Cheese Rheology and Texture

Cheese Rheology and Texture Sundaram Gunasekaran M. Mehmet Ak

CRC PR E S S Boca Raton London New York Washington, D.C. © 2003 by CRC Press LLC

Library of Congress Cataloging-in-Publication Data Gunasekaran, Sundaram, 1957Cheese rheology and texture / Sundaram Gunasekaran, M. Mehmet Ak. p. cm. Includes bibliographical references (p. ). ISBN 1-58716-021-8 (alk. paper) 1. Cheese—Texture. I. Ak, M. Mehmet. II. Title. TX382 .G86 2002 637′.3—dc21

2002034861

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Visit the CRC Press Web site at www.crcpress.com © 2003 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 1-58716-021-8 Library of Congress Card Number 2002034861 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper

Dedication To: My parents, Raga Palanisamy Sundaram and Kamala Sundaram, for inspiring me to always strive for excellence. My wife, Sujatha, and children, Suvai and Suman, for their love, support, and patience. — SG

My father, Haci Ak, and mother, Zeynep Ak, for giving me the opportunities they never had. My wife, Nese, who continuously supported my efforts and patiently endured the time I spent working on this book. My daughter, Asli, and my son, Efe, who cheered me up in times the situation looked hopeless. — MMA

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Foreword Two complex scientific areas, cheese and rheology, create an exponential increase in complexity when combined. This text makes a significant contribution to an understanding of this complexity. It underscores limitations and considerations in evaluating and conducting research on cheese rheology, points out some important gaps in our understanding of cheese rheology, and thoroughly reviews methods, theories, and applications of rheology in general and specifically for cheese. Rheologists will gain a better understanding of the physicochemical properties of cheese, and cheese researchers will be exposed to the wide range of rheological methods and the theoretical bases of those methods. Both groups should realize the need for collaborative research after exposure to the individual complexities of cheese and rheology. The diversity of observations, and seemingly contradictory observations, on the physical and chemical properties of cheese that appear in this text should not be surprising since many of the observations were made before instruments were improved and were specifically adapted to deal with unique properties of cheeses. Also, confusion resulted from: cheese scientists who used techniques inadequate to definitively measure physical properties of cheese; rheologists who chose test samples of cheese that did not possess comparable chemical properties except for the property to be measured; and inadequately defining the chemical properties of cheese. The authors have discussed unique characteristics of cheese that rheologists should be cognizant of in designing experiments. Comments on merits and deficiencies of wide range of rheological test methods as applied to cheese should assist cheese scientists in appropriately using the procedures. The chronology of cheese rheology research outlined in this book is encouraging as evidenced by the increase in collaborative research groups or research groups with better understanding of both research areas. The physicochemical properties of cheese have always been an important component in assessing cheese quality and value. The assessment was usually done by sensory evaluation, which was quite adequate because cheese was generally consumed in its “original” state. Development of heat-processed cheese products in the early 1900s prompted some research on the physical properties of cheese, primarily by modifying chemical properties, however, only limited research was done on rheological properties. The last several decades have greatly changed the forms and uses of cheese in the market place. Cheese has to be sliced or shredded by highspeed cutting devices; the melt and flow properties of cheeses have to be more carefully controlled; flavor intensities and flavor profiles have to be modified without adversely affecting physical properties of cheese; and cheese products must possess adequate stability, often under wide ranges of environments. This myriad of desired properties greatly increases the need for procedures to independently control specific properties and the need for adequate methods to measure the properties specifically © 2003 by CRC Press LLC

being controlled. The authors of this book have facilitated attainment of these goals by their thorough review of the present status of cheese rheology research and by providing guidance for further research efforts. Norman F. Olson Department of Food Science and Center for Dairy Research University of Wisconsin-Madison

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Preface Rheology of cheese has been studied since the early 1950s. In fact, “Cheese Rheology” is the name of a chapter in the 1958 FAO Report*. Since then, many advances have taken place both in cheese technology and rheology. As cheese became an important part of the diet in many parts of world, the cheese industry responded by manufacturing new types of cheeses with varying textures to suit varied needs and to promote cheese use both as a table cheese and as an ingredient food. This flurry of new cheeses and applications and cheesemaking technologies has also brought about an acute need to characterize the rheological and textural attributes of cheeses to ensure their high quality. Thus, for food rheologists and food scientists, cheese is among the most popular subjects of study. In this book, we have attempted to summarize the vast literature available on cheese rheology and texture. Needless to say, the sheer volume of information available and the complexity of both cheese and rheology made this a particularly difficult task. Our goal was to bring together many of the dispersed published information on cheese rheology and texture in one book to serve as a comprehensive reference source. A unique aspect of this book is that it contains detailed descriptions of several methods to study rheology of foods in general and cheese in particular. This is to provide the interested readers the necessary basic information on many techniques reported in the literature which often do not have adequate explanation. Chapter 1 provides an overview of cheesemaking technology. Fundamental rheological test methods are described in much detail in Chapter 2. This chapter will facilitate the readers to gain a deeper understanding of the various rheological test methods. The uniaxial testing, one of the most widely used classes of rheological and texture testing methods, is the focus of Chapter 3. The fracture mechanics are an extension of the uniaxial test methods. These are discussed in Chapter 4. In Chapter 5, linear viscoelastic methods are described. This is now among the most popular rheological test performed on cheeses, and is also known as dynamic testing. Both the theory and applications are discussed in a manner benefiting those who are already familiar and those who are new to the subject. Chapter 6 focuses on nonlinear viscoelasticity of cheeses. This subject has not received much attention due to the lack of available instrumentation and the complexity of data analysis. This chapter will be more useful to those familiar with rheological analysis than to the casual reader. The discussion on cheese texture in Chapter 7 is limited to mechanical texture of cheese, as it is more in line with rheological measurements. Cheese meltability and stretchability, two of the most important properties of cheese used in prepared foods, are the topics of Chapters 8 and 9. The emphasis in these chapters is on measurement methods. The effects of various factors on cheese functional properties are addressed in Chapter 10. * Kosikowski, F.V. and G. Mocquot. 1958. Advances in Cheese Technology, FAO Studies No. 38. Food and Agriculture Organization of the United Nations. Rome, Italy. © 2003 by CRC Press LLC

Acknowledgments We would like to acknowledge many individuals who have contributed directly or indirectly toward making this book a reality. First and foremost, we would like to express gratitude to Professor Norman F. Olson, who was instrumental in helping us to initiate our first project on cheese rheology in 1989, when S.G. was a new assistant professor and M.M.A. was a graduate research assistant. Since then, with his expert knowledge and friendly personality, Professor Olson has been a source of great support. Thanks are also due to Dr. Mark Johnson, Dr. Rusty Bishop, John Jaeggi, and other past and current staff at the Wisconsin Center for Dairy Research. These people are invaluable resources for cheese research. This book draws from much of the research performed in S.G.’s laboratory. As such, the efforts of many graduate students and post-doctoral research associates are deeply appreciated. They include: Chyung Ay, James Colby, Kexiang Ding, Chang Hwang, Sun Young Kim, Sanghoon Ko, Gul Konuklar, Meng-I Kuo, Laura Marschoun, Kasiviswanathan Muthukumarappan, Hongxu Ni, Ramesh Subramanian, Salman Tariq, Deepa Venkatesan, Ya-Chun Wang, and Chenxu Yu. Thanks are also due to S.G.’s colleagues, Professors A. Jeffrey Giacomin and Daniel Klingenberg at the Rheology Research Center, University of Wisconsin-Madison, and Professor Karsten B. Qvist of KVL, Denmark. Thanks to Hallie Kirschner for typing parts of the manuscript. The financial support of Wisconsin Milk Marketing Board and Dairy Management Inc. for many of S.G.’s projects is also deeply appreciated. M.M.A. wishes to thank each member of his family for their full support and patience during the writing of this book. He expresses appreciation to the following: Suat Yasa and Murat Yasa of Aromsa Limited Company, for their interest in the book; friends Elsie and Warren Sveum, Sarah and Alvaro Quinones, Mar GarcimartinAkgul, and Arzu and Yann LeBellour for their constant encouragement; and former students Filiz Lokumcu and Metin Yavuz for their valuable assistance in gathering some of the publications. Sundaram Gunasekaran M. Mehmet Ak

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Table of Contents Chapter 1

Cheesemaking — An Overview

Cheese Types Cheesemaking Milk Pretreatment Coagulation Syneresis Shaping and Salting Ripening Process Cheese References Chapter 2

Fundamental Rheological Methods

Definition of Rheology Basic Concepts Strain Stress Strain Rate Fundamental Methods Uniaxial Compression Uniaxial Tension Bending Test Specimen with a Rectangular Cross-Section Specimen with a Circular Cross-Section Torsion Test Vane Method Stress-Relaxation Test Analysis of Relaxation Behavior Creep Test Analysis of Creep Behavior Shear Rheometry Sliding-Plates Geometry Concentric-Cylinders Geometry Cone-and-Plate Geometry Parallel-Plate Geometry Capillary Rheometry Extensional Rheometry Lubricated Squeezing Flow Equations for Different Fluids in Lubricating Squeezing Flow References © 2003 by CRC Press LLC

Chapter 3

Uniaxial Testing of Cheese

Uniaxial Compression Measurements Structure and Composition Effects Stress-Relaxation Measurements Torsion Measurements Tension Measurements Creep Measurements Bending Measurements Vane Measurements Shear Measurements Lubricated Squeezing Flow Measurements References Chapter 4

Fracture Properties of Cheese

Fracture Mechanics Brittle Fracture Griffith Criterion Determination of KI Fracture Tests on Cheese Notch Tests Cutting, Slicing, and Shredding Cutting with Wire and Blade Eye/Slit Formation and Growth References Chapter 5

Linear Viscoelasticity of Cheese

Mathematical Relations in Linear Viscoelasticity Types of SAOS Measurements Strain (or Stress) Sweep Frequency Sweep Temperature Sweep Time Sweep Time–Temperature Superposition Application of SAOS in Cheese Rheology Linear Viscoelastic Region of Cheeses Cheddar Cheese Gouda Cheese Mozzarella Cheese Mozzarella: Time–Temperature Superposition Example Feta Cheese Imitation Cheese Quarg Cheese Processed Cheese Cox–Merz Rule References © 2003 by CRC Press LLC

Chapter 6

Nonlinear Viscoelasticity of Cheese

Pipkin Diagram Sliding Plate Rheometer Large Amplitude Oscillatory Shear Flow Spectral Analysis Discrete Fourier Transform Determining Material Properties Amplitude Spectrum Stress–Shear Rate Loops Effect of Wall Slip Constitutive Model for Cheese Relaxation Modulus Obtained from SAOS Relaxation Modulus Conforming to LAOS References Chapter 7

Cheese Texture

Texture Development in Cheese Cheese Manufacturing Factors that Affect Texture Textural Changes during Storage Measurement of Texture Texture Profile Analysis TPA Testing of Cheese Uniaxial Tests for Cheese Texture Measurement Compression Test Wedge Fracture Test Torsion Test and Vane Rheometry Texture Map Dynamic Tests Empirical Tests Crumbliness Cone Penetrometer Stringiness References Chapter 8

Measuring Cheese Melt and Flow Properties

Meltability Empirical Tests Objective Tests Steady Shear Viscometry Capillary Rheometry Squeeze-Flow Rheometry UW Meltmeter Viscoelasticity Index for Cheese Meltability Dynamic Shear Rheometry Helical Viscometry © 2003 by CRC Press LLC

Cheese Melt Profile Measurement UW Melt Profiler Determination of Melt Profile Parameters Graphical Method Modeling Melt Profile Constant Temperature Test Transient Temperature Test Conduction Heating References Chapter 9

Measuring Cheese Stretchability

Empirical Methods Instrumented Methods Vertical Elongation Horizontal Extension Compression Tests Helical Viscometry Fiber-Spinning Technique The Weissenberg Effect References Chapter 10 Factors Affecting Functional Properties of Cheese Properties of Milk Cheesemaking Procedures Addition of Starter Culture and Coagulants Curd Handling Cooking, Stretching, and Cooling Cheese Composition Moisture Content Fat Content Salt Content pH Post-Manufacturing Processes Aging/Ripening Freezing and Frozen Storage Heat Processing Other Factors References

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1

Cheesemaking — An Overview

Cheese is one of the first and most popular manufactured food products. What perhaps started out as an accidental curdling of milk has been further refined into cheesemaking. Over several thousand years, cheesemaking has advanced from an art to near science. Cheese varieties have proliferated to suit varied conditions and requirements, especially during the last decade or so. It is estimated that more than 2000 varieties exist (Olson, 1995), and the list may still be growing. Cheese is now an important part of foods consumed in many countries (Table 1.1). In a recent survey, after spices, cheese was named the top ingredient that makes cooks feel more creative (Doeff, 1994). Several cheeses satisfy varied requirements in order to be used as suitable ingredients in various dishes from baby foods to baked products (Table 1.2). Battistotti et al. (1984) described the history of cheese and cheesemaking in much detail. This chapter provides a broad overview of cheesemaking. For further details, readers are referred to many recent books on the subject (Scott et al., 1998; Spreer, 1998; Law, 1999; Walstra et al., 1999; Fox et al., 2000).

