven. A continuing evolution of understanding and innovation led to commercially viable packages that played an important role in changing the way consumers prepared popular food items.

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10.2.4 Commercializing thick metal packages The Pillsbury Company introduced the first widely distributed disposable microwave shielding component as part of the package for a 10 cm square frozen microwave pizza commercialized for convenience stores about 1980. Foil laminated paperboard folded and glued into an inverted tray served as the lid for what also was the first commercial metalized film susceptor package. Apertures in the lid vented moisture and permitted controlled ingress of microwave energy to cook the pizza toppings while diverting the majority of the energy to the susceptor pad under the pizza crust. Patents describing a multi-component package (using a different susceptor technology) and specifics of the shielding lid issued to Pillsbury and American Can, respectively.19,20 The lid and a simple tray for containing food are illustrated in Fig. 10.3. This shielding lid was produced from an overall lamination of aluminum foil to paperboard by die cutting circular apertures in the top panel and rounded corners on the periphery of the blank, and required well-adhered glue tabs to create a low impedance electrical connection between the foil on the glue tabs and the foil of the sidewalls of the lid which the tabs overlay. This low impedance connection minimized the possibility of creating a sufficiently high electric potential between two foil layers that could lead to arcing. The patent specifically taught the risk of arcing from glue tabs that became detached and also described shielding lids using glued web corners instead of glued tabs.

10.3 Apertured foil laminated shielding lid and microwave transparent food support tray (from US Patent 4,345,133).

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Overall foil laminations patterned with post die cutting, while effective for relatively simple applications like this first use (single, small and uniform product), fail to provide sufficient versatility for larger, multi-component products and more complex heating requirements. The foil needs to be combined with other continuous layers or structures resistant to food penetration or leakage if the thick metal functionality is to be incorporated into barrier packaging components such as trays or lids. Other means to selectively incorporate patterns of thick metal films with intricate shapes were needed to satisfy the requirements of food developers. Alcan patented a series of structures incorporating large-scale patterns of thick metal films primarily aimed at field modification through the creation of higher mode heating configurations in a container.21±26 The fundamental energy mode in the body of a substance to be heated is characterized by a concentration of energy at the periphery of the substance, or the container if the substance fills the container. Higher heating modes increase the number and reduce the scale of the standing waves that develop. A producer of aluminum foil and pressed foil containers, one of Alcan's primary objectives was overcoming the very poor temperature profiles that develop in foods microwave heated in these trays. Much of Alcan's technology was based on the concept of conductive elements placed above the food creating a multiplicity of smaller standing waves beneath them, leading to smaller dimensions for heating variations. Smaller variations should result in more uniform temperatures at the end of the cook cycle, and should equilibrate more quickly during post-heating rest or wait time than larger-scale variations resulting from unmodified microwave energy distributions. While improved cook performance was achieved using these elements, no simple, cost-effective and robust methods were developed to place the required multiple small aluminum patches into either rigid or flexible lid structures. Adhesive-backed patches are susceptible to mechanical damage and variability in placement; adhesive failures, particularly at patch edges could lead to arcing. This technology was widely evaluated by food companies, but little commercial activity resulted. Chemical etching of largely opaque evaporated aluminum coatings on film was introduced to create patterns that served as decorative windows in bags and pouches. Sodium hydroxide readily reacts with and dissolves aluminum, offering the potential to create patterns in sheets of the metal. Previously available etching technology was largely confined to batch processing, which was unsuitable in both capacity and cost for the large areas required for high-volume food packages. Beckett Packaging developed a high-productivity roll-fed process to etch patterns in evaporated aluminum coatings, which served as the launching point for extending etching to thick metal films; this important process will be described in more detail later in this chapter.27 Concurrent with the development of this process came package designs capable of providing functional, reasonable cost shielding and field modification

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effects in paperboard based structures.28±34 Introductions came first in Europe, for high-value frozen foods enabled by this technology, but introductions were limited by sufficient converting capability to translate the complex foil patterns now available into commercial packages. The etching hardware and technology were acquired by Fort James Corporation, later part of Graphic Packaging International. Its further research, investment and access to downstream converting capability have resulted in significant commercialization activity for food products in Europe and North America, with growing activity on other continents. This remains the primary thick metal patterning capability for microwave packages today, and introductions continue for new products.

10.3

Physics and design principles

10.3.1 How thick is a thick metal film? For the purposes of microwave package design, metal films become `thick' when they move from the realm of having meaningful transmittance or absorbance of 2450 MHz microwave energy to being effectively 100% reflective. This reflectance corresponds to the metal films being essentially completely conductive and not generating bulk-resistive losses as they carry the electrical component of the microwave field in the oven. Complete conductance or reflectance at the expected field strength exposure is the property that matters, and care must be taken when measuring the performance of potential structures to understand reflective performance at real world oven field strengths. Most often, the reflectance, absorbance, transmittance (RAT) properties of microwave packaging materials are non-destructively characterized in low-power microwave network analyzers. While useful for characterizing initial properties of materials, the low electric currents induced in such units fail to identify potential electric breakdown of materials at typical oven cooking conditions. Practically, what this means for metal films is that to be considered `thick', they should be at least one skin depth thick, as discussed below, preferably at least two skin depths thick. For this discussion, skin depth is defined as the thickness of the layer at the surface of an electrically conductive material in which a large portion of microwave-induced electric currents are contained and carried. The skin depth can be calculated as follows: s 2 10:1 s ˆ !a where s ˆ skin depth,  ˆ conductivity, ! ˆ angular frequency, and a ˆ absolute permeability. Inserting the properties of pure aluminum at 2450 MHz yields a skin depth of 1.7 m for the material of most commercial interest and practicality for

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microwave packaging. The skin depth equation is developed for radiation incident from one side and as microwave field exposure may occur from both sides of the metal layer, thicknesses below two skin depths, or roughly 3.4 m for aluminum, may experience stress amplification in the bulk and risk breakdown at power levels normally experienced in microwave oven heating. Standard 7.24 m thick packaging grade aluminum foil exceeds two skin depths in thickness, is largely free of structural defects and easily handled on common packaging converting equipment. Properly designed microwave packaging elements from this material provide stable performance at required oven power levels. High optical density evaporated aluminum layers have been proposed for use as shielding materials due to their foil-like appearance and temptingly high reflectance characteristics as measured on low-power network analyzers. To date, however, these materials fail to perform as effective shields at commonly encountered electric field strengths in typical domestic or food service microwave ovens. Previously published data showed a sharp drop-off in reflectance for 3.5 optical density metalized films laminated to paperboard at incident power levels between 100 and 200 W in a VR430 waveguide.35 For this waveguide, these power levels represent electric field strengths between 5600 and 7900 V/m. To put this in perspective, electric field strengths of 9400 V/m and higher are measured in typical domestic microwave ovens, placing the reflectance breakdown power level squarely in the range of expected field strength exposure.36 Owing to the low loss factors of frozen foods, interactive microwave packaging components are subjected to almost all of the electric field intensity immediately after power is applied in the heating cycle. It is at this earliest portion of the heating cycle that the reflectance properties of high optical density evaporated films are lost, rendering them ineffective as shielding devices and incapable of carrying sufficient current to act much different from partially degraded standard thin film susceptor materials. By comparison, in these same tests standard thickness foil showed no deterioration at the full power capability of the test equipment (2300 W, which corresponds to field strength of 26 700 V/m). It should be noted that the reason this test data indicated less than 100% reflectance for foil is that a 3.175 mm gap was left around the edge of the foil or metalized film sample so perimeter currents characteristic of microwave oven operation would be imposed on the material, which factor into the total electric stress experienced by fully or partially conductive elements. Despite the lack of demonstrated success for the high optical density evaporated films as conductive and reflective elements at real world oven conditions, researchers continue to explore means to employ them. Lower initial cost and relative ease of patterning these thinner films compared with 7.24 m foil are powerful incentives for the development of creative solutions to their

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power handling shortcomings. There is no present commercially demonstrated solution to this shortcoming; therefore, the remainder of this chapter focuses on the use and preparation of metal films greater than two skin depths in thickness.

10.3.2 The roles of thick metal films in microwave packaging Thick metal films provide valuable options to the package designer, expanding available package functions beyond those achievable in passive, transparent containers or in packages solely incorporating energy absorbing susceptor elements. Modest shielding and field modification occur when using susceptors, but rarely to the extent necessary to make significant energy distribution changes. Susceptor placement is also often not consistent with the needed placement of shielding or field modification elements. The early microwave pizza example demonstrates this dilemma well; the susceptor was placed under the bottom of the crust to assist browning and crisping, while the pizza topping required shielding located above the pizza to prevent overcooking. Reflect, conduct, redirect, redistribute and reradiate are a few of the terms that can be used to describe the effects thick metal film elements have on microwave energy in microwave packages incorporating them. These effects lead to three main results in microwave packages: · even heating; · controlled differential heating; · browning and crisping. While the first two effects can most often be achieved solely with thick metal elements, browning and crisping effects are typically achieved in conjunction with susceptor elements. Even heating Large-scale thick metal patterns exclude incident energy from adjacent sections of a food product; proper placement of the metal reduces the heating rate of those food sections absolutely compared with an unmodified package and also relatively compared with non-shielded areas. Where the unmodified heating of the food product or products is known to result in undesirable temperature distributions, designs can be created that generate proper distributions through the redistribution of energy to overcome common tendencies for edges (especially corners) to be overcooked and centers (especially the bottom center of the food mass) to be undercooked. The simplest shielding approaches provide shielding on sidewalls of trays while leaving the majority of the tray floor transparent. An example of this approach is shown in Fig. 10.4, where the rim, sidewalls and a small portion of the edges of the floor of the tray (areas numbered 3, 4 and 5) have a layer of foil,

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10.4 Tray with foil shielding on sidewalls, rim and extending partially into base (from US Patent 4,351,997).

while the majority of the tray floor (area numbered 2) does not have this metal layer and is completely transparent.37 A tray with this type of thick metal pattern would be best used for a product that is relatively uniform in thickness and whose heating characteristics in the length and width dimensions vary little, and may also incorporate a shielding lid to force more energy through the microwave transparent bottom of the tray. Food weights above roughly 350 g exceed the ability of this relatively simple design to provide even heating.38 Smaller-scale metal patterns aim to modify the microwave energy pattern more locally, and are also aimed at creating even heating of relatively homogeneous foods. The arrays of foil patches applied to the lids of containers mentioned earlier were designed to create higher order modes of heating than would occur with purely passive packaging. The theory behind these approaches is to create smaller heating `cells' in the food, yielding smaller temperature differences over smaller dimensions and resulting in more uniform final temperature profiles. Figure 10.5 illustrates an array of such patches (squares numbered 606 in a regular array adhered to a rigid lid on a tray) designed to create higher order heating modes and greater temperature uniformity.39 More complex patterns can be used in conjunction with large-scale shielding to enhance the transfer of energy to the most difficult place to reach in a food item, the center of the bottom. In addition to providing more uniform heating, such systems can make the heating results more tolerant of variations in oven performance, product or total load in the oven (i.e. cooking more than one item, including cooking several different items). Resonant loops can be used to increase energy absorption as well as conduct energy across the floor of a tray, biasing the distribution of energy to the portion of the food needing the largest heating boost. Figure 10.6 shows an example of an oval tray combining sidewall

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10.5 Top view of field effect foil patch array on tray lid (from US Patent 4,831,224).

10.6 Tray with shielded sidewall and containing resonant loop in base (from US Patent 5,593,610.

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shielding extending just into the bottom wall (areas 32 and 34) with an annular ring (area 36) in the base of the container; the tray was designed for use in conjunction with a lid incorporating cooperating conductive elements to provide a robust heating packaging system.40 De-tuning unloaded resonant elements To reiterate a previous important point, the larger the total food load, the more likely thick metal elements are required to achieve even heating results consistent with minimum consumer quality, cook time and food safety requirements. As the food load increases, however, so does the likelihood that consumers may eat only a portion of the food at the first sitting and place the remaining food in the refrigerator in the original package for later reheating. This practice presents a significant safety challenge when highly interactive resonant loops or other field modification features have been incorporated into a package. These features must interact strongly to function effectively to modify the field or transmit energy when adjacent to a meaningful food load, but in the absence of such a load into which energy can be constructively dissipated, have the potential to cause excessive local energy concentration and heating of the package and any remaining food residue during a subsequent microwave heating cycle. Package damage and food residue scorching or even burning could result where food has been completely or partially removed. In the highly unlikely instance that a consumer would cut through the protective film layer and damage the thick metal element, it could lead to arcing in an unloaded condition. A solution has been created for this problem that uses the presence or absence of food adjacent to the loops to selectively tune or de-tune their functionality.41 By appropriately segmenting loops or other conductive metal elements, DC electrical discontinuity is created between the segments, rendering them largely inactive in the absence of an adjacent load. When food is adjacent to the loops, it dielectrically loads the gaps between the segments, raising the capacitance and creating a continuity effect or coupling between the segments. This capacitive coupling allows the segments to function as effective resonant loops, power transmission lines or reflective areas, albeit at lower efficiency than unsegmented features of similar overall dimensions. In the absence of an adjacent food load, the pattern is detuned from a resonant state and becomes effectively non-interactive with incident microwave energy, preventing arcing, overheating, scorching or burning. Figure 10.7 shows an example of segmented patterns which provide shielding that automatically tunes and de-tunes depending on whether a food load is present or absent.42 Further work has resulted in a growing number of abuse-tolerant structures incorporating patterns of thick metal films.43±46

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10.7 Pattern of repeated segmented metallic interactive elements (from US Patent 6,204,492).

Controlled differential heating Highly heterogeneous or multi-component food products represent a more complex heating challenge; different food items react very differently to microwave energy and can heat at significantly different rates. Differences in shapes and sizes of different components further complicate finding an optimal heating protocol, with the unfortunate outcome of sub-optimizing the heating and resultant quality of all components. Different target temperatures (such as desired in the earlier ice cream sundae example) are likely for the different food products as well. Creating differential heating microwave packages starts with creating an in-depth understanding of the cooking dynamics of each component and the optimal end state at the time of serving. Food density and moisture content, microwave absorption characteristics, thermal conduction, tendency to crisp, brown, toughen, etc., all of which change as the food heats, affect the final results. Cooking individual components separately begins the process of understanding the nuances of how each component behaves in a microwave oven, and also begins to quantify the nature and complexity of the challenge being faced. Once the heating performance parameters for each component are understood, the next step is to determine how the components will be arrayed in the final package. Multi-compartment trays or separate containers for each component

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may be used, or the components may just be arranged in a predictable (sometimes not so predictable!) way in a single-compartment tray. Interactions between the individual items must be accounted for and first approximation packaging elements are then designed and tested. Sound experimental procedures that include monitoring oven power input, cook time, resultant food temperature profiles and food product characteristics accelerate the iterative process of tuning conductive elements to optimize performance. Once performance is satisfactory in the single oven that should be used for first evaluations, it is prudent to test performance in a selection of relatively popular ovens known to represent a wide variety of cook behavior. Conductive element design changes to accommodate the expected range of consumer oven variability can improve predictability of heating results, making consumer heating instructions simpler and more reliable, and increasing the likelihood of satisfied customers. The photo in Fig. 10.8 of a simple two-compartment paperboard tray with full bottom and sidewall shielding in the smaller compartment shows the low end of the range of pattern complexity that can be envisioned. The more complex patterns presented in other figures and references represent the wide range of design possibilities available for the package designer. Different patterns can be incorporated into different compartments or sections of the package to overcome heating shortcomings that might otherwise have to be dealt with through the inclusion of additional package components or more complex handling requirements on the part of the consumer. Since simple package designs that minimize the number of discrete package components and manipulation by the consumer before, during or after heating

10.8 Two-compartment paperboard tray with full shielding in smaller compartment (courtesy Graphic Packaging Int'l, Inc.).

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offer the best chance for commercial success, building functionality in through complex thick metal patterns is a powerful route to packages that robustly satisfy cooking and safety requirements. An additional differential heating (and browning and crisping) concept to be considered is that of evanescent propagation heating.47 Properly sized apertures in reflective material create limited propagation on the side of the reflector opposite the incident microwave radiation. The energy that can be transferred decays exponentially with distance and can be used to increase the ratio of surface to bulk heating. The previously cited popcorn package used this mechanism to limit the exposure of popped kernels to energy while maintaining energy transfer to the microwave susceptor to complete the popping cycle.48 Browning and crisping The susceptors of Chapter 9 cannot provide browning and crisping for all food items. As product mass, dimensions and moisture content increase, standard susceptors are less able to raise the temperature of all the surfaces to be browned or crisped. Once again, bottom centers represent the greatest geometry challenges in heating, and creating satisfactory texture and color development completely across crusts for large pies or pizzas has proven especially difficult. High moisture content breaded or enrobed dough products require a delicate balance between creating appropriate color and texture on the surface while avoiding drying out or toughening the center of the product. Thick metal films offer the ability to enhance the heating of standard susceptors by helping to ensure that all portions of a susceptor are exposed to the energy required to raise their temperature to desired levels. Figure 10.9 shows a blank for a rectangular pressed paperboard tray that incorporates complex combinations of conductive element patterns that can be used alone or in hybrid structures when positioned to overlay a metalized film susceptor.49 Designs of this type can operate by exploiting multiple functionalities, combining shielding and field modification with fringe heating to enhance susceptor performance and energy transfer (see Section 10.5) to activate susceptor areas that otherwise would experience very little incident microwave energy and would have little ability to convert sufficient energy to achieve browning and crisping temperatures in the food. Fringe heating with thick metal films can occur when elongated apertures or spaced transmission lines are created in reflective material.50 Strong energy dissipation occurs when a product is immediately adjacent to these apertures or lines and these elements have been explored in the search for a means to create grill marks on food placed adjacent to such elements. Unfortunately, the thermal mass of foods typically desired to exhibit such marks, such as meat portions, has exceeded the ability of these constructions to create this effect. They are,

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10.9 Blank for rectangular pressed tray with conductive element apertures, arrays and segmented transmission loops (from US Patent 6,677,563).

however, capable of increasing surface heating, and if used with susceptors can enhance susceptor performance.

10.4

Patterning thick metal films

10.4.1 Patterning approaches explored Several patterning approaches were discussed in Section 10.2, and represent a subset of the approaches proposed by those who recognized the importance of patterning thick metal films for microwave packaging. A more complete listing with brief comments on each technique follows. · Die cutting rigid metal sheets to be formed into sleeves or boxes. These early, permanent appliances were durable, but costly to manufacture and limited in flexibility for different foods or arrangements. Since they were not suitable for disposable packaging, they principally found use in food service applications.

Shielding and field modification ± thick metal films

255

· Post-trimming apertures in formed foil trays or containers. While effective in providing transmission openings on the bottom of foil containers, this approach is cumbersome since the resulting structure is not capable of holding food unless a leak-proof insert is sealed over the opening or the apertured tray is used to hold a separate, microwave transparent tray. Recently, a metal can with a microwave transparent bottom and selectively removable metallic lid has been proposed, which would essentially leave a continuous sidewall shield with microwave transparent ends.51 · Die cutting or punching apertures in self-supporting foil or foil/film laminates subsequently laminated to flexible films and/or rigid non-interactive sheets. Although mechanically removing segments from self-supporting foil or laminates with film is less capital intensive than chemical etching, cut quality is critical to avoid defects that can lead to arcing. There is also a limit to how large the apertures can become before web handling difficulties arise, and fine detailed patterns are difficult to achieve. · Die cutting foil (preferably mounted on carrier substrates) and spot adhering the resulting patch to a carton blank for later folding and setup. Suitable only for extremely simple, large-scale patterns, this simple process must be implemented carefully to avoid cut quality issues or edge damage to the foil during package fabrication and filling. · Laminating foil to paperboard or paper and die cutting the combined structure. The approach used for the first major commercial shielding introduction is relatively simple to implement, but patterning an overall foil lamination requires creating apertures in the structure. Unless these apertures are subsequently covered, other packaging components must provide barrier to contamination or permeation during storage. Strip laminating foil followed by die cutting can result in selective placement of foil on package blanks that can be subsequently folded to provide large-scale, simple patterns in trays.52 · Chemically etching patterns in foil mounted to film and post-laminating the structure to paper or paperboard. This versatile process has become the predominant choice for patterning thick metal and is discussed in more detail below. · Using pressure-sensitive label processes to create self-adhering patches of foil (generally laminated to a carrier substrate) that are attached to formed package components. With an understanding of the previously discussed limitations (potentially prone to damage, placement error and generally restricted to simple patterns), this approach may have merit for applications where the simplest shielding or field modification effects are desired. Application complexity grows when multiple patches are required on a single package, requiring either pre-patterning of one large pseudo-label or multiple application stations. A recent patent proposes applying a shield label to the cover or sidewall of an already filled food package.53 This patent anticipates possible damage to the foil and teaches foil thicknesses between 25 and

256

Packaging and products for use in microwave ovens

500 m, 3 to 70 times the thickness of the foil used in commercial packages prepared by chemical etching. · Pattern adhering foil to paperboard, die cutting or laser cutting the foil component in register with the edge of the adhesive pattern and stripping the loose foil away to leave a solidly adhered pattern on the board, which can then be over-laminated with a protective film.54 This process simplifies foil handling compared with the pre-punching of foil described earlier, and is not as limited in terms of the amount of foil to be removed, but is still limited in the resolution of patterns that can be produced. For patterns of simple or moderate complexity, this process is attractive as it uses proven process elements, can conceptually be retrofitted into existing adhesive lamination equipment, and offers the opportunity to recycle unneeded foil. Mechanical die cutting is expected to result in a faster process, while laser cutting could offer the ability to create more complex patterns. · Using a laser to vaporize unwanted foil from a laminated structure to leave behind the desired foil pattern.55 Potentially only useful for patterns in which minimal foil is to be removed due to the high power requirements to remove large sections of metal. · Printing a shielding material in a pattern on a package member and protecting the shield from subsequent damage. While periodically claimed in patents,56 the paucity of specific formulation and performance data provided suggests that this elusive objective has yet to be achieved from a performance point of view, much less by using materials compatible with producing food packages at reasonable cost. The discussion in the previous chapter on printed susceptor structures described the difficulties in achieving practical formulations for these resistive structures; achieving highly conductive printable formulations capable of robustly carrying high current loads has yet to be demonstrated on a practical basis for packaging, although it will remain an objective for researchers.

10.4.2 Chemical etching Commercially, chemical etching is the method of choice for producing packaging structures incorporating thick metal films. The use of an aggressive chemical to selectively remove metals is well known in the art, and some of the difficulties associated with etching aluminum with hot aqueous alkali such as sodium hydroxide were being addressed in the 1950s.57 The growing availability of vacuum metalized films for packaging opened the door for high-speed, lowcost roll to roll selective etching of thick metal films to be developed. The basic process steps for selective patterning are: 1. 2.

mount the etchable metal film on an etchant resistant carrier web; print a chemical resist in a pattern corresponding to desired final metal pattern;

Shielding and field modification ± thick metal films 3. 4. 5.

257

expose the structure to an etchant capable of dissolving the metal to be removed; neutralize any etchant remaining after the web exits the etchant exposure area to prevent any further etching; and protect and prepare the etched pattern for subsequent converting operations.

Steps 1 and 2 are easily accomplished on separate lamination and printing hardware, but from a practical and cost-effectiveness point of view, steps 2 through 5 are best combined into a single continuous process which minimizes extra handling between key steps in the process. The continuous process avoids contamination or damage to surfaces that could take place during winding of rolls prior to or after etching and prior to protection of the etched pattern. Figure 10.10 shows a schematic of the etching process. The brevity of this description belies the complexity associated with consistently and economically operating this process. Aqueous sodium hydroxide, often referred to as caustic soda, or simply caustic, is the etchant of choice for etching aluminum foil laminated to oriented PET film. This strong base aggressively attacks aluminum-generating reaction products of aluminum hydroxide, aluminum oxide and hydrogen gas; the reaction is exothermic. Coatings resistant to caustic are readily printable using conventional application methods. Achieving high-speed etching of 7.24 m foil requires, in addition to very good web handling and tension control (especially in the caustic exposure area): means to contain the concentrated (~50%) caustic at elevated temperatures to increase reaction kinetics; sufficient exposure time to the caustic to completely remove the aluminum foil in the areas unprotected by the pattern resist coat; make-up caustic addition to replenish the strength of the etchant working on the exposed foil; means to extract the heat generated by the reaction; the ability to capture and neutralize any caustic mist and to react evolved hydrogen gas to prevent explosions; and filtration means to remove precipitated reaction products or other solid contaminants that would affect etching quality. Ultimately,

10.10 Schematic of chemical etching process.

258

Packaging and products for use in microwave ovens

10.11 Packages containing thick metal film elements (courtesy Graphic Packaging Int'l, Inc.).

dissolved contaminants reduce etching efficiency and quality, requiring complete replacement of the etching bath; fortunately the neutralized spent etchant has value as a raw material for other industrial processes, eliminating potential disposal problems for this complex solution. With proper process control and selection of raw materials, precise replication of high-resolution patterns can be consistently reproduced and the resulting lamination to rigid substrates can be converted into a variety of packaging forms, including cartons, sleeves, cards, inserts, pressed and folded trays. Figure 10.11 illustrates examples of thick metal containing packages, including packages that combine thick metal elements with susceptors.58 While paper and paperboard have provided the structural rigidity for commercial packaging articles to date, combinations of thick metal elements with polymeric packaging components have been considered in the past and continue to be pursued.59,60

10.5

Antennas

It is not surprising that package designers have thought in terms of antennas as they attempted to incorporate thick metal films into packages to capture, transmit and reradiate energy; the basis for microwave cooking came out of work done during World War II to optimize performance of radar defense systems, systems which ultimately were a key element in the Allies' crucial victory in the Battle of Britain.61 By definition, an antenna is simply an arrangement of conductors that can either generate an electromagnetic field in

Shielding and field modification ± thick metal films

259

response to alternating voltage applied to the conductors or, when placed in such an electromagnetic field, have induced in the antenna an alternating current. This reminds us that the magnetron of a microwave oven is a field-generating antenna. The circuits discussed above created from thick metal films have primarily acted as receiving antennas, activated by incident electromagnetic radiation and dissipating energy into nearby food, or at most, food located a short distance away. Typically, in the package structures illustrated and referred to above, the receiving points are located immediately adjacent to the food load. Partly inspired by early and periodic examples of receiving antennas which were intended to protrude directly from food items,62±64 or which were incorporated into permanent browning or cooking dishes,65 package designs have been proposed which incorporate antennas with receiving or collection points separated from the food and generating or dissipating points adjacent to the food.66 Figure 10.12 is illustrative of this effort, with loop 10 representing the collection portion and lines 20 and 22 representing dissipation portions underlying a susceptor disk 40.67 The concept is to capture energy at a point substantially removed from the food product, where the strong receiving characteristics of the antenna can capture significant energy and transmit the power in current form down the linear tracks where it can interact with the food, a susceptor or other structures as desired. In this particular execution, the impedance of the dipole antenna is matched to the impedance of the destination transmission portion to minimize reflection and re-radiation by the antenna.