CHEESE TYPES Today’s wide array of cheeses may be classified according to the country of origin, manufacturing process, or some end-use property. Classifying cheeses based on manufacturing and maturation processes by Olson (1979) produces a succinct list. A classification based on firmness and the maturation agent used produces a longer list but may be more relevant if textural and rheological properties are important (Figure 1.1). A classification based on the distinctive manufacturing process involved is also useful to understand the effect of the process on the cheese texture (Table 1.3). Other classifications of cheeses, e.g., according to milk source, overall appearance (color, size, shape), chemical analysis, etc., are also possible. Davis (1965) recognized the difficulty in classifying cheeses and attempted to group them based on the nature and extent of chemical breakdown during ripening or according to flavor. Such a classification is still not available. Fox (1993) proposed that the products of proteolysis could be most useful for classification. One of the main difficulties when using classification schemes is that differences exist in the moisture range allowed within various categories published in the literature (Banks, 1998). Davis (1965) assigned some empirical texture/rheological parameter values to the terms from very hard to soft (Table 1.4). The United States Code of Federal Regulations (CFR, 1998) stipulates certain standards of identity for cheeses classified according to their consistency, as listed in Table 1.5. The typical composition of milk and several cheese varieties is given in Table 1.6. In the United States, the cheese market is dominated (almost equally) by Cheddar and Mozzarella cheeses. They comprise about twothirds of the total cheese production over the past several years (Figure 1.2).

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TABLE 1.1 Consumption of Cheese in Selected Countries Consumption per Capita (kg) Country North America Canada Mexico United States South America Argentina Brazil Venezuela Western Europe Denmark France Germany Ireland Italy Netherlands Spain Sweden Switzerland United Kingdom Central Europe Poland Balkans Romania Eastern Europe Russia Ukraine North Africa Egypt Southern Asia Japan South Korea Oceania Australia New Zealand a

1995

2000a

10.86 1.47 12.26

10.76 1.61 13.75

10.35 2.82 3.48

11.06 2.72 2.76

16.84 21.51 11.90 5.54 18.66 14.68 5.46 16.14 14.28 8.75

16.22 22.49 12.50 6.70 20.38 14.97 6.25 16.12 14.31 9.88

2.90

3.87

4.05

4.26

2.03 1.26

1.41 0.79

5.27

5.83

1.46 0.27

1.77 0.70

8.25 8.17

11.10 8.48

Preliminary

Source: After International Dairy Federation (www.dairyinfo.gc.ca/).

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TABLE 1.2 Typical Requirements of Cheese as a Food Ingredient Requirement Crumbles when rubbed Sliceability

Shreddability

Flows freely when shaken

Examples of Food Applications Mixed salads Soup Filled cheese rolls (finger foods) Sandwiches (filled, open, toasted) Cheese slices in burgers Cheese slices on crackers Consumer packs of sliced cheese Pizza pie (frozen/fresh baked) Pasta dishes (lasagna, macaroni and cheese) Cheese sprinklings (on lasagna) Snack coating (e.g., popcorn) Dry soup/sauce mixes

Flowability when blended with other raw materials Ability to “cream” or to form a paste when sheared Nutritional value

Fresh cheese desserts

Meltability upon grilling or baking

All cooked dishes (including sauces, fondues, pizza pie)

Flowability upon grilling or baking

Most cooked dishes (e.g., pizza pie, cheese slices on burgers) Chicken cordon-bleu Deep-fried breaded cheese sticks Deep-fried burgers with cheese inserts Fried cheese dishes

Flow resistance upon deep-frying

Stretchability when baked or grilled Chewiness when baked or grilled Limited oiling-off when baked or grilled Limited browning when baked or grilled

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Cheesecake Tiramisu Homemade desserts Baby foods

Examples of Cheese or Cheese-based Ingredient Feta, Cheshire, Stilton Stilton Swiss-type, Gouda, Edam Swiss-type, Cheddar, Mozzarella Cheddar Cheddar Swiss-type, Cheddar, Mozzarella Mozzarella, Provolone, Cheddar, analog pizza cheese, Monterey Cheddar, Romano, Provolone Grated Parmesan and Romano Cheese powders Cheese powders, enzyme-modified cheese Quark, Fomage frias, Cream cheese

Pizza pie

Cream cheese, Ricotta Mascarpone Cream cheese Dried cheeses, esp. rennet-curd varieties (high in calcium) Mozzarella, Cheddar, Raclette, Swiss, Romano, analog pizza cheese, PCPsa Mozzarella, Cheddar, Swiss, Romano, analog pizza cheese PCPs, Cream cheese PCPs, analog pizza cheese, custom-made Mozzarella or string cheese PCPs, analog pizza cheese Paneer, acid-coagulated Queso Blanco Mozzarella, Kashkaval, young Cheddar, analog pizza cheese Halloumi, Mozzarella, Provolone, Kashkaval, young Cheddar Mozzarella, Kashkaval

Macaroni and cheese Lasagna Pizza pie

Cheddar, Romano Cheddar, Romano, Parmesan Mozzarella, analog pizza cheese

Pizza pie Pizza pie

TABLE 1.2 (continued) Typical Requirements of Cheese as a Food Ingredient Requirement

Examples of Food Applications

Viscosity

Soups Sauces Cheesecake

Flavor

Most cheese dishes, soups Baked products Snack coatings Dressings Baby food Ready-made meals

a

Examples of Cheese or Cheese-based Ingredient Cheese powders, PCPs Cheese powders, Cheddar, Blue cheese, PCPs Cream cheese Cheddar, Romano, Swiss-type, Parmesan Cheese powders, enzyme-modified cheese Cheese powders Cheese powders Dried cheese Cheese powders

Pasteurized process cheese products.

Source: After Fox et al., 2000. With permission.

CHEESEMAKING Though there are numerous cheese varieties, the manufacturing processes of most of them share several common steps. Variations at one or more steps during manufacture produce cheeses of different textures and flavors. The essential steps in cheesemaking and some variations for a few types of cheeses are schematically illustrated in Figure 1.3. These steps are as follows.

MILK PRETREATMENT Milk used for cheesemaking is normally standardized and heat treated. In some cases, milk is homogenized. An acid-producing starter culture is then added. The standardization of milk has become necessary to ensure that milk obtained from several producers or dairies is of a “standard” composition and condition throughout the year. This is critical in cheesemaking because the legal standards of various cheeses specify certain fat-to-protein ratios. The fat-to-protein ratio is determined mainly by the fat-to-casein ratio in the milk (Fox et al., 2000) which can be modified by removing fat or by adding cream or skim milk or skim milk powder, etc. It is also common to add color (annatto or carotene) and calcium (in the form of CaCl2) to the milk and to adjust milk pH to a desired level, known as preacidification. Adding calcium speeds up coagulation or reduces the amount of rennet needed and produces a firmer gel. Heat treatment of milk is primarily intended to destroy the harmful microbial population and enzymes in raw milk to assure product safety and quality. Pasteurization is the most commonly used heat treatment (72°C with 15 s holding time). It © 2003 by CRC Press LLC

Acid Coagulated Soft Cottage Cream Quark Queso Blanco Baker’s Neufchatel Ricotta (Acid and heat coagulated from whey)

Surface Ripened

Semi-soft Brick Bel Paese Havarti Limburger Munster Oka Port du Salut St. Paulin Trappist Taleggio Tilsiter Soft Liderkranz

Concentrated (from Whey)

TYPES OF NATURAL CHEESES

Gjetost Myost Primost Enzyme Coagulated

Internal Bacteria Ripened Very Hard Asiago Grana Parmesan Parmigiano Romano Sabrinz Sardo Hard Caciocavallo Cheddar Cheshire Colby Graviera Ras Cheese with eyes Edam Emmental (Swiss) Gouda Gruyere Maasdam Samsoe

Mould Ripened

Internal Mould Semi-soft Blue Danablu Gorgonzola Roquefort Hard Stilton

Surface Mould Soft Brie Camembert Coulommiers Carre de l’Est

Semi-soft

Soft Salt-cured/ Pickled Domiati Feta

Caerphilly Mahon Monterey Jack Pasta filata Mozzarella Provolone Caciocavallo

FIGURE 1.1 Natural cheeses classified according to the maturation agent used and firmness. (After Vedamuthu and Washam, 1983; Fox et al., 2000.)

not only destroys most of the bacteria present, including lactic-acid bacteria, but also inactivates many enzymes. A gentle heat treatment, known as thermization (60 to 65°C with 15 to 30 s holding time) may also be used advantageously before or after pasteurization (Spreer, 1998). However, many cheeses are still produced from raw milk, especially in Europe (Fox et al., 2000). If the cheeses are made from unpasteurized milk, they must be cured for at least 60 days at not less than 1.7°C (35°F), and the label should indicate the manufacturing date or state “held for more than 60 days.” (NDC, 2000). In traditional cheesemaking, the acid produced by microorganisms present in raw milk lowers the milk pH to a level sufficient for subsequent coagulation. However, if the milk undergoes a heat treatment, selected cultures of lactic-acid bacteria

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TABLE 1.3 Classification of Cheeses by the Distinctive Manufacturing Process Involved Distinctive Process Involved Curd particles matted together Curd particles kept separate Bacteria-ripened throughout interior Prolonged curing period Pasta filata Mold-ripened throughout interior Surface-ripened mainly by bacteria and yeasts Surface-ripened mainly by mold Curd coagulated mainly by acid

Characteristics

Example Cheeses

Close texture, firm body Slightly open texture Gas holes or eyes with eye formation throughout cheese Granular texture; brittle body Plastic curd; stringy texture Visible veins of mold (blue-green or white); piquant, spicy flavor Surface growth; soft, smooth, waxy body; mild to robust flavor Edible crust; soft, creamy interior; pungent flavor Delicate soft curd

Cheddar Colby, Monterey Jack Swiss (large eyes), Edam or Gouda (small eyes) Parmesan, Romano Mozzarella, Provolone Blue, Gorgonzola, Roquefort Brick, Limburger Brie, Camembert Cottage, Cream, Neufchatel

Source: After NDC, 2000. With permission.

TABLE 1.4 Empirical Texture/Rheological Parameter Values Used in Cheese Classification Logarithmic Scale Values Cheese Type Very Hard Hard Semihard Soft

Moisture (%)

Viscosity Factor

Elasticity Factor

Springiness Factor

< 25 25–36 36–40 > 40

>9 8–9 7.4–8 < 7.4

> 6.3 5.8–6.3 < 5.8 < 5.8

> 2.3 2–2.3 1.8–2 < 1.8

Source: After Davis, 1965.

TABLE 1.5 United States Federal Standards for the Maximum Moisture and Minimum Milk Fat for Classes of Cheese Designated by Consistency Consistency

Maximum moisture content (%)

Minimum milk fat in solids (%)

Hard grating Hard Semisoft Semisoft part skim Soft

34 39 50 (>39) 50 Not specified

32 50 50 45 (<50) 50

Source: After CFR, 1998.

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TABLE 1.6 Typical Composition (% by Weight) of Milk and Some Cheese Varieties Moisture

Protein

Total Fat

Total Carbohydrate

Fat in Dry Matter

Ash

Calcium

Phosphorus

Salt

pHa

Cow Goat Sheep Buffalo

87.3 87.7 80.7 82.8

3.4 2.9 4.5 4.8

3.7 4.5 7.4 7.5

Milk 4.8 4.1 4.8 4.8

29.1 36.6 38.3 41.7

0.7 0.8 1.0 0.8

0.12 — — —

— — — —

0.90 0.95 1.10 0.85

6.7 — — — —

Dry curd cottage Creamed cottage Quark Cream Neufchatel

79.8 79.0 72.0 53.7 62.2

17.3 12.5 18.0 7.5 10.0

0.42 4.5 8.0 34.9 23.4

Acid Coagulated 1.8 2.7 3.0 2.7 2.9

2.1 21.4 28.5 75.4 62.0

0.7 1.4 — 1.2 1.5

0.03 0.06 0.03 0.08 0.07

0.10 0.13 0.35 0.10 0.13

nil 1.00 — 0.73 0.75

5.0 5.0 4.5 4.6 4.6

Chhana Queso Blanca, acid Ricotta from 3%-fat milk Ricotone from whey and milk

53.0 55.0 72.2 82.5

17.0 19.7 11.2 11.3

25.0 20.4 12.7 0.5

Heat-Acid Coagulated 2.0 3.0 3.0 1.5

53.2 44.8 45.7 2.9

— — — —

— — — —

— — — —

— 3.00 <0.5 <0.5

— 5.4 5.9 5.8

Queso Blanco-rennet Queso de Frier Italian fresh cheese

52.0 52.4 49.0

23.0 23.0 28.0

Unripened-Rennet Coagulated 20.0 — 42.0 19.5 — 41.0 16.0 — 31.4

— — — —

— — —

— — —

2.50 3.00 nil

5.8 5.8 6.5

Type and Cheese

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TABLE 1.6 (continued) Typical Composition (% by Weight) of Milk and Some Cheese Varieties Type and Cheese

Total Fat

Total Carbohydrate

Fat in Dry Matter

Ash

Calcium

Phosphorus

Salt

pHa

50.3 47.5 50.0 50.0

3.7 5.2 5.1 5.0

0.39 0.49 0.53 —

0.35 0.34 0.39 —

2.10 — 3.50 —

6.9 4.4 6.5 — —

51.7 46.9 47.6 44.6 46.9 51.6

3.4 3.9 4.2 3.3 2.8 3.7

0.68 0.70 0.73 — — 0.72

0.46 0.55 0.54 — — 0.47

0.65 0.82 0.96 1.20 2.20 1.80

5.3 5.8 5.7 5.6 5.9 6.2

24.9 28.1 25.6 19.4

Hard Cheese Low Temperature 33.1 1.3 52.4 26.9 — 45.2 26.6 2.1 45.1 21.6 2.2 47.1

3.9 3.6 4.7 2.6

0.72 — 0.76 0.52

0.51 — 0.50 0.37

1.80 1.50 2.20 1.00

5.5 5.8 5.4 5.3

35.7 31.8 28.4 24.8

Hard Cheese High Temperature 25.8 3.2 36.5 26.9 3.6 39.0 27.4 3.4 43.7 28.3 — —

6.0 6.7 3.5 4.7

1.18 1.06 0.96 —

0.69 0.76 0.60 —

3.00 3.00 1.20 —

5.4 5.4 5.6 5.2

Moisture

Protein

Camembert Feta Blue Gorgonzola

51.8 55.2 42.0 36.0

19.8 14.2 21.0 26.0

Soft Ripened High Acid 24.3 0.5 21.3 — 29.0 2.3 32.0 —

Colby Gouda Edam Fontina Havarti-Danish Munster

40.0 41.5 41.4 42.8 43.5 41.8

25.0 25.0 25.0 24.2 24.7 23.4

31.0 27.4 27.8 25.5 26.5 30.0

Cheddar Manchego, Spain Provolone Mozzarella

36.7 37.9 40.9 54.1

Parmesan Romano Swiss Kaflatyri, Greece

29.2 30.9 37.2 34.2

a

pH at time of retailing.

Source: After Hill, 1995; Fox et al., 2000.

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Semihard Washed 2.0 2.2 1.4 — — 1.1

FIGURE 1.2 United States total (excludes cottage cheese) and Cheddar and Mozzarella cheese production trends. (After Annual Summary of Dairy Market Statistics of years 1997 through 2001. Agricultural Marketing Service, USDA. Mozzarella data from University of Wisconsin Dairy Marketing Web site: www.aae.wisc.edu/future.)

must be added. The type of bacteria added depends on the cheese type and cheesemaking protocol used. These bacteria break down the milk sugar, lactose. Lactic acid produced during this process lowers the pH. An alternative to adding starter culture is to acidify the milk directly by adding lactic acid or hydrochloric acid or gluconic acid-δ-lactone, an acidogen. Though this direct acidification allows better control, starter culture remains active in the cheese during ripening, months after cheese manufacture, and contributes to cheese flavor. Therefore, direct acidification is used primarily when manufacturing cheese varieties for which texture is more important than flavor, e.g., cottage cheese, quark, Mozzarella, etc. (Fox et al., 2000). Walstra and Jenness (1984) reported an increase in cheese yield when using pasteurized milk. This is due to casein–whey protein interaction and greater moisture retention. One disadvantage of pasteurization, however, is that aged cheeses develop their flavors more slowly and to a lesser extent than cheeses made with raw milk (Kristoffersen, 1985). This has led many cheesemakers to use milk heated to 60 to 68.5°C for 15 s or less instead of pasteurized milk (Johnson, 1998).

COAGULATION Since pretreating milk is a fairly recent practice relative to the history of cheesemaking, many consider coagulation as the first and most important step in cheesemaking. Coagulation is the step during which milk undergoes a profound physical and rheological change, that is gelation. Milk gel is formed by aggregation of milk protein, the caseins. This can be accomplished by: 1. The action of a proteolytic enzyme 2. Lowering the pH below the isoelectric point of protein (~ 4.6) 3. Heating to about 90ºC at a pH of about 5.2 (i.e., higher than the isoelectric point)

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Milk

Pretreatment (Standardization, Homogenization, Heat treatment, Starter addition)

Coagulation (Rennet /Coagulant addition)

Syneresis (Cutting, Stirring, Scalding/cooking, Whey removal)

Soft Cheese (e.g., Camembert)

Semi Hard Cheese (e.g., Gouda)

Hard Cheese (e.g., Cheddar)

Pasta Filata Cheese (e.g., Mozzarella)

Moulding

Hot water Washing

Cheddaring

Heating & Stretching

Brining

Pressing & Moulding

Milling

Moulding

Storage

Brine Salting

Dry Salting

Brine Salting

Turning

Waxing & Wrapping

Ripening

Packing

FIGURE 1.3 Major steps in cheesemaking (actual steps and/or conditions for a particular cheese may vary). (After Scott et al., 1998; Fox et al., 2000.)

Among these, enzymatic coagulation is the most popular. Acid coagulation via food-grade acidulants is used to manufacture quark, cottage, and cream cheeses. Heat coagulation is used for Ricotta and Queso Blanco cheeses (Johnson and Law, 1999; Fox et al., 2000). Enzymatic coagulation is accomplished by enzymes from animal (e.g., calf rennet, porcine pepsin), plant (e.g., Cynara Cardunculus from Cardom, Circium and

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Carlina Spp. from thistle), or microbial (e.g., Endothia parasitica, Rhizomucor miehei) origin. Enzymatic coagulation consists of two phases. During the first or primary phase, the hydrophilic hairy structure, stabilized by steric hindrance, of κ-casein is cleaved off at Phe105-Met106 bond. The secondary or clotting phase is initiated as 85 to 90% of the κ-casein is cleaved and results in the aggregation of the altered protein micelles. The κ-casein loses its ability to stabilize the remainder of the caseinate complex. The result is soluble glycomacropeptides (residues 106–169), and hydrophobic, para-κ-casein (residues 1–105). As the protein micelles continue to aggregate, a loose network forms, entrapping fat globules, water, and water-soluble materials. The para-κ-casein left on the micelle is still connected to α- and β-casein, but it is highly hydrophobic and basic, leading to destabilization of the micelle. Gel formation by association of the modified micelles in the secondary phase is highly dependent on the milk’s temperature and calcium content. The coagulation rate is also highly dependent on the concentration and activity of the enzyme solution. Increases in both of these factors shorten coagulation time and increase firmness. Although it is not clear how the micelles aggregate, there are two hypotheses. One is that hydrophobic bonding occurs between the para-κ-casein. The other is that calcium and calcium phosphate bonding occurs in α- and β-caseins. Other factors that affect aggregation are casein concentration and milk pH. The aggregation rate is proportional to the square of casein concentration (Lomholt and Qvist, 1999). As discussed previously, the effect of renneting action strongly depends on milk pH. Each milk-clotting enzyme has an optimum pH at which it is most active. Extremes in acid or base also denature the enzymes but not as irreversibly as high temperatures. Lowering the pH leads to a decrease in coagulation time mainly due to increased enzyme activity, but rate of aggregation is also affected (Lomholt and Qvist, 1999). The aggregation of casein micelles forms strands of casein particles of about three particles wide and 10 particles long, alternated by some thicker nodes of particles (Walstra et al., 1999). After this, the aggregates grow more compact (Bauer et al., 1995). The time when aggregates become visible is known as the flocculation time or rennet coagulation time (RCT). When the flocs grow to occupy the entire volume, the gel is said to have been formed. The gel network is very irregular, with many pores several micrometers in width (Walstra et al., 1999). Aggregation of casein micelles into chains, then into strands and clusters, and eventually into an amorphous mass has been observed by microscopic evaluation in both acid- and enzyme-coagulated systems (Kimber et al., 1974; Glaser et al., 1980). From a rheological standpoint, casein aggregation and gel formation represent an increase in viscosity and gel modulus, respectively. The viscosity increase in renneted milk, however, is observed after an initial lag time (~ 60% RCT) during which the viscosity may actually decrease slightly due to a decrease in voluminosity of the casein micelles following the release of macropeptides (Fox et al., 2000). After this, the viscosity increases exponentially up to the onset of gelation (i.e., 100% RCT). The viscosity increase and the concomitant change in physical properties have been used to identify the RCT (Kopelman and Cogan, 1976; Ay and Gunasekaran, 1994; Fox and McSweeney, 1998; Konuklar and Gunasekaran, 2002). The modulus of the gel increases markedly at gelation time. In fact, gelation time is defined as the time at which the gel modulus increases rapidly. The initial

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102 80 101 70

G′ G′′ δ

gel point

10 –1

10 –2

60

50

δ(°)

G′, G′′ (Pa)

100

40

10 –3

30

10 –4

20 500

1000

1500

2000

2500

3000

3500

Time (s)

FIGURE 1.4 Changes in storage (G′) and loss (G″) moduli and phase angle (δ) of the rennetted milk during coagulation. The gel point is identified at G′–G″ crossover which occurs at δ = 45°. (After Uludogan, 1999.)

increase in modulus is due to the increase in number of contacts between micelles. Subsequently, the strengthening of intermicellar bonds translates into increased gel modulus (Walstra et al., 1999). It has been premised that the increase in gel firmness is due to the increase in the number of bonds with time (Lomholt and Qvist, 1999). This premise was based on the observation that, though the modulus continues to increase, the phase angle stays relatively constant, i.e., the nature of the bonds does not change (Dejmek, 1987; Lopez et al., 1998). Figure 1.4 shows a typical plot depicting changes in viscoelastic moduli and the phase angle of the coagulating milk gel system. As more micelles aggregate, they may fuse together and strengthen the bonds (Lomholt and Qvist, 1999). The modulus continues to increase for several hours after gelation time, signifying gel firming. The microstructure of the gel has been observed to become coarser with larger pores and thicker strands (Lomholt and Qvist, 1999). Carlson et al. (1987) presented a detailed analysis of all aspects of milk coagulation kinetics in a four-part series of papers.

SYNERESIS Due to its porous nature, the coagulum has the propensity to contract and expel entrapped liquid. This is known as syneresis, an important step in concentrating the milk. To a great extent, the success of the remaining cheesemaking steps depends on satisfactorily draining the whey. Also, most of the lactose, a substrate for postproduction microbial activity, is lost in the whey, which helps to prevent some

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adverse effects (Scott et al., 1998). In an undisturbed gel, however, syneresis occurs very slowly. Therefore, during cheesemaking, syneresis is accelerated by cutting the coagulum into small cubes, which increases the surface area and reduces the distance for the diffusion process to facilitate whey removal. Syneresis can also be enhanced by decreasing the pH or increasing the temperature of the coagulum (Walstra et al., 1999). Cutting the coagulum to facilitate faster whey removal must be timed precisely. If the coagulum is cut too soon, some milk solids leave the curd along with whey. Whey normally carries water-soluble components including lactose, whey proteins, salts, peptides, and other nonprotein nitrogenous substances (Scott et al., 1998). If it is cut too late, more water gets trapped in the matrix, resulting in high-moisture cheese. Therefore, cheesemakers have been striving for many years to identify the correct curd-cutting time. Since the coagulum firmness continues to increase uneventfully over several hours, it is hard to determine an optimal curd-cutting time. Many instrumented and so-called objective curd-cutting-time predictions have been made (Hori, 1985; Payne et al., 1993; Gunasekaran and Ay, 1996; O’Callahan et al., 1999). Some commercial units are available based on some of these techniques (Fox and McSweeney, 1998; O’Callahan et al., 1999). However, there is still no universal procedure to identify optimal curd-cutting time. Most large factories apply a set time schedule, depending on the cheese type, to cut the curd after adding the rennet. In many smaller cheesemaking facilities, cutting time is still determined by the subjective judgment of the cheesemaker. Recently, Konuklar and Gunasekaran (2002) reported a novel rheological technique for identifying the curd-cutting time. They observed that the viscosity versus time curves during coagulation under continuous steady shear exhibit several abrupt peaks. The first peak over 40 kPa.s coincides with cutting time determined by an experienced cheesemaker during Cheddar, Swiss, and Gouda cheesemaking (Figure 1.5.) Syneresis is the process that a cheesemaker can use to closely control the moisture content of the cheese and hence the microbial and enzymatic activity in the cheese, which affects ripening, stability, and quality of the cheese (Fox et al., 2000). Therefore, it is specific to a particular cheese type or cheese family. Walstra et al. (1999) listed the following factors as affecting syneresis: firmness of gel at cutting; surface area of the curd; any applied pressure; acidity; temperature; composition of the milk; and other variables. Pearse and Mackinlay (1989) discussed the mechanism and biochemical aspects of syneresis. Stirring exerts pressure, causing curd particles to collide, and facilitates their compression for a short time. Stirring also keeps the curd from settling in the vat. For Cheddar- and Swiss-type cheeses, the cut coagulum is not stirred immediately after cutting. The curd–whey mixture is cooked (at about 40ºC for Cheddar-type and 50ºC for Swiss-type) and vigorously agitated during cooking. For soft cheeses, the curd is ladled and hooped which allows whey to drain without stirring. Cooking the curd, also known as scalding, enhances syneresis by facilitating contraction of the protein matrix. Heating further enhances acid production by the starter organisms. Lowering pH, combined with increased temperature, not only helps to expel more whey but also affects the dissolution of calcium phosphate, and thus has major implications for characteristics of the cheese (Johnson and Law, 1999). The scalding

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FIGURE 1.5 Viscosity (η) of coagulating milk system vs. time after rennetting measured under a continuous steady shear stress of 0.2 Pa. The first viscosity peak over 40 kPa.s coincided with the cutting point (CTP) determined manually during (a) Cheddar; (b) Swiss; and (c) Gouda cheesemaking. (After Konuklar and Gunasekaran, 2002. With permission.)

step can be used to distinguish four major groups of cheese — excluding soft cheeses, some of which may be scalded (Scott et al., 1998): 1. Textured cheeses such as Cheddar or Cheshire 2. Pasta filata types or kneaded cheeses 3. Cheeses untextured in the vat (e.g., Edam and Gouda) and those which acquire texture later (e.g., Tilsiter and Emmental) 4. Blue-veined cheeses

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To manufacture some cheeses (e.g., Edam, Gouda, or Havarti), the curd is washed by adding water to the curd–whey mixture. This accomplishes two things: 1. It adjusts the pH of the cheese independently of its moisture content by removing lactose and other solubles from the curd. 2. It enhances whey removal by adding hot water to raise the curd temperature, as is the case during direct heating. It should be noted that using hot water to stretch pasta filata cheeses (e.g., Mozzarella, Provolone, etc.) is not considered as washing (Scott et al., 1998).