10.12 Conductive metal antenna with dipole collecting loop and linear transmission/dissipation lines (from US Patent 5,322,984).

260

Packaging and products for use in microwave ovens

Since the antenna loops are intended to be strongly interactive as receivers of microwave energy, one of the difficulties in applying them practically to packages has been to find ways to limit the interactions when food loads are reduced, as has been done in segmented active thick metal elements as described above. The development of segmentation technology has been important in permitting the use of this special subset of antennas in packages.

10.6

Application examples

While packages incorporating thin film susceptors of the type described in Chapter 9 represent by far the largest commercial volume of interactive microwave packages, growing application is being made of packages exploiting the performance advantages of thick metal films. The ability to create uniform temperature distributions in large, multi-serving sized products offers the opportunity to dramatically reduce cook time compared with conventional oven cooking while achieving similar or even improved cook performance. This discussion will highlight the dramatic results achievable for large products, but single serve items can also be improved by the use of these designs; examples of a single serve style tray are shown in Figs 10.11 and 10.13 and a planar card for an enrobed dough hand-held snack is shown in the lower right corner of Fig. 10.11. The poor cook performance of large products, such as a 1 kg family size lasagne, in microwave transparent trays (the overdone edges and top surface experience excessive moisture loss while centers are undercooked) largely prevented these products from being viable microwave products, and relegated consumers to greater than one hour conventional oven preparation times when oven preheat cooking time is included. Dramatic cook time reductions and better

10.13 Trays with sidewall shields and segmented resonant loops in base (courtesy Graphic Packaging Int'l, Inc.).

Shielding and field modification ± thick metal films

261

product quality are achieved when thick metal patterns are incorporated into trays for this product. Table 10.1 provides data for four commercial packages, comparing cook time in a conventional oven with cook time in packages incorporating aluminum foil elements, some also including susceptor film.68 In all cases, product weight loss during cooking was similar in the thick film containing microwave packages to conventional oven cooking. For the lasagne cooked in the passive microwave package, product weight loss was twice that in the pattern foil shielding package. Customers and consumers judged product quality of the food prepared in the thick metal microwave packages to be equal or superior to the products prepared in the conventional oven. The 1.1 kg lasagne was cooked in the tray on the left of Fig. 10.13, which incorporates partial sidewall shielding with segmented resonant loops on the package bottom wall.69 The design used for the rectangular meat pie with top and bottom raw dough crusts combines the unique challenge of balancing heating in a shape lacking radial symmetry with that of cooking, browning and developing texture in a frozen raw dough crust in contact with a moist filling; the complex structure is illustrated in the upper left corner of Fig. 10.11 and described in an issued patent.70 This product enablement offers the opportunity for food manufacturers to extend their range of convenient prepared food products when microwave cooking becomes a high-quality, time-saving way to heat products that previously required heating in a conventional oven. Reductions in preparation time of at least 70% compared with conventional ovens, and elimination of all too common requirements for constant consumer attention and package manipulation during cooking for passive packages creates a powerful tool for food manufacturers to convert long preparation time products into fast preparation foods competitive with the time and energy (and often higher cost) associated with stopping for take-out food. Instead, popular family meals and foods can be prepared quickly and simply from pre-purchased frozen foods. Growing sensitivity to energy use in the home also benefits from transitioning foods from conventional oven preparation to the microwave. Initial power consumption studies show reductions of at least 70% in the energy required to cook these products result from avoiding the conventional oven and using microwave cooking.71 This is consistent with power company published guidance to consumers suggesting microwave cooking uses 75% less energy than conventional ovens.72

10.7

Conclusions

From heavy, rigid metal sleeves with limited product adaptability, the use of thick metal films in microwave cooking to achieve shielding and field modification has evolved to a highly flexible system capable of incorporating a wide range of custom designs tailored to the specific needs of individual food

Table 10.1 Examples of benefits gained from thick metal containing microwave packages (data from Graphic Packaging International, Inc.) Product (all cooked from frozen)

Product weight

Thick metal film package

Conventional oven cook conditions

Passive package microwave cook conditions

Thick metal film package microwave cook conditions

Cook time savings, thick metal microwave vs. conventional oven (including preheat)

Lasagne

1100 g

Pattern foil pressed paperboard tray

10 min preheat + 60 min @ 190 ëC

24 min total 12 min on high, 12 min @ 50% power

15 min on high

78%

Round meat pie, raw dough bottom crust

625 g

Pattern foil and overall susceptor pressed paperboard tray

10 min preheat + 35±40 min @ 177 ëC

Not applicable, passive package unable to cook the crust properly

10 min on high

78±89%

Rectangular meat pie with raw dough top and bottom crusts

900 g

Pattern foil and overall susceptor pressed paperboard tray cooked in carton containing pattern foil and overall susceptor insert on inside cover

10 min preheat + 50±60 min @ 205 ëC

Not applicable, passive package unable to cook the crust properly

18 min on high

70±74%

Round fruit pie with raw dough top and bottom crusts

685 g

Pattern foil and overall susceptor pressed paperboard tray cooked in carton containing pattern foil and overall susceptor insert on inside cover

10 min preheat + 50±60 min @ 205 ëC

Not applicable, passive package unable to cook the crust properly

15 min on high

75±79%

Shielding and field modification ± thick metal films

263

products. Contrasted to mechanical fabrication of expensive implements unsuitable for consumer packages, chemical etching technology permits costeffective production and utilization of shielding and field modification packages for high-volume, fast-moving consumer goods. When this technology is combined with smart food formulation, more products can enter the realm where high quality and convenience are combined, increasing value for consumers. Shielding and field modification will continue to be valuable tools for microwave package designers and that interest will drive further evolution of structures and production approaches. Alternatives to foil will continue to be explored, with printable shielding materials or creation of shielding from thick evaporated layers requiring significant breakthrough technology before viable solutions are realized. Cross-fertilization of materials and fabrication methods from radio frequency identification (RFID) and other `smart' electronics technologies will require adding the ability to retain conductivity at much higher current densities than these emerging low-power technologies currently require. Creation of packages with more complex shapes than currently offered may attract interest and effort, and the extension of shielding and field modification technology using thick metal films into the use of microwave packages or components for health care or industrial processing applications could drive additional utilization and growth. In many respects, although this technology has been of interest since microwave cooking was discovered in the late 1940s, it has remained largely behind the scenes until more recently. A number of factors, including the increasing realization that the microwave oven is an energy-saving appliance compared with conventional hot air ovens, are favorable for increased utilization of this powerful technology.

10.8

Sources of further information and advice

This section provides several additional selected resources the reader may wish to examine to pursue specific interest and is followed in Section 10.9 with the references cited in the body of the chapter. Bouirden A, Ouacha A, Lefeuvre S and Keravec J (1989), `Microwave browning of foods', KEMA High Frequency/Microwave Processing Conference. Brody A L, Strupinsky E R, and Kline L R (2001), Active Packaging for Food Applications, Lancaster, PA, Technomic Publishing Company, Inc. Buffler C R (1993), Microwave Cooking and Processing, New York, Van Nostrand Reinhold. Collin R E (1998), Foundations of Microwave Engineering, New York, McGraw-Hill. Decareau R V (1992), Microwave Foods: New Product Development, Trumbull, CT, Food & Nutrition Press, Inc. Jackson J D (1992), Classical Electrodynamics, 3rd edn, New York, Academic Press. Maygar R J (2004), `A companion to Classical Electrodynamics 3rd edn by J.D. Jackson', Rutgers University, http://www.scribd.com/doc/SO9827/A-Companion-

264

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to-Classical-Electrodynamics-3rd-Edition-by-J-D-Jackson Osepchuk J M (1995), `Microwave technology', in Kirk-Othmer Encyclopedia of Chemical Technology, vol. 16, 4th edn, 672±700. von Hippel A R (1954), Dielectrics and Waves, New York, Wiley.

10.9

References

1 Moffett Jr. F W, `Method of heating frozen food packages', US Patent 2,600,566, 1952 2 Welch A E, `Microwave heating apparatus and method of heating a food package', US Patent 2,714,070, 1955 3 Bohrer T H and Brown R K (2001), `Packaging techniques for microwaveable foods', in Datta A K and Anantheswaran R C, Handbook of Microwave Technology for Food Applications, New York, Marcel Dekker, 444±467 4 Stevenson P N, `Container and food heating method', US Patent 3,547,661, 1970 5 Stevenson P N, 'Selective cooking apparatus', US Patent 3,615,713, 1971 6 Pothier R G, et al., `Partially shielded food package for dielectric heating', US Patent 3,865,301, 1975 7 MacMaster G H, et al., `Microwave browning utensil', US Patent 3,946,187, 1976 8 Derby P P, `Microwave heating apparatus with browning feature', US Patent 3,946,188, 1976 9 Copson D A, `Heating method and apparatus', US Patent 2,830,162, 1958 10 Anderson G R, `Microwave heating device and method', US Patent 4,266,108, 1981 11 Fabish T J, et al., `Microwave absorber designs for metal foils and containers', US Patent 5,258,596, 1993 12 Gelman S S, et al., `Microwave energy moderating bag', US Patent 4,144,438, 1979 13 Leveckis A S, et al., `Microwave energy cooking bag', US Patent 4,196,331, 1980 14 Leveckis A S, `Microwave energy moderating bag', US Patent 4,204,105, 1980 15 Clark C O, `Dynamic microwave energy moderator', US Patent 4,228,334, 1980 16 Flautt Jr., et al., `Microwave energy moderator', US Patent 4,268,738, 1981 17 Ji H, et al., `Food package for microwave heating', US Patent 6,231,903, 2001 18 Raughley K D, `Container for preparing a comestible article in microwave oven, and a self-contained comestible article utilizing the same', US Patent 7,253,382, 2007 19 Turpin C H, et al., `Microwave heating package and method', US Patent 4,190,757, 1980 20 Cherney J A, et al., `Partially shielded microwave carton', US Patent 4,345,133, 1982 21 Keefer R M, `Container for microwave heating including means for modifying microwave heating distribution, and method of using same', US Patent 4,841,568, 1989 22 Keefer R M, `Package of material for microwave heating including container with stepped structure', US Patent 4,831,224, 1989 23 Keefer R M, `Microwave container and method of making same', US Patent 4,866,234, 1989 24 Keefer R M, `Microwave container with dielectric structure of varying properties and method of using same', US Patent 4,888,459, 1989 25 Lorenson C P, et al., `Improved uniformity of microwave heating by control of the depth of a load in a container', US Patent 4,990,735, 1991 26 Hewitt B C, et al., `Microwave heating device with microwave distribution modifying means', US Patent 4,992,638, 1991

Shielding and field modification ± thick metal films

265

27 Beckett D E, `Formation of packaging material', US Patent 4,398,994, 1983 28 Beckett D G, `Controlled heating of foodstuffs by microwave energy', US Patent 5,117,078, 1992 29 Beckett D G, `Microwave cooking container cover', US Patent 5,126,518, 1992 30 Beckett D G, `Microwave oven packaging', US Patent 5,213,902, 1993 31 Beckett D G, `Microwave heating structure', US Patent 5,260,537, 1993 32 Beckett D G, `Microwave heating element with antenna structure', US Patent 5,278,378, 1994 33 Beckett D G, `Control of microwave energy in cooking foodstuffs', US Patent 5,310,980, 1994 34 Beckett D G, `Microwave heating structure comprising an array of shaped elements', US Patent 5,354,973, 1994 35 Bohrer T H and Brown R K (2001), `Packaging techniques for microwaveable foods', in Datta A K and Anantheswaran R C, Handbook of Microwave Technology for Food Applications, New York, Marcel Dekker, 433 36 Data courtesy private communication Graphic Packaging International, Inc. 37 Mattisson L, et al., `Food package', US Patent 4,351,997, 1982 38 Data courtesy private communication Graphic Packaging International, Inc. 39 Keefer, R M, `Package of material for microwave heating including container with stepped structure', US Patent 4,831,224, 1989 40 Minerich P L, et al., `Container for active microwave heating', US Patent 5,593,610, 1997 41 Zeng N, et al., `Abuse-resistant metallic packaging materials for microwave cooking', US Patent 6,204,492, 2001 42 Zeng N, et al., `Abuse-tolerant metallic packaging materials for microwave cooking', US Patent 6,204,492, 2001 43 Lai L, et al., `Microwave oven heating element having broken loops', US Patent 6,114,679, 2000 44 Zeng N, et al., `Abuse-resistant metallic packaging materials for microwave cooking', US Patent 6,433,322, 2002 45 Zeng N, et al., ` Abuse-tolerant metallic packaging materials for microwave cooking', US Patent 6,552,315, 2003 46 Lai L M C, `Abuse-tolerant metallic pattern arrays for microwave packaging materials', US Patent 6,677,563, 2004 47 Keefer R M, et al., `Methods and devices used in the microwave heating of foods and other materials', US Patent 5,591,195, 1996 48 Ji H, `Food packaging for microwave heating', US Patent 6,231,903, 2001 49 Lai L M C, `Abuse-tolerant metallic pattern arrays for microwave packaging material', US Patent 6,677,563, 2004 50 Beckett D G, `Controlled heating of foodstuffs by microwave energy', US Patent 5,117,078, 1992 51 Richardson M D, et al., `Microwavable metallic container', US Patent 7,112,771, 2006 52 Lafferty T P, et al., `Partially-shield microwave heating tray', US Patent 6,102,281, 2000 53 Kennedy M, `Method for applying microwave shield to cover of microwaveable food container', US Patent 6,696,677, 2004 54 Schmelzer M A, `Patterned metal foil laminate and method for making same', US Patent 5,759,422, 1998 55 Habeger C C, et al., `Patterned metal foil laminate and method for making same', US

266

Packaging and products for use in microwave ovens

Patent 5,800,724, 1998 56 Kennedy M, `Method for applying microwave shield to cover of microwaveable food container', US Patent 6,696,677, 2004 57 Clark F E, `Apparatus and method for removing metal from the surface of a metal object', US Patent 2,895,814, 1959 58 Photograph courtesy of Graphic Packaging International, Inc. 59 Germain A, `Microwave heating container', US Patent 6,852,958, 2005 60 O'Hagan B R, et al., `Container with microwave interactive web', US Published Patent Application 2007/0215611, 2007 61 Buderi R (1996), The Invention that Changed the World, New York, Simon & Shuster, Inc. 62 Spencer P L, `Food cooking', US Patent 2,540,036, 1951 63 Diesch B J, et al., `Oven antenna probe for distributing energy in microwave', US Patent 4,460,814, 1984 64 Notsaka C, `Cooking with the use of microwave', US Patent 5,582,854, 1996 65 Dehn R A, `Cooking utensil for uniform heating in microwave oven', US Patent 4,320,274, 1982 66 Habeger C C, et al., `Antenna for microwave enhanced cooking', US Patent 5,322,984, 1994 67 Habeger C C, `Antenna for microwave enhanced cooking', US Patent 5,322,984, 1994 68 Data courtesy of Graphic Packaging International, Inc. 69 Photograph courtesy of Graphic Packaging International, Inc. 70 Lai L, et al., `Microwaveable container having active microwave energy heating elements for combined bulk and surface heating', US Patent 6,150,646, 2000 71 Data courtesy of Graphic Packaging International, Inc. 72 Upper Peninsula Power Company website http://www.uppco.com

11

Package and product development testing in a microwave oven M L O R E N C E , General Mills Inc., USA

Abstract: Variability stands in the way of delivering consistent product quality from microwave ovens. A good microwave product developer takes into account all the sources of variability in the test system that an end user may see. The two largest sources of variability are the differences in microwave ovens in the marketplace and the end users themselves. This chapter outlines a test procedure that aids the developer in determining the robustness of a product/package design and if an applied fix improves performance in all of the variability found in the marketplace. Key words: microwave product development, microwave package development, microwave tolerance testing, microwave variability.

11.1

Introduction

Variability is the nemesis standing in the way of delivering consistent product quality from microwave ovens. Contrast this with developing products for a consumer gas or electric conventional oven or stove top where the temperatures can be set and the delivered heat fluctuates within a narrow range. A good microwave product developer must take into account all possible sources of variability in the test system. The two largest sources of variability are the end users and the many microwave ovens in the marketplace. Other chapters in this volume treat the differences in microwave ovens themselves, the largest source of variability in this testing system ± power levels, oven age effects, standing wave patterns, microwave interactions with multiple foods which have varying dielectrics, heat capacities, shapes, weights, etc. Consumers provide variability in how they handle the product ± starting temperature, package venting or set up, direction following before and during heating, set time before consumption, etc. Previous chapters address the understanding of foods, packaging and their interactions with a microwave field. With this background, key questions still remain for the developer: 1. 2.

Is the proposed product and package robust enough for all this variation? When a solution is applied to better the performance, is it truly a statistically significant difference?

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Packaging and products for use in microwave ovens

11.2

Realities of heating food in microwave ovens

There are some realities around microwave heating that need to be understood from the outset in order to control expectations and steer the developer to focus on solutions for particular inherent problems. As a review: 1.

2.

3.

4.

5.

6.

Food heats differently in microwave ovens ± energy interacts with the product differently from common heating methods that conduct heat from the outside surface inwardly moving moisture away from the surface. Microwave heating affects the product deeper, moving moisture to the outside surface. With this difference in how energy is applied and that the surface is wet, it will be difficult to mimic conventional oven and stove top finished product attributes. Food heats unevenly in microwave ovens ± owing to standing wave patterns in ovens, how microwave energy impinges the product edges, penetration depth, the geometry of the food, package design, location within the oven, etc. Very few food forms do well in microwave ovens ± browning, baking and drying are very difficult to achieve in a microwave oven. Foods more tolerant to steaming and general reheating do well ± popcorn, entreÂes, and vegetables. Even with packaging and formulation assistance the list of foods is short ± pizza, handheld sandwiches, pot pies and French fries. Microwave ovens are not created equal ± products will not work well in all ovens ± since there are many makes and models of ovens with varying design features; products will not perform well in some ovens and expect a low percentage of product failures. Packaging alone cannot fix product performance issues ± both need to coevolve ± an important reality that product and packaging developers need to work in concert to create the best performing products out of the largest number of ovens. Variability is the foe of design robustness ± as stated earlier; differences in ovens, consumer interaction with the product, etc. create the need for the developer to be an excellent experimenter.

11.3

Consumer microwave oven variability

Microwave ovens in the US consumer marketplace are estimated at 117 000 000. Some 96% of households have at least one microwave oven. An average life expectancy of a microwave oven is 9 years. A 2005 estimate of ovens being replaced is 9 000 000 annually. When considering the makeup of microwave ovens in the marketplace there is a wide range of oven wattages, cavity sizes, in-feed location, turntable or mode stirrer, etc. Consider also the special array of feature buttons as well ± defrost, variable power, popcorn, frozen entreÂe, etc.

Package and product development testing in a microwave oven

271

Table 11.1 5 Year AHAM microwave oven shipments ending 2004 (Association of Home Appliance Manufacturers) Size

Cubic feet*

Percentage

Est. power (W)

Compact Mid Family Full Over range

0.60±0.89 0.90±1.29 1.30±1.79 1.80±2.20 Various

32.8 28.3 12.9 6.9 19.1

600±800 900±1000 1100 1200 900±1000

* 1cubic foot ˆ 0.0283 m3.

Table 11.1 shows industry data of consumer ovens sold over 5 years (Association of Home Appliance Manufacturers (AHAM) shipments ending in 2004). This gives an indication of the distribution of cavity sizes and wattages recently purchased in the marketplace. This will be useful when considering how to outfit a testing lab and is discussed later in this chapter. Microwave ovens also decrease in output power as they age and their frequency of use. There is an excellent treatment of this in Chapter 12 of The Microwave Processing of Foods, Measuring the Heating Performance of Microwave Ovens, by Swain and James, Woodhead Publishing. Every oven in the testing lab should be occasionally baselined using a standard microwave oven wattage test such as ASTM F1317. This will be the most accurate method for determining an oven average output wattage considering the design and age effects mentioned earlier. How well the available microwave power in an oven couples with the product depends also on the size of the food load. Larger products utilize more of the available power and smaller products couple with a smaller percentage of it. This may not influence the heating rate of the product within the oven but the product itself can affect the power distribution within the oven. Since ovens have standing waves that create hot spots due to areas of intensified field strength, variation can occur from the size of the product and where it is placed within the oven. Later a test method will outline dealing with both oven-to-oven variation and within-oven variation.

11.4

Commercial microwave oven variability

Development for commercial microwave ovens is somewhat easier since restaurants, fast food chains and convenience stores purchase the same industrial models in order to reduce oven-to-oven variability and deliver similar product quality store to store, regardless of location. Most of these ovens are higher in power output so product is heated very rapidly. These types of ovens and their features (i.e. addition of infrared heaters, convection heaters, and higher

272

Packaging and products for use in microwave ovens

wattages) are discussed by Cooper in Chapter 4. Testing in these ovens can also follow the methods outlined in this chapter.

11.5

Consumer variability

There are many sources of consumer variability. This variability consists of all changes to the product after it leaves the manufacturer. As an example, variability is seen in a frozen distribution system. Shipping, warehousing, displaying, shopping and home storage conditions allow parts of frozen products to thaw and refreeze. A May 2003 Refrigerated & Frozen Foods article by Paula Frank states that repeated temperature fluctuations can cause a number of degradative effects. Even minor temperature changes cause water to form ice crystals, then melt, then recrystallize, and so forth. During this process, a variety of damaging things can occur, including dehydration, oxidation, syneresis, off-flavor development and textural breakdown, depending on the extent of freeze/thaw cycling and the type of food in question.

Home freezer temperatures fluctuate between ÿ23 ëC to ÿ7 ëC. Initial temperature will affect overall heating times, the final temperature distribution and product quality. Much confusion comes from interpretation of on-package heating instructions. Many have found that diagrams or pictures along with words work better than using words alone. Questions from the International Microwave Power Institute's 2007 consumer survey gives an indication of how well consumers follow printed directions. Notice in Table 11.2 that up to 15% of the consumers do not follow the directions on the package. Table 11.3 indicates that when a range of heating times is given, a majority of consumers will use the middle time followed by the shortest and longest times listed. This source of variability needs to be accounted for when testing the robustness of a product to assess the risk of under or overheating. Notice in Table 11.4 that when the consumer is requested to change power settings or to stop and start the oven that 30% of consumers do not follow these directions. These missed steps need to be studied to determine product robustTable 11.2 2007 Consumer Survey, International Microwave Power Institute If you purchase foods with microwave directions, such as frozen entre¨es or popcorn, how do you decide about heating time? Follow the directions on the package Use the special feature on the oven Estimate the time Use a pre-set time key

85% 8% 4% 3%

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Table 11.3 2007 Consumer Survey, International Microwave Power Institute If package directions give a range of heating times, what do you do? Use the shortest time Use the longest time Use a middle time None of the above

29% 15% 44% 12%

Table 11.4 2007 Consumer Survey, International Microwave Power Institute When package instructions indicate multiple steps that require stopping and restarting the oven, such as changing power levels and stirring, what do you do? Follow instructions Partially follow instructions Disregard instructions

70% 26% 4%

ness within the marketplace and the effect on product quality and human safety. The package directions reflect the manufacturer's best estimate of when the product will be optimally heated. An additional source of variability is determining when a product is adequately heated and delivers the best eating quality. Most directions give a time range which can lead to parts of the product being underheated or overheated. Some directions, such as for pizzas, ask the consumer to look through the front of the oven to judge complete cheese melt. With uneven heating patterns in the oven, waiting for all the cheese to melt can lead to overheated areas and tough or burnt spots. Popcorn directions instruct consumers to listen for the frequency of popping to slow to 1±2 pops per second. When the bag is opened the corn may be perfectly popped, partially scorched and there may be an unacceptable amount of un-popped kernels in the bottom of the bag. Doneness or temperature indicators and how they are made and function are well documented in literature. The basic operating premise is to use a thermochromatic ink which changes color with temperature. Depending on where the indicator is placed it can show when the product is hot, like a popular microwaveable syrup in the market. Placement on the lidding film of a frozen entreÂe could misinform the consumer because it is measuring the surface temperature of the film heated by steam and not the entreÂe components themselves. These indicators give the temperature at a localized point and do not address the evenness of heating over the entire product. Some packages require venting, peeling or assembly before the product is heated. If these steps are missed there is a potential for poor product perform-

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ance or they may create a safety issue such as burns or even fires. Placement of product within an oven, typically on the glass turntable can cause variation due to how the product interacts with standing wave patterns that form `hot spots' in ovens. Placing a product in the middle of the oven may give one heating profile while placing it towards the edge may give another, and in other cases the heating profile may not depend strongly on where the product is placed (Chapter 3). These consumer variations need to be accounted for in robustness testing as well. Some products require elevation from the oven floor by use of packaging. This primarily helps products with susceptors. The heat generated in a susceptor will conduct to any surface it is in contact with. Elevation helps to better transfer that heat to the product and not allow heat to transfer to the glass turntable or oven floor. It may also allow some additional microwave energy to get to the raised susceptor by spacing the product farther away from the microwave reflective metal surface of the oven cavity under the glass turntable or floor. Fairly large items tend to shadow their bottom sides making for hotter edges and a cooler center the closer they are to the floor of the oven cavity. Plate XIV shows infrared images of the bottoms of 180 mm (700 ) pizzas heated on susceptors. These data demonstrate a 25 ëC increase in average temperature when a pizza on a susceptor disc is raised 25 mm off the oven floor. This increase is primarily due to insulating the susceptor from the glass floor. These images also demonstrate a center to edge temperature difference from the shadowing effect and how the product interacts with the available energy. The red portions of the images are hotter than the lighter areas. The circles represent the area of interest from which the noted temperature statistics were derived. These images were taken 10 seconds after the same heating time in the same oven (proper between run cooling of the oven was observed). The pizza was flipped upside down off its susceptor on to a non-infrared reflective surface (i.e. a piece of corrugated kraft paper board) and was placed under the lens of the IR camera where the data was captured. Variation can occur with the pre-consumption hold time: how long the product is allowed to stand after microwaving before being consumed. Because of heat conduction, hot areas of the product will equalize with cooler areas. This is one of the ways to help mitigate within-product temperature variation. When running experiments and measuring product temperatures out of any oven, take the readings after the same standing time. Consumers will not eat product within a short time after heating. Allow for a realistic time (minutes) before taking final temperatures.

11.6

Product variability

The effect of the thickness of the dielectric (food product) on heating rates and evenness of that heat has been mentioned in earlier chapters. This is the situation

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when putting dissimilar dielectric materials in different locations on a plate in the oven. This could very well be a frozen dinner in a multi-compartment tray where each food has a different heating rate. Imagine now all the ways natural product variability can make the products perform slightly different. Variability can be found in geometry, thickness, weight, moisture content, age of flavors and ingredients, age of product, coverage of gravies and sauces, etc. With all of the sources of variation previously mentioned (ovens, consumers, product, distribution, etc.) good experimentation is the only way to statistically verify the robustness of a product in the marketplace and if any applied fixes make a significant difference to better the finished product attributes.

11.7

Measurable responses

Performing good experimentation around all these sources of variation will require ways to measure finished product attributes. If a browning agent is added to a pizza crust or a susceptor is added underneath it, how might it improve crispness or browning in the myriad of ovens in the marketplace? Perhaps the addition of a foil antenna array under the susceptor to equalize the temperature distribution on the bottom of the crust needs assessment to determine the benefit of improved quality vs. cost. Perhaps a package is invented that more evenly heats a frozen lasagne entreÂe. How will these be evaluated in order to determine whether these fixes make a difference? Most microwave products are evaluated by temperature. There are multiple ways to measure temperature. One of the most common methods is the use of a single thermocouple. This will give a direct temperature for almost any point in the product. However, to get a good feel of the temperature distribution of the product at a certain time out of the oven it is a more difficult method owing to the time required to take multiple readings and the speed of heat conduction equilibrating in the product. While measurements with a single thermocouple can provide a quick initial assessment, it is difficult with this method to create a reliable statistical temperature profile of the product. A thin thermocouple will produce a faster and more accurate reading due to a smaller probe head which must be heated by the product. Because they are metal and will interact with the electromagnetic field, these cannot be used in a microwave oven. They are useful only for end heating results. Another single point method of measuring temperature is the use of fiber optics. This enables temperature measurements in the microwave oven during or after heating. Since the fiber optic probes are derived from glass they are transparent to the electromagnetic field, unlike typical thermocouples. These probes are much more expensive and fragile than a thermocouple. Fiso Technologies, Inc. has a device that allows the fiber optic probes to rotate in the oven with the product that is sitting on the turntable below it. This allows real time point temperature measurements while the food heats. Again, only a few

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points can be measured. An apparatus or frame that is transparent to microwave energy must be constructed to hold the probes in place while cooking. This holder cannot inhibit heat or steam migration and affect the product performance. An array of thermocouples can be used to get a better statistical picture of temperature distribution within a product after heating in a microwave. As an example, arrange a set of thermocouples in a 3  4 array to fit the surface area of the product. The tips of the thermocouples typically are on the same horizontal plane. The array can use more thermocouples and they can be placed as close to each other as necessary. The beauty of this approach is that temperature readings can be established at different depths throughout the product. At each depth the array would acquire readings and calculate an average and standard deviation for each level. Perhaps all the temperatures from all the levels could be combined to give overall statistics. These statistics can be used in analyzing how different treatments or fixes of the product and packaging affect temperature distribution. An array of thermocouples may not work well for flat products such as a pizza or where there is interest in surface temperatures for drying and crisping. In this case an infrared camera works well as seen in Plate XIV. With this approach every pixel indicates a temperature giving hundreds of readings. In Plate XIV an average temperature and standard deviation was determined to see the effect of elevating a pizza 25 mm from the glass floor. This works well in this oven but how might it work in other ovens? Does this fix work in all or most ovens? How to test in multiple ovens and statistically determine if fixes tested make a difference will be addressed later in this chapter. Temperature is one measurable response. Others may be sensory attributes. Even though a pizza crust is made hotter as in Plate XIV, can a sensory panel pick up a difference? Maybe there is an increased crispness but there could be more tough or burned areas. Good sensory testing with multiple ovens would be helpful in determining the benefit of any fixes. Other analytical techniques can be used such as texture analyzers, weight loss, percent browned area, color, popcorn pop volume, number of un-popped kernels, etc.

11.8

Basic experimentation in microwave ovens

To perform the best microwave product and package development and to test for robustness in quality and human safety, a lab should be outfitted with at least 20 ovens. This will give an idea of how the product will perform in the marketplace. The distribution of ovens could follow the segmentation of ovens that is outlined in Table 11.1 with a mix of cavity sizes, wattages, features, etc. Consider finding older ovens. There are ovens that are 20 years and older still in the marketplace. Find ones with and without turntables. This wide variety of ovens allows the experimenter to test the boundaries of the product and package to identify limitations and what might need to be fixed. Each oven should be on

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its own circuit breaker so many ovens can be run in sequence, shortening the analysis time of experimental treatments to be tested. A frozen lasagne entreÂe will be used as an example for the test procedure. The temperature distribution on the top of the product will be the focus by using an infrared camera that can give an average and standard deviation of the top surface area. The first step is to establish a baseline for these ovens. Determining when the product is done for each oven can be somewhat tricky and different approaches can be taken. If this is a product in the marketplace, follow the packaging directions. If it is a new product make some estimates by testing the product in some of the different ovens and use a single point thermocouple in different areas of the product or an IR camera to establish reasonable heating times. Determining doneness is a large source of variability. The more work done with product in multiple ovens, the better the experimenter will get in determining the heating end point. There will be hot edges and cold centers. Each oven will have a different heating time. Heat to doneness, as a consumer would, as best as possible. It makes sense at this point to discuss some good microwave oven testing procedures so variability in data collection is minimized. If the product is shelf stable, refrigerated or frozen make sure all products have reached temperature equilibrium before testing. Let each oven cool at least 30 minutes between uses. One reason for resting between runs in the same oven is that the magnetron drops in power output when it becomes hot. Going back to a cold oven state allows experiments to be repeatable and this mimics true consumer behavior. If a susceptor is used and is specifically placed on the oven floor, that floor will become rather hot. If experiments are conducted one right after the other in the same oven you will get a result where residual heat from the glass floor is available from previous experiments and will contribute to heating the product, biasing the data. Again, this does not reflect typical consumer behavior (oven, magnetron and oven floor all initially cold). Practice the same handling procedure for preparing the product to be microwaved, before, during and after heating. When the oven timer beeps, start counting to a reasonable amount of time before a temperature measurement will be taken. If it takes 10 seconds to pull the entreÂe out of the oven and position it under the IR camera, then use 10 seconds for all the ovens before capturing an IR image or a thermocouple array. If different depths of the product are being tested make sure data are captured at the same time intervals out of the oven. Alternatively, the temperature measurements could be taken at a longer interval out of the oven representing a typical hold time before consumption. This allows for some temperature equilibration to occur. For the first heating test choose a relatively new middle of the road oven. Establish the transfer and hold time to collect the IR image. With the statistics generated you will have a temperature distribution represented by the normal curve of oven 1 in Fig. 11.1. The standard deviation represents

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11.1 Normal curves, average entre¨e temperature, two ovens.

within-oven variability and for this product manifests itself in hot edges and a cold center. Figure 11.1 demonstrates the surface temperatures of heated lasagne out of two different ovens. These ovens happen to have the same overall average temperature but oven 2 has a greater swing in temperatures, giving it a higher standard deviation or within oven variation. Figure 11.2 demonstrates oven-tooven variations when comparing oven 3 with the other two ovens. The start of the overall experimental process is to heat the product in all of the microwaves to their particular times that yield similar doneness, measure product surface temperatures, calculate the statistics for each oven and plot the averages of the ovens against the standard deviations of each oven as illustrated in Fig. 11.3.

11.2 Normal curves, average entre¨e temperature, three ovens.

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11.3 Oven-to-oven variability vs. within-oven variability.

The x axis represents each of the oven's average temperatures or oven-tooven variability. The y axis represents each of the oven's standard deviation or within-oven variability. The ranges of temperature in Fig. 11.3 are rather large and consumers will be disappointed in finished product quality. In a more ideal case by using an innovative package or product fix, the range of average temperatures will be narrowed and the within-oven standard deviations minimized. A good rule to follow in improving microwave performance is to let the product tell what needs to be fixed. This entreÂe has hot edges and a cold middle. One possible fix for all of this variation is to add aluminum foil to the outside edge of the package, cutting down the amount of microwave energy getting in from the sides and forcing more energy to the top and bottom center of the entreÂe. Figure 11.4 shows that when a middle oven from the tested oven set is chosen a significant improvement is seen when applying this fix.

11.4 Middle oven with shielding fix.

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11.5 Normal curves, middle oven with shielding fix.

Notice by using the shielding technique the average temperature is increased and the within-oven variability is reduced dramatically. Figure 11.5 illustrates the fix using normal curves. Do not stop with designing a product and package after having a success in one oven. Try different solutions. Repeated experiments with different fixes in this one oven can help determine which solution should next be tested in a larger set of ovens. Tests in larger sets of ovens determine how well the solution fixes the problem. The experimenter must not develop or optimize a product and/or a fix in just one oven. The largest source of variability in the testing system is in the consumers' homes with all of the different microwave ovens. When a desired fix is determined it is best to try heating the product in a subset of ovens to confirm the one oven result. Figure 11.6 illustrates picking

11.6 Four oven subset representing larger data set.

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11.7 Four oven set representing larger data set with fix.

four ovens that represent the majority of the other ovens. This testing will give more insight into the robustness of the product/package system. Figure 11.7 demonstrates the effect of using perimeter shielding with the four oven set. Notice the oven-to-oven temperature range for all ovens is slightly narrower than the control ovens and that the within-oven variability for all ovens is dramatically reduced. If the product in these ovens is giving hotter overall average temperatures, then the heating time may be reduced, or perhaps additional fixes to the heating pattern should be tested to see if there is a better solution. Some compromises in quality may need to be taken from good performing ovens so poor performing ovens can work better. One compromise in quality may be with the total cost of the product or package in order to make it profitable at a certain price point. To determine overall robustness, the next step in this procedure is to heat the product in all 20 ovens and see what the total population looks like with the fix. These data sets, before and after a fix, may be analyzed in order to confirm that the fix is statistically significant at the desired confidence level. There may be some ovens that are not affected or made worse by the fix. Not all products turn out well in all ovens. This product may always fail in that oven due to its unique heating characteristics. A business risk assessment would be appropriate to determine if the amount of suboptimal performing ovens is acceptable. The next phase of testing, after the final fix is applied, is to test for quality and safety robustness of the product/package system. In a four oven set or even larger, test the effect of adding 1, 2 or 3 minutes to all of the cook times. When does the product quality drop off? Are there burned areas? Does the package catch fire? Are there odd odors coming from the oven? Subtract time and see how exacting the preparation directions need to be. Think of ways the consumer may not follow the directions, abuse the product or package and test in these

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ovens to understand the risks with product quality and consumer safety (spills, burns, etc.) What happens when the product starts at different temperatures? Once the experimenter is feeling confident in the final product and package design it is wise to send a product home with consumers to gauge their overall liking of the product, ease of preparation, etc. Always confirm the final design with consumers. What safety issues does this research reveal? How are the heating instructions followed? Are they confusing? Are there sensory attributes that need improvement and further development? The test process in summary: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Establish a 20 oven heating laboratory. Establish the desired finished product attributes. Heat in 20 ovens to establish baseline by doneness. Let the product tell you areas of improvement. Choose a middle oven to test fixes and give direction. Choose corner ovens ± designed testing. Confirm the final solution in the 20 oven set. Understand main drivers of product quality, safety. Get feedback from consumers ± in-home testing. Repeat as necessary to optimize the product offering.

11.9

References

Frank, P. (2003) `Refrigerated and frozen foods', Refrigerated & Frozen Foods, 14(5), 40, 42±45. Swain, M.J. and James, S.J. (2005) `Measuring the heating performance of microwave ovens', in H. Schubert and M. Regier (eds), The Microwave Processing of Foods, Woodhead, Cambridge, pp. 221±242.

Plate XIV Infrared image of pizza bottoms, oven floor and elevated 25 mm (1 inch).

12

Regulatory issues in microwave packaging

S R I S C H , Michigan State University, USA

Abstract: This chapter reviews the main regulations in the US covering packaging for microwave products. It discusses their development and the current situation in such areas as safety and food contact materials. Key words: microwave foods, regulation, packaging.

12.1

Introduction

Packaging materials for food products are designed to protect foods during distribution and storage. The packages are designed primarily to protect the quality of the food by inhibiting or limiting any chemical, microbiological or physical changes. Materials may serve as barriers to compounds such as moisture or oxygen moving in or out of the product and can provide a barrier to light which can have a detrimental effect on food quality. Packages can prevent foods from being crushed or broken during shipping. They can also protect products that have been heat processed to prevent any microbial contamination. The atmosphere within packages can be modified with carbon dioxide or other gases to either prevent or slow down any microbial growth to extend the shelf life of a product. While these issues are important for foods designed for the microwave oven, the packaging materials serve an additional role in that they are the cooking or heating container. The packages used for these applications need to hold up to the heat that is generated as the foods cook in the microwave oven. The overall premise for packaging regulations which have been developed by the US Food and Drug Administration (FDA) is that the packaging material does not contaminate the food product and does not impart any type of off-odor to the product. The regulations are based on knowing the composition of the packaging material and how that will act when in contact with different types of foods and used in different applications. There are regulations that indicate what can be used in terms of both polymers and additives to the packaging materials. Any packaging used for food products in the United States must comply with the regulations that are published in the Title 21 of the Code of Federal Regulations.

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History of microwave package regulations

In 1988, as the market for microwave food products was growing dramatically, the US FDA observed some of these packages and realized that existing regulations had not contemplated packaging materials reaching temperatures higher than 120 ëC, the temperature that is expected to be reached in containers to be retorted. One initial memorandum from the Food and Color Additives Review Section to the Food Formulation Branch of FDA specifically addressed the increased use of microwave susceptor packaging (Cramer, 1988). As discussed in the packaging chapters in this book, a susceptor is a metallized film. It is typically a polyethylene terephthalate (PET) film with a vacuum deposited layer of metal, usually aluminum. This layer of film is then laminated to paper or paperboard. There are two main configurations of this package. In one, the layer of film is laminated to paperboard with the non-metallized surface of the PET film in direct contact with the food product. This has been used for products such as pizza, fish and sandwiches. In the other construction, the susceptor film is laminated between two sheets of paper so that the food contact layer is paper and not the polyester film. The materials used in this type of packaging complied with existing regulations and companies were using those regulations as the basis for introducing the packaging with no further testing than what those regulations required. The main concern that the FDA had was that the temperatures reached during microwave heating were much higher than those considered for resins cleared for use in cooking and holding food. As mentioned above, this temperature is 120 ëC. In addition to concern about the higher temperatures that the polymers reached, there was concern about adhesives being used. One specific example was the possible use of adhesives that were covered by 21 CFR 175.105 or 175.125 (21 CFR, 1987). One of the requirements for these adhesives was that there must be a functional barrier between the adhesive and the food product. In the type of susceptor construction that was being used for products including pizza, sandwiches, and fish, the susceptor was in direct contact with the food product. During microwave heating, the polyester film would crack and craze. This would result in the adhesive being in direct food contact and the adhesives were only approved for indirect food contact. In addition, there was concern that the higher temperatures could result in degradation of the adhesives and other package components to create new compounds which may not yet have been identified and could result in food safety issues if they became a part of the food product. In September 1988, the FDA held a public meeting to notify industry of its concerns regarding microwave susceptors packaging and to provide guidance on how to generate suitable data to evaluate the safety of these materials (Machuga, 1988). It should be noted that some companies had anticipated that there could be FDA concern and had started evaluations of the safety of microwave susceptors prior to the FDA public meeting. Golden Valley Microwave Foods,

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now part of ConAgra, had worked specifically on popcorn bags and did share the data that had been generated with the FDA prior to the public meeting. The FDA also announced at the meeting their intention to publish an advance notice of proposed rulemaking (ANPR). The concern that the FDA conveyed at that meeting was that some of the packages on the market used materials that were approved for food use but reached much higher temperatures during microwave heating than the regulations had contemplated. In their initial work prior to the public meeting, they did abuse the packaging materials to the point that they were severely scorched. Many regulations do use abuse conditions to give a margin of safety; however, when microwave susceptors are abused to the point that they are severely scorched, the food in contact with them will also be severely scorched to the point of not being edible. In addition to being severely scorched, the products will also be dried out and tough, adding to their being inedible. At the time, the FDA also envisioned that the packaging would be very widely used by consumers, resulting in a large proportion of their diet coming from packages of this type. The FDA looks at consumption factors which take into account what percentage of a person's diet is in a particular type of package when evaluating possible exposure to any materials that may migrate from the package. There was some speculation that as the market was growing rapidly and might continue to grow at that pace, as much as 30% of a person's diet might be heated in microwave packaging. This would have resulted in much higher exposure to any compounds that migrated from the package into the food. The ANPR was finally published in 1989 (Federal Register, 1989). The focus of the ANPR was 21 CFR Parts 174, 175, 176 and 177 for indirect food additives. In the ANPR, the FDA stated that they were considering establishing maximum temperatures of use for microwave packaging materials. When the ANPR was published, the FDA had conducted preliminary studies on susceptor packaging. Some of the things that they found were that parts of the package could reach temperatures in excess of 260 ëC, there was breakdown of the PET film, and there could be blackening of the paper or paperboard used as a base material. The FDA studied both non-volatile and volatile components that could come from the package. In particular, one study found that a component of the PET film, a specific short chain oligomer, PET cyclic trimer, migrated into corn oil in contact with package. In 3 minutes of heating, approximately 95% moved from the film to the corn oil. The FDA also found volatile compounds that came from adhesives and paper in the corn oil heated in contact with the susceptor. Based on their testing, the FDA had three major concerns that were outlined in the ANPR. The first was that significantly higher levels of the non-volatile compounds would migrate into foods. When PET was approved for food use, the FDA had anticipated that some of the oligomers would migrate but the susceptor packaging showed levels six to ten times higher than what had been considered. The second concern was the PET did crack during microwave heating, resulting in direct food contact for adhesives that were not approved for that use. The

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higher temperature could also result in unregulated degradation products. The third concern highlighted in the ANPR was that the higher temperatures would result in higher migration of components of the paper or paperboard that was used. In the ANPR, the FDA requested that companies submit information on the chemical composition and construction of the packages and identity of breakdown products that might be formed during use as well as any toxicological data available on the compounds present. They wanted migration data for compounds when the packages were used for the maximum time and temperature that could be expected. The FDA requested information on temperatures of the package during actual use conditions and anticipated use of the packaging. They wanted to know what products were likely to use susceptors and how widely they might be used. While the ANPR was not published until 1989, the industry had formed a coalition prior to the 1988 public meeting to address the issue. The group was led by the Society of the Plastics Industry and the National Food Processors Association. The companies that joined the effort included those from every aspect of the microwave package and product including resin, ink and adhesive suppliers, converters, paper companies, and end users. The group met regularly to review data being developed and discuss appropriate testing procedures to supply the FDA with the data that they had requested in the ANPR. The group submitted its first report to the FDA on December 7, 1989, which included temperature measurement data, the methodology that had been developed to analyze volatile migrants and a preliminary report on the volatiles analysis. The first supplemental report was submitted on April 7, 1990. This had further information on volatile analysis and preliminary non-volatile work. The final report was submitted July 30, 1990, and had the final volatile work and the report on non-volatiles analysis. The method developed for measuring temperature of the packaging and the results that were obtained from those measurements were published in 1990 (Kashtock et al., 1990). A summary of the findings was presented at the TAPPI Conference on Polymers, Laminations and Coatings Conference in 1991 (Breder, 1991). In addition to information on both the volatile and non-volatile potential migrants from susceptor packaging, one member company was able to submit to the FDA a 90-day feeding study of PET oligomers that had been conducted in the 1970s which showed a no observable effect level. Many of the companies who submitted samples for analysis also submitted confidentially to the FDA the compositional data for the susceptors that they were using. One other important piece of information for the FDA was marketing data that showed that less than 1% of an average person's diet would be in contact with a susceptor package. Using this information and the data on the amount of different volatile compounds that were generated by the packaging, it was shown that the dietary concentrations of different potential migrants would be less than 0.5 ppb

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(Breder, 1991). This consumption data helped the FDA to realize that the packaging was not in as broad a use as they had thought. The FDA never did establish any temperature limits for susceptor packaging and did not publish any regulations until sometime well after 2000. While the FDA's major concern was with susceptor packaging, they also wondered about the temperatures reached by passive packaging materials that would be heated only by transfer of heat from the food product. In general, any product in a passive container will not get much above the temperature of boiling water or 100 ëC as the high moisture content of most foods moderates the heating of the product. In foods that have localized areas that are high in fat, the temperatures can be higher than that of boiling water but do not reach anywhere near the temperatures that are reached in microwave susceptors.

12.3

Current regulations

There are a number of different regulations that are pertinent for microwave packaging. Some of these apply to all food packaging and some are specific to higher temperature use. One general regulation is for what is termed secondary direct food additives (21 CFR Part 173, 2008). A secondary food additive is a material that is not used as an ingredient in the food but is likely to become a part of the product during processing and packaging. In Subpart C of Part 173, there is a listing of solvents, lubricants, release agents, and related substances. These materials are used on equipment and on packaging materials to help the processing and packaging machinery run more smoothly and allow packaging materials to move smoothly over surfaces. These substances must meet the requirements of food additives as being safe for human consumption since they are reasonably expected to become part of the food product. Some of the different substances listed are ethyl acetate (21 CFR 173.228, 2008), hexane (21 CFR 173.240, 2008) and methylene chloride (21CFR 173.255, 2008). In these regulations, there may be limits on the amount that is allowed in the food product and each would have to be looked at specifically for each application. 21 CFR 174.5 lists the general provisions that are applicable to indirect food additives. Good manufacturing practices must be followed and any substance used must be pure enough for inclusion in food products. Any substances used in packaging materials for any purpose must meet one of several criteria: they must be generally recognized as safe as a food ingredient, generally recognized as safe as part of a packaging material, approved by prior sanction, permitted under sections 175, 176, 177, 178, or 179.45 of 21 CFR or have a proper pre-market notification filed with the FDA. The last category is for materials that a company believes are safe for use in packaging materials and has generated what they believe to be appropriate data to support the position that has been filed with the FDA. In 1995, the FDA published the threshold of regulation for substances used in food contact articles (60 FR 36596, July 17, 1995). This regulation is contained

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in 21 CFR 170.39 and 174.6 and states that if a compound migrates at what is considered to be negligible levels, then it is not subject to the requirements that a food additive petition be filed prior to use. While this was not in effect when the initial data on potential levels of volatile migration into foods from susceptor packaging was submitted in 1990, it allowed materials that were being used to fall into this category so no further testing would be needed. As mentioned, most of the volatiles that were identified would be present in a person's diet at less than 0.5 ppb (Breder, 1991). In addition to representing a dietary concentration of less than 0.5 ppb, any compound that is exempted under the threshold of regulation must not be a carcinogen, shows no other health or safety concerns, does not serve any functional purpose in the food product, and has no adverse effect on the environment. Sections 175, 176, 177, and 178 of 21 CFR (2008) address the requirements for adhesives and components of coatings, paper and paperboard components, polymers and adjuvants, production aids and sanitizers, respectively. A detailed discussion of all of these regulations is beyond the scope of this chapter. CFR 179.45 is specifically for packaging materials that are used for food to be irradiated. This would be applicable to microwave food products only if they are irradiated as a means of preservation and then meant to be heated in a microwave oven by the final consumer. All of these regulations can be accessed at http://www.access.gpo.gov/cgi-bin/cfrassemble.cgi. Each material that is to be used in a package designed for the microwave oven must be listed in the CFR and must meet the criteria specified. These criteria can limit the amount of an additive that may be used or may specify purity of a polymer. It is still incumbent on the user of the material to be able to show that no components enter the product at a level that would be equivalent to a dietary concentration higher than 0.5 ppb. If any compound does migrate at a higher level, then the company must have safety data to show that the material is safe for human consumption and must file a food additive petition for that material. Safe microwave food packaging requires that the manufacturer consider how the product is going to be used and what part of the package will be in contact with the food product. These materials must be properly evaluated. The one final consideration that overrides all regulations is that the package cannot cause an off-flavor in the food. If any component of the package does create an undesirable flavor, no matter what level is present, the food would be considered adulterated. People do continue to question the safety of materials used in the microwave oven. One problem that has occurred is that many containers that are used for other products end up being re-used by consumers as storage and potentially heating containers. It is important to use only materials that have been designed for microwave use.

Regulatory issues in microwave packaging

12.4

289

References

21 CFR 175.105, 1987, US Government Printing Office, Washington, DC. 21 CFR 175.125, 1987, US Government Printing Office, Washington, DC. 21 CFR 173, 2008, US Government Printing Office, Washington, DC. 21 CFR 173.228, 2008, US Government Printing Office, Washington, DC. 21 CFR 173.240, 2008, US Government Printing Office, Washington, DC. 21 CFR 173.255, 2008, US Government Printing Office, Washington, DC. 21 CFR 174.5 2008, US Government Printing Office, Washington, DC. 21 CFR 174.6, 2008, US Government Printing Office, Washington, DC. 21 CFR 175, 176, 177, 178, 179.45, 2008, US Government Printing Office, Washington, DC. Breder, C.V. 1991, Proceedings of the TAPPI Polymer, Coatings, and Laminations Conference, San Diego, CA. Cramer, G.M. 1988, Memorandum to Food Formulation Branch, Department of Health and Human Services, Washington, DC. Federal Register 1989. US Government Printing Office, Washington, DC. Vol. 54, No 173, pp. 37340±37342. Federal Register 1995. US Government Printing Office, Washington, DC. Vol. 60, 36596. Kashtock, M.E., Wurts, C.B., Hamlin, R.N. 1990, `A multi-lab study of food/susceptor interface temperatures measured during microwave preparation of commercial food products', J. Packaging Tech. Vol. 4(2), pp. 14±19. Machuga, E. 1988, Memorandum of Conference, `Microwave Susceptor Packaging Meeting', Washington, DC.