SHAPING

AND

SALTING

When the curd is at the desired moisture content and pH, it is separated from the whey. The curd particles are subsequently shaped into some form and salted (primarily by NaCl), not necessarily in that order. These steps, though common for most cheeses, are performed very differently, depending on the cheese type. As Johnson and Law (1999) stated, the manner in which cheese curd and whey are separated can affect texture as well as color and flavor. When manufacturing hard cheeses such as Cheddar, the curd–whey slurry is pumped into a vat with a perforated bottom for whey removal. The curd is “cheddared” for about 90 min. Cheddaring is the process in which curd particles are allowed to fuse or “mat” together. The mats are then cut into slabs and stacked on top of each other. Physical properties and pH of the curd at this stage affect curd fusion and appearance of the finished cheese (Olson, 1995). When the desired pH has been reached, the slabs are milled into small pieces. At this stage, the curd may be sprayed with warm water and stirred for further whey removal. Salt is sprinkled on at a level of about 2 to 3% which expels additional whey. The salted curd is then hooped in molds and pressed overnight. Manufacturing steps for Mozzarella and other pasta filata cheeses differ markedly after the milling stage described above. The milled curd is “kneaded,” i.e., heated and stretched in warm water (about 60 to 70°C) using an open-channel, single-screw or twin-screw extruder/auger. This transforms the curd into a cohesive, viscoelastic mass. Due to the conveying action of the auger, the curd mass gets stretched into a continuous stream of molten material. This stretching step is unique to Mozzarella manufacturing. It imparts the characteristic oriented microstructure and related textural attributes of these cheeses (Oberg et al., 1993; Ak and Gunasekaran, 1997). The molten cheese is then placed into molds and cooled. When the cheese is cool enough to keep its shape, the mold is removed and the cheese is salted by dropping it in a nearly saturated brine solution (about 25% salt) at 1 to 4°C. The cold brine temperature cools the cheese further. In fact, much of the total cooling of Mozzarella occurs during brining (Nilson, 1968). Brine salting is a slow process, taking several days for uniform salt distribution within a cheese block. It should be noted that, concomitant with salt intake, the cheese loses moisture. The salt and moisture gradients in a cheese during salting are opposite of each other (Turhan and Gunasekaran, 1998; Walstra et al., 1999;

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Fox et al., 2000). Though brine salting is the traditional method, salting of Mozzarella can also be done by adding salt directly to the curd just before stretching, during stretching, or between stretching and molding. This direct salting reduces the subsequent brining time. Another major variation is surface salting. Salt is rubbed directly on the cheese surface (e.g., Romano and Gorgonzola). This is repeated for several days so the salt diffuses throughout. In many other cheeses, surface salting and brining are used in combination (e.g., Gruyere and Emmental). Regardless of the method used, salting is a vital step in cheesemaking because unsalted cheese is virtually tasteless (Olson, 1995). Salt also plays a major role in the texture, flavor, and microbial quality of cheese (Kindstedt et al., 1992; Paulson et al., 1998; Fox et al., 2000). Salt inhibits the growth of certain bacteria, which are harmful to the cheese and cause spoilage, especially on the surface. It further assists in dissolving the casein and in rind formation, as well as in slowing down enzyme activity. Salt concentration in cheese varies greatly from less than 1% in Emmental to 7 to 8% in Domiati (Fox and McSweeney, 1998). The salt content may also vary considerably within a cheese block due to the slow diffusion of salt. Thus, there is more water and less salt at the center of a cheese block compared to at the surface (Prentice, 1993). This unevenness in the salt (and water) distribution also leads to variation in the rheological properties of the cheese within the block (Visser, 1991). As already noted, hard and semihard cheeses are shaped by applying external pressure. Pressing expels whey and facilitates faster curd fusion into an integral mass of a desired shape with a rind. Though simple enough, pressing is perhaps the least understood step in cheesemaking (Scott et al., 1998). The time, pressure, and efficiency of pressing are related to the condition of the curd at pressing time and the decrease in pH during pressing (Johnson and Law, 1999). Sometimes pressing is done in conjunction with vacuum to force out any entrapped air. The complex nature of the interrelationships among many of the cheesemaking parameters makes controlling cheese properties very hard. Tables 1.7a to 1.7d present how various cheesemaking and technological factors affect cheese quality. This set of four tables was prepared in 1961 for the Danish Samso cheese (Birkkjaer et al., 1961), but the information it contained is generally valid for other hard/semihard cheeses (e.g., Gouda).

RIPENING Ripening is the natural process of microbial and biochemical reactions that occurs in a cheese after its manufacture and during storage. Ripening gives different cheeses their unique flavors, textures, and appearances. Except for some soft cheeses (e.g., cottage cheese, cream cheese, quark, etc.), almost all cheeses are held under controlled conditions to develop distinct attributes. Ripening essentially results from the action of microorganisms present within the curd mass and on its surface. Ripening is also influenced by residual enzymes present in the cheese curd. Cheeses are ripened over a range of time from several days (e.g., Mozzarella) to more than a year (e.g., Cheddar).

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Fox et al. (2000) list the following ripening agents in cheese: 1. 2. 3. 4.

Coagulant — chymosin or other suitable proteinase Milk — some indigenous enzymes contained in milk, e.g., plasmin Starter culture — host of enzymes released upon cell death and lysis Secondary microflora — microflora that perform some specific secondary function (e.g., propionic acid, bacteria, and yeasts and molds) 5. Exogenous enzymes — proteinases, peptidases, and lipases added by cheesemakers to accelerate ripening

TABLE 1.7A Effect of Cheesemaking Parameters on Cheese Quality (Prepared for Danish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Harder Cheese and Their Primary and Secondary Effects Factor No. Efficiencya 1

2

+

3c

+

4

+

5c

(+)

6c

+

Modifications

Primary Effect

Secondary Effectb

Use fresh milk or Slightly improves whey Cheese becomes slightly pasteurize at expulsion less acid. Ca content approx. 70ºC increases slightly (158ºF) Reduce or omit Improves whey expulsion Cheese becomes more acidic. Ca content addition of water to increases the milk Add CaCl2 to the Improves whey expulsion Ca content increases. milk Adding more than 40 g/100 kg milk (0.68 oz/110 lbs milk) may give an off flavor Increase amount of Slightly improves whey Cheese becomes more acidic. culture/starter or expulsion from the curd Ca content decreases. prolong preToo much culture/starter or ripening period of too long a preripening the milk makes cheese sour, short, and flaky Lower renneting At the same cooking A renneting temperature temperature temperature, whey drain that is too low results in in the vat increases weak curd and thus a slightly due to a greater bigger loss in the whey. rise in temperature. If no Ca content decreases cooking occurs, whey is reduced, and cheese becomes softer Cut curd into Improves whey expulsion Very fine cutting may result smaller cubes in a bigger loss in whey. Many of the “grains” may retain some of the whey during molding/pressing, so cheese may be softer

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TABLE 1.7A (continued) Effect of Cheesemaking Parameters on Cheese Quality (Prepared for Danish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Harder Cheese and Their Primary and Secondary Effects Factor No. Efficiencya 8

+

9

+++

10

+++

12

++

13c

+++++d

14

++

15c

+

Modifications

Primary Effect

Secondary Effectb

Reduce or omit addition of water during cooking

Improves whey expulsion Cheese becomes sour and of curd, esp. by reducing may eventually become relatively large additions too firm in the curd and of water thus will often break. Ca content increases Increase cooking Increases whey expulsion Cheese becomes less acidic and tougher At high temperature in the vat temperatures, esp. above 40ºC (105ºF); cheese may develop an off flavor Avoid a temperature Increases whey expulsion Cheese becomes less acidic. drop during final in the vat and during Ca content increases stirring pressing Reduce or omit salt Cheese “grains” swell less Cheese becomes less acidic. addition to whey and thus retain less whey Ca content increases. Brine salting may be prolonged during final stirring to get adequate salt content Leave cheese at Cheese liberates a Ca content decreases cooking relatively large quantity considerably temperature in of whey before rind is water or whey after closed pressing in the vat Increase Increases amount of whey Cheese becomes slightly temperature in draining during pressing less acidic. If it is not pressing room cooled longer, the risk of cracked rind and gas from coliforms may increase Prolong pressing Increases amount of whey You might see adhesion, time (possibly until draining during pressing especially when using the next morning) cotton cloths and a relatively high pressing temperature. Counteract this by using nylon cloths and cooling during last part of pressing

a

+ Represents relative efficiency, the higher the better. (+) means that the effect depends on other conditions. Shaded effects reduce acidity; bold-faced effects increase acidity. c Factor numbers 3, 5, 6, 13, and 15 show modifications that influence either acidity or firmness but not both. All other factors influence both. d An extraordinary change in technique, 3 hours at 38ºC. b

Source: After Birkkjaer et al., 1961. With permission.

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TABLE 1.7B Effect of Cheesemaking Parameters on Cheese Quality (Prepared for Danish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Softer Cheese and Their Primary and Secondary Effects Factor No. Efficiencya 1

Modifications

Primary Effect

Pasteurize at 65ºC Slightly reduces whey (150ºF) or above expulsion (above 80ºC 75ºC (166ºF), esp. [175ºF] somewhat) above 80ºC (175ºF)

2

+

3c

+

4

+

5c

(+)

6c

+

8

+

Add water to the milk Reduce or omit addition of CaCl2 to the milk Reduce amount of culture/starter or shorten or omit preripening period of the milk

Reduces whey expulsion Reduces whey expulsion

Slightly reduces whey expulsion

Secondary Effectb Cheese becomes (above 80ºC [175ºF] somewhat) more acidic. Ca content decreases. High pasteurization temperatures often lead to weak eye formation Cheese becomes less acidic. Ca content increases Ca content decreases

Cheese becomes less acidic. Ca content decreases. Not enough culture/starter or a pre-ripening that is too short may produce a tough cheese with an off flavor A renneting temperature that is Raise renneting At the same cooking too high will cause cutting temperature temperature, whey problems since the coagulum expulsion in the vat is slightly reduced due to a will be too firm during cutting. Ca content increases smaller rise in slightly temperature. If no cooking occurs, whey expulsion increases and cheese is firmer Cut curd into bigger Reduces whey expulsion Big curd cubes can be easily cubes stirred into smaller pieces, causing greater whey drain than intended and greater loss in the whey. Many “grains” may retain some whey when cheese is molded so cheese becomes softer than intended Add more water Reduces whey expulsion, Cheese becomes less acidic. Ca content decreases. If you during cooking esp. when relatively add more than 20% of the large amounts of water quantity of milk, cheese often are added develops an off flavor

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TABLE 1.7B (continued) Effect of Cheesemaking Parameters on Cheese Quality (Prepared for Danish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Softer Cheese and Their Primary and Secondary Effects Factor No. Efficiencya

Primary Effect

Secondary Effectb

Reduces whey expulsion

Cheese becomes more acidic. Cheese which is already acidic may crack easily Cooling without water leads to acidic cheese. Cooling with water leads to small or no change in acidity, depending on amount of water. Ca content decreases Cheese becomes more acidic. Ca content decreases. Shorten brine salting so cheese is not too salty. Heavy salting in the vat may restrain fermentation, producing cheese with high pH Ca content increases

Modifications

9

+++

Lower cooking temperature

10

+++

Cool curd cubes for Reduces whey expulsion about 15 min before in the vat and during final stirring ends pressing

12

++

Add more salt to whey during final stirring

Curd cubes swell more and retain more whey

13c

+++++d

Rind closes earlier, slowing whey expulsion

14

++

Reduce pressing temperature or drain the whey faster Lower temperature in pressing room

15c

+

Use low pressure to start or shorten pressing time

Less whey is pressed out of the cheese

Reduces whey expulsion during pressing

a

Moderate cooling yields more acidic cheese. Cooling too soon retards fermenting and gives high pH cheese. Cooling after or during last part of pressing, if long enough, slows rind cracking and coliform production Low pressure and short pressing time may cause bad rind closing, fermenting in rind (cracked rind) and open texture

+ Represents relative efficiency, the higher the better. (+) means that the effect depends on other conditions. Shaded effects reduce acidity; bold-faced effects increase acidity. Shaded and bold-faced effects may result in more or less acidity. c Factor numbers 3, 5, 6, 13, and 15 show modifications that influence either acidity or firmness but not both. All other factors influence both. d An extraordinary change in technique, three hours at 38ºC. b

Source: After Birkkjaer et al., 1961. With permission.