13

Microwave oven safety D B A R O N , dBEMF, USA

Abstract: Microwave oven safety is predicated on careful design and manufacturing criteria based on well-defined safety standards. Emission and exposure safety criteria are used to quantify the performance of consumer and commercial ovens and industrial applications, respectively. Measurements from operating units are compared with safety standards to determine the operating compliance of microwave heating applications. Typical government performance standards for ovens, such as those of the US CDRH/FDA/DHHS, are presented along with consensus safety standards, such as the IEEE ICES C95.1-2005 safety standard, which quantify maximum permissible exposure levels for industrial applications. Key words: safety, radiation, leakage, emission, exposure, measurement.

13.1

Microwave safety basics

Microwave ovens are arguably the safest cooking appliance in the home. The combination of rigorous design, production, and quality controls by the manufacturer and the regulatory oversight by governmental agencies truly minimizes risks or concerns over any potential hazards. Microwave energy `cooks' when lossy dielectric materials (food) absorb energy from the electromagnetic field and get hot. Separating the high-level fields in the cooking cavity of the oven from the user is the result of extensive engineering and careful safety regulation. Virtually all currently available microwave ovens, both consumer and commercial, operate at 2.45 GHz or 2450 MHz, meaning the electric field inside the oven changes at nearly 2.5 billion times a second. This rapidly changing electromagnetic field causes the molecules in many substances to vibrate rapidly, resulting in heating. The same physical mechanisms that cause food materials to heat can cause energy to be absorbed by biological tissue (people). Some industrial cooking equipment operates at 915 MHz as well. When consumer ovens were first introduced in the late 1960s, there was concern over possible safety hazards. These concerns resulted in the introduction of regulatory requirements to insure against any possible hazard. A general RF (radio frequency) and microwave safety requirement was applied to microwave ovens. Continued concern by members of the public led to the introduction of the Radiation Control for Health and Safety Act of 1968 in the United States.

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This regulation sets standard emission or `leakage' limits for microwave ovens manufactured in or exported to the United States. These general guidelines have been adopted in most countries of the world. The guidelines, codified in the US regulation, 21CFR1030.10, state that: The equivalent plane-wave power density existing in the proximity of the external oven surface shall not exceed 1 milliwatt per square centimeter at any point 5 centimeters or more from the external surface of the oven, measured prior to acquisition by a purchaser, and, thereafter, 5 milliwatts per square centimeter at any such point.

These 1 and 5 mW/cm2 limits are present in most all microwave oven performance standards. The relaxation of the leakage limit value from 1 to 5 was intended to address the potential of early ovens to emit or leak at greater levels as the oven door seal began to wear with increased usage. In the United States, microwave oven testing and usage is regulated by the Center for Devices and Radiological Health, a bureau of the Food and Drug Administration (FDA), under the Department of Health and Human Services (CDRH/FDA/DHHS). All ovens manufactured for sale in the United States are required to meet the US regulations. Emission measurements are intended to provide a repeatable means of characterizing the performance of a particular oven. A standardized test procedure is needed to maximize the repeatability of the testing. The US requirement specifies a 275 mL water load in a low-form beaker located in the center of the oven cooking cavity during testing. The oven is to be operated at its rated input voltage and at full operating power. Leakage testing is performed with a microwave survey meter having operating specifications listed in the US guidelines. Because of the evolution of the microwave oven markets starting in the United States, the US requirements have been adopted by most regulatory agencies worldwide. When performing oven leakage testing, look for an instrument acceptable to the US CDRH for leakage measurements. Some instruments are acceptable for final compliance testing of ovens, with performance criteria specified by the CDRH (refer to Figs 13.1 and 13.2). Others are suitable only for `in use or after repair' measurement applications. Some more fully featured leakage measurement instruments have a Response setting or selection. The response time of a microwave oven survey meter is required by the CDRH to respond to a sudden change in microwave leakage by reaching 90% of the new steady state value within 3 seconds. Typically, a faster response, less than 1 second, is used for turntable ovens, while the slower 3 second response was used primarily for ovens having a mode stirrer in the top of the oven cavity to provide a smoother cooking pattern. Any response time, up to the 3 second maximum, is acceptable to the CDRH for final compliance oven testing. Refer to the operating or user instruction manual of the survey meter being used. Refer to Appendix on page 301 for a list

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13.1 Hand-held microwave oven survey meter: HI-1501.

13.2 Production line survey meter: HI-1710A.

of survey instruments suitable for leakage testing of microwave ovens to CDRH requirements. During the testing, the sensing probe of the instrument is moved slowly across the leakage surfaces of the oven. The probe is held perpendicular to the leakage surfaces and, with the spacer cone lightly touching the oven, moved at not more than 25 mm per second. The spacer cone maintains a 50 mm spacing between the oven surface and the detection array of the sensing probe. The location and magnitude of the maximum leakage observed are recorded while scanning. The typical surfaces measured include the gaps between the oven door and the front panel surface of the oven, the control panel, and any air vents and lamp changing access panels. It is recommended that the probe be moved across the door viewing screen as well, often in a `W' pattern, to detect any defects in the viewing area. The oven should be located on a non-metallic surface and may need to be moved forward to the edge of this surface, if the gap along the bottom of the door is facing down, in order to provide measuring access to the gap. This is so that the probe may be held perpendicular with this gap. Observe the water load inside the oven. If the water begins to steam, it may be necessary to replace the load with cool (room temperature) water and continue the test. Steam from hot or boiling water may affect the leakage values observed. The steam in the

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oven cavity and condensation on the cavity walls can affect the microwave field distribution and affect the leakage readings. The maximum leakage allowed by US regulatory agencies, during the standard leakage test, is 1 mW/cm2 for ovens when first received by the end user and 5 mW/ cm2 during the life of the oven. Typical emission values for ovens, on the market today, are well below the 1 mW/cm2 value over their total operating life. Finally it is necessary to perform a `Burst' test to verify the proper operation of the total door safety interlock system. To do this, have the oven operating in a full-power condition. Locate the survey meter sensing probe at a position at a door leakage surface having a higher leakage value. Slowly open the oven door by pulling on the door handle or pressing the door release button and observing the leakage as indicated by the survey meter. As the door opens, observe the highest leakage during the opening process. The objective of this test is to assure that the oven door safety interlocks are operating properly and turn off the oven before the leakage becomes excessive. The maximum leakage allowed by the US Government during this test is 5 mW/cm2. Typically, with today's microwave ovens, the `burst' values observed will be the same as, or very similar to, the normal leakage tests. As will be noted in the following section on `exposure' evaluation, the emission limits and testing described above are more severe and restrictive than the exposure limits described for industrial applications. How often should microwave ovens be tested? In practice there is seldom a need to periodically test microwave ovens in good operating condition. Many ovens include a series of recommendations for safe operation of the oven. These recommendations typically include: · Do not attempt to operate with: o any object caught in the door o if the door does not close properly o with a damaged door, hinge, latch, or sealing surface. This is good advice, follow it. A visual check of the door and seal system of any microwave oven, from time to time, is worthwhile. Are there special situations where it may be advisable to test microwave ovens? · When new equipment is put into operation in a commercial or technical facility: a test documenting the initial operation of the oven can be filed for future reference. It is a simple test and the documentation may be welcome in the future. · Periodically during heavy, repetitive use: if ovens are being used in a laboratory or test kitchen environment, especially if by the same personnel, it may be advisable to test the ovens periodically, perhaps annually, as a verification and assurance of a safe workplace.

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· After modification for special testing: if an oven is modified for special testing, typically with an opening in the interior cavity wall, a test of the modified area and a filed test report provides assurance of a safe workplace. · When damage is observed: ovens that have been subject to abnormal operating conditions or otherwise physically damaged or altered should be tested for microwave leakage before returning to operation. Refer to the safe operating conditions described above. Microwave ovens operating within these guidelines should present no hazard to those present even during extended, repetitive operation.

13.2

Microwave ovens and pacemakers

It is not uncommon to see advisory or warning signs in restaurants, lunch rooms, and other public places regarding the presence of microwave ovens and possible problems with pacemakers or other active medical implants such as ICDs (implantable cardioverter defibrillators). Should an employer or facility manager be concerned regarding such a situation? The short answer to the above question is, No. The FDA offers the following comments on its website: Center for Devices and Radiological Health, US Food and Drug Administration: · At one time there was concern that leakage from microwave ovens could interfere with certain electronic cardiac pacemakers. · Similar concerns were raised about pacemaker interference from electric shavers, auto ignition systems, and other electronic products. · FDA does not specifically require microwave ovens to carry warnings for people with pacemakers. The problem has been largely resolved because pacemakers are now designed to be shielded against such electrical interference. · However, patients with pacemakers may wish to consult their physicians if they have concerns.

At any normal operating distance, the leakage from a typical microwave oven is below the recommended maximum exposure guidelines of pacemaker manufacturers.

13.3

Electromagnetic field exposure ± industrial applications

In evaluating potential safety concerns in industrial heating applications, it is often not feasible to use emission measurements as described for consumer and commercial microwave ovens. For workplace safety, actual exposure measurement is typically required for a proper workplace evaluation. For consideration

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under OSHA (Occupational Safety and Health Administration) in the United States or the European Union Workplace Safety Directives, actual exposure evaluation is the required protocol. To understand electromagnetic field safety in the workplace, several additional concepts are helpful. When discussing electromagnetic energy safety, the non-ionizing portion of the electromagnetic spectrum is typically divided into three sections. In the frequency range below 100 kHz, the primary interaction mechanism is electro-stimulation of nerve and muscle cells. Above approximately 100 kHz and up to about 3 GHz, the primary mechanism is bulk tissue absorption. This is the area where microwave ovens operate. Above 3 GHz, superficial or surface tissue heating becomes the dominant mechanism. Electromagnetic energy penetrates into the material being heated to varying depths depending on the wavelength of the energy and the dielectric properties of the material. The wavelength of a propagating field can be calculated from the fact that the frequency times the wavelength is equal to the velocity of propagation. Electromagnetic energy propagates at the speed of light (3  108 m/s). At 2.45 GHz (2:45  109 ) the wavelength is equal to: 3  108 ˆ 0:122 m ˆ 12:2 cm (about 4.8 inches) 2:45  109 The penetration of electromagnetic energy into a material is usually described by a variable called penetration depth, defined as the distance from the surface of the material at which the power density of the field has decreased to 1/e (approximately 37%) of the level at the surface. At 2.45 GHz, the penetration depth of the electromagnetic energy, into typical muscle tissue, is approximately 7 mm (see Fig. 13.3).

13.3 Microwave penetration depth vs. frequency.

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In characterizing microwave energy regarding its health hazard potential, the following measurement units are typically used. Electric field strengths (E) are measured in units of volts per meter (V/m). Magnetic field strengths (H) are measured in units of amperes per meter (A/m). Magnetic fields are also described in terms of magnetic field flux density (B). Magnetic flux densities are measured in units of tesla (T) or sometimes in units of gauss (G). The magnetic field units are simply related by the equation B ˆ H where  is the magnetic permeability of the material or medium. In most materials, other than ferrous and some other unique materials,  is the permeability of free space (and air and water and meat and etc.) which is 4  10ÿ7 henries per meter or about 1/800 000. A third measure of the magnitude of an electromagnetic field is the power density (S). The units of power density are watts per square meter (W/m2) or, sometimes, milliwatts per square centimeter (mW/cm2). For the purposes of our discussion, we will assume that these electromagnetic fields are well-behaved plane wave fields and we can relate power density to electric and magnetic field intensity by the equations: E2 ˆ H 2  377 ˆ S 377 where the electric field, E, is in V/m, the magnetic field, H, is in A/m, and the power density is in W/m. For example, an electric field of 100 V/m has a planewave power density of 1002/377 ˆ 26.5 W/m2. It can be shown that a power density of 26.5 W/m2 is equal to 2.65 mW/cm2. Power densities are stated in both units of W/m2 and mW/cm2 (10 W/m2 ˆ 1 mW/cm2). The correct SI unit is W/m2; however, units of mW/cm2 are often used in discussing microwave oven measurements. At microwave frequencies, typical field measurements are stated in terms of electric field (V/m) or power density (mW/cm2). A last metric is also of interest for a discussion of electromagnetic field safety, the specific absorption rate (SAR). This is a measure of the absorption of energy by some material. This material can be hamburger or soup; it can also be muscle tissue. The units of specific absorption rate are watts per kilogram (W/kg). The specific absorption rate is described as a `basic restriction' for safety purposes. In all our safety efforts, we seek to control the absorption of energy by the human body. Significant amounts of research have shown that, if the specific absorption rate is limited to less than about 4 W/kg, the human body will be able to absorb this energy and safely maintain its core body temperature. As the energy absorption rate exceeds this value, the core body temperature will tend to increase, causing potential health problems. Simply stated, limiting the SAR will control the potential for hazard to an exposed person. To this 4 W/kg value, a safety factor of 10 is typically applied, limiting the SAR to less than 0.4 W/kg for actual exposures. Laboratory testing and modeling have determined the variation in SAR with frequency and, hence, wavelength. From these variations, typical maximum

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Table 13.1 MPE values ISM microwave bands ± IEEE C95.1 Frequency (MHz)

General public exposure Power density Electric field (V/m) (W/m2)

2450 915

10 4.6

61.4 41.6

Controlled/occupational exposure Power density Electric field (W/m2) (V/m) 81.7 30.5

175 107

permissible exposures (MPEs) to electromagnetic fields have been developed and codified into exposure safety standards. Two main safety bodies have developed safe exposure recommendations for exposure to electromagnetic energy, the IEEE (Institute of Electrical and Electronic Engineers) International Committee on Electromagnetic Safety (ICES) and ICNIRP (International Committee on Non-Ionizing Radiation Protection). These groups have published standards for safe exposure to electromagnetic energy by living beings. These MPE values are frequency dependent as the human body absorbs energy more efficiently at some frequencies than others. Where the absorption is more efficient, the MPE value must be lower to maintain the same level of protection. At the microwave frequencies of interest for cooking, 2.45 GHz and 915 MHz, the recommended MPE values from the IEEE C95.1 standard are as shown in Table 13.1. 915 MHz and 2450 MHz are two designated ISM (industrial, scientific, and medical) bands set aside specifically for power or heating applications of electromagnetic energy. Because the human body absorbs electromagnetic energy more effectively at 915 MHz, the MPE values are lower to maintain a sufficient safety margin. Note also that two limits are provided for different exposure populations. The controlled/occupational exposure situation is for workers or other informed individuals who are aware of the exposure conditions, of possible ill effects, and of controls that are required for a safe workplace environment. Persons operating in a controlled environment are generally required to be under a documented RF safety plan such as that outlined in IEEE C95.7. General public or uncontrolled exposure limits (MPEs) apply to all others and may be employees without RF safety training or casual passers-by. It is important to note that these MPE values are averaged over the whole body of an exposed individual. An exposure measurement is affected by the location of the exposed person and can vary significantly over the body of the exposed individual. In addition to spatial or whole-body averaging, exposure may also be time averaged depending on the particular exposure situation. If the exposure varies over time and the exposure timing can be controlled, a total exposure period, consisting of exposed and unexposed times or times of variable exposure, of up to

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13.4 Microwave oven leakage vs. distance from oven surface (example).

6 minutes can be used for time averaging. For example, if the exposure were cyclic and with an ON time of 3 minutes and an OFF time of 3 minutes, the total cycle time would be six minutes and the duty cycle would be the ON time divided by the total cycle time (3/6 ˆ 50%). Because of the time averaging possible in this example, the exposure during the ON time could be twice the calculated MPE and the exposure would still comply with the requirements of the standard. An example can illustrate a comparison between microwave oven `emission' requirement and the industrial application `exposures'. In Fig. 13.4, the leakage from a microwave oven is plotted as a function of distance from the oven. At the oven surface (measured at 5 cm with a standard microwave oven survey meter), the leakage value was 0.7 mW/cm2. This is compared with a maximum emission of 5 mW/cm2 for an oven in use and an emission limit of 1 mW/cm2 for a `new' oven. The curve plots the reduction in leakage measured as the sensor is moved away from the oven surface (distance in meters). A special measurement instrument was used for these values as the standard microwave oven survey meter is not sufficiently sensitive for such measurements. At a distance of 0.4 m from our typical oven, the leakage value would be approximately 0.002 mW/cm2 (2 milliwatts per square centimeter). From our conversion equations, we can calculate the plane wave electric field intensity of this power density value: p E ˆ 0:002  3770 ˆ 2:75 V/m (0.02 W/m2 ) Compare these estimated `exposure' values from a typical microwave oven with the MPE values for the general public of 61 V/m and 10 W/m2. The added safety factors present in the microwave oven emission requirements provide additional assurance of operating safety under any anticipated conditions including children `viewing' the cooking process by looking through the oven window.

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13.5 Dielectric `stick man' substituted for subject.

Proper evaluation of potential exposure from an industrial microwave heating application requires more complex instrumentation and evaluation procedures. Measuring exposure rather than emission requires characterizing the electromagnetic fields existing at the exposure location (where the subject is standing or sitting). The microwave fields present are measured continuously or at a number of discrete locations over the space occupied by the subject. As the MPE values are specified for unperturbed fields, the measurements are completed with the subject not present. For measurement reference purposes, a dielectric stickman is often located at the exposure location (see Fig. 13.5). To determine the spatially averaged field intensity, a series of field measurements are recorded at intervals over the exposure space (see Fig. 13.6). The IEEE C95.1 safety standard requires that the measured data be spatially averaged over the exposure area based on power density (W/cm2). Power density is proportional to the square of the electric field strength so it is possible to measure exposure in field strength units (V/m for electric fields) and average the squares of the individual field values. The spatially averaged value can be compared with the MPE value

Location Foot Ankle Calf Knee Thigh Groin Belly Chest Shoulder Head

Field strength (V/m) 22 34 47 58 69 75 81 75 66 58

Average

59

jFSUj2 484 1156 2209 3364 4761 5625 6561 5625 4356 3364 3751 61.2

13.6 Spatially averaged field measurement example.

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to determine compliance with the safety guidelines. In the example, the average of the squared field values (in V2/m2 or |FSU|2) is 3751 V2/m2 which equals 61.2 V/m (|FSU|2 ˆ field strength units squared). This calculated spatial average value is slightly higher than the value of 59 V/m obtained by averaging the actual field values. The spatially averaged value may then be modified by any temporal (time) averaging that may be present in the exposure situation. The final exposure values are compared with the MPE values for uncontrolled (general public) or controlled (occupational) exposures. Using the higher, controlled exposure limits implies that those present in such conditions are participating in a workplace RF Safety Program. IEEE C95.7 provides outlines and guides for developing such a safety program for occupational industrial exposures. Evaluations using exposure criteria imply the presence of a subject (the person being exposed); no subject present ± no exposure. Emission measurements focus on the emitting device, the microwave oven, and apply without regard to the presence, location, or size of a potentially exposed individual.

Appendix: Microwave oven survey meters 1.

Acceptable for final compliance testing of microwave ovens, microwave oven servicing and in-home testing: HI-1501 Microwave Oven Survey Meter, ETS-Lindgren, 1301 Arrow Point Drive, Cedar Park, TX 78613, USA +001 (512) 531-6400 http://www.etslindgren.com/ HI-1710A Microwave Oven Survey System, ETS-Lindgren, 1301 Arrow Point Drive, Cedar Park, TX 78613, USA +001 (512) 531-6400 http:// www.ets-lindgren.com/

2.

Suitable for microwave oven servicing and in-home testing: HI-1801 Microwave Oven Survey Meter, ETS-Lindgren, 1301 Arrow Point Drive, Cedar Park, TX 78613, USA +001 (512) 531-6400 http://www.etslindgren.com/ Narda 8201 Microwave Survey System, Narda Safety Test Solutions GmbH, Sandwiesenstrasse 7, 72793 Pfullingen, Germany, +49 (0) 7121-97 32-777 http://www.narda-sts.de

14

Modeling microwave heating in foods M C E L U C H and P K O P Y T , Warsaw University of Technology, Poland

Abstract: The chapter addresses electromagnetic (EM) modeling of microwave food heating scenarios with the use of two popular computational methods: the finite difference time domain (FDTD) method and the finite element method (FEM) in the frequency domain. Principles behind FDTD and FEM are discussed first, with focus on their numerical accuracy bounds. Theoretical considerations are illustrated with practical examples involving a commercially available domestic microwave oven loaded with a beef load. Two popular EM solvers are applied and shown consistent in predicting matching characteristics and field patterns: HFSS (FEM) and QuickWave-3D (FDTD). Multiphysics functionalities of QuickWave-3D are further utilized to demonstrate the effects of temperature-dependent materials, load rotation, heat flow and magnetron detuning. Key words: electromagnetic (EM) modeling, multiphysics modeling, finite difference time domain method (FDTD), finite element method (FEM), numerical accuracy, microwave heating.

14.1

Introduction

Electromagnetic (EM) modeling gained great popularity long ago with the telecommunications community, which pioneered its use for practical design of radio frequency (RF) systems, antennas and similar devices in 1980s. The advantages of an approach that puts an EM solver in the role of a testing platform for concept verification as well as troubleshooting prototypes encouraged other practitioners in the field of microwave hardware design to accept it. As a result, the numerical modeling algorithms have spilt into the microwave power area, where they have become a tool used on a regular basis in the design of components for microwave power applicators. This has been made easier by the fact that such elements are often similar to their counterparts in telecommunications and virtually the same design tools can be used without much need for modification. This increased penetration of the EM modeling techniques into the microwave heating domain leads to a demand for more customized tools that would extend pure EM solvers. Instead of just modeling the performance of feed systems or cavities, complete processes where the EM energy is used can be modeled. With constantly growing computing power of standard widely available PCs as well as falling prices of hard disk drive storage and computer memory, it has become

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Packaging and products for use in microwave ovens

possible to develop and use truly multiphysics solvers consisting not only of the EM computational kernel but also of additional modules responsible for phenomena from other domains such as thermo- or fluid dynamics. As found in the comprehensive review of available commercial electromagnetic codes published in Yakovlev (2006), two major methods have gained notoriety and are employed in almost all such tools being used nowadays. They are the finite difference time domain (FDTD) method and the finite element method (FEM). Although, based on Yakovlev (2006), it has been suggested that microwave heating scenarios are more efficiently handled with FDTD- rather than FEM-based methods, both approaches are very often used in R&D as well as commercial projects that involve microwave heating. Examples can be found in Ma et al. (1995), Torres and Jecko (1997), Risman and Celuch-Marcysiak (2000), Ratanadecho et al. (2002), Al-Rizzo et al. (2007) and Kopyt and Celuch (2007), where the FDTD algorithm has been employed to predict temperature profiles in media heated with microwaves, or in Pangrle et al. (1991), Sekkak et al. (1994), Zhang and Datta (2000) and Akarapu et al. (2004) who employed the FEM method in the coupled analysis of microwave heating. Despite the amount of research into coupled simulation techniques reported every year in the literature, as well as the quick rate at which the existing commercially available solvers are being extended with new features, it is unlikely that such packages will ever reach a point where a large majority of practical problems can be solved with default settings. The ability to model processes of growing complexity comes at a price of increased requirements for an operator of such modeling tools. Practitioners in the field are not surprised to learn how quickly computer resources can be exhausted by models of modest looking scenarios when they are not properly set up. Thus, the ability to take advantage of recent developments in the area will, to a growing extent, depend on the overall knowledge-based skills and proficiency in building adequate multiphysics models. This chapter aims at providing an insight into simulations of microwave heating scenarios with both the FDTD and FEM algortithms in order to make advanced modeling easier. Several examples are provided to better illustrate the basic concepts of the modeling methods. Properties important in the analysis of microwave power phenomena are stressed and shown to affect the computational accuracy when handled improperly. The specific topics presented in subsequent sections include: · short background of the modeling methods, with emphasis on mechanisms useful in coupled multiphysics analysis; · error bounds due to numerical dispersion inherent in numerical algorithms; · modeling of lossy and dispersive media crucial in the analysis of the microwave heating effect; · modeling of lossy cavity walls;

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· coupled analysis of microwave heating involving heat conduction and load rotation effects besides the EM phenomena. The examples analyzed in the chapter are solved with a numerical package based on the FDTD method and also with a FEM-based solver. As an FDTD method implementation, the QuickWave-3D package version 7.0 (QuickWave3D, 1997±2008) is chosen. It is based on the conformal FDTD method (Gwarek, 1985) with additional features including the coupled heat diffusion module or load rotation during heating. The FDTD-based numerical tools are frequently compared using a parameter that expresses computational speed of such software as a number of FDTD cells calculated per second (cell/s). For example, solving a problem built out of 1 million cells and where reaching the electromagnetic steady state requires 10 000 iterations will take approximately 2 hours 45 minutes, with a package granting the speed of 1 million cells/s. The experiments show that the speed typically achieved on a regular PC with QuickWave-3D is circa 30 million cells/s. Discussions among FDTD software users and vendors, such as those held at the Seminar `Computer Modeling & Microwave Power Engineering' (Yakovlev, 2008), indicate that this is one of the fastest FDTD implementations on the market. It can be, thus, considered as a good representation of tools based on the FDTD algorithm to be considered in this chapter. The experiments performed by the authors using test cases designed to check the computational speed of HFSS (HFSS, 1990±2008) and ANSYS Multiphysics (ANSYS Multiphysics, 1993±2008) solvers suggest that the developers of the HFSS package have reached the theoretical speed limits for FEM-based methods. This has been achieved by putting great efforts into development of effective problem preconditioning mechanisms and adaptive mesh generation routines. As a result, the solution process in HFSS consists of several stages that precede the actual electromagnetic fields calculation. Such an approach proves beneficial in scenarios where performing multiple simulations for the same problem is necessary, such as during S-parameter extraction in a wide frequency band. Although the preconditioning requires additional computation, it takes place only once and, to a great extent, enhances the computational speed at the subsequent stages. Our experiments show that other FEM-based environments, which do not use such elaborated computational schemes, offer less competitive speed in computations. The HFSS package version 11, which uses the above preprocessing schemes, was found to be the fastest among the tools of this class. It is therefore chosen here as a representative of the FEM method, despite the fact that it offers fewer features oriented towards handling multiphysics scenarios than the ANSYS Multiphysics environment. Both QuickWave-3D and HFSS are available on the market and the survey (Yakovlev, 2006) found them suitable for applications in the microwave heating area, which further explains the decision made by the authors to make use of these two packages.

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14.2

Packaging and products for use in microwave ovens

FDTD versus FEM

This section presents aspects of numerical methods typically employed for modeling of purely electromagnetic effects in microwave power systems. Although other effects ± e.g. heat transfer ± also play a role, they will be introduced only in subsequent sections of the chapter. This is to recognize that Maxwell's equations will always remain at the heart of a microwave heating problem, and their accurate and effective solution is a prerequisite for any further analysis of a more general multiphysics scenario. Both the FDTD method and FEM are representative of a larger class of modeling approaches where the considered space is divided into small nonoverlapping sub-volumes known as cells or elements. The solution of a problem is found as linear or low-order polynomial functions approximating the field inside each of the sub-volumes. Such methods are called space-discrete and are particularly popular in modeling microwave heating problems. They are flexible enough to model loads of arbitrary shapes without requiring that the loads be homogeneous. They also allow monitoring of field intensities, dissipated power or specific absorption rate (power dissipated per unit mass, denoted by SAR and expressed in W/kg) in space in a very straightforward manner. In the next two sections the FDTD method and the FEM will be presented to a greater detail showing the equations that are solved with the numerical packages based on the algorithms.

14.2.1 The FDTD method In the FDTD method (Kunz and Luebbers, 1993; Taflove and Hagness, 2005), Maxwell's equations are discretized in space and time, and a response to any particular excitation is obtained by explicit simulation of signals propagating across the circuit. An electromagnetic problem in the 3D space is converted into a 4D problem, with time being the fourth variable. Refinement of space discretization requires proportional refinement of the time step due to the Courant stability criterion (Taflove and Hagness, 2005, 4.7). Consequently, the computing time for any particular 3D problem with N3 FDTD cells is always predictable and proportional to N4. This makes FDTD advantageous with respect to FEM for electrically large problems since (as discussed in Section 14.2.2) in FEM the dependence on N is more rapid and burdened with uncertainty. Moreover, since the FDTD algorithm reproduces a natural process of wave propagation, convergence to the steady state depends on the Q-factor of the modeled structure. Simultaneously, in microwave heating scenarios structures loaded with lossy media are typically considered, which naturally lowers the Qfactor and leads to speeding up the FDTD simulation convergence. The structure of a basic FDTD cell usually referred to as Yee's cell is well known (Taflove and Hagness, 2005, 3.6). It is also called a staggered or

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expanded node since each of the six field components is calculated at a different position in space. Consider one component of one of Maxwell's equations: @Ez ˆ …r  H†z 14:1 @t where "z is the relative permittivity of the medium (for the Ez field component), H is the magnetic field vector, and subscript (..)z denotes the z-component of the expression. Assuming that the Ez component is placed at a point in space …k
x; l
y; …m ‡ 0:5†
z† at the instant of time n
t, one discretizes (14.1) into a finite difference form: " n‡0:5 ÿ kÿ0:5;l;m‡0:5 Hyn‡0:5 k‡0:5;l;m‡0:5 Hy n‡1 ‡ ˆ k;l;m‡0:5 Ezn ‡ k;l;m‡0:5 Ez
x  n‡0:5 ÿ k;l‡0:5;m‡0:5 Hxn‡0:5
t k;lÿ0:5;m‡0:5 Hx 14:2
y k;l;m‡0:5 "z "0 "z "0

which may be a function of space variables and time (Celuch-Marcysiak et al., 2006). Alternatively, one may multiply both sides of (14.2) by
z=…
x
y† and use the following auxiliary variables instead of the field components ez ˆ Ez
z;

hx ˆ Hx
x;

hy ˆ Hy
y;

cz ˆ

"z "0
x
y 1
z
t

to obtain: n‡1 k;l;m‡0:5 ez

ˆ k;l;m‡0:5 enz ‡ n‡0:5 k‡0:5;l;m‡0:5 hy

ÿ kÿ0:5;l;m‡0:5 hn‡0:5 ‡k;lÿ0:5;m‡0:5 hn‡0:5 ÿk;l‡0:5;m‡0:5 hn‡0:5 y x x k;l;m‡0:5 cz

14.3

Equation (14.1) and its discretized form (14.3) do not account for media losses, which are of primary importance in microwave power problems. Modeling the losses requires that equation (14.1) be modified. Thus, when considering point …k; l; m ‡ 0:5† within a lossy dielectric, the following form must be used: @Ez ‡ z Ez ˆ …r  H†z 14:4 @t where z stands for conductivity of the medium. After discretization and transformation into an integral form, it can be expressed as follows: "z "0

n‡1 k;l;m‡0:5 ez

ˆ k;l;m‡0:5 enz k;l;m‡0:5 s0z ‡ n‡0:5 k‡0:5;l;m‡0:5 hy

ÿ kÿ0:5;l;m‡0:5 hn‡0:5 ‡k;lÿ0:5;m‡0:5 hn‡0:5 ÿk;l‡0:5;m‡0:5 hn‡0:5 y x x 0 k;l;m‡0:5 cz

14.5

where

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Packaging and products for use in microwave ovens c0z ˆ cz ‡ sz ;

s0z ˆ

c z ÿ sz ; c z ‡ sz

sz ˆ

z
x
y
z

and cz is defined as in (14.3). Formulation (14.3), while being formally equivalent to (14.2), can be interpreted somewhat differently. Here the variables are field integrals along the cell edges. This may be considered as an integral formulation of the FDTD method, bringing immediate numerical advantages. Parameters cz are calculated at the preprocessing stage and stored. In the vicinity of a media interface, the value of "z is averaged through vectorial integration over the cell. Even in the case of variable meshes, the operation count remains at 30 flops per cell per iteration, while it would reach 36 with the classical implementation of (14.2). The cz coefficients are stored locally for each cell, and multi-level indexing to look-up tables is avoided, further improving the algorithm efficiency. Coefficient cz can be interpreted as capacitance of the FDTD cell, with virtual perfect electric conductor (PEC) plates of a capacitor on its z-boundaries (perpendicular to the considered Ez field component) and perfect magnetic conductor (PMC) walls surrounding it, divided by the time step. This interpretation encourages a natural move to modify the coefficient cz when the shape of the FDTD cell changes to match a curved boundary. This possibility was noticed at the early stage of FDTD research (Gwarek, 1985) opening the way to conformal boundary approximations (Taflove and Hagness, 2005, 10). Equation (14.5) is consistently reduced to (14.3) in lossless dielectrics, and formally speaking, (14.5) can be applied to all components within lossy as well as lossless regions. This simplifies the coding and is indeed applied in basic FDTD programs. In more advanced software packages, a preprocessor assigns the `lossless' and `lossy' components to separate classes, to be later separately processed with (14.3) and (14.5) respectively. This further improves the numerical efficiency: while 33 flops and 39 memory reads per cell per iteration are needed in a lossy dielectric, 30 flops and 36 reads are maintained in a typically dominating air environment. It is noteworthy that this is the number of memory read/write operations, and not the arithmetic operation count that determines the speed of FDTD simulations on contemporary computers. Lossy and dispersive media The algorithm described by (14.4) and (14.5) approximates Maxwell's equations assuming that conductivity and permittivity do not vary with frequency. In other words, the real part of complex permittivity is constant and the imaginary part is inversely proportional to frequency. This may be true when losses are caused predominantly by conduction currents and there are no effects of molecular resonances. However, many media involved in microwave heating do not meet these assumptions. In such cases, frequency dependence of media parameters is often

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14.1 Frequency-dependent real and imaginary parts of relative permittivity of water described by the Debye model with "0 ˆ 81, "00 ˆ 1:8, t ˆ 0:0094 ns: dots ± analytical values, lines ± extracted from the FDTD simulation of a waterfilled coaxial line (radii of 300 mm and 75 mm).

described by the Debye, Drude or Lorentz models of dispersion. For example, a typically used Debye approximation of water parameters (Kunz and Luebbers, 1993, 8.2) provides relative permittivity of 81:0 ÿ j0:13 at 27.12 MHz, 79:38 ÿ j11:23 at 2.45 GHz, and 2:05 ÿ j4:46 at 300 GHz as shown in Fig. 14.1. However, practical microwave power installations do not work across such a broad band, and for the bandwidth of interest (e.g., 2.45 GHz  50 MHz) electromagnetic analysis with constant parameters is representative. Then the first approximation of complex permittivity for a typical microwave heating problem consists in taking "z in (14.5) from "0 material data, and  is calculated as  ˆ 2f "0 "00 . This is illustrated in Fig. 14.2. A short-ended coaxial line is analyzed for reflection coefficient in the frequency band of 1 GHz±5 GHz in two cases: the line filled with water modeled as a Debye medium and as lossy dielectric characterized by relative permittivity at the frequency of 2.45 GHz. As shown, the differences in this particular case are not large, and in the vicinity of 2.45 GHz the relative error of approximation is only about 1.5%. The Debye, Drude and Lorentz media models have been implemented in the FDTD context (Kunz and Luebbers, 1993, 8; Taflove and Hagness, 2005, 9).

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14.2 A comparison of S11 parameters of the line filled with Debye medium (dashed line) or a lossy dielectric (solid line).

The most numerically effective implementation of dispersive media models results from using the integral notation of (14.3) and (14.5) with equivalent capacitance interpretation of the FDTD cell. This approach also provides intuitive insight into the various FDTD equations. The original expression (14.3) for lossless media describes charging of a lossless capacitor C. Equation (14.5) describes charging a capacitor C connected in parallel with a resistor G (see Fig. 14.3a). By analogy, the Debye, Drude and Lorentz models describe the equivalent circuits of Fig. 14.3(b)±(d), respectively, where C1, L, r denote capacitor, inductor and resistor in the additional parallel branch modeling the dispersive and resonant effects. Numerical error bounds Numerical dispersion of the FDTD algorithm is a problem essentially different from the physical dispersion of media parameters or dispersive characteristics of waveguide structures. Numerical dispersion is inherent in any space discrete method, causing the EM waves to propagate with a different phase velocity on the discrete mesh than in the continuum. The phase velocity error transforms to an equivalent error of calculated resonant frequencies. Thus the same dispersion curves show phase velocity error, wavelength error, resonant frequency error or (with reversed sign) wavenumber error. The level of dispersion depends on the direction of wave propagation, time step
t and steps in space
x,
y,
z. Assuming a lossless homogeneous

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14.3 Models of lossy media: (a) a simple model of constant conductivity, (b) Debye model, (c) Drude model and (d) Lorentz model.

medium and
x ˆ
y ˆ
z ˆ a, one obtains well-known (see, e.g., Taflove and Hagness, 2005, 4) dispersion relations exemplified in Fig. 14.4(a). The dispersion error is plotted versus the ratio of cell size to wavelength. Two directions of propagation are distinguished: axial (that is, along one of the main axes of the FDTD grid) and diagonal (at equal angle to each of the three Cartesian coordinate axes). Time step influence is demonstrated by the curves for three different values of stability factor r defined as: r ˆ v…a=
t†

14:6

where v is phase velocity in the continuum. The Courant criterion dictates r  31=2 for stable operation of the 3D FDTD algorithm on homogeneous, lossless and equidistant meshes. Comparing the curves for r ˆ 31=2 , r ˆ 2 and r ˆ 1, one observes that dispersion errors increase with decreasing time step. This effect may be counterintuitive with the reference to the circuit-theory computer-aided design (CAD) where accuracy tends to improve with time step reduction. In FDTD modeling of distributed structures, too small
t not only prolongs the simulation but also reduces the accuracy.

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14.4 (a) Absolute value of relative frequency error caused by FDTD dispersion in a lossless medium, plotted versus cell size to wavelength ratio, for three values of stability coefficient: r ˆ 31=2 (continuous), r ˆ 2 (dashed), and r ˆ 1 (dotted); (b) relative wavenumber error caused by FDTD dispersion in a lossy medium, plotted versus time step to period ratio, for r ˆ 31=2 and five values of the loss tangent.

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The question concerning whether these simple error estimates retain adequacy in the case with lossy media is important for modeling of microwave power scenarios. Major observations by Celuch-Marcysiak (2004) are presented in Fig. 14.4(b). The change of coordinates in this figure, with respect to Fig. 14.3(a), is prompted by changes of wavelength due to the losses, which makes presentation in the coordinates of Fig. 14.4(a) unclear. The dotted line repeats the lossless case predictions; other lines correspond to the loss tangent increasing up to 0.1. Unlike the lossless case, where the phase error is always positive (and resonant frequency error always negative), in the lossy case we observe a bilateral dispersion phenomenon ± positive phase errors in the axial and negative in the diagonal direction. In other words, the calculated resonant frequencies of a microwave heating system may be either underestimations or overestimations of their physical counterparts. However, from the practical viewpoint, the most important conclusion is as follows: absolute values of numerical dispersion errors do not increase in lossy media. This is also true for materials of loss tangent above 0.1, such as beef characterized by approximately 0.3 at 2.45 GHz. Interestingly, in such high-loss regions the numerical anisotropy of the FDTD mesh decreases and the simulated results are less dependent on the direction of wave propagation Therefore, simple error estimates of the lossless case may be considered as sufficiently reliable error bounds for microwave heating applications. Following the above predictions, discretization with ten cells per wavelength is often proposed by automatic mesh generators, as 1.5% accuracy appears adequate in many engineering tasks. This entails higher absolute mesh resolution in high permittivity loads than in the cavity. One may accept the above `rule of thumb' as a starting point for a new microwave system analysis. However, if one knows that a particular system behavior is determined by cavity modes, rather than load focusing or diffraction effects, it may be more effective to maintain the same absolute mesh resolution throughout the computational volume. Conformal meshing and material boundary modeling In early FDTD codes, all circuit boundaries and media interfaces were modeled in a staircase manner. In that approach, any curved or oblique sections were replaced by linear ones, parallel to one of the coordinate axes, with all FDTD cells cubical and homogeneous. This constituted a basic limitation of the FDTD approach, hindering its applications in many areas. In microwave heating, the complaints concentrated around the jaggedness of the food load models, and the simulated heating patterns (Risman, 1998). As a means to alleviate the problem, non-equidistant and variable meshing was introduced. Cell sizes could then be controlled as
x ˆ
x…x†,
y ˆ
y…y†,
z ˆ
z…z†, allowing for better resolution in the proximity of structure boundaries or higher permittivity

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14.5 (a) Coaxial line (radii 300 and 75 mm); (b) discretization of the coaxial line cross-section using conformal FDTD cells of dimensions 37:5  37:5 mm.

regions. The variable meshing is an improvement over uniform equidistant meshing but the staircase and jaggedness problems essentially remain. On the other hand, even early FDTD literature (Gwarek, 1985) suggested more flexible boundary approximations with conformal cells. However, there is also a hidden catch in some of those techniques and their implementations. Owing to the previously mentioned Courant stability criterion, a maximum FDTD time step for stable operation is bounded by the smallest cell size (14.6). Now, the value of a in (14.6) should be taken as an effective dimension of this portion of the cell where the electromagnetic fields exist ± remember that the fields exist throughout the dielectric regions but vanish in metal. Consider the coaxial line of Fig. 14.5(a). Its conformal meshing of Fig. 14.5(b) clearly represents the shape, but some boundary cells are partially filled with metal, and hence their effective cell size decreases. As metal protrudes deeper into a cell, a straightforward conformal FDTD implementation would result in the time step decreasing to zero, and the computing time increasing to infinity. There are two basic ways of resolving the problem in two groups of the existing FDTD solvers: either the time step is reduced down to some predefined limit beyond which the small cell is neglected, or the small cells (smaller than, for example, half of the basic discretization) are merged into their neighbors. The first approach is easier to program and sufficient in terms of certain accuracy criteria (Railton and Schneider, 1999). However, it essentially amounts to a refined version of staircasing, and slows down the simulation due to the reduced time step. The latter approach ensures smoother convergence of boundary approximation errors with discretization (Celuch-Marcysiak, 2001), at the expense of more complicated coding. The effectiveness of the conformal meshing approach is illustrated with the coaxial line example shown in Fig. 14.5(a). The medium properties extracted in a wide frequency band based on simulation employing the meshing presented in

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Fig. 14.5(b) match exactly the theoretical predictions despite modestly dense mesh employed in the example. The meshing of 37.5 m that was used corresponds only to approximately 200 cells used to discretize the cross-section of the line of quite complex geometry.

14.2.2 FEM In the FEM (Silvester and Ferrari, 1996; Zienkiewicz et al., 2005), the electromagnetic problem consisting of the geometry, boundary conditions and excitation defined at one particular frequency is converted into a set of linear algebraic equations. Such a conversion is defined as a process where a problem described by Maxwell equations is solved by seeking its approximate solution. In general, two procedures to obtain this goal exist (Zienkiewicz et al., 2005). The first one consists in determination of variational functionals for which stationarity is looked for. The other one is the method of weighted residuals (also known as the Galerkin method), which aims at minimizing the spaceweighted error of the sought-for approximation. Such an approach differs to a large extent from the finite differences formulation where the problem solution is found through simulating the actual physical process of wave propagation. The resulting set of linear equations is a standard problem in linear algebra. What makes it difficult is its size. Each element of the discretized 3D space brings several variables into the system while a typical microwave heating problem may consist of as many as millions of elements. This means that even with modern supercomputers solving such a huge system directly would be impractical. Iterative methods are therefore employed, but they also have disadvantages. The speed of convergence depends on an initial estimate and matrix preconditioning, which are problem-dependent (Silvester and Ferrari, 1996, 10.4). This is further confirmed in Shewchuk (2002), where the effect of matrix preconditioning in case of most popular tetrahedral (unstructured) computational meshes used by the EM FEM-based solvers is shown to lead to a drastic increase in computational time. As a result, in case of complicated structures, it is difficult to estimate if and when an analysis will terminate successfully or even accurately predict how the computing time will rise with mesh refinement. It has been estimated (Lynch and Paulsen, 1990) that with a problem of N3 elements, the simulation time may be proportional to N 4 . . . N 6 , depending on the problem type and the quality of preconditioning. The Galerkin method seems more straightforward to explain than the variational formulation, and the results of both are equivalent. For this reason the Galerkin method will be presented in this section as a brief introduction to FEMbased examples presented further in this chapter. Since the standard FEM applied to electromagnetic problems assumes frequency domain formulation, the Maxwell equations assuming a periodic solution in time eÿj!t will be the starting point for the following discussion:

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Packaging and products for use in microwave ovens r  E ˆ j!H

14:7a

r  H ˆ ÿj!"E

14:7b

where " and  are complex permitivitty and permeability, respectively. In order to make the FEM introduction simpler the equations can be combined so that magnetic field is eliminated. As a result a second-order partial differential equation known as the vector Helmholtz equation with the electric field E unknown is obtained: r  …r  E† ÿ k 2 E ˆ 0

14:8

where k is the complex wavenumber defined as k 2 ˆ !2 ". In the weighted residual formulation scalar basis function j is defined in the solution domain following an observation that a solution of (14.8) will also fulfill the following condition: h‰r  …r  E†Št i ÿ hk 2 Ei i ˆ 0

14:9

where h i indicates integration over the volume. With integration of the first term by parts one gets h‰r  …r  E†Št i ˆ hr  …i r  E†i ÿ hri  …r  E†i H ˆ n  …i r  E†ds ÿ hri  …r  E†i; 14:10 where n is the outward-pointing unit vector normal to the surface containing the volume. As a result, the so-called weak formulation is obtained, in which the expression n  H is exposed as a boundary condition for electric field E and allows applying boundary conditions where E is unspecified or calculating n  H where E is given: H 14:11 h…r  E†  Ei i ÿ hk 2 Ei i ˆ j! n  Hi ds The solution is looked for in the expanded form in terms of weighting functions j , such that Eˆ

N X

Ej j …x†

14:12a

jˆ1

nH ˆ

N X jˆ1

…n  H†j j …x† ˆ

N X

F j j …x†

14:12b

jˆ1

After (14.12) is substituted into (14.11), and (14.11) is defined for i ˆ 1 to N, where N is the number of nodes used in the discretization, the problem can be stated in the following matrix form with Ae ˆ Bf where A, e, B and f contain the following complex sub-matrices:

14:13

Modeling microwave heating in foods 2 D@

j

6 6 Aij ˆ 6 6 4

@y

@i @y

@

2 i ‡ @zj @ @z ÿ k j i D E @ i ÿ @yj @ @x D E @ i ÿ @zj @ @z

E

D D

@j @i @x @x

ÿ

@j @i @x @y

E

@

2 i ‡ @zj @ @z ÿ k j i D E @ i ÿ @zj @ @y

D @ ÿ @xj D @ ÿ @yj

E D

@j @i @x @x

‡

@i @z @i @z

@j @i @y @y

319

E

3

E

7 7 7 7 E5

ÿ k 2 j i

14:14a 2

3

Exj 6 7 ej ˆ 4 Eyj 5; Ezj

2 6 Bij ˆ 4

H

j! i j da 0 H 0 j! i j da 0

0

0 0

H j! i j da

3 7 5;

2

3

Fxj 6 7 f j ˆ 4 Fyj 5 Fzj

14:14b

Equation (14.13) is solved for e in a process where known vector f constitutes the right-hand side of the jth equation. For equations where the right-hand side ± the vector f ± remains unknown, the electric field E must be explicitely defined so that such equations can be removed from the matrix and solved for f separately. As already stated, the above procedure is repeated for each value of ! from the band of interest. There exist approaches aimed at improving the convergence rate of such problems by employing smart meshing mechanisms combined with procedures improving the conditioning of the A matrix. Again, a detailed discussion of such methods lies outside of the scope of this chapter. What needs to be explained is the construction of shape functions j further used in the solution process. Most EM solvers based on FEM use tetrahedral elements (HFSS), hexahedral elements or both (ANSYS Multiphysics also allows elements degenerated into prisms or pyramids) leaving the choice at the discretion of the user. Consider a coaxial line cross-section, as an example of simple 2D object discretization and the shape functions. The line of radii 300 and 75 m discretized with 48 basic triangular elements is presented in Fig. 14.6(a). The example given with triangular elements and linear functions was chosen because of its simplicity. Although most FEM packages use higher-order shape functions, they would be much more difficult to present. Figure 14.6(b) presents typical linear shape functions. For reasons of clarity only a fragment of the function that is defined over the element marked as `1' is shown. This means that function j assumes non-zero values also over all elements which share the jth node. For example, a function defined for the first node assumes non-zero value at this node and zeros at all other nodes. Thanks to this feature it is easier to numerically calculate values of the integrals defined for each of N linear equations in (14.11). The calculations must account only for an area of several neighboring elements because on the remaining part of the volume the shape functions are zero. This leads to a limited number of non-zero elements in each row of matrix A in (14.14). The exact number of such elements depends on the type of finite elements used for domain discretization, while the overall number of nodes affects the size of the problem matrix. The approach described above has two major differences with respect to the finite difference time domain approach presented before. First, the discretization with varied shapes makes modeling of any complex geometry a straightforward

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14.6 (a) An example FEM discretization of coaxial like cross-section using triangular elements; (b) linear shape functions fj defined for all the nodes of element `1'.

task. Contrary to the elaborate conformal FDTD formulations, geometries with curved boundaries (e.g. coaxial line) can be discretized with a modest number of elements relatively easily and without additional difficulties caused by possible existence of PEC (perfect electric conductor) boundary condition within a cell.

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At the same time, the basic FEM approach and algorithms implemented in ANSYS or HFSS packages are rooted in the frequency domain. This fact has farreaching consequences when modeling scenarios that involve dispersive media. In FEM, no particular treatment of such materials is necessary because circuits are characterized in a given frequency band using multiple simulations performed with monochromatic excitation of a frequency chosen from that band. The media can be defined separately for each simulation based on their predefined dispersive characteristics. On the other hand, inability of the FEM approach to apply wide-band excitations leads to prolonged simulations if fine frequency resolution in wide band is necessary. Although methods exist (Bracken et al., 1998) to minimize the number of frequency points at which monochromatic excitation has to be applied to the circuit, they are most efficient in modeling circuits with a limited number of resonances in the frequency band of interest. In such cases rational functions of a limited number of poles can be employed to provide highly accurate approximation of the complete curve. However, in case of multiple-resonance circuits like a microwave oven cavity such approaches may not work faster than the standard methods based on the discrete frequency sweep. Constructing a good approximation of such curves requires that many samples be collected, which necessitates performing separate simulations at all these frequencies. FEM error bounds Similarly to the FDTD formulation, the computational accuracy of FEM depends on the discretization employed in a modeled scenario. Because in FEM various elements with a varying number of nodes can be used, the error figure will depend not only on the number of elements in a given volume, but also on the element type as well as on the assumed shape functions. All these factors make it difficult to formulate guidelines valid for all possible cases. For this reason, two simple scenarios are chosen as examples based on the analyses performed in Lynch et al. (1985) and Lynch and Paulsen (1991). The first case is a 2D mesh consisting of triangular elements while in the other one square-like elements are used. In both scenarios linear shape functions are employed for simplicity. The dispersion errors that are inherent in such cases are plotted in Fig. 14.7 against the ratio between the element size and the wavelength. The greatest difference in the dispersion analysis of basic formulation of FEM is that no influence of the stability factor on computational accuracy is considered, because time is neglected in FEM-based simulation. Although timedomain FEM schemes are sometimes formulated and successfully used (Lynch and Paulsen, 1990), they lie out of the scope of this chapter. The accuracy analysis presented here is done for FEM employing the socalled nodal elements, while some of the FEM packages (e.g. HFSS) use an alternative approach based on edge elements. In the nodal element approach,

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14.7 Relative frequency error caused by FEM dispersion in a 2D lossless problem, plotted versus cells size to wavelength ratio for two directions of wave propagation and for two discretizations: (a) mesh consisting of triangular elements of height equal to a; (b) mesh consisting of squares with side dimension equal to a.