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TABLE 1.7C Effect of Cheesemaking Parameters on Cheese Quality (Prepared for Danish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Less Acidic Cheese and Their Primary and Secondary Effects Factor No. Efficiencya

Modifications

Primary Effect

Use raw milk or Slightly improves whey pasteurize at approx. expulsion 70ºC (158ºF) Add water to the milk Reduces whey expulsion

Secondary Effectb

1

+

2

++

4

++

Reduce amount of culture/starter, or shorten preripening period of the milk

7c

++

8

+++

9

++++++

10

++

11c

+

Start cooking earlier Development of lacticby shortening acid bacteria is prestirring or restrained and whey intermediate stirring, is expelled and prolong final stirring correspondingly Add more water Greater diffusion of sugar Adding more than 20% during cooking and Ca from curd cubes water may produce a to the whey cheese with an off flavor. Increasing the water added produces cheese with a higher water content and lower Ca content Raise cooking Development of lacticCheese becomes firmer temperature acid bacteria in the vat is and tougher. At high slowed. Whey is temperatures, especially expelled earlier above 40ºC (105ºF), cheese develops an off flavor Avoid a drop in Development of lacticCheese becomes firmer. temperature during acid bacteria is slowed Ca content increases final stirring Prolong the time for Acidity is slightly Cheese consistency final stirring so total changed because becomes more supple stirring time is longer development of lactic(flexible), so cheese is acid bacteria is slowed. easier to cut But because curd cubes are kept in the whey longer, more Ca is discharged

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Less acidification

Cheese becomes slightly firmer. Ca content increases slightly Cheese becomes softer. Ca content decreases Cheese becomes a little softer. Ca content increases. Not enough culture/starter and a weak preripening produces a tough cheese with an off flavor Ca content increases

TABLE 1.7C (continued) Effect of Cheesemaking Parameters on Cheese Quality (Prepared for Danish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a Less Acidic Cheese and Their Primary and Secondary Effects Factor No. Efficiencya 12

14

Modifications Reduce or omit addition of salt to whey during final stirring

+

Cool cheese early, or carry through pressing at high temperature 40ºC (105ºF)

Primary Effect

Secondary Effectb

Curd cubes swell less and Cheese becomes firmer. thus retain less whey Ca content increases. Brine salting should be prolonged to get an adequate salt content Development of lacticCooling results in a softer acid bacteria is slowed cheese. Cooling too early may result in high pH cheese. High pressing temperature makes a firmer cheese, and the danger of a cracked rind and fermentation is increased if it is not cooled after pressing

a

+ Represents relative efficiency, the higher the better. Shaded effects result in softer cheese; bold-faced effects result in firmer cheese. Shaded and bold-faced effects may result in softer or firmer cheese. c Factor numbers 7 and 11 show modifications that influence either acidity or firmness but not both. All other factors influence both. b

Source: After Birkkjaer et al., 1961. With permission.

Various methods of influencing cheese ripening are summarized in Table 1.8. The primary factors in this process are (Scott et al., 1998): 1. Storage temperature and humidity, humidity being less important for cheeses hermetically packed (e.g., with a wax coating). 2. Chemical composition of the curd — fat content, level of amino acids, fatty acids, and other by-products of enzymatic action. 3. Residual microflora of the curd — primarily from the starter culture. The cheesemaker can do little to influence it except in the case of blue-veined or surface-ripened cheeses. Temperature and humidity are factors that cheesemakers can control during ripening. In general, higher temperatures increase the microbial growth rate and other biochemical reactions occurring in the curd. Thus, cheeses matured at different temperatures can have different flavor profiles. Accordingly, proper control of storage temperature is essential. Variety-specific storage temperature control protocols have

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TABLE 1.7D Effect of Cheesemaking Parameters on Cheese Quality (Prepared for Danish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a More Acidic Cheese and Their Primary and Secondary Effects Factor No. Efficiencya 1

+

2

++

4

++

7c

++

8

+++

9

++++++

10

++

11c

+

Modifications

Primary Effect

Secondary Effectb

Pasteurize at 65ºC Slightly reduces whey Cheese becomes slightly (150ºF) or above 75ºC expulsion (above 80ºC softer (above 80ºC [175ºF] (166ºF), esp. above [175ºF] somewhat) somewhat). Ca content 80ºC (175ºF) decreases slightly Reduce or omit addition Improves whey expulsion Cheese becomes a little of water to the milk from the curd firmer. Ca content increases Increase amount of Increases acid production Cheese becomes a little culture/starter or firmer. Ca content prolong preripening of decreases. Too much the milk culture/starter and too strong preripening causes cheese to be sour, short, and flaky Cook longer by Lactic-acid bacteria have Ca content decreases. A prolonging prestirring better growth conditions long intermediate stirring or intermediate stirring, in the vat. Whey time increases the loss in and shorten final stirring expulsion occurs later the whey because curd is correspondingly easily stirred into pieces Reduce or omit addition Less diffusion of sugar Cheese retains more Ca and of water during and Ca from curd cubes less water. It may become cooking to the whey too acidic and stiff and break. Cheese becomes softer. Cheese which is already acidic may crack Lower cooking Lactic-acid bacteria have Cheese becomes softer. temperature better growth conditions Ca content decreases in the vat. Whey expulsion occurs later Cool curd cubes for Lactic-acid bacteria have A short stirring time about 15 min before better growth conditions produces a tough cheese. end of stirring. A small Cut surface often gets amount of water is horny and greasy after optional storage Shorten the time of final Acidity is changed Cheese becomes softer. stirring so total stirring slightly because Ca content decreases. time is shorter development of lacticBrine salting should be acid bacteria is shortened so cheese is not improved. But because too salty curd cubes are kept in the whey for a shorter time, less Ca is discharged

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TABLE 1.7D (continued) Effect of Cheesemaking Parameters on Cheese Quality (Prepared for Danish Samso Cheese, a Gouda-Type Semihard Cheese) Modifications Needed to Produce a More Acidic Cheese and Their Primary and Secondary Effects Factor No. Efficiencya 12

14

Modifications Increase amount of salt added to the whey during final stirring

+

Primary Effect

Secondary Effectb

Curd cubes swell more and thus retain more whey

Too heavy salting in the vat restrains acidification, which may produce a high-pH cheese Take care that cheese Lactic-acid bacteria have Since rind fermentation can temperature during better growth conditions be prevented rather pressing stays near the during pressing. Pressing effectively by cooling, optimum temperature at high temperatures, or cheese should be cooled of the bacteria cooling too early to low after pressing or during temperatures in the curd, the last part of pressing, restrains acidification if this is long enough

a

+ Represents relative efficiency, the higher the better. Shaded effects result in softer cheese; bold-faced effects result in firmer cheese. c Factor numbers 7 and 11 show modifications that influence either acidity or firmness but not both. All other factors influence both. b

Source: After Birkkjaer et al., 1961. With permission.

been developed to optimize cheese quality. For example, Swiss-type Emmental is held at a low temperature initially (10 to 15°C) to facilitate the growth of lactic-acid bacteria. Later, the temperature is increased (20 to 24°C) so that propionic bacteria can grow. These are essential for the characteristic Emmental flavor and “eyes.” For blue-veined cheeses (e.g., Gorgonzola, Roquefort, Stilton), warm-temperature storage is followed by low-temperature storage (Scott et al., 1998). Prevailing relative humidity during storage (80 to 85%) helps to control the moisture content of cheeses not covered with moisture barriers such as a wax coating. The moisture equilibrium in the cheese changes due to reactions occurring that require or release water. Increase in moisture content during storage affects the solute concentration and microbial growth rate. In general, higher moisture content promotes more vigorous growth of microorganisms than does lower moisture content. In addition to temperature and moisture, other factors such as curd pH, inhibitory substances (e.g., antibodies and salts), and oxidation–reduction potential affect the microbial population in the cheese (Scott et al., 1998; Fox et al., 2000). The enzymes relevant for maturation in most hard cheeses are active in the pH range of 4.9 to 5.5, and in soft cheeses from pH 5.3 to 6.0 (Scott et al., 1998). Protein, fat, and lactose are hydrolyzed (i.e., proteolysis, lypolysis, and glycolysis, respectively) to varying extents during cheese ripening. Among these, proteolysis of casein is the most important. Proteolysis of α- and β-casein occurs due to any

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TABLE 1.8 Methods of Influencing Cheese Ripening and Their Advantages and Disadvantages Method of Influence

Advantages

Increased storage temperature Increased inoculation level in starter culture

Easy to perform No aspects determined by law Natural enzyme balance No aspects determined by law

Proteases/peptidases Lipases, animal, and microbial

Addition of Enzymes Relative low cost Specific effect

Lactobacillus/pediococci Brevibacterium lines Mold Propionic-acid bacteria

Cold/warm treated Lysozyme treated Nonacidic producing

Special Cultures Naturally balanced No aspects determined by law

Modified Starter Cultures Natural enzyme balance Easy to conform to

Disadvantages No specific effect Risk of destroying bacteria Influences pH and consistency

Few usable enzymes Risk of over-ripening Aspects determined by law Use of whey

Opposite effect on pH and consistency Different taste profile

Technologically complex

Source: After Kristensen, 1999. With permission.

residual rennet from what was added for coagulation, natural proteases, and proteases and polypeptidases from starter or adventitious bacteria (Scott et al., 1998). This is essential for cheese flavor development. Fat contains lipophilic flavor compounds, which develop or are released by microbial or enzymatic action through oxidation, decarboxylation, and eventually reduction of decarboxyl compounds. Glycolysis is also initiated by adding a starter culture and reaches its peak in the milk during the preripening stage. Here lactic acid, acetic acid, and CO2 are produced. In some cheeses, citrate is also metabolized into citric acid. Proteolysis is also mainly responsible for changes in the body and texture of cheeses. The breakdown of proteins first involves the conversion of casein fractions into large peptides. These peptides are later broken down to lower molecular weight products. The primary proteolysis in ripening has been defined as the changes in caseins, which can be detected by polyacrylamide gel electrophoresis. The products of secondary proteolysis include the peptides and amino acids that are soluble in the aqueous phase of the cheese. In mature Cheddar, approximately one-third of the protein has been broken down to forms that are soluble at pH 4.6 (Banks, 1998).

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PROCESS CHEESE Process cheese is manufactured from one or more of the natural cheeses described thus far. The basic premise is to stabilize the proteins that are normally affected already during one or more of the cheesemaking steps (Shimp, 1985). This is accomplished by heating and mixing cheeses with some emulsifying salts. The careful selection of cheeses, emulsifying salts, and processing factors allows making process cheeses of varied textures suitable for many end uses. The primary reasons for manufacturing process cheese are (Spreer, 1998): 1. 2. 3. 4.

Long shelf life due to heat treatment and hot filling Wide variety due to a multitude of ingredients and composition Efficient utilization due to spreadable consistency and small portions Upgrading of defective rennet cheese products if the defects limit the shelf life but the products are still edible

The basic steps in the manufacture of process cheese are selecting and blending raw materials, heat processing, and forming and packaging. The raw materials include the natural cheeses, emulsifying salts, and other ingredients. Using the appropriate cheeses in the blend is very critical to obtain the desired texture and flavor. The emulsifying salts, primarily phosphates and citrates, are selected for their ability to disperse and increase hydration of the cheese proteins, which creates smoothness and fat emulsification (Olson, 1995). Other ingredients vary, from dairy and nondairy products such as skim milk powder, whey protein concentrate, spices and vegetables, and muscle food ingredients, etc. In general, good quality raw materials ensure good quality process cheese. Process cheeses can be grouped into three major categories based on composition and consistency: process cheese block, process cheese food, and process cheese spread. The selection of type of heat processing and raw materials for each are done accordingly. A fourth group, process cheese analog based on vegetable fat-casein blend, is also manufactured. Specific manufacturing steps, ingredient selection, etc., are detailed in Caric and Kalab (1993). The manufacturing conditions for sliceable and spreadable process cheese are summarized in Table 1.9. The heat-processing step converts the raw material into a homogeneous product. Heating is performed under atmospheric pressure or vacuum at 85 to 95°C or under pressure at 105 to 120°C. Temperatures under 90°C are desirable to avoid a browning reaction when the raw materials are high in lactose. During heating, the mix is continuously stirred at 60 to 140 rpm. The process duration varies from 4 to 8 min for processed cheese blocks to 8 to 15 min for processed cheese spread (Caric and Kalab, 1993). After heat processing, the melt is conveyed to filling machines where it is molded into different shapes or put into containers. It can also be spread on conveyor belts and sliced. The cheese is then cooled. Cooling is performed fairly slowly (10–12 h) for process cheese blocks and very quickly (15–30 min) for process cheese spread to facilitate softening of the product.

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TABLE 1.9 Manufacturing Conditions for Sliceable and Spreadable Process Cheese Process Cheese Type Condition Average age of the raw material Relative casein content structure Melting salt

Water, how added Temperature Time for melting, stirring pH Process cheese Whole milk powder or whey powder Homogenization Packaging (filling) Cooling Treatment

Sliceable

Spreadable

Fresh to half-mature; mostly fresh 75–90%, mostly long

Combination of fresh, half-mature, and over-ripe 60–75%, short to long

Structure: not creamy Emulsifier: high molecular Polyphosphate, etc.

Structure: creamy Emulsifier: lower or medium molecular Polyphosphate, etc. 20–45%, in portions 85–98ºC/150ºC (185–208ºF/302ºF) 8–15 min, fast 5.7–5.9 5–20% 5–10% Desirable

10–25%, all at once 80–85ºC (176–185ºF) 4–8 min, slow 5.4–5.6 0–2% 0 None 5–15 min Slow (10–20 h) at room temperature Very careful

Fast (15–30 min) in freezing conditions (cool air) Intensive (powerful)

Source: After Kristensen, 1999. With permission.

REFERENCES Ak, M.M. and S. Gunasekaran. 1997. Anisotropy in tensile properties of Mozzarella cheese. Journal of Food Science 62(5):1031–1033. Ay, C. and S. Gunasekaran. 1994. An ultrasonic attenuation measurement for estimating milk coagulation time. Transactions of the ASAE 37(3):857–862. Banks, J.M. 1998. Cheese. In The Technology of Dairy Products, Ed. R. Early, 81–122. London, U.K.: Blackie Academic and Professional. Battistotti, B. et al. 1984. Cheese: A Guide to the World of Cheese and Cheesemaking. New York: Facts on File Publications. Bauer, R. et al. 1995. The structure of casein aggregates during renneting studied by indirect Fourier transformation and inverse Laplace transformation of static and dynamic light-scattering data, respectively. Journal of Chemical Physics 103:2725–2737. Birkkjaer, H.E. et al. 1961. The influence of the cheesemaking technique upon the quality of cheese. Report No. 128, Danish Government Research Institute for Dairy Industry, Hillerod, Denmark. (Translated from Danish and reprinted with permission in the Dairy Pipeline, 1998, Center for Dairy Research, University of Wisconsin-Madison, Madison, WI, 53706, U.S.A.)

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Caric, M. and M. Kalab. 1993. Processed cheese products. In Cheese: Chemistry, Physics and Microbiology, Vol. 2, Major Cheese Groups, 2nd ed., Ed. P.F. Fox, 467–505. New York: Chapman and Hall. Carlson, A., C.G. Hill, Jr., and N.F. Olson. 1987. Kinetics of milk coagulation: I-IV. Biotechnology and Bioengineering 29(4):582–589, 590–600, 601–611, 612–624. CFR, 1998. Cheeses and Related Cheese Products. Code of Federal Regulations, Title 21, Part 33, pp 294–346. United States Department of Health and Human Services, Food and Drug Administration, Washington. Davis, J.G. 1965. Cheese, Vol. 1, Basic Technology. London: Churchill Livingstone. Dejmek, P. 1987. Dynamic rheology of rennet curd. Journal of Dairy Science 70:1325–1330. Doeff, G. 1994. Cheese in the U.S.A. Dairy Foods Sept., p. D. Fox, P.F. 1993. Cheese: an overview. In Cheese: Chemistry, Physics and Microbiology, Vol. 1, General Aspects, Ed. P.F. Fox, 1–32. London: Chapman and Hall. Fox, P.F. et al. 2000. Fundamentals of Cheese Science. Gaithersburg, MD: Aspen Publishers, Inc. Fox, P.F. and P.L.H. McSweeney. 1998. Dairy Chemistry and Biochemistry. London: Blackie Academic and Professional. Glaser, J., P.A. Carroad, and W.L. Dunkley. 1980. Electron microscopic studies of casein micelles and curd microstructure in cottage cheese. Journal of Dairy Science 63:37–48. Gunasekaran, S. and C. Ay. 1996. Milk coagulation cut-time determination using ultrasonics. Journal of Food Process Engineering 19(3):331–342. Hill, A.R. 1995. Chemical species in cheeses and their origin in milk components. In Chemistry of Structure-Function Relationships in Cheese, Eds. E.L. Malin and M.H. Tunick, 43–58. New York: Plenum Press. Hori, T. 1985. Objective measurements of the process of curd formation during rennet treatment of milks by hot wire method. Journal of Food Science 50:911–917. Johnson, M.E. 1998. Part II — Cheese chemistry. In Fundamentals of Dairy Chemistry, Ed. N.P. Wong, 634–654. New York: Van Nostrand Reinhard Co. Johnson, M. and B.A. Law. 1999. The origins, development and basic operations of cheesemaking technology. In Technology of Cheesemaking, Ed. B.A. Law, 1–32. Sheffield, England: Sheffield Academic Press Ltd. Kimber, A.M. et al. 1974. Electron microscope studies of the development of structure in Cheddar cheese. Journal of Dairy Research 41:389–396. Kindstedt, P.S., L.J. Kiely, and J.A. Gilmore. 1992. Variation in composition and functional properties within brine-salted Mozzarella cheese. Journal of Dairy Science 75:2913–2921. Konuklar, G. and S. Gunasekaran. 2002. Rennet-induced milk coagulation by continuous steady shear stress. Journal of Colloid and Interface Science (in press). Kopelman, I.J. and U. Cogan. 1976. Determination of clotting power of milk clotting enzymes. Journal of Dairy Science 59(2):196–199. Kristensen, J.M.B. 1999. Cheese Technology — A Northern European Approach. Aarhus, Denmark: International Dairy Books. Kristoffersen, T. 1985. Development of flavor in cheese. Milchwissenschaft 40:197–199. Law, B.A. (ed.) 1999. Technology of Cheesemaking. Boca Raton, FL: Sheffield Academic Press. Lomholt, S.B. and K.B. Qvist. 1999. The formation of cheese curd. In Technology of Cheesemaking, Ed. B.A. Law. Sheffield, England: Sheffield Academic Press Ltd. Lopez, M.B., S.B. Lomholt, and Q.B. Qvist. 1998. Rheological properties and cutting time of rennet gels: effect of pH and enzyme concentration. International Dairy Journal 8:289–293.

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NDC. 2000. Newer Knowledge of Dairy Foods/Cheese. National Dairy Council (www.nationaldairycouncil.org). Managed by Dairy Management Inc., Rosemont, IL. Nilson, K.M. 1968. Some practical problems and their solutions in the manufacture of Mozzarella cheese. In Proc. 5th Annual Marschall Italian Cheese Seminar, 1–7. Madison, WI. Oberg, C.J., W.R. McManus, and D.J. McMahon. 1993. Microstructure of Mozzarella cheese during manufacture. Food Structure 12:251–258. O’Callaghan, D.J., C.P. O’Donnell, and F.A. Payne. 1999. A comparison of on-line techniques for determination of curd setting time using cheese milks under different rates of coagulation. Journal of Food Engineering 41(1):43–54. Olson, N.F. 1979. Cheese. In Microbial Technology II, Eds. H.J. Peppler and D. Perlman, 39–77. New York: Academic Press. Olson, N.F. 1995. Cheese. In Biotechnology, Vol. 9, Eds. H.-J. Rehm and G. Reed, 355–384. Weinheim, Germany: Verlag Chemie. Paulson, B.M., D.J. McMahon, and C.J. Oberg. 1998. Influence of sodium chloride on appearance, functionality and protein arrangements in non-fat Mozzarella cheese. Journal of Dairy Science 81:2053–2064. Payne, F.A. et al. 1993. Fiber optic sensor for predicting the cutting time of coagulating milk for cheese production. Transactions of the ASAE 36(3):841–847. Pearse, M.J. and A.G. Mackinlay. 1989. Biochemical aspects of syneresis: A review. Journal of Dairy Science 72:1401–1407. Prentice, J.H. 1993. Cheese rheology. In Cheese: Chemistry, Physics & Microbiology, Vol. 1, General Aspects, Ed. P.F. Fox, 303–340. Elsevier Applied Science, London. Scott, R., R.K. Robinson, and R.A. Wilbey. 1998. Cheesemaking Practice. Gaithersburg, MD: Aspen Publishers, Inc. Shimp, L.A. 1985. Process cheese principles. Food Technology 39(5):63–69. Spreer, E. 1998. Milk and Dairy Product Technology. New York: Marcel Dekker, Inc. Turhan, M. and S. Gunasekaran. 1998. Analysis of moisture diffusion in white cheese during salting. Milchwissenschaft 54(8):446–450. Uludogan, G. 1999. Evaluation of Milk Coagulation Using Ultrasonic and Rheological Methods, Ph.D. thesis, University of Wisconsin-Madison. Vedamuthu, E.R. and C. Washam. 1983. Cheese. In Biotechnology — A Comprehensive Treatise, Vol. 5, Eds. H.-J. Rehm and G. Reed, 231–313. Weinheim, Germany: Verlag Chemie. Visser, J. 1991. Factors affecting the rheological and fracture properties of hard and semihard cheese. Bulletin of the International Dairy Federation No. 268, 49–61, IDF, Brussels, Belgium. Walstra, P. and R. Jenness. 1984. Dairy Chemistry and Physics. New York: John Wiley and Sons. Walstra, P. et al. 1999. Dairy Technology — Principles of Milk Properties and Processes. New York: Marcel Dekker, Inc.

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2

Fundamental Rheological Methods

Fundamental rheological methods are performed under well-defined and controlled conditions. Though some assumptions about the materials and test methods may be made, calculations of material properties are based on well-defined rheological terms (e.g., strain, stress). Moreover, material properties determined by fundamental methods are independent of the apparatus used for measurements, which allows comparison of data from different research groups (Mitchell, 1984; Shoemaker et al., 1987; Tunick and Nolan, 1992; Tunick, 2000). These fundamental methods help researchers study cheese properties and effects of many manufacturing factors, and eventually develop cheeses with desired and consistent textural and rheological properties. Few reviews have been published on the fundamental rheological methods employed in cheese research (van Vliet, 1991a; Konstance and Holsinger, 1992; Luyten et al., 1992).

DEFINITION OF RHEOLOGY The term rheology was coined by Professor E.C. Bingham to represent a new branch of mechanics concerned with the study of deformation and flow of matter (Reiner, 1964). This definition was accepted at the inaugural meeting of the Society of Rheology (then, the American Society of Rheology) in 1929. Although significant rheology research has been performed prior to this date, the progress in the field of rheology seems to have greatly accelerated after its inception in 1929 as a separate discipline (Doraiswamy, 2002). Rheology is now a well-recognized field with many applications in different industries. Professionals from various disciplines (e.g., physicists, chemists, biologists, engineers, mathematicians) are interested in the theoretical and practical aspects of rheology. As stated in the definition, rheology aims at measuring those properties of materials that control their deformation and flow behavior when subjected to external forces. Thus, rheology is mainly concerned with the relationship between strain, stress, and time. When subjected to external forces, solids (or truly elastic materials) will deform, whereas liquids (or truly viscous materials) will flow. However, contemporary rheology is more interested in the behavior of real materials with properties intermediate between those of ideal solids and ideal liquids (Doraiswamy, 2002). These industrially important materials are called viscoelastic materials, which include almost all real materials.

BASIC CONCEPTS Rheology deals with the relationship between three variables: strain, stress, and time. Strain and stress are related to deformation and force, respectively. Strain accounts

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for the size effect on material deformation due to difference in length (or height) of specimens, whereas stress accounts for the size effect on applied force due to difference in cross-sectional area of specimens. Using strain and stress, rheologists are able to obtain true material properties independent of the sample size and geometry, and compare test results for samples of different sizes and geometries. Many rheological terms are defined and described by van Vliet (1991b).

STRAIN When a material is subjected to an external force, individual points of the body will move relative to one another causing a change in the size and shape of the material. The deformation is the measure of such a change in size and shape. Deformation, however, is not uniquely related to force as illustrated in the following example. Two specimens (A and B), made of the same material and having identical shape and size, are subjected to the same axial force, F, applied perpendicular to the material surfaces (Figure 2.1). This will result in the same amount of extension Lo A

Before deformation

F

F

L A

After deformation

Deformation = ∆L

∆L/2

∆L/2 Lo

F

Before deformation

F

B

L After deformation

B

Deformation = ∆L

∆L/2

∆L/2 2 Lo

F

Before deformation

A

Before deformation

B

F

2L After deformation ∆L

A

After deformation

B

∆L Total deformation = 2∆L

FIGURE 2.1 Effect of test specimen length on force–extension relationship. (After Hall, 1968).

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(or deformation), denoted by ∆L. Let us now imagine that we join the two specimens end to end and again apply the same axial force F. Since each specimen will experience the same axial force as they did when stretched separately, they each will extend to the same amount as before (i.e., ∆L) giving a total extension of 2∆L. However, when we divide the total extension 2∆L by the total original length 2Lo, the resulting quantity has the same numerical value as when the specimens were stretched separately (i.e., ∆L/Lo). This way, we arrive at a quantity that is independent of original specimen length (or height) and is referred to as strain. Thus, strain is a quantitative measure of the intensity of deformation. When the deformation is divided by the initial length of a specimen, as illustrated above, the resulting strain is known as the engineering strain (or nominal strain, Cauchy strain). The average engineering axial strain is then given by: ε=±

L − Lo ∆L =± Lo Lo

(2.1)

This expression defines the tensile engineering strain (+) when L (current length or height) is greater than Lo (original length or height), or compressive engineering strain (-) when L is smaller than Lo. Both of these strains are known as normal strains or axial strains. There is also another kind of strain, the shear strain, which exists when the force is applied parallel to the material surfaces. This is depicted in Figure 2.2. A shear strain is defined as the change in angle between two lines originally at right angles in the undeformed state, that is, γ ≡ θ (Fletcher, 1985). The angle θ may be difficult to measure. Hence, the average shear strain (γ) is obtained by dividing the deformation, δ, by sample height, h: γ=

∆δ δ = = tan θ ∆h h

(2.2) δ

F

θ

h

∆δ

∆h

FIGURE 2.2 Simple shear deformation. When the deformation is uniform, shear strain is independent of size of element taken. Thus, shear strain γ = (∆δ/∆h) = (δ/h).