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each component of the field is represented by an expansion of scalar basis functions, whereas in the edge-element approach, the vector field is approximated by an expansion of vector basis functions. Despite these differences, the errors due to dispersion are on similar levels in both techniques (Warren and Scott, 1995). Thus, a general rule of thumb can be deduced which is similar to the one observed in the FDTD method: to use at least ten elements per wavelength while preparing the mesh. This guarantees that the numerical dispersion error will not exceed 2%. This requirement is normally built into automatic mesh generators in the FEM-based commercial solvers which use this suggestion as the starting point for automatic mesh refinement schemes. Additionally, the presented results confirm the practical observation that although 2D triangular or 3D tetrahedral elements are easy to employ by automatic meshing mechanisms, their use is burdened with several consequences. As shown in Fig. 14.7, the dispersion error for the two orthogonal directions of wave propagation is comparable when mesh of triangular elements is considered. It is, however, twice as big as the error obtained for diagonal wave propagation on the mesh consisting of square elements. This may translate into an increased number of triangular elements that must be used to achieve accuracy similar to that granted by square elements.

14.3

Coupled electromagnetic±thermodynamic simulation

A graphical representation of the microwave heating phenomena is presented in Fig. 14.8. The heat generated in the load by means of microwaves becomes subject to thermal diffusion. As shown, the strongest link between the electromagnetic and thermal problems is through any of the medium properties, which can be a function of temperature. The thermal and electromagnetic parts are bilaterally coupled as long as there is a temperature dependence of the properties of the medium. The wave propagation through the medium does depend on boundary conditions, the excitation and the media properties. Although in practice one can assume that the first two factors do not depend on the temperature, the third one ± media properties ± does, which means that the distribution of the electromagnetic field in the computational domain continuously changes as the temperature rises (or falls). The coupling also works in the opposite direction. The heat generation rate strongly depends on the electric field amplitude, so the changes in the EM field distribution can increase or decrease the rate of temperature changes. The coupled mathematical model that is used to describe the thermal part of the coupled problem is based on Maxwell equations complemented with the heat transfer equation together with appropriate boundary conditions and an initial condition:

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14.8 Physical phenomena and their interaction in microwave heating effect.

du ÿ r…kth ru† ˆ q…u†cp  14:15 dt where medium properties ± thermal conductivity kth, specific heat cp and density  ± are functions of temperature u: cp 

kth ˆ f …u†;

cp ˆ f …u† and  ˆ f …u†

14:16

One way coupling of the processes (thermal ! EM coupling) results from the temperature dependence of the electric properties of the medium: " ˆ f …u†

14:17

The reverse coupling (EM ! thermal) stems from the source term function q…u† ˆ

1 !"o "00r …u†jE…u†j2 2cp 

14:18

In all cases where the electric properties of the medium are constant with regard to the temperature, the microwave heating problem can be solved as decoupled. In such scenarios the only interface between the electromagnetic and thermal part is the source term function q which does not change in time. This means that once the initial medium properties are known, it is possible to obtain the electromagnetic field distribution which will not change in time. This also means that the source term function will be constant; thus the temperature function can be obtained solely through solving the heat flow equation (14.12). In all other situations a bilaterally coupled simulation is required. Coupled numerical models of microwave heating typically use the same numerical

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algorithm, either FDTD or FEM, in the electrodynamic and thermodynamic parts. Such an approach makes it easier to exchange the information on the fields between the electromagnetic and thermal solvers and also allows reusing fragments of the numerical routines, which speeds up implementation work and testing. It also offers greater accuracy. The most popular approach to running a coupled simulation of the microwave heating effect takes advantage of the significant difference between the timescales of the electrodynamic and thermodynamic phenomena. All the simulation methods based on this feature of microwave heating perform steps summarized below: 1.

2. 3. 4. 5.

The solution of the electromagnetic part of the problem is found with solving the Maxwell equations. It is important to obtain fields which have already stabilized in the electromagnetic steady state as only then a valid electromagnetic field magnitude in the whole domain can be calculated. With the electric field magnitude and media properties known, one derives the source term function q given with (14.15). Assuming that the source term function q obtained in step 2 stays constant over some time
T, the new temperature field approximation ^u…t ‡
T† can be calculated through solving equation (14.15). Using the advanced-in-time temperature field approximation ^u…t ‡
T† one obtains thermal and electromagnetic medium properties given with (14.16) and (14.17). Steps 1 to 4 are repeated until the distribution of all fields is obtained for total heating time TTot.

The assumption made in step 3, about source term function constant over period
T, stems from the fact that the function may change as a result of a change in medium properties and the development of electromagnetic field distribution in reaction to these changes. However, this may happen only as a result of a temperature rise that would be large enough to cause a significant modification of medium properties. Such a temperature growth needs time to build up due to finite thermodynamic inertia of the medium (thermal diffusivity). Because of the unequal timescales of the electromagnetic and thermodynamic processes the temperature changes are much slower than variation of the electromagnetic field (seconds compared to picoseconds). Thus, even with adopting the time-step
T large in electromagnetic scale, the approach described above is characterized with good accuracy. Regardless of the chosen method, the electromagnetic steady state should be reached in order to proceed with the coupled simulation process. In most formulations of FEM the steady state is obtained naturally. In FDTD the steady state can be reached after a sufficiently large number of iterations. In a microwave circuit to which excitation has been applied, a transient state first appears and gradually develops into the steady state. The time needed to reach

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the steady state physically depends on the coupling between the circuit and the source. From the authors' experience, from 10 to 100 periods of the excitation signal must elapse in practical microwave heating scenarios. Note that the FDTD simulation time additionally depends on the time step, determined by the meshing. The user may watch the fields or construct consecutive heating patterns to confirm whether the transients have expired (Celuch-Marcysiak et al., 2006)

14.4

Computational examples

A few test cases will now be provided in order to illustrate approaches to solving typical problems that a microwave heating engineer is likely to encounter in their work. The defined problems are solved, whenever possible, with both solvers selected to represent the FDTD method and FEM ± the QuickWave-3D and HFSS v.11 packages. As an environment in which the features of the selected methods and solvers are demonstrated, a domestic microwave oven named MAX (courtesy of Whirlpool, Inc.) is selected. The oven is presented in Fig. 14.9. It is an example of a carefully designed microwave oven. Because of its complex geometry, it is computationally more demanding than the designs normally used in microwave heating benchmarks that typically consist of a simple rectangular cavity fed through a piece of a straight waveguide. Such examples rarely illustrate in full the accuracy of EM solvers employed as they do not take into account real shapes of cavities and feeding systems in their full complexity. The MAX oven consists of a semi-cylindrical cavity fed through two apertures located at the bottom and the top. A waveguide power splitter is employed to guide the microwave power to the apertures from the magnetron. In order to further improve the ability of the oven to heat bottom side of loads, a post is located in

14.9 The MAX microwave oven: (a) overall view; (b) top view.

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the center of the cavity, which further contributes to the geometrical complexity of the modeled object. The cavity walls and the feed system are modeled as PECs. The cavity contains a turntable built of quartz with dielectric constant "0 ˆ 6 and relatively low losses represented with electric conductivity  ˆ 0:01363 S/m (Wheaton Glass Warehouse, 2008). The geometry of the turntable is prepared based on measurements of the real object that is provided together with the MAX oven. The turntable supports a load placed within the cavity. It is a cylindrical piece of beef with radius of 60 mm and height of 6 mm centrally located on the rotating tray, circa 20 mm above the cavity floor. Properties of the medium assumed in the example were defined based on measurements performed in temperature range of ÿ20 to ‡80 ëC by Risman (1997) and additionally linearly extrapolated in the range ‡80 to ‡100 ëC so that longer heating times or higher power levels can be analyzed without saturating the temperature field in the load. The beef properties employed in the scenario are presented in Fig. 14.10(a). As shown in Fig. 14.10(b), the original temperature range covers the temperature where the medium undergoes a phase change (in the vicinity of ÿ2 ëC) as it thaws during heating. This slows down the heating process and makes the computations more demanding. Because of the assumed properties of the load material, not only the specific heat ± defined here via enthalpy ± changes significantly in the vicinity of the melting temperature, but also electric parameters (e.g. electric losses) grow significantly. As a result, one can expect relatively slow heating of the object while it is frozen, and a rapid increase in its heating rate as soon as areas of the product absorb the amount of energy comparable to the latent heat of phase change typical for meat. Then increasing electric losses in these portions of the load will lead to even faster temperature rise and more intensive heating of the neighboring areas thanks to the heat conduction effect. The examples in the next sections of the chapter have been selected so that the solvers are employed in two roles: first, to investigate the reflections from the cavity and analyze sources of computational errors that may decrease accuracy of the model; and then to predict the temperature evolution within the load.

14.4.1 Wide-band modeling of a microwave oven Contrary to some opinions, the ability to efficiently perform wide-band simulation of a microwave circuit is of importance also in case of microwave power systems, which operate at one of the ISM frequencies. As indicated in Risman and Celuch-Marcysiak (2000) and Yakovlev (2006), the magnetron is an imperfect device which changes its frequency depending on the reflection factor and may even `jump' from one oscillating frequency to another, over a range of tens of MHz (Buffler and Risman, 2000). For this reason it is a common practice

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14.10 Properties of beef as a function of temperature: (a) dielectric constant and electric conductivity; (b) enthalpy.

to use a network analyzer to inspect the system performance over such a band. By measuring the level of reflections from the input port of the analyzed structure, it is possible to ensure the stability of operation and the microwave efficiency. Thus, if a numerical EM model is to be a significant help for the designer, it must offer an efficient approach to the S11 curve extraction in a relatively wide band. It can then be used as a virtual equipment replica for a similar laboratory task.

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The ability of the selected solvers to calculate the reflection characteristics of the modeled microwave oven is therefore demonstrated. The FDTD software is expected to be more efficient than FEM as it employs a pulse source and the Fourier transform processing as presented in Gwarek and Celuch-Marcysiak (2003). It can provide wideband frequency domain results with negligible overhead in terms of CPU time compared with the monochromatic regime typically implemented in FEM tools. The aim of the simulation is to indicate the resonances in the vicinity of the operation frequency of the magnetron. The short timescale of the dominating effects as well as low power that is normally utilized during the S-parameters measurements justify disregarding the thermodynamic phenomena in this case. In other words, the measurement takes such a short time that the energy delivered to the lossy circuit is insufficient to visibly raise the load temperature. It is possible to concentrate on the characteristic features of the sole EM modeling algorithms employed to solve the test problem. As illustrated in Fig. 14.1, in narrow frequency bands Debye media can be modeled as lossy dielectrics without significantly affecting the accuracy of computations. With this in mind, one performs S11 simulations with a load medium characterized only with a pair of dielectric constant and electric conductivity values selected from the curves in Fig. 14.10(a) at the temperature of interest and dispersive characteristics of beef are not accounted for. In the wide-band low-power simulations of the MAX oven scenario the dielectric constant and electric conductivity of beef at 20 ëC are assumed as 48.2 and 2.194 S/m, respectively. The FDTD model is discretized with hexahedral conformal cells. The cells are made smaller in the feed system where large EM field gradients are expected due to the presence of metal parts of the power divider protruding from the waveguide walls. The mesh is also denser in the turntable and load areas. Although the wavelength within the quartz shelf is almost four times longer than in beef, the dimensions of cells used in these media are comparable so that all tiny geometrical details of the shelf are accurately modeled. This keeps the FDTD and FEM geometry approximations as close to each other as possible. A similar mesh is also employed directly under the shelf owing to the complex shape of the cavity floor. Disregarding this area of the model would strongly corrupt the final output due to the presence of PEC. The remaining parts of the cavity are discretized using cells of dimensions corresponding to approximately one-tenth of the free-space wavelength in vacuum at the highest frequency of the excitation. In the case of the FEM-based model, tetrahedral elements are employed by the automatic mesh generator. The final mesh is obtained through an automatic iterative process, which also leads to a mesh consisting of smaller elements in the feed and turntable areas than in the empty parts of the cavity. The mesh generation is started from solving the problem on the initial rough mesh based

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14.11 The S11 curve obtained for the example microwave oven using HFSS with three refinement passes (dashed line), four passes (solid line) and five passes (dash dot line).

solely on media permitivitty data. This stage is needed to locate areas where field gradients are largest. In such areas, elements are added and the process is repeated until the difference between solutions obtained in two consecutive runs is smaller than a predefined margin. In case of the MAX microwave oven simulations, as many as four iterations (so-called refinement passes) of the process are performed. This is needed to construct a mesh consisting of a sufficient number of elements to obtain final S11 of accuracy similar to that granted by the FDTD solver. With the default settings of three iterations, accuracy is too low, especially for small and large frequencies, while five iterations lead to extremely long computational times without any significant improvement over the case with just four passes. The results obtained for various number of refinement passes are shown in Fig. 14.11. Although automatic mesh generation is also available in the FDTD package, it can be turned off. Because FDTD meshes are structural and easy to control, the MAX scenario is meshed by a human operator instead. The resulting S11 curves obtained with the FDTD and FEM solvers in the frequency band between 2 and 3 GHz with the resolution of 10 MHz are shown in Fig. 14.12. The curves remain in good agreement and all resonances are properly identified. In view of the observations regarding FDTD and FEM algorithms presented in the previous sections, it is expected that an accurate solution should lie between the FDTD- and FEM-based approximations owing to the sign of dispersive errors inherent in these methods. The curves are close to each other even in the upper part of the frequency spectrum, where the cell-size to wavelength ratio is lowest, which proves that the employed meshes are properly defined. Some discrepancies (e.g. a rise in the level of reflections at 2.85 GHz

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14.12 The S11 curve obtained for the example microwave oven using the QuickWave-3D (dashed line) and HFSS (solid line) with four refinement passes.

indicated by the FDTD method) may be attributed to better mesh refinement in FEM, as FEM calculations show the reflections to fall with increased number of passes. However, others (e.g. slight differences between the FDTD- and FEMgenerated curves in the middle of the band) are more probably caused by other factors such as boundary condition approximations. The summary including calculation times, the number of elements or cells employed by the two models as well as requirements for memory and disk space is presented in Table 14.1. In case of the FDTD solver the field corresponding to the hard disk usage is left intentionally blank as, contrary to the FEM-based tool, no intermediate data must be written to a temporary storage on the hard drive during calculations. Of course, in both cases the hard disk is used to store the information on the models for future use. The difference in the number of elements or cells in the scenario is most striking in this comparison. The reason is more flexibility to adjust a FEM mesh so that it matches shapes of discretized objects, as illustrated with the coaxial line example in the previous section. Such meshes typically require fewer elements than structural meshes typical for the FDTD formulations. However, this difference does not translate into a shorter computation time, which in this case is about seven times longer for the FEM model. The RAM usage is also seven times larger for FEM than for FDTD. Although the HFSS package version 11 has been previously chosen as a representative FEM tool, the results obtained with HFSS version 9 are also included in Table 14.1, in order to illustrate the progress made by FEM analysis and preconditioning mechanisms over a relatively short period of several years. This also corroborates some of the findings in Yakovlev (2006) regarding the computational speed of FEM and FDTD.

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Table 14.1 Comparison between the FDTD- and the FEM-based solver for the wideband analysis of the MAX scenario considered herein

QW3D HFSS v11 HFSS v9

Computation time*

Element/ cell count

RAM usage

Hard disk usage

39 min 17 s 300 min 8 s 1128 min 45 s

1 323 120 31 000 38 190

136 MB 955 MB 650 MB

± ± 760 MB

* The calculations were performed on a 2.21GHz AMD Athlon 3500+ platform. In the case of HFSS v9 calculations were performed on a 2.4 GHz Intel Pentium IV platform and the calculation time was scaled down properly.

The observations presented in Table 14.1 regard only the wide-band excitation case. The overall computation time for the FEM solver is long because as many as 101 separate simulations are performed. The situation changes when the model is solved for field distribution within the cavity in a monochromatic regime, as it takes place when microwave heating is modeled. A single simulation run consists of the preprocessing stage when the mesh is iteratively defined, followed by the actual modeling performed on the final discretization, at the selected frequency. In the MAX scenario the complete FEM monochromatic simulation lasts 13 min 8 s or almost 23 times shorter than when the wide band circuit response is sought for. If a 2.45 GHz signal is used as an excitation, the computation time of the FDTD solver will fall by approximately 25% compared with the figure presented in the table. In FDTD, the electromagnetic steady state is obtained after simulation time equal to a multiple of periods corresponding to the lowestfrequency component in the excitation signal (unless there are high-Q resonances, in which case their frequencies are decisive). In the MAX scenario excited with the wide-band signal (2±3 GHz), there are no high-Q resonances within the band, and the steady state can be achieved after 60 periods of a 2 GHz signal (circa 30 000 iterations). Also in the case of a 2.45 GHz monochromatic excitation, the steady state is achieved after 60 periods, but only 24 000 iterations will be needed this time, which translates into the run time of 31 min 25 s. The next example is aimed at demonstrating the relationship between dispersion errors and the extracted S11 characteristics. This effect can be shown with a model employing larger cells leading to a bigger ratio between the cellsize and the wavelength. As a result, the S11 curves are shifted as compared with the accurate finer-mesh solution. This is shown in Fig. 14.13 for the FDTD method. The results obtained with the finer discretization are compared with those from a model employing twice as large cells above the turntable. The conclusion is that the coarse meshing of the cavity shifts the frequency domain results down by about 20 MHz, which lies within the dispersion predictions of

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14.13 The S11 curves obtained for the MAX oven using various dicretisations: (a) model calculated with the QuickWave-3D where the cavity is discretized with cells of 10 mm in the z-direction (solid line) or cells of 20 mm in the zdirection (dashed line).

Fig. 14.4. This effect will not manifest itself when a similar modification is done to the mesh within the load area. The reason is that a cavity mode is considered with most of its energy stored outside the load. Modifying the discretization in the feed system may lead to significant changes in the modeled circuit behavior; however, this will not be an effect of numerical dispersion but rather of improper treatment of field singularities in the vicinity of metal elements. It is expected that the opposite effect should be observed in case of FEMbased models. However, demonstrating this feature with a package integrated with the automatic mesh generator is impossible as the generator does not allow defining a poor mesh in one portion of the circuit while enforcing proper discretization in the other regions. Another important effect in microwave power analysis and observed using a wide-band excitation of a circuit is the dependence of reflection curves and resonant frequencies on temperature levels in the load. A change in the load temperature modifies electric properties of its medium, thus detuning the cavity. This means that the load heating rate will not only depend on thermodynamic medium properties such as specific heat, or thermal conductivity at the current temperature, but will also be affected by electromagnetic properties of the load, which besides determining the amount of dissipated power further affect the amount of power actually delivered to the cavity. This can be demonstrated by modifying the temperature of beef and observing the reflection curve. In case of beef, using the relationship between the medium properties and temperature as in Fig. 14.10(a), one identifies that medium properties are significantly different at ÿ20 ëC than at the room temperature. The two curves are presented in Fig. 14.14. As shown, a rise in temperature affects the shape of S11 curve leading to

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14.14 The S11 curves obtained for the MAX oven loaded with beef at two temperatures: +20 ëC (solid line) and ÿ20 ëC (dashed line).

lower reflections at the frequency of 2.45 GHz (from ÿ5 dB at ÿ20 ëC to ÿ4 dB at ‡20 ëC) and while at the lower temperature one notes a deep resonance at the frequency of 2.47 GHz which may detune the magnetron. This may affect the heating process, not only by reducing the power entering the cavity by increased reflections, but also by modifying the field distribution through a change of the operating frequency.

14.4.2 Coupled EM-thermal modeling of microwave heating process Another important factor besides the frequency response of the microwave oven is the uniformity of heating of loads. In the laboratory, the oven performance and its ability to heat loads without creating cold- and hot-spots can be verified with direct temperature measurements or infrared photography. Again, if a numerical model is to be a valuable tool in the designer's hand, it must allow inspecting the evolution of the temperature field within the heated object. Then the heating process can be well understood and, if necessary, improvements can be introduced into the system design. Additionally, through modeling approximate answers can be obtained to questions that often arise while designing heating processes: `How long will it take to heat the load up to the safe temperature?' or `Given the magnetron power, what temperature level can we expect within a steady load?' The microwave oven used previously to demonstrate wide-band modeling is also used to show basics of the coupled process simulation. This time the lossy medium is defined in a full temperature range according to the data presented in Fig. 14.10. The initial temperature ÿ20 ëC is assumed, which means that the

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load will undergo a phase change. This will slow down the temperature rise within the object. Compared with the previous scenario, the excitation is modified. Sinusoidal excitation is now needed since even when the magnetron's frequency shifts, the heating continues in another monochromatic regime. Instead of the low-power signal used previously, a 500 W input signal is employed. It corresponds to parameters of typical microwave ovens on the market. It is low enough to avoid rapid temperature field evolution that would make observation of the heating effect difficult. In this section the FDTD solver is mostly employed. Based on the comparison made in the previous section, the FEM solver may work faster than the FDTD-based package in the monochromatic regime. However, performing a coupled analysis requires that the EM module be coupled to an additional heat flow solver capable of handling non-linear media. The module available for the HFSS package offers only the unidirectional coupling to the EM solver. With such coupling governed with equation (14.18), the EM fields affect the heat generation rate q and, in turn, the temperature field. Since the reverse coupling (equation (14.17)) is not implemented, the EM properties do not follow changes of the temperature field. Such an approach is useful when modeling media of neglibible dependence between their EM parameters and temperature. However, it is insufficient in our case since EM parameters of beef strongly depend on temperature. On the other hand, full bilateral coupling between the EM and thermal solvers is in-built into the QuickWave-3D package, which makes it possible to model scenarios where the temperature dependence of media EM properties is strong (e.g. water undergoing phase-change). The model is further extended with mechanisms that facilitate modeling scenarios with rotated loads and possible detuning of the magnetron's operating frequency. For this reason the FDTD package was employed to model a scenario where frozen beef is heated with microwaves. In such a case, it is expected that an accurate solution can be obtained only using the fully coupled model. The FEM performance was demonstrated with a simplified example, where the initial temperature of beef was raised well over the freezing point so that a (more favorable) medium characteristic slowly changing with temperature is guaranteed. This also shows that even a modification of the initial temperature of loads may affect problem complexity. The influence of model discretization on the extracted reflection curve was described in the previous section, and shown in Fig. 14.13. The shift of this curve towards lower frequencies resulting from the numerical dispersion errors in computational algorithms may change the heating rate in the load. In order to check how this can further affect the temperature distribution within the load, a simple coupled simulation is performed on the two meshes. Since heat diffusion would obscure features of the effect, a model is constructed that accounts only for the heat generation and thermal dependence of media parameters and neglects the heat flow.

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14.15 Temperature distribution obtained for cavity discretized with cells of 10 mm in the z-direction.

Results obtained with this approach using the FDTD package are shown in Figs 14.15 and 14.16 for the two meshes used in the previous section. They present the two-dimensional temperature distribution within beef on a horizontal plane passing through the load in the middle of its height and also the distribution on a vertical plane parallel to the x-axis and passing through the load

14.16 Temperature distribution obtained for cavity discretized with cells of 20 mm in the z-direction.

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center. In both scenarios, heating lasted 2.5 min and the employed heating time step
T was equal to 10 s. As expected, higher reflections from the cavity obtained with a coarser mesh led to a visible slow-down in temperature rise. Not only the values of temperature in several hot-spots are different, but also the location of some of them is offset towards the outer boundary of the load. This can be attributed to a less accurate approximation of the electric field distribution in the load, and especially at its boundaries. The accuracy of the coupled microwave heating model depends on the heating time step
T as well as on the spatial and temporal discretization. In the coupled process, data between the EM or thermal solvers are exchanged periodically with a time step
T. Too large a value of this parameter will inevitably lead to deteriorating accuracy of the final temperature distribution. The processes employing media with highly non-linear temperature dependence of electromagnetic or thermophysical properties will be most sensitive to this effect. On the other hand, very short heating time steps will prolong calculations without significant improvement of computational accuracy. As shown in Kopyt and Celuch (2006) an accurate solution can be obtained as the heating time step becomes smaller, which agrees with intuitive expectations. However, no exact rules can be given to effectively adjust the heating time step to the properties of particular scenarios as its value depends on medium properties and the electric field values within the load. Because most often these factors are mutually coupled, they can be monitored only in the course of the coupled simulation and are not known a priori. For typical food media and typical domestic ovens the time step of several seconds is normally appropriate, but it must be kept in mind that higher non-linearity of media and stronger electric field intensities within the load require heating time step reduction. This can be illustrated with another example solved with FDTD. The heat conduction is still neglected to keep the model simpler and to clearly illustrate the influence of the heating time step. First, the model utilized the finer discretization so that the numerical dispersion effect is suppressed. The simulation covers 2.5 min of heating, but it is repeated for two different heating time steps of 5 s and 10 s, which correspond to 30 and 15 heating iterations respectively. The results of the computational experiment are shown in Fig. 14.17(a) where temperature evolution in one of the hot-spots within the load is presented for the two cases. The influence of the time step is strongest when beef undergoes the phase change, as then the medium exhibits highly non-linear behavior. For other temperatures the difference between the two curves is not significant, which suggests that the relatively long time step is appropriate for scenarios where fully thawed beef is heated as its properties are nearly linear. A similar curve obtained for a model employing large cells in the z-direction that is presented in Fig. 14.17(b) suggests slower heating of the load, which corroborates expectations.

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14.17 Comparison of temperature evolution in a hot spot: (a) simulated with
t ˆ 10 s (solid line) and
t ˆ 5 s (dotted line) for small cells-size; (b) simulated with
t ˆ 10 s for small cell-size (solid line) and large cell-size (dotted line).

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14.18 Temperature distribution in the load cross-sections when the coupled model accounts for heat flow effect.

Accurate modeling of a microwave heating process requires that the heat conduction be accounted for. Thus, in the next two examples the coupled simulation is performed, where besides the EM solver also the thermal solver is employed. Again, the FDTD environment was employed. The media properties as well as the excitation are kept unchanged as in the previous scenarios. The heating time step of 10 s is selected. Figure 14.18 presents the resulting temperature field distribution in the same cross-section of the load as before. As expected, the temperature rise in the hot-spot is significantly slowed down, because the heat conduction transfers energy from the areas that heat fastest to the neighboring portions of the load that are cooler. This leads to a more uniform heating than in the cases without heat diffusion. However, the general temperature distribution as well as the location of hot- and cold-spots remains essentially the same. A complete model of microwave heating in a domestic microwave oven requires that the load rotation also be accounted for, as in many such appliances the temperature distribution uniformity is improved with this approach. Thus, the ability to also include this effect in a coupled model is crucial if the behavior of real-life systems is to be analyzed. The effect of load rotation is illustrated with the already known example with heat transfer included in the model. The rotation speed of the load is 1 revolution per minute (rpm). The mechanism accounting for the load rotation requires that yet another discretization-related parameter be introduced. The continuous load movement needs to be discretized by defining a set of finite number P of distinct positions the load can assume within the cavity. The time period when the load

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is located idly in one of them depends only on the number P and the revolution speed. Using such an approach one full revolution is represented by a finite number of steps with instantaneous transition between them. It can be expected that with growing number of angular steps the accuracy of the result can be improved. As in previous cases, increasing the number of steps beyond a certain limit does not bring on any accuracy improvement and leads only to prolonged computations as demonstrated in Kopyt and CeluchMarcysiak (2003). It is difficult to define general rules for choosing the proper angular discretization but in most cases 12 or 16 angular positions will grant reasonable accuracy, and thus the angular step of 30ë is selected for the MAX model. During the heating period of 2.5 min the load rotating at 1 rpm will make 2.5 full revolutions. With the assumed angular step modification of the load, status changes every 5 s. It is reasonable to assume the same heating step. As shown previously, the reduction of the heating time step to 5 s does not constitute a major change of the model, so the introduction of load rotation can be still regarded as the only significant difference. The resulting temperature distribution within the load is shown in Fig. 14.19. A much more uniform temperature distribution is observed due to load rotation, which perfectly agrees with intuition as well as with what the oven designers were aiming to achieve. As the last example of the fully coupled model, a coupled analysis of the heating process performed with FDTD is presented, where the operating frequency is modified according to the reflections of the cavity. As already explained and illustrated in Fig. 14.14, a changing temperature of the load modifies matching of the cavity, which ± in turn ± may affect the operating

14.19 Temperature distribution in the load cross-sections when the coupled model accounts for the heat flow effect accompanied with load rotation.

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frequency of the energy source. In order to simulate such a scenario and check how this influences the temperature distribution within the load, the heating process of the beef sample is modeled with settings employed previously. For simplicity, the rotation of the load is disregarded although the model accounts for the heat flow effect. Between each heating step of 10 s, a wide-band analysis of the cavity is performed in order to find the minimum reflections in a band of 100 MHz centered around 2.45 GHz. In the consecutive heating step, the monochromatic excitation signal will be assigned to this frequency. As a result, each heating step is performed with a slightly different excitation frequency. Although it has not been strictly validated by theory and experiments, the assumption that the domestic oven magnetron tunes to the deepest in-band resonance seems reasonable. For the purpose of this review, it allows the demonstration of whether, and to what extent, changes in the operating frequency may change the heating patterns in the load. The results of such an advanced coupled modeling with interleaved monochromatic and wide-band analyses are shown in Fig. 14.20. The presented temperature distribution differs from results obtained using simpler constant-frequency approaches. As already explained, a model where the EM solver is unidirectionally coupled to the thermal model can be useful for the class of problems where the temperature dependence of the EM properties of media is weak. For this reason the microwave heating scenario analyzed previously ± heating of beef from the initial temperature of ÿ20 ëC ± cannot be accurately solved with the selected FEM-based solver. It is a result of particularly strong dependence between dielectric constant and dielectric loss in the vicinity of 0 ëC, where beef

14.20 Temperature distribution in the load cross-sections when the coupled model accounts for the heat flow and the magnetron detuning effects.

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14.21 Dissipated power density distribution in the cross-section of the load heated from the temperature of +20 ëC: (a) the distribution obtained with the HFSS package (values given in W/m3); (b) the distribution obtained with the QuickWave 3D package (values given in W/mm3).

undergoes a phase change. However, as shown in Fig. 14.14, in the temperature range starting from ‡20 ëC the EM properties of the medium change slowly. This means that the problem of heating beef patties in a domestic microwave oven starting from the room temperature can be analyzed with reasonable accuracy also using the FEM package. Such a simplified simulation does not consist of several cycles where the EM and thermal parts of the problem are solved. Instead, the EM fields are derived only once with values of media properties assumed to be constant in temperature. Based on the result, the dissipated power density is calculated and used by the coupled thermal solver as an excitation of the load over the whole heating period. In this case the heating period is no longer divided into a number of heating time steps. This corresponds to performing only three first steps defined in Section 14.3.2. The results of the numerical experiment are shown in Fig. 14.21, where dissipated power density in the load cross-section is presented. The obtained distributions are the decisive factors in the temperature field calculations performed as the next step. As shown in Fig. 14.21, also in this case both the FDTD- and FEM-based solvers offer comparable results. The final temperature distributions obtained based on the power densities are presented in Fig. 14.22. Although both thermal solvers co-operating with the EM packages are capable of handling non-linear thermal problems, also in this case beef properties were assumed independent of temperature. This is justified as in the assumed temperature range starting from ‡20 ëC the medium is already fully thawed while the evaporation is not a dominating process so it does not yet significantly affect the heat capacity of beef. The time of calculations was recorded in two presented cases. As expected, the EM solution was obtained faster with FEM (after 13 min 8 s) than with

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14.22 Temperature distribution in the cross-section of the load heated from the temperature of +20 ëC: (a) the distribution obtained with the HFSS package; (b) the distribution obtained with the QuickWave 3D package.

FDTD (after 31 min 25 s). The complete simulation requires that besides pure calculations of the EM fields the dissipated power density be calculated based on them and the thermal modeling be completed. This part took 5 min 7 s when the FDTD environment was employed or 1 min 37 s in the case of the FEM environment. The longer time needed to complete the thermal calculations by the FDTD solver results from the lengthy process of calculating the time averaged dissipated power density within the whole volume of the load, which in FDTD-based solvers requires recording maximal values of the field over at least one period of the excitation signal. In order to analyze the accuracy of the solution obtained with a simplified model, several simulations were performed using the FDTD package. The heating period of 100 s was divided into one, two, and five heating steps. The first scenario corresponds to the microwave heating model using unidirectional coupling (a single thermal step), whereas the other two cases represent the more general approach based on a fully bilaterally coupled model. The resulting temperature histories recorded in a hot-spot for each case are presented in Fig. 14.23. The increasing number of heating time steps leads to a lower final temperature at 100 s. This is not surprising, when we consider that dielectric losses of beef fall with temperature as depicted in Fig. 14.10. With the unidirectional coupling between the EM and the thermal parts of the model this effect cannot be properly accounted for, leading to higher final temperatures recorded in the hot-spot. Each time step is an opportunity to properly adjust the heat generation rate and bring the model closer to the physical scenario. However, small differences in final temperatures in all three cases confirm that owing to weak temperature dependence of the EM properties of beef in the selected temperature range, the problem can be analysed also with simplified models. Figure 14.23

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14.23 Temperature history recorded in a hot-spot of the load for unidirectional coupling (circles), full coupling with two heating time-steps (triangles), and full coupling with five heating time steps (squares).

also shows that in the early stages of heating the temperature calculated with greater number of time steps is higher than the temperature predicted with linear interpolation between initial and final temperatures given with the unidirectionally coupled model. This is hardly surprising because of the finite thermal inertia of the medium, which does not allow the heat generated in the hot-spot to flow to cooler regions instantaneously. A combination of the heat diffusion effect acting during the whole duration of heating and the falling heat generation rate leads eventually to lower final temperatures.

14.5

Conclusions

In this chapter the authors have provided an insight into modeling of microwave heating scenarios with both the FDTD and FEM algorithms. The presentation of strengths and limitations of both numerical techniques has been backed with theoretical predictions as well as several computational examples. Based on dispersion error analysis, meshing criteria for effective FDTD and FEM simulations have been formulated, with the same basic rule of at least ten cells per wavelength. In the case of the FDTD approach irregular and conformal meshing techniques have been discussed as a significant extension of traditional FDTD formulations. For FEM, recent progress in terms of adaptive meshing and

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effective preconditioning has been demonstrated. Additionally, an approach to coupled EM±thermal analysis has been introduced. The numerical examples have been designed in order to show major types of analyses often performed by microwave power systems designers. A scenario consisting of a commercial domestic microwave oven has been modeled using two commercial packages: QuickWave-3D and HFSS, considered as a good representation of a large class of tools based on FDTD and FEM, respectively. The monochromatic and wide-band excitation of the oven has been considered. It has allowed demonstrating the influence of selected physical properties of the modeled system as well as numerical properties of the model itself onto the final results. The results obtained with the FDTD- and FEM-based tools have been compared in terms of accuracy, computational speed and memory usage. The following conclusions can be formulated: · The FDTD method offers the best computational effectiveness in terms of CPU and RAM requirements in cases where the results are required over a frequency band. In the considered example of the reflection coefficient extraction at approximately 100 frequency points, FDTD in QuickWave-3D v.7.0 is seven times faster and less memory consuming than the most recent FEM formulation in HFSS v.11. · For single frequency analysis, FEM algorithms may become competitive to FDTD in terms of speed, provided that they are preceded by adaptive mesh generation and effective matrix preconditioning. In the considered example of EM field calculations at 2.45 GHz, FEM in HFSS v.11 performs 2.5 times faster than FDTD in QuickWave-3D v.7.0. However, this is a feature of this particular FEM implementation, and not of the finite element method itself. An earlier version 9.0 of HFSS was shown nearly four times slower, and a similar observation was made for other FEM solvers. Moreover, FEM requires several times more RAM than FDTD for comparable accuracy. The coupled modeling of the scenario has also been discussed. Several cases have been considered in order to show the effect of extending the basic model with mechanisms accounting for the heat flow effect, load rotation or magnetron detuning during the heating process. It has been shown that accurate analysis of a microwave heating effect over a temperature range including phase changes, where the material parameters rapidly change, requires a bilaterally coupled electromagnetic±themrodynamic model. Among the two FDTD and FEM solvers considered, only the FDTD one in QuickWave-3D meets this requirement. The FEM model produces consistent results only over a limited sub-range of temperature above the thawing point. This is a feature of the considered software package, and not of the FEM itself. There exist other FEM packages on the market, more devoted to the multiphysics approach. However, their speed in the EM analysis is significantly inferior to that of HFSS v.11.

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Acknowledgements

The authors wish to thank Whirlpool Sweden AB for providing CAD files with the MAX microwave oven geometry. They want also to kindly acknowledge help received from Space Research Center (SRC) of the Polish Academy of Sciences in joint modeling of selected microwave problems using the SRC's ANSYS Multiphysics v 11 license performed in order to gather material for this publication. The authors also wish to ackowledge help obtained from Ansoft Corporation in the form of trial versions of the HFSS v11.0 and ePhysics v3.0 products.

14.7

References

Akarapu, R., B.Q. Li, Y. Huo, J. Tang and F. Liu (2004), `Integrated modeling of microwave food processing and comparison with experimental measurements', J. Microwave Power and Electromagnetic Energy, 39(3±4), 153±165. Al-Rizzo, M., J.M. Tranquilla and M. Feng (2007), `A finite difference thermal model of a cylindrical microwave heating applicator using locally conformal overlapping grids: Part I ± theoretical formulation', J. Microwave Power and Electromagnetic Energy, 40(1), 17±29. ANSYS Multiphysics (1993±2008), ANSYS, Inc., http://www.ansys.com. Bracken, J.E., D.K. Sun and Z.J. Cendes (1998), `S-domain methods for simultaneous time and frequency characterisation of electromagnetic devices', IEEE Trans. Microwave Theory Tech., 46(9), 1277±1290. Buffler, C.R. and P.O. Risman (2000), `Compatibility issues between Bluetooth and high power systems in the ISM band', Microwave J., 43(7), 126±133. Celuch-Marcysiak, M. (2001), `Evaluation and enhancement of supraconvergence effects on nonuniform and conformal FDTD meshes', 2001 IEEE MTT-S Int. Microwave Symp. Dig., Phoenix, AZ, pp. 745±748. Celuch-Marcysiak, M. (2004), `Extended study of Poynting theorem and reciprocity on non-uniform FDTD meshes', IEE Proc. ± Sci. Meas. Technol. 151(6), 452±455. Celuch-Marcysiak, M., W.K. Gwarek and M. Sypniewski (2006), `A novel FDTD system for microwave heating and thawing analysis with automatic time-variation of enthalpy-dependent media parameters', in: Advances in Microwave and Radio Frequency Processing, M. Willert-Porada (ed.), Springer, pp. 199±209. Gwarek, W.K. (1985), `Analysis of an arbitrarily-shaped planar circuit ± a time-domain approach', IEEE Trans. Microwave Theory Tech., 33(10), 1067±1072. Gwarek, W.K. and M. Celuch-Marcysiak (2003), `Wide-band S-parameter extraction from FD-TD simulations for propagating and evanescent modes in inhomogeneous guides', IEEE Trans. Microwave Theory Tech., 51(8), 1920±1928. HFSS (1990±2008), Ansoft, Inc., http://www.ansoft.com Kopyt, P. and M. Celuch-Marcysiak (2003), `FDTD modeling and experimental verification of electromagnetic power dissipated in domestic microwave ovens', J. Telecommun. Inform. Soc., 1, 59±65. Kopyt, P. and M. Celuch (2006), `One-dimensional fully analytical model of microwave heating effect', Proc. 15th International Conference on Microwaves, Radar and Wireless Communications MIKON, Cracow, Poland, May 22±24, pp. 581±584. Kopyt, P. and M. Celuch (2007), `Coupled electromagnetic-thermodynamic simulations

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of microwave heating problems using the FDTD algorithm', J. Microwave Power and Electromagnetic Energy, 41(4), 18±29. Kunz, K. and R. Luebbers (1993), The Finite Difference Time Domain Method for Electromagnetics, CRC Press. Lynch, D.R. and K.D. Paulsen (1990), `Time-domain integration of the Maxwell equations on finite elements', IEEE Trans. Antennas Propagat., 38(12), 1933±1942. Lynch, D.R. and K.D. Paulsen (1991), `Origin of vector parasites in numerical Maxwell solutions', IEEE Trans. on Microwave Theory Tech., 39(3), 383±394. Lynch, D.R., K.D. Paulsen, and J.W. Strohbehn (1985), `Finite element solution of Maxwell's equations for hyperthermia treatment planning', J. Comput. Phys., 58, 246±269. Ma, L., D.-L. Paul, N. Pothecary, Ch. Railton, J. Bow, L. Barrat, J. Mullin and D. Simons (1995), `Experimental validation of a combined electromagnetic and thermal FDTD model of a microwave heating process', IEEE Trans. Microwave Theory Tech., 43(11), 2565±2572. Pangrle, B.J., K.G. Ayappa, H.T. Davis, E.A. Davis and J. Gordon (1991), `Microwave thawing of cylinders', AIChE Journal, 37, 1789±1800. QuickWave-3D (1997±2008), QWED Sp. z o.o., ul. Nowowiejska 28, lok. 32, 02-010 Warsaw, Poland, http://www.qwed.com.pl/. Railton, C.J. and J.B. Schneider (1999), `An analytical and numerical analysis of several locally conformal FDTD schemes', IEEE Trans. Microwave Theory Tech., 47(1), 56±66. Ratanadecho, P., K. Aoki and M. Akahori (2002), `A numerical and experimental investigation of the modeling of microwave heating for liquid layers using a rectangular waveguide', Applied Mathematical Modeling, 26, 449±472. Risman, P.O. (1997), private communication. Risman, P.O. (1998), `A microwave oven model ± examples of microwave heating computations', Microwave World, 19(1), 20±23. Risman, P.O. and M. Celuch-Marcysiak (2000), `Electromagnetic modeling for microwave power applications', Proc. 13th Intern. Conf. Microwaves, Radar and Wireless Communications (MIKON-2000), Wroclaw, Poland, 3, pp. 167±182. Sekkak, A., L. Pichon and, A. Razek (1994), `3-D FEM magneto-thermal analysis in microwave oven', IEEE Trans. Magnetics, 30(5), 3347±3350. Shewchuk, J. (2002), `What is a good linear element? Interpolation, conditioning, and quality measures', 11th International Meshing Roundtable, Ithaca, New York, pp. 115±126. Silvester, P.P. and R.L. Ferrari (1996), Finite Elements for Electrical Engineers, 3rd edn, Cambridge University Press. Taflove, A. and S.C. Hagness (2005), Computational Electromagnetics ± The FiniteDifference Time-Domain Method, 3rd edn, Artech House. Torres, F. and B. Jecko (1997), `Complete FDTD analysis of microwave heating processes in frequency-dependent and temperature-dependent media', IEEE Trans. Microwave Theory Tech., 45, 108±117. Warren G.S. and W.R. Scott Jr. (1995), `Numerical dispersion in the finite-element method using triangular edge elements', Microwave Opt. Technol. Lett., 9(6), 315± 319. Wheaton Glass Warehouse (2008), Technical information, http://www.glasswarehouse.com Yakovlev, V.V. (2006), `Examination of contemporary electromagnetic software capable of modeling problems of microwave heating', in: Advances in Microwave and

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Radio Frequency Processing, M. Willert-Porada (ed.), Springer, pp. 178±190. Yakovlev, V.V. (2008), Seminar chair. Digest of 10th Seminar `Computer Modeling and Microwave Power Engineering', University of Modena and Reggio Emilia, Modena, Italy, Feb. 28±29. Zhang, H. and A.K. Datta (2000), `Coupled electromagnetic and thermal modeling of microwave oven heating of foods', J. Microwave Power Electromagnetic Energy, 2, 71±85. Zienkiewicz, O.C., R.L. Taylor and J.Z. Zhu (2005), Finite Element Method ± Its Basis & Fundamentals, 6th edn, Elsevier Butterworth-Heinemann.

15

Modelling the effects of active packaging of microwaved foods P R I S M A N , Microtrans AB, Sweden

Abstract: After an introduction about microwave absorption in thick metal layers, metal containers and shielding metal frames are dealt with. Metalisation patterns on containers (ameliorators) are then discussed, with some modelling examples. Modelling of continuous and fractured susceptors is then addressed and susceptor behaviour close to food loads is exemplified. Finally, a susceptor retro-modelling cavity is described and some remarks on thermal modelling are given. Key words: microwave, metal containers, susceptor, modelling, ameliorator.

15.1

Introduction

From a microwave perspective, active packaging can be divided into three groups: · shielding devices ± reflecting the impinging microwave energy away from parts of the food load; · ameliorators ± in essence receiving microwave energy and conveying it to the food load, to improve the evenness of heating of the load. · susceptors ± absorbing microwave energy and conveying the heat to the food load, by heat radiation, conduction or convection. Shielding devices and ameliorators are metallic and of such thickness that they become passive in the sense that they do not themselves absorb microwaves. Susceptors are typically thin metal layers deposited onto a polyethylene terephthalate (PET) film. The layers are continuous, or consist of small, closely located `metal islands' which are so thin that they are heated by their electrical resistance. Whereas the microwave properties of shielding devices and ameliorators do not vary during the heating process, susceptor surfaces rupture by the film locally heating the PET above the heat-set temperature and this then relaxing locally. Small gaps between metal islands are created, changing the microwave properties. This chapter deals with modelling of these systems and not with optimisation procedures. The QuickwaveTM commercially available software (QWED, 1997) was used in constructing and running all modelling scenarios. This chapter is ß Per Olov Risman and printed with his permission.

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As in all microwave modelling, one must have a basic experimental or theoretical knowledge about what to look for or verify. Descriptions and characterisations of the basic properties of active packaging devices and their interaction with the microwave fields in typical microwave ovens are therefore necessary. Since the characterisations and modelling techniques and what to look for is typically quite different for the three types of active packaging, this chapter is divided into four sections: · · · ·

microwave properties of metals; shielding devices; ameliorators; susceptors.

There are also some final comments at the end of the chapter.

15.2

Microwave properties of metals

Metals are highly conductive, by electronic conduction. Whereas the ionic conductivity  of foods may be some few units of 1/ m, that of metals is in the range 106 to 108 1/ m. The electric properties of metals is often specified by their resistivity, in  m (micro-ohm metre). Since resistivity is the inverse of conductivity, the resistivity of nickel (see Table 15.1) is 0.068  m. The conductivity of metals dominates completely over the relative real permittivity "0 , so different formulas for the penetration depth than for foods are to be used. For non-magnetic metals, p p (metres) 15:1 dp  0 =…2 2"00 † ˆ 1= 4 f 0 where dp is the power penetration depth (power density reduction to 1/e of that at the surface), 0 the magnetic constant defined to be 4  10ÿ7 s/m, 0 the free space wavelength, "00 the relative loss factor, and f the frequency. For magnetic metals, 0 is replaced by 0 0 where 0 is the relative magnetic permeability of the metal, at the operating frequency (note that  is the relative permeability,   10ÿ6 ). dp is thus reduced for magnetic metals. At 2450 MHz, equation 15.1 is simplified to dp2 ˆ 1=386 90

(metres, at 2450 MHz)

15:2

For typical metals, dp is in the order of 1 to 5 m ± see Table 15.1. A layer with a thickness of 10dp will therefore in practice not let any microwaves through, but such thin sheets may not be mechanically safe as shields.

15.2.1 Power absorption in a thick metal layer Since dp is much smaller than a typical metal sheet thickness, there is no reflected wave from the back of it, even if it is only a fraction of a mm thick. The

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Table 15.1 Conductivity data for selected metals Material Silver Gold Aluminium Brass Zinc Nickel Titanium Stainless steel

Conductivity  (1/ m)

dp (m) at 2450 MHz

6.29  107 4.10  107 3.50  107 1.62  107 1.69  107 1.46  107 2.38  106 1.40  106

0.64 0.79 0.86 1.26 1.24 1.33 3.3 4.3

Notes Best of all; pure Pure >99.5% purity 70% copper Pure Pure Pure Type 304

Note: dp data are for very flat surfaces.

transmitted ± and thus absorbed ± relative power flux density into the metal then becomes, to the first order and for a non-magnetic metal: p p (perpendicular incidence) 15:3 Pabs =Pi  8="00  16 f "0 = where "0 is the electric constant  8:85  10ÿ12 s/ m and Pi the incident power flux density. Different results are obtained with oblique incidence for the two kinds of polarisation of the impinging wave. The absorption becomes larger for the transverse magnetic (TM)-polarised case (the magnetic field parallel to the surface) than for the transverse electric (TE)-polarised (the electric field parallel to the surface), since the impedance component of the impinging wave in the direction perpendicular to the metal surface is lower in the former than in the latter case. The following is obtained, in the TM-polarised case: p 8="00 i (TM-polarised case) 15:4 Pabs =P  cosi where i is the angle of incidence (ˆ 0 for TEM incidence). In the TE-polarised case, the factor cosi is multiplied instead of divided with the base expression. Equation [15.4] implies that infinite power transmission takes place for TMpolarised waves when i ! 90ë. This conclusion is of course wrong; one has to multiply by cosi to obtain the power flux density transmission with the surface normal as reference. Interestingly, this also shows that the absorbed power density per metal surface unit becomes constant for TM-polarised incidence, independently of the incidence angle if the metal surface is thought to be rotated in an illuminating microwave plane wave. But the absorbed power density per metal surface unit falls off as cos2i under TE-polarised incidence. p The expressions in equations [15.3] and [15.4] are to be multiplied by  for a magnetic substance; the power absorption increases. The penetration depth in metals is generally very short in relation to the overall dimensions. A surface resistance Rs in ohms per square, /ú), may then be calculated. This corresponds to fictitiously replacing the conducting

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halfspace or thick sheet by a thin sheet with such a thickness and surface resistance that the total power absorption becomes unchanged. The thickness of this equivalent thin layer becomes 2dp (ˆ ds ) where ds is the so-called skin depth, and Rs ˆ 1=…
ds †

( =ú; thick surface)

15:5

Since the surface current density jJs j ˆ jHk j, where Hk is the magnetic field component parallel to the metal surface, one also obtains Pabs ˆ 12 Rs
jHk j2

15:6

This equation permits the study of power losses in smaller surface regions than the plane wave case in equations [15.3] and [15.4]. Equation [15.4] gives the absorbed power (per surface area) in relation to the impinging power flux density Pabs/Pi becomes 0.018% for aluminium and 0.088% for the stainless steel, for perpendicular incidence and using the data in Table 15.1. In the optical region, even the best metal reflectors absorb more than 1%. That there may still be significant wall losses in microwave oven cavities often depends on the field amplification by resonances and low equivalent cosi values of TM-polarised modes. There may also be impedance transformations by irregularities and increased current path losses by metal crevices and surface roughness.

15.3

Shielding devices

15.3.1 Metal containers The fact that a closed metal box completely shields against microwaves has been known for more than 100 years ± by the so-called Faraday cage. Actually, a very important category of shielding devices was in use in microwave ovens already in the 1950s: metal containers. The reasons for using these were the advantages of cost, impenetrability and mechanical stability. Microwaves could not heat from below, which limited the useful thickness of the food load and also caused a reduction of microwave power efficiency. Using some characteristics of multimode ovens, a typical such reduction for a 400 g load was shown to be about 15% (Risman, 1992), in good agreement with typical experimental results. But there was also a positive shielding effect which essentially eliminated the edge overheating effect (see Chapter 3, Section 3.9).

15.3.2 Shielding frames Intentional shielding devices for microwave oven use were introduced in the 1960s, when it became clear to many users that there was very often a tendency for edge regions to overheat and the central area to be cold in packaged slab-

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15.1 Metal shielding frame with open bottom.

shaped food items such as ready meals. Experimenting with shielding devices could create a risk of failure of the early and sensitive magnetrons, and metalisation of packaging material was not well developed, so shielding frames tested and supplied by oven manufacturers became quite popular, particularly in Europe; see Fig. 15.1 (Risman, 1973). The function is not complicated: food load corners are shielded by three metal surfaces being joined there and waves impinging from above are allowed to heat the centre portions of the load, as are trapped surface waves or cavity volume modes from below. The electric fields parallel to food edges which would otherwise cause edge overheating (see Chapter 3) are essentially shortcircuited. In the context of this chapter, shielding is by a metal surface which reflects microwaves. A metal mesh or grid may transmit some part of the microwave energy, but there will then also be a nearfield around such partially open structures. They are therefore categorised as ameliorators, and dealt with in Section 15.4. Metal films with a thickness comparable to or less than the penetration depth dp will be heated by microwaves ± they are dealt with in Section 15.5.