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It is assumed that the strain is uniform and each small element of the material is subjected to the same local deformation, and that is also equal to the overall strain. Hence, we can write (∆δ/∆h) = (δ/h). In writing Equation (2.2), it is also assumed that the deformation, δ, is small. From the definition of strain it is evident that both normal strain and shear strain are dimensionless quantities. Sometimes, normal strain is expressed in units of, for instance, mm/mm or as a percentage, and shear strain in radian. The utility of engineering strain is limited to very small deformations (typically < 1% in tension), and the meaning becomes distorted when L becomes appreciably larger than Lo during the test (and also in fluid flows). The following two cases demonstrate why engineering strain is not appropriate for large deformations. First, we consider a tensile test where the specimen is stretched from Lo to 2Lo. According to Equation (2.1), the engineering strain is equal to 1 (i.e., ε = 1). However, let us now consider that the test is done in two steps, such that the specimen is first stretched from Lo to 1.4Lo and then from 1.4Lo to 2Lo. In the first step, the engineering strain is calculated to be ε1 = 0.4, whereas in the second step it is ε2 = 0.43. When we add these two strains we obtain ε = ε1 + ε2 = 0.83, which is less than the expected value of 1. Second, when engineering strain is equal to 1 in a tensile experiment, it means L = 2Lo, that is 100% extension. On the other hand, an engineering strain of 1 in compression gives an awkward result as: ε = −1 =

L − Lo Lo

(2.3)

This yields L = 0, which is physically impossible. There are a number of ways to measure strain when the deformations are large. For up to about 25% deformation all measures of strain yield similar stress–strain relationships in an ideal compression (Peleg, 1984). However, when deformations involved are large, the stress–strain relationships differ depending on how strain (and stress) is measured. In food rheology, the so-called Hencky strain (or true strain, natural strain) is most commonly used when large deformations are involved. Hencky strain is a better measure of strain than engineering strain because deformations are referenced to the current specimen length (or height) rather than to the initial specimen length. Using Hencky strain can eliminate the problems associated with engineering strain such as the ones encountered in the two illustrative examples above. Let us consider that a uniaxial extension experiment is performed in many small steps from the initial specimen length Lo to the final length L. In each step, one can define an incremental engineering strain (∆ε) as follows: ∆ε =

∆Li Li

(2.4)

where, ∆Li is the differential increase in the length during the ith step and Li is the length of specimen at the beginning of that step. The total strain is obtained by summing all the incremental strains from Lo to L, thus: © 2003 by CRC Press LLC

εH =

∑

L

L ∆Li dL = = ln   Li L  Lo 

∫

(2.5)

Lo

This is known as Hencky strain, εH. If we reconsider the two examples given earlier, we see that Hencky strain is additive. That is:  2L  ε H ,total = ln  o  = ln[2] and,  Lo  ε H = ε H1 + ε H 2

(2.6)

1.4 Lo   2 Lo  = ln   + ln   = ln[1.4] + ln[2] − ln[1.4] = ln[2]  Lo  1.4 Lo 

Furthermore, when εH = –1, this means that L = 0.37Lo, which is a meaningful result. Both relations, Equations (2.1) and (2.5), represent average quantities and valid only when strain is uniform all along L as illustrated in Figure 2.3. Whenever there is necking in the gage length in a tensile specimen, or bulging in a compressive specimen (Figure 2.4), these strain calculations become inaccurate or invalid. It can be shown that, engineering strain (ε) and Hencky strain (εH) are related as: ε H = ln(1 + ε ) = ε −

ε2 ε3 + ... 2 3

(2.7)

Equation (2.7) is valid for both in tension and compression as long as the magnitude of ε is used with appropriate sign (i.e., plus (+) for tension and minus (–) for compression). We should point out that Hencky strain is larger in compression and smaller in tension than the corresponding engineering strain. The difference between Hencky strain and engineering strain steadily increases with deformation (Figure 2.5). Hencky strain is approximately equal to engineering strain up to about Before deformation A

F

B

C

F

D

L

After deformation A + ∆A

B + ∆B

C + ∆C

D + ∆D

L + ∆L

FIGURE 2.3 Description of uniform deformation along a tensile test piece. For uniform strain: ∆L/L = ∆A/A = ∆B/B = ∆C/C = ∆D/D.

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TENSION Gage length F

F

Necking F COMPRESSION

Bulging

FIGURE 2.4 Necking in tension and bulging in frictional compression. 0.25 Engineering

0.2

Hencky

Strain

0.15

0.1

0.05

0 0

5

10

15

20

Deformation (%)

FIGURE 2.5 Comparison of engineering strain (ε) and Hencky strain (εH) of a specimen in tension (Note: in tension εH < ε; in compression εH > ε).

5% deformation, but the difference increases so that, for instance, ε = –0.25 (25% compressive strain) corresponds to nearly εH = –0.29 (about 16% difference). The use of Hencky strain is also convenient when considering the constant-volume assumption, which is frequently used in the calculation of true stress (see below). For this assumption Hencky strain yields: ε H , x + ε H , y + ε H ,z = 0

(2.8)

where, the subscripts x, y, and z for εH refer to the three orthogonal directions of strain in a volume element.

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F

F

∆L1

L0

∆L2

L0

D

Thicker specimen

d

Thinner specimen ∆L1 < ∆L2

FIGURE 2.6 Effect of cross-sectional area of test piece on force–deformation relationship.

STRESS Stress is defined as force per unit area over which the force is applied. Thus, the unit of stress in SI system is Pa ( = N/m2). The concept of stress is developed to eliminate the artificial effect of sample size on the material properties. Let us consider two cylindrical specimens of same material but different diameters subjected to an axial force, F (Figure 2.6). We will measure different deformations although specimens are made of the same material. The reason is that although the force is the same on both specimens the intensity of the force, or force per unit area, is higher for the thinner specimen. Therefore, stress, instead of force, is a parameter that includes the effect of specimen dimensions and can be used to evaluate the mechanical response of a material. Two types of stress can act on a surface: normal stress and shear stress. Normal stress acts perpendicular to the surface whereas shear stress acts parallel to the surface (Figure 2.7). Normal stress is further classified as tensile and compressive depending on the directions of force and unit normal vector of the surface. In tension these two vectors are in the same direction (angle 0°) while in compression they are in opposite directions (angle 180°). In simple shear the force is applied tangentially to the surface as shown in Figure 2.8. The solid lines indicate the original shape of the element. The deformation of the element is such that there is a change in the shape but not in the volume of the element. The tangential force divided by the area (of the x–y plane) it acts on gives the shear stress, denoted by σxy = τ: τ=

Ft A

(2.9)

In fact, stress and strain at a point in a material are tensorial quantities having nine components as shown in Figure 2.9.

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Normal force, F

Unit normal vector, n Tangential force, Ft Area, A

F

F

n

n

n

Ft

Tension:

Shear:

Compression:

FIGURE 2.7 Normal (tension and compression) and shear stresses acting on a surface and the unit normal vector. y

Surface area

A d

q

Ft

A

q

h

z

FIGURE 2.8 A cubic element undergoing simple shear due to tangential force, Ft.

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x

y σyy; εyy σyx; εyx σxy; εxy

σyz; εyz σzy; εzy σzx; εzx

σxx; εxx σxz; εxz

σzz; εzz

x

z

FIGURE 2.9 General state of stress acting on a cubic element (all stresses have positive sense). The corresponding strains are also indicated.

When stress calculation is based on the initial cross-sectional area of a specimen it is known as engineering stress, σ: σ≡

F Ao

(2.10)

Since the cross-sectional area of a test piece is changing continuously during a large deformation test, the engineering stress may not precisely represent the state of stress in the material. Thus, stress calculation based on the current cross-sectional area, known as true stress, σt is used more commonly: σt ≡

F A

(2.11)

The true stress and engineering stress are related to each other by the following expression: σ t = σ(1 + ε ) = σ ⋅ exp(ε H )

(2.12)

Here, exp(εH) = 1 + εH + εH2 /2!… Therefore, for small strains the true and engineering stresses are essentially the same (i.e., σt .σ). Equation (2.12) is valid

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for both in tension and compression as long as the magnitude of ε is used with appropriate sign (i.e., plus (+) for tension and minus (–) for compression). We should point out that true stress is smaller in compression and larger in tension than the corresponding engineering stress. After defining strain and stress, it is useful to demonstrate with an example why it is better to use stress–strain relations rather than force–deformation relations. For this, let us consider force–deformation graphs of three cylindrical specimens of the same material but different dimensions undergoing a tensile deformation (Figure 2.10A) (Riley et al., 1995). At first sight we cannot guess that all three curves describe the same material behavior. In the next figure (Figure 2.10B) the same data are replotted as stress vs. deformation. Here, we see that two of the previous graphs overlay, but the third one still appears to be different. Finally, we plot the data as the stress vs. strain (Figure 2.10C) to see that all three previously separate curves in fact form a single graph. This example illustrates that stress and strain are better parameters to use in evaluating and classifying the response of materials to applied forces.

STRAIN RATE The third important rheological variable, “time,” is introduced in the measurement of strain rate. The concept of strain rate is necessary to describe flow behavior of materials. In flow situations, since the strain will attain very large values with increasing time, it is preferred to discuss material behavior in terms of stress–strain rate rather than stress–strain. The strain rate is simply the time derivative of strain. For instance, strain rate in compression, and strain rate in simple shear, are given by: ε˙ H =

(dL L) = dt

1 dL Vz = L dt L

(2.13)

and γ˙ =

1 dδ Vx = h dt h

(2.14)

where, Vz = axial velocity and Vx = velocity of the moving plate.

FUNDAMENTAL METHODS UNIAXIAL COMPRESSION Uniaxial compression is the most popular test for determining rheological properties of foods, including cheese. This test is popular probably because it is easy to execute and there is no need for sample gripping (Luyten et al., 1992). Nearly all compression tests on cheese are done using one of the versatile instruments commonly referred to as Universal Testing Machine (UTM) (Figure 2.11). The UTM provides precise control of deformation while accurately measuring force.

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Force (kN)

9 8

No: 1

7

No: 2

6

No: 3

A

5 4 3 2 1 0 0

0.05

0.1

0.15

Deformation (mm) 500 No: 1

Stress (MPa)

400

B

No: 2 No: 3

300 200 100 0 0

0.05

0.1

0.15

Deformation (mm) 500 C

No: 1

Stress (MPa)

400

No: 2 No: 3

300 200 100 0 0

0.1

0.2

0.3

0.4

0.5

Strain (%)

FIGURE 2.10 Diagrams for accounting the height and cross-sectional area effects of three specimens (No. 1, No. 2, and No. 3) of same material but different dimensions. No. 1: area = 10 mm2, length = 30 mm; No. 2: area = 10 mm2, length = 60 mm; No. 3: area = 20 mm2, length = 30 mm. (After Riley et al., 1995.)

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Load cell

Moving crosshead

Specimen

FIGURE 2.11 Schematic view of a universal testing machine (UTM).

TABLE 2.1 Some Major Manufacturers of Universal Testing Machines (UTMs) Company

Web Site

ATS Applied Test Systems Instron Lloyd Instruments M&L Testing MTS Shimadzu Stable Micro Systems Tinius Olsen Thwing-Albert United Testing Systems Zwick

http://www.atspa.com http://www.instron.com http://www.lloyd-instruments.co.uk http://mltest.com http://www.mts.com http://www.shimadzu.com http://www.stablemicrosystems.com http://www.tiniusolsen.com http://www.thwingalbert.com http://www.tensiletest.com http://www.zwick.com

UTMs can be used to conduct compression as well as tension, bending, and shear tests. A number of companies (Table 2.1) are making computer-controlled UTMs with many useful features for operating the machine and acquiring, storing, analyzing, and reporting of the data. The UTMs are designed for various materials such as metals, concrete, ceramics, papers, polymers, and foods.

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F F: Force Vz: Deformation rate Upper Platen (moving) Cheese specimen

Vz

Lower Platen (stationary) BEFORE COMPRESSION

Without friction (homogeneous deformation)

With friction (inhomogeneous deformation)

AFTER COMPRESSION

AFTER COMPRESSION

FIGURE 2.12 Schematic drawing of uniaxial compression test with and without frictional effects. proportional limit for A

Elastic limit for A

lB

proportional limit for B

m

at

er

ia

al A teri ma

Stress

Elastic limit for B

Slope A > Slope B (A is stiffer than B) Slope gives Young’s modulus Strain

FIGURE 2.13 Linear elastic constants to be obtained from stress–strain curve.

A typical arrangement for a compression test is shown in Figure 2.12. In this test, a specimen of known shape and size is placed between two parallel rigid plates of a UTM, and often the upper plate is moved downward at a constant (crosshead) speed (i.e., constant deformation rate) while recording the force as a function of time. The resulting force–time data pairs are converted into corresponding stress and strain values from which other rheological quantities such as Young’s modulus or modulus of elasticity can be calculated (Figure 2.13). A higher value of modulus of elasticity

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Specimen with ends not parallel

Force

Force

Specimen with parallel ends

Deformation

Deformation Tail

FIGURE 2.14 Effect of shape of test piece on the force–deformation diagram. The “tail” at the beginning of the curve on right is due to specimen ends not being parallel. (After Bourne, 1982.)

corresponds to a higher material stiffness, as shown schematically in Figure 2.13 for materials A and B. It is important to note that since Young’s modulus is calculated from the initial part of the stress–strain data the test piece must have perfectly flat and parallel ends for accurate determination of this property (Figure 2.14). For highly nonlinear stress–strain curves, the Young’s modulus is sometimes expressed as the 5% strain secant modulus (Charalambides et al., 1995). Since food materials are viscoelastic and the stress–strain curve is nonlinear, the existence of a true elastic limit, as seen in Hookean solids, is questionable. Therefore, to maintain the purity of the term modulus of elasticity, representing rigidity or stiffness of a material, Mohsenin and Mittal (1977) proposed the term “modulus of deformability” to be used when dealing with stress–strain curves of food materials. The point at which the linearity between stress and strain ceases to exist is called the proportional limit (Figure 2.13). Said differently, the Hooke’s law is applicable only up to the proportional limit of the material. On the other hand, the elastic limit is the greatest stress, which a material is capable of sustaining without any permanent strain remaining upon release of the stress (ASTM, 1995). Thus, if a stress is applied to a specimen and then removed, the specimen will return to its original shape and size as long as the stress did not exceed the elastic limit. In general, the elastic limit is greater than the proportional limit, but for some materials they are difficult to distinguish. In addition to the proportional limit and elastic limit, several other significant parameters, particularly for engineering materials, can be determined from the stress–strain curves such as yield point or yield strength, ultimate strength, resilience, toughness, etc. Each of these parameters is described in Table 2.2 and its calculation illustrated in Figures 2.15–2.18. In uniaxial compression tests on cheese, mostly cylindrical specimens are preferred, except few cases where cubic samples are used. It must be noted that sharp corners in cubic samples are prone to stress concentrations. The tools to