15.3.3 Modelling of metal frames This is straightforward, since the metal thickness is not sensitive. As an example, the scenario in Fig. 15.2 uses 1 mm thick metal; the oven is the same as that used in many other examples in Chapter 3; see Fig. 3.9. Figure 15.3 shows the heating pattern in the horizontal layer about 2 mm from the top of the food, without and with the frame. The intensity scale is the same in the two images. Since the load area that is accessible to impinging microwaves is reduced by the frame, a reduction of the overall microwave efficiency occurs. This decrease varies greatly with the type of oven; in the case of this model oven test the power reflected back to the magnetron increased

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15.2 A modelling scenario with the oven of Fig. 3.9, the IEC batter load (IEC, 2006) and a shielding frame with an elliptical top hole.

15.3 The heating pattern in the top region of an IEC batter load in the scenario of Fig. 15.2. (a) without frame; (b) with frame.

from 5 to 20% with or without the frame ± which is a quite typical value for a single load. It should, however, be pointed out that much of the `extra power' in the frameless case is actually wasted by edge overheating and evaporation. A longer heating time is then also needed, to compensate for the cold centre region.

15.4

Ameliorators

15.4.1 General aspects Whereas shielding devices can be classified as reflectors (quasi-optically reflecting away the microwaves), ameliorators are far more complicated and can

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be characterised as deflectors, as defined in the International Electrotechnical Vocabulary (IEC, 2007), in entry 841-09-25 as a `device which is normally smaller than the wavelength of the microwaves and changes the microwave relationship in its vicinity by diffraction and/or resonance'. The term ameliorator stems from the Latin word melior and means to make better. The simplest form is as a metal plate with small, regularly spaced holes ± a holefield. If the metal sheet is continuous and the holes are small, the meshplate will act as a hole-screen such as those employed in microwave oven doors. The leakage through such screens can be quite accurately calculated by analytically derived equations (Otoshi, 1972). The following equation gives good results for holes which are so small that no diffraction other than that of the first order occurs, for example mesh screens in microwave oven doors: TdB ˆ ÿ20  10 log…3ab0 =2d 3 † ‡ 32t=d

15:7

where TdB is the relative intensities on the two sides, expressed in power decibels (i.e. ÿ10 dB means a tenfold reduction of the power transmission), a and b are the distances between adjacent hole centres in Cartesian co-ordinates, d is the hole diameter, 0 is the free space microwavelength, and t is the plate material thickness. Since the equation is dimensionless, it is only necessary to express all dimensions above in the same units, e.g. mm. Furthermore, the equation stipulates that scaling up the dimensions of the holes and the distances between them so the pattern remains unchanged will result in an increase of transmission which is proportional to the linear scaling factor, at constant microwave frequency. Obviously, this cannot hold if the hole size is a significant fraction of the wavelength. The equation is based on a perpendicularly impinging plane wave, i.e. a wave having both the electric and magnetic fields parallel to the meshed metal surface. This gives the strongest coupling. As can be shown by modelling, the mesh plate transmits much less for `striking' incidence (i.e. with the electric field perpendicular to the mesh plane), but there are also nearfield effects which will modify the behaviour of the mesh plate considerably if there is an absorbing load close to it. The inverse kind of ameliorator function is obtained by patterns of metal islands on a microwave transparent substrate, i.e. replacing metal by air. The metal and air island structures have theoretical similarities, in accordance with Babinet's principle. This states that the fields transmitted by an aperture (or array of apertures) in a plane conducting screen are equal to the negative of the field diffracted by the complementary obstacle (Harrington, 1961). In the case of hole-field symmetry in two perpendicular directions parallel to the plane, this means that the sum of transmission in the hole-field and metal island field cases is one.

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15.4.2 Modelling and properties of regular island fields Numerical microwave modelling can be used to quantify all aspects of ameliorator behaviour, with and without food loads. But complete microwave oven scenarios are not always practical to use, since the distance between metal (or air) islands may be quite small, requiring small cells which in turn require many time steps per microwave cycle ± the number of cells becomes extensive, as does the number of time steps per cycle. Instead, scenarios employing short waveguides are used for ameliorator patterns consisting of metal objects that are small, and in particular closely located. A sufficiently large number of the small islands must then be used, so that edge effects at the pattern periphery become insignificant. Since two polarisations (in effect TE and TM) must be used, two scenario categories are needed. In the TE case, a vertical waveguide with cross-section dimensions 86 mm  30 mm may be used; see Fig. 15.4. It is fed from the top with the TE10 mode, and there is another mode matching at the bottom.

15.4 TE incidence towards a mesh plane.

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15.5 TM incidence (the electric field perpendicular to the mesh plane).

In the TM case, a horizontal waveguide with the same dimensions and characteristics is used; the same mesh plane sub-scenario constitutes a part of the waveguide bottom, below which there is a space with all five walls being perfectly absorbing planes; see Fig. 15.5. The top waveguide is fed by the TE10 mode and there are perfectly absorbing scenario boundary planes below. The actual fields are observed, in both cases, mainly the dominating magnetic fields near the centre of the mesh plane, on both sides. Comparisons with the undisturbed field (no mesh plane, i.e. an opening) and with a metal plate in the TM case are to be made, to separate out the reflections by the mesh plane. Other measurement structures are more accurate; see Section 15.5.4, where a circular TM012 cavity method is described. In a first example, square holes with 2.8 mm side are in a regular square pattern as shown in Figs 15.4 and 15.5, with 0.2 mm metal in between. The software allows superconducting metal sheets with zero thickness in one plane, so this is used. Equation [15.7] then gives ÿ34.4 dB attenuation, with the surface area of the air squares converted to corresponding circle diameters. If the pattern is inverted (to metal islands) and the TM-type scenario in Fig. 15.5 is instead used, the parallel magnetic field is attenuated by a factor of about 2; this can be interpreted as about 25% of the power being transmitted when there is no food load close to the metal island plane.

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In a second example, the metal islands are 10 mm  10 mm squares, with 3 mm air in between, in the TM case. The parallel magnetic field is now attenuated so that 60% remains after transmission through the field; this can be interpreted as about 35% of the power being transmitted. The coupling to a food load close to a grid of air holes or metal islands varies both with TE or TM polarisation, the distance and the load permittivity. The coupling is stronger for the TE case (impinging electric field parallel to the grid), if the load is touching or close to the grid, since the coupling to a dielectric is then better; it can be said to partially take over the displacement current in the grid voids. As an example of modelling with the 10 mm  10 mm square metal islands with 3 mm distance, the field coupling results in 58% `power coupling efficiency' in a load with " ˆ 52 ÿ j20 located 2 mm away from the grid in the TE case, and 47% in the TM case.

15.4.3 Other ameliorator geometries More generalised geometries of metalisation on microwave transparent containers are of course possible. Owing to the nearfield interaction with adjacent loads, the limitation on size of the individual metal islands and their airgaps is related mainly to the negative effects of shielding by large islands, and small distances between islands causing local overheating or even arcing between them. And total structures of multiple islands may become resonant or antiresonant, further complicating the analysis and synthesis of practical ameliorator systems. A first example is a metal island pattern on a previously commercially available container shown in Fig. 15.6. It has a continuous metallisation on the sloping sides, and a bottom pattern of hexagonal metal islands with 9 mm maximum diameter and 1 mm air gaps. This bottom pattern was used in direct contact with the IEC batter load (IEC, 2006); the load is about 150 mm 100 mm  20 mm and has " ˆ 35 ÿ j15 in the model microwave oven in Fig. 15.2, with an additional equal pattern 4 mm above the top surface of the load. It is seen in Fig. 15.7 that there is mainly a shielding and no improvement of the heating pattern. However, the actual ameliorator container is smaller than the IEC batter load, and also has metallised side walls. Therefore two modelling runs were made with a 105 mm  75 mm  20 mm batter load with the same bottom metal island pattern only, without and with four vertical metal plates contacting the load. The power density pattern in a horizontal plane 3.5 mm above the bottom is shown in Fig. 15.8(a), with only the pattern of hexagonal metal islands (top image) and with also the four vertical sides contacting thin metal (bottom image). Figure 15.8(b) shows the power density in a plane 1 mm below the top of the load, in the same two cases. The reflected power back to the magnetron was 6% with the bottom metal island pattern, and the added metal walls. With no metal at all it was 16%. This result indicated that the ameliorator system is receptive to one or several of the

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15.6 An ameliorator container. The wide inner dimension is about 150 mm.

particular volume mode resonances in the cavity. As seen in Fig. 15.8, the system also promotes heating from below, which is generally more favourable since less energy is then wasted by surface evaporation and cooling. The example above shows that the heating pattern can be modified considerably by surrounding food loads with ameliorators. The concept is sometimes called `an oven within the oven', and can improve the heating evenness, particularly in microwave ovens with relatively poor `intrinsic' heating evenness. However, as a consequence of the descriptions of underheating trapped surface waves (LSM) modes in Chapter 3, Section 3.6, the heating result in microwave ovens with inherently strong such modes may actually deteriorate and the oven efficiency may also be reduced, if a large part of the container bottom has metal islands. In practice, ameliorator systems with a strong function

15.7 The heating pattern about 3 mm from the bottom of an IEC batter load, without (a) and with (b) the metal island pattern of Fig. 15.6.

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15.8 (a) The heating pattern 3.5 mm above the bottom of a food load (see text), with the bottom ameliorator pattern of Fig. 15.6; without (top) and with (bottom) vertical metal sides surrounding the food load, (b) the heating pattern 2 mm from the top of the food loads, with the same ameliorators as in (a).

can be said to improve the heating result in poorly performing microwave oven models, but be less favourable with some well-performing microwave oven models. It is therefore important that ameliorator systems are tested in a range of microwave oven models with different microwave systems.

15.4.4 Some comments on ameliorator modelling The small scenario in Fig. 15.5 has about 1.5 million cells, with the smallest cell dimension 0.2 mm. It runs in less than 15 min on a computer with a 2 GHz processor. The small oven scenario used for obtaining the results in Fig. 15.8 has a smallest cell dimension of 0.5 mm, and is improved with so-called special planes outside which larger cells (1.5 mm) are used. It has about 7 million cells and runs in 1 to 2 hours, since many more cycles are needed due to the oven cavity resonances. The oven cavity has a volume of only about 14 dm3 and a very simple feed. Therefore, a typical oven with small pattern ameliorators around the load may need up to 3 hours. However, parallel processing using for example the multiple processors in advanced graphics cards is now coming into use and already a speed-up of a factor 25 has been reported (Dziekonski et al., 2008). Scenarios with up to 30 million cells (there may then be a memory limitation), requiring 30 000 time steps, are now, in 2008, able to run fast enough for run times not to be an obstacle.

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15.9 The heating pattern in the same load as in Fig. 15.8a, but now in the plane of the metal islands. The scale is now extended by a factor 15.

As mentioned earlier, very strong heating may occur in small parts of food loads close to ameliorator edges. As an example, Fig. 15.9 shows the heating pattern just at the bottom metal island pattern at the 100 mm  75 mm  20 mm batter load, in which the heating pattern 3.5 mm above the metal island plane is shown in the bottom image in Fig. 15.8(a). The scale is now set for maximum to be 15 times higher than that in Fig. 15.8. It is obvious that microwave modelling alone cannot describe the heating situation. There is a need to couple the microwave heating to load enthalpy and heat conduction, and then to also introduce realistic heating times. This can be done with the QuickwaveTM software, and some data are given in Chapter 6, Section 6.8. The method uses enthalpy data to calculate the temperature rises in all load cells over a step in real time of 5 to 30 seconds, then, in a second step, changes the dielectric data accordingly in all these cells individually, and in a third step uses heat conductivity data to even out temperatures between the load cells before the microwave heating is resumed.

15.5

Susceptors

15.5.1 General A susceptor is a thin microwave-absorbing device which is primarily intended to absorb microwaves and convey the heat to the food load. The Latin word suscipere means to take up, but the term susceptance is used in electrical engineering and is then the imaginary part of the admittance, which is in turn the inverse of the impedance. Susceptance is therefore a property which is not related directly to power absorption.

15.5.2 Power absorption in a thin metal layer ± a continuous metal susceptor Exact analytical calculations can be performed for the limiting case of a conductive film, under free space plane wave conditions, as well as with a

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homogeneous dielectric of any microwave property, extending over the whole cross-section of a waveguide. Matching of the parallel electric and magnetic fields at the boundaries, and the source, are then introduced into a linear matrix equation which can readily be solved (Balanis, 1989). For a single susceptor in free space there is, however, a simpler method. The resulting equations include the film resistance Rf in ohms per square, /ú) of the film which is Rf ˆ 1=t

…t  dp †

15:8

where t is the film thickness and dp the penetration depth of the conductive substance at the frequency under study. The unit /ú refers to the resistance of the sheet, measured between two conductors contacting opposite side peripheries; the resistance is then independent of the side length of the square sheet. Actually, the wave impedance of free space (0  377 ) is also `per square', and it is a vector in the direction of propagation. Even if `per square' is dimensionless, it has to be observed when making calculations, as with the surface resistance Rs. Next, the incidence and polarisations have to be included. The free space wave impedance is 0 . The angle of incidence is i . The wave impedances perpendicular to the film surface are to be considered, since only that propagation component induces a current in the film. These incident impedances become, as for the thick metal surface in equation 15.4, for the TM-polarised case: ?0 ˆ 0
cosi

15:9

i

As before, the factor cos is multiplied instead of divided with the base factor in the TE-polarised case. The impinging wave encounters the film and the reflection is caused by the component of space impedance perpendicular to the film. Since the film is very thin, the strength of the electric field in it and also that emitted from its back side are equal. One then directly obtains the absorption of power flux in the film, from the parallel `connection' of the impedance of free space and the susceptor, as Pf =Pi ˆ

4Rf
?0

…2Rf ‡ ?0 †2

(both polarisations)

15:10

This absorbed power per unit area is maximum (50%) when Rf ˆ 12 0 =cosi

(TE-polarised case)

15:11

Rf ˆ 12 0
cosi

(TM-polarised case)

15:12

Equation 15.10 is an approximation for the thickness t  dp . Numerical comparisons with the exact matrix solutions show that the approximate solutions are valid for  > 105 [1/ m] and t < 0:1dp with less than 1% error of the totally 100% of the power which is reflected, absorbed and transmitted. A thickness up

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to 0.3 mm can normally be used with less than 5% error. However, using an anisotropic conductivity of the film in the model will result in a significant reduction of the error; see Section 15.5.4. These restrictions are important for the modelling, which uses a volume rather than surface concept. It must also be noted that equations 15.10 to 15.12 apply only in the unrealistic free space case without an adjacent load; see the next section.

15.5.3 Continuous metal susceptor with an adjacent load In real heating situations, the susceptor will of course be placed near the food item which is supposed to heat up. Complicated standing wave and impedance relationships then appear and there is not much use for the idealised free space case. In the analysis of multilayer systems with a susceptor, the linear equation matrix format can again be used for the solution of the properties of the whole system. It is then convenient to introduce a susceptor with a larger thickness than its real, which is about 10 nm. Starting with a suitably small t value, for example 0.2 mm, and inserting the actual Rf value in equation [15.8], the corresponding equivalent  is calculated. The equivalent permittivity to be inserted in the equations is then obtained from the basic relationship "00 ˆ =2 f "0 "00

(at 2450 MHz:   0:136 300
"00 )

15:13

is the loss factor of the metal, f the frequency and "0 the electric where constant. There is no need to add a real part "0 other than 1, since "00  1 and will completely determine the propagation. The computational t value is normally chosen much larger (as above) than the real value for a high- film, to avoid numerical problems in the computation by too small cell dimensions. The scenario is given in Fig. 15.10 and what may happen is illustrated in Figs 15.11 and 15.12. A relevant piece of information is the power absorbed by the susceptor, in relation to that totally absorbed by the system (the susceptor and the adjacent food item). By this, the reflectivity of the system is partially compensated for, so that realistic power sharing data for a microwave oven situation are obtained. In Fig. 15.11 the distance D between the susceptor and the dielectric slab is 10 mm. The susceptor absorption is a monotonous function of its film resistance; when this is low its shielding effect causes less power to be absorbed by the dielectric. Interestingly, there is not much difference in absorption between the widely different dielectrics. In Fig. 15.12 the same components are used, but the susceptor±dielectric distance D is now only 2 mm. The difference in susceptor absorption between the cases with different dielectrics is now more pronounced. This is, however, mainly by the susceptor absorption being lower with the high-" dielectric, which thus absorbs a higher share of the power.

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15.10 Irradiated susceptor at a distance from a lossy dielectric slab. S is the Poynting vector (in the direction of incidence).

15.11 Power absorption in a susceptor film, in relation to the totally absorbed power, for 10 mm distance susceptor±dielectric.

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15.12 Power absorption in a susceptor film, in relation to the totally absorbed power, for 2 mm distance susceptor±dielectric.

In many practical situations the susceptor will be at the bottom of the package, below the food item. Since the distance to the oven cavity bottom is then rather short, modes which are rather dissimilar to plane waves dominate. These LSM modes (longitudinal section magnetic modes, see Chapter 3) are characterised by an absence of vertically directed magnetic fields (with a horizontal food and container bottom surface). There is then a strong vertical electric field component in the airspace, but this is weakened inside the shelf or p food load by a factor between " and ", depending on their thicknesses. A useful way of describing the LSM mode behaviour with regard to the flat shelf and load on it is to employ an almost striking angle of incidence of a plane wave, from below into the shelf and food item. A value of 85ë can be used to represent the behaviour of a reasonably typical oven cavity underheating LSM mode. Computer runs using this value show rather small differences to the data for 60ë in Fig. 15.12. In both Figs 15.11 and 15.12 the angle of incidence is 60ë and the impinging wave is TM-polarised. Since there may be situations where the equivalent angle of incidence is less than 60ë, the perpendicular incidence (i ˆ 0, TEM) is also of interest. The major difference from Fig. 15.12 is then that the susceptor absorbs much less power if its Rf is about 100 and the permittivity of the food load is large. The total power absorption by the system consisting of the susceptor and the load is of course of interest. This is shown in Fig. 15.13 for two incidence angles

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15.13 Total power absorption (susceptor plus load) as function of film resistance, for 2 mm distance susceptor±dielectric.

(0ë and 80ë TM-polarised), with the load permittivities as parameter, as in the previous figures. The drastic difference in absorption efficiency between the two incidence angles has some similarities to that shown in Fig. 3.4 in Chapter 3. The data clearly show that TEM incidence will not be likely to contribute to the heating much, if there are simultaneous waves with 80ë TM-polarised incidence available. Furthermore, the efficiency varies very little with the load permittivity for the 80ë TM-polarised incidence and the susceptor does not influence this negatively. It is concluded that very insufficient information on the behaviour of the susceptor-food system is obtained by using only the simplistic perpendicular free space incidence model without a food load. The fact that susceptors may function well anyway is explained by microwave field interactions between the susceptor and the adjacent food load.

15.5.4 Fractured susceptors and multilayer structures These are as such addressed in Chapter 9, so this section deals with the behaviour using the fractured susceptors with the linear equation matrix method and with numerical modelling using FDTD methods such as QuickwaveTM. It is then necessary to use a complex permittivity " ˆ "0 ÿ j"00 (or, equivalently, a real permittivity "0 and a conductivity ).

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15.14 Microstructure of a fractured 8 nm thick susceptor (from Ball et al., 1993).

As can be deduced from Fig. 15.14, a fractured susceptor can be described as resistive islands in series with capacitive gaps. Its impedance thus becomes reactive. When this is to be converted to a volume property for modelling, a parallel conductivity and real permittivity have to be used. At a fixed frequency this does not cause any problems; when measuring a fractured susceptor in a waveguide set-up as described in Chapter 9 or by von Hippel (1954), one can as well use distributed circuit concepts and arrive at a complex permittivity. But it is then to be noted that these circuit elements are only in the plane of the susceptor ± what is studied is only the case of TE-polarised incidence, i.e. the behaviour of the induced currents in the plane of the susceptor. One must of course assume a thickness of the material under test (MUT), and this thickness must not be very small in order not to cause any numerical problems in the modelling. As mentioned above, thicknesses of up to 0.3 mm can then be used if errors up to about 5% are acceptable; this is only 0.2% of the 2450 MHz wavelength and does not change the system geometry significantly. This thickness is thus possible to use in most scenarios. For a susceptor film with Rf ˆ 100 /ú the corresponding conductivity then becomes (equation [15.8]) about 30. The QuickwaveTM and other FDTD software allow the use of anisotropic media. In particular a fractured susceptor provides a good opportunity for this. The capacitance is essentially between the flake edges, and there are methods to calculate it with some approximations (Habeger, 1997). The short distance may provide condition for a quite high equivalent permittivity "0 , in particular for multilayer metal flakes in a resin (Pesheck and Lentz, 1992; Ball et al., 1993). Values of for example "  500 ÿ j60 were reported by Pesheck and Lentz (1992) to be achievable. Figure 15.15 shows an example of such a structure. Additional examples are given by Pesheck and Lentz (1991). Quantifying the anisotropic behaviour of this kind of structures by retromodelling requires the use of both TE- and TM-polarised incident free space waves or waveguide modes. The TE-polarised case is that which is used in the

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15.15 Example of a multilayer artificial dielectric structure; plan and cross section views (from Ball et al., 1993).

standard waveguide methods (von Hippel, 1954) and is outlined in Fig. 15.4. The TM case requires a more well-defined set-up configuration than that shown in Fig. 15.5: a circular TM012 mode cavity is then suitable, with a circular flat MUT. Note that the measurement cavity is different from that which is most suitable for low loss MUTs such as plastics and is described in Chapter 5, Section 5.6.4. This is because the electric field should now be perpendicular to the MUT surface. A circular TM012 mode cavity is shown in Fig. 15.16. For the 2450 MHz ISM band, a suitable diameter is 120 mm, with a height of 196 mm. The MUT has a diameter of 30 . . . 40 mm and is located at half the cavity height, on two crossed PTFE threads. The access opening is at three-quarters height, as for the TM012 mode cavity described in Chapter 5, Section 5.4. The system is of the transmission type, with coaxial probe antennas positioned axially and protruding about 2 mm into the cavity.

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15.16 A resonant TM012 cavity set-up for retro-modelling of the across anisotropic permittivity of fractured or composite susceptors.

Extraction of data for MUTs is by retro-modelling, mapping the performance of the set-up by using a series of `test MUTs' with given data, and then comparing/interpolating with experimentally obtained data. The resonant frequency and either the Q value or transmission at resonance are then used. Since a complex permittivity in the directions of the susceptor plane has been obtained with the TE-polarised measurement set-up, the anisotropic permittivity in the axial direction of the cavity can then first be set to 1 ÿ j0. Initially, the `horizontal' values are used with the TM012 cavity set-up, and then complemented with values in the axial direction obtained by retro-modelling in that setup. If needed, one may then iteratively use the overall anisotropic data in the TEpolarised set-up.

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15.17 A susceptor±ameliorator combination. The major axis is about 170 mm.

The metal layer thickness in single and multilayer structures may of course be made different, to achieve a combination susceptor±ameliorator effect. An example of combined thin and thick layer metallisation is shown in Fig. 15.17. This can in principle be modelled in the same ways as previously described, but one will of cource have to consider that the retro-modelling results apply only to MUTs which have homogeneous properties over the whole area.

15.5.5 Modelling of susceptor heating As mentioned at the end of Section 15.4.4, the QuickwaveTM software package ± and some other commercially available software packages ± allow the use of enthalpy, specific heat (per volume unit) and heat conductivity data to calculate the temperature rises in all individual load cells. This can be extended to susceptors. Susceptors can be considered to have a heat conductivity comparable to that of typical foods with a high water content, and there will typically be a much stronger heating of the susceptor than of the food. However, the susceptor may not be touching the food, and this may also dry out. The drying-out can be dealt with in the same way as for white bread: ascribing a very high enthalpy density to an evaporating load (see Chapter 6, Section 6.8, Table 6.5). The heat transfer from the hot susceptor to a load nearby can be included by ascribing a strongly temperature-dependent heat transfer coefficient from the susceptor to a layer of `special air' between it and the food load, and from that special air layer to the food. The heat capacity of the special air can be set to zero, as can its enthalpy change with temperature. Its heat conductivity is set to a high value, to represent spreading-out of steam.

15.6

Final comments

The dielectric properties of food materials are highly variable, as quantified in Chapter 6. Thawing and evaporation ± i.e. the dynamic heating process ± further complicate the situation. Heat transfer becomes crucial with susceptors. The problems are then not in setting up the scenarios and carrying out the modelling

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computations as such, but to obtain reliable physical input data of what materials and processes one wants to model. Modelling mimics the behaviour of nature, and by that basically replaces experiments. But experiments do not allow complete studies of microwave fields and their behaviour. Microwave modelling is therefore an invaluable tool for improved understanding and by that also for improved and more reliable optimisation work.

15.7

References

Balanis C (1989) Advanced Engineering Electromagnetics. John Wiley & Sons, USA, pp. 220±236. Ball M et al. (1993) Materials choices for active packaging. Microwave World (IMPI), No. 1, pp. 24±28. Dziekonski A et al. (2008) Implementation of matrix-type FDTD algorithm on a graphics accelerator. XVII International conference on Microwaves, Wroclaw, Poland, paper A8/1. Habeger C (1997) Microwave interactive thin films. Microwave World (IMPI), No. 1, pp. 8±22. Harrington R F (1961) Time-harmonic Electromagnetic Fields (reissue 1968). McGrawHill, USA, pp. 365±373. von Hippel A (1954) Dielectric Materials and Applications. The MIT Press, Cambridge, MA, pp. 63±68. IEC (2006) Household microwave ovens ± methods for measuring performance. Consolidated edition 3.2, IEC, Geneva. IEC (2007) International Electrotechnical Vocabulary, www.electropedia.org Otoshi T Y (1972) Microwave Transmission Through Holes. IEEE-MTT, Boston, USA, pp. 235±261. Pesheck P and Lentz R (1992). WO patent application No. 92/08565. QWED Sp. z o.o. (1997) QuickWaveTM software for electromagnetic design, www.qwed.eu. Risman P O (1973) Swedish patent No. SE 353640. Risman P (1992) Metal in the microwave oven. Microwave World (IMPI), Vol. 13, No. 1, pp. 28±33.