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TABLE 2.2 Description of Some Commonly Encountered Terms in Analysis of Stress–Strain Curves of Engineering Materials Parameter

Description

Young’s modulus or modulus of elasticity

It is a measure of material’s resistance to axial deformation. It represents the stiffness of the material to an applied load. The larger the stiffness, the higher the force or stress needed to cause a given deformation or strain. Its value is calculated as the slope of the stress–strain curve in the linear section. In shear loading it is called Rigidity Modulus. See Figure 2.13. It is defined as the slope of a line drawn tangent to the stress–strain curve at a particular stress (or strain) level. Thus, the tangent modulus can have different values according to the point at which it is calculated. When this point falls within the linear part of the stress–strain curve, the tangent modulus is equal to the Young’s modulus. In general, the tangent modulus describes the stiffness of a material in the plastic region. See Figure 2.15. It is the slope of a line connecting the origin of the stress–strain curve and any point (e.g., 5% strain) on the curve. It is therefore true that the secant modulus takes different values depending upon the strain at which it is evaluated. The secant modulus also describes the stiffness of a material in the inelastic region of the stress–strain diagram. See Figure 2.15. It is the highest stress at which stress is directly proportional to strain. Hooke’s law applies up to the proportional limit. The proportional limit also marks the start of nonlinearity in the stress–strain curve. See Figure 2.13. It is the maximum stress the material can sustain without any measurable permanent strain remaining upon the full release of load. Thus, the material will return to its original shape/size when the stress is removed. To determine the elastic limit, one conducts a cumbersome incremental loading–unloading test procedure until a permanent (or plastic) deformation is detected. See Figure 2.13. A small increase in stress above the elastic limit results in a relatively large increase in strain. The specimen is permanently deformed even if the load is reduced to zero. The stress that causes this yielding is termed the yield stress or yield strength. Some materials exhibit a distinct yield point, but many others do not have a welldefined yield point. Therefore, it is common practice to define a yield strength using a procedure called the offset method. In this method, most commonly a 0.2% strain offset is applied. For that, a line parallel to the initial straight-line portion of the stress–strain curve is drawn starting from point 0.002 (or 0.2%) on the strain axis. The point where this line intersects the stress–strain curve is taken as the yield strength. The 0.2% strain offset is arbitrarily chosen and it can be different. Note that the offset method requires a linear portion in the stress–strain curve. For materials showing no linear portion it is practical to define the yield strength as the stress to produce a certain strain (e.g., 0.5%). See Figure 2.16. It is the highest stress reached in the stress–strain curve before fracture. The important point is that the ultimate strength is based on the original cross-sectional area of the test piece. If the specimen develops necking (e.g., ductile materials), then the engineering stress will decrease with further increase in strain, but the true stress will continue to increase until fracture. See Figure 2.16. It is the amount of energy absorbed by a material in the elastic range. Its value is obtained from the area under the stress–strain curve up to the elastic limit of a material. Materials with a high-yield stress and a low modulus of elasticity will have good resilience. See Figure 2.17. It is the amount of energy absorbed by a material until fracture (or the amount of work per unit volume). Its value is equal to the total area under the stress–stain diagram. The larger the area, the tougher the material. See Figure 2.17.

Tangent modulus

Secant modulus

Proportional limit

Elastic limit

Yield point/yield strength

Ultimate strength

Resilience

Toughness (or modulus of toughness)

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TABLE 2.2 (continued) Description of Some Commonly Encountered Terms in Analysis of Stress–Strain Curves of Engineering Materials Parameter

Description

Brittle material

It is a material that fractures before undergoing little or no plastic deformation. See Figure 2.18. It is a material that exhibits yield point and undergoes significant plastic deformation before failure. The usual measures of ductility are the engineering strain at fracture and the reduction of area (particularly for tension) at fracture. See Figure 2.18.

Ductile material

Slope = Young’s modulus

Stress

Slope = Tangent modulus at selected location (e.g., at 8% strain)

Slope = Secant modulus at selected location (e.g., at 5% strain)

5% Strain

8%

FIGURE 2.15 Different ways of obtaining modulus from stress–strain relationship.

Stress

Ultimate strength Offset (e.g., 0.2%) yield strength

0.2%

Fracture stress

Strain

FIGURE 2.16 Schematic illustration of yield strength, ultimate strength, and fracture stress on the stress–strain curve.

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Fracture

Stress

A

Proportional limit

Modulus of resilience

Strain

B

Stress

Fracture

Modulus of toughness

Strain

FIGURE 2.17 Description of modulus of resilience (A) and modulus of toughness (B).

prepare cylindrical cheese specimens typically include a cork borer and a wire cutter (Figure 2.19). The cork borer is useful for cutting out uniform cylinders of certain diameter from a cheese block, and the wire cutter is good to obtain a certain height (or length) from the cheese cylinders. The success of a compression test depends largely on the quality and accuracy of the test specimen. It is therefore important that the samples maintain true cylindrical shape with perfect parallel end faces. This is easier said than done, especially when preparing cylindrical cheese specimens. Van Vliet and Peleg (1991) made a number of recommendations to ensure proper sample preparation and, consequently, correct experimental data. They state that after boring or cutting an elastic material the shape and dimensions of the resulting test piece are different from that of the borer or cutter used to produce it. A similar concern is expressed in ASTM Standard

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Brittle material

Stress

Fracture

Ductile material

Strain

FIGURE 2.18 Schematic drawing of stress–strain curves for brittle and ductile materials.

(1996) for sample preparation in compression testing of rubber, where the suggestion is to use a cutting tool (Figure 2.20) that is larger in diameter than the specimen to allow for cutting pressure. This hollow cutting tool is rotated in a drill press and lubricated with soapy water to obtain a smooth-cut surface. Luyten (1988) used a similar borer shown in Figure 2.21 for cutting cylindrical specimens of Gouda cheese without compression and erosion at the sides of the specimens. This borer has an inner diameter slightly larger than the diameter of the cutting part. Cheese boring or cutting should be carried out as slowly as possible. Other recommendations for proper cheese sample preparation are listed in Table 2.3. A wide range of test conditions has been used in uniaxial compression of cheese (Ak and Gunasekaran, 1992). A brief list of experimental conditions is presented in Table 2.4. Since most food products are viscoelastic, and therefore strain-rate sensitive, they can produce significantly different responses according to the crosshead speeds involved. For instance, it is shown that White Stilton cheese is firmer or less firm than Gouda cheese depending on the compression speed and the degree of compression (Shama and Sherman, 1973). It is considered crucial to know the conditions prevailing (e.g., strain rates) during sensory evaluation in order to select the optimum conditions for instrumental measurements (Sherman, 1975; Voisey, 1975). Bourne (1977) remarked that the rate of compression of solid foods in the mouth varies widely with many factors such as variations in chewing speeds from person to person, length of stroke of the jaws, type of food, etc. It is reported that the maximum rate of jaw movement during chewing ranges from 15 mm/s to 30 mm/s, with males chewing at a faster rate than females (Langley and Marshall, 1993). We shall note, as an exception, that for UF-Feta cheese it is not necessary to run uniaxial compression testing at the chewing rate to get a good correlation with sensory evaluation, provided that the crosshead speed is greater than 50 mm/min (Wium et al., 1997).

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FIGURE 2.19 Tools that can be used for sample preparation for compression testing of cheese. A: a cork-borer machine (from www.hmc-hsi.com, with permission); B: set of cork borers and sharpener (from www.boekelsci.com, with permission); C: table-top wire cheese cutter (from www.ashtongreen.com); D: cheese specimens for compression (after Ak, 1993).

Obviously, accurate control of test temperature is extremely important as physical properties of cheeses (and foods in general) are greatly affected by temperature changes. It is equally important to make sure that the specimen and the platens are maintained at the same temperature during a compression test. The choice of specimen dimensions requires special care. Buckling may occur if the aspect ratio (ratio of sample length or height, L to its diameter, D) is relatively large (e.g., L/D > 2). On the other hand, if L/D ratio is small (e.g., L/D < 1) the test results may be greatly affected by the specimen end conditions (e.g., friction effects). For instance, Chu and Peleg (1985) examined apparent deformability modulus, (determined as the engineering stress divided by engineering strain at 20% deformation) and failure conditions (i.e., failure stress and failure strain) of potato, bologna sausage, and process American cheese as a function of height-to-diameter ratio in the range 0.12 ≤ L/D ≤ 1.00. The flat (i.e., lower L/D ratio) specimens exhibited higher apparent deformability modulus (i.e., higher stiffness). This is particularly

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ASTM Cutting Tool

DTOOL

DTOOL = 28.804 mm (+0.000/−0.025) DSPECIMEN = 28.6 ± 0.1 mm LSPECIMEN = 12.5 ± 0.5 mm

FIGURE 2.20 The ASTM cutting tool for cutting cylindrical compression test specimens. (Per ASTM D638.) (After ASTM, 1996. With permission.) 17 to 21 mm

14.7 mm

14-mm diameter Cheese sample Cheese borer

Cheese block

14 mm

FIGURE 2.21 Cork borer for cutting cylindrical cheese specimens. (After Luyten, 1988; van Vliet and Peleg, 1991.)

the case when there is considerable friction between the specimen ends and the machine plates (e.g., when plates are coated with emery cloth). For instance, the apparent deformability modulus of the cheese sample with L/D = 0.12 is about 3.5 times greater than that for the sample with L/D = 1.0. Culioli and Sherman (1976) examined the effect of contact surface conditions on force–compression behavior of Gouda cheese at crosshead speeds of 2.5, 10, and 50 cm/min and L/D ratio of 1.0. At any of three crosshead speeds the level of friction

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TABLE 2.3 Recommendations for Cheese Sample Preparation for Uniaxial Compression Tests If it exists, remove hard rind of cheese Prepare specimens when they are cold (refrigeration temperature) Take sample from the same location in a cheese (e.g., center) and in the same direction Take samples from locations that are sufficiently away from each other since fracture may occur in the cheese loaf during previous sampling Cut specimens as slowly as possible, preferably using a motorized borer and cutting tool Lubricate all surfaces of the borer with mineral oil to minimize distortion during cutting out Use a tightly stretched, thin wire cutter, lubricated with mineral oil Measure actual dimensions of each specimen before testing Make sure that the size of specimen is large compared to the size of the heterogeneity Source: After van Vliet and Peleg, 1991.

at contact surfaces (i.e., with emery paper or with oil) exerted no influence on the force–compression behavior until 40% compression. At fracture point the force was lower when an emery paper was used at the interface than when the specimen ends were lubricated with oil. However, when the true stress is plotted against percent compression, the stress was greater when an emery paper was used at the interface than when the specimen ends were lubricated with oil. On the other hand, Luyten et al. (1992) found no clear effect of using emery paper or oil at the specimen–machine interface on the fracture stress of Gouda cheese. Moreover, they recalculated stress–strain curves from the data of Culioli and Sherman for emery paper and oil, and found no difference between them. The effect of aspect ratio on the fracture stress of young Gouda cheese is depicted in Figure 2.22. In this figure, data for different friction conditions (i.e., normal plates, lubricated, and emery paper) are pooled together since no clear effect of friction on the fracture stress is reported (Luyten et al., 1992). It is seen that the fracture stress of this cheese shows a tendency to become constant beyond the L/D ratio of 1.5. Although the uniaxial compression test appears simple in principle and practice (e.g., no need to grip the sample), the data analysis is complicated by the effect of friction between the specimen and the testing machine platens. Friction influences not only the magnitude of the force for compression but also the appearance of the compressed specimens (Culioli and Sherman, 1976). Barreling due to friction (Figure 2.12) is an indication of nonhomogeneous deformation. During compression the cheese specimen is to move relative to the platens and thus the force required to achieve a certain level of compression depends also on the friction. Therefore, stresses in the presence of friction (i.e., shear-plus compression) are always greater than in the absence of friction (i.e., shear-free compression). The common practice of reducing the friction is to lubricate the sample–platen interfaces with low-viscosity oil. It has been shown that type of lubricating oil can have a significant impact on the measurements (Charalambides et al., 1995). An alternative way of accounting for friction is to bond the sample to the platens using adhesives such as cyanoacrylate (Casiraghi et al., 1985). Charalambides et al. (2001) described a method based on the Cooke and Larke procedure to account for friction.

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TABLE 2.4 Experimental Conditions Used in Uniaxial Compression Testing of Cheese Cheese Type Cheddar Leicester Brie UF-Feta Immature Cheddar, Cheshire, Leicester Mozzarella cheese analogs Camembert

Crosshead speed (mm/min)

Temperature (°C)

Sample Diameter, D (mm)

Sample Height, L (mm)

Aspect ratio: L/D

2.5, 6.4, 12.7, 25.4, 50.8, 127 25, 50, 250, 500, 1000 33.3

22

19

19, 29

1, 1.53

Room, 23–26, 30–37 5, 20

25

25

1

15

19.5

1.3

100, 200, 300, 400

13

15.3

15.3

1

Mineral oil; emery sheet Smooth hydrophobic paper Low-viscosity oil

5–1000

0–40

28.5–29.5

30

~1

Machine plates

20

20

23

20

0.87

Machine plates

10

20

13.8

10

0.72

Machine plates

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Surface Condition Mineral oil

Reference Ak and Gunasekaran (1992) Vernon-Carter and Sherman (1978) Molander et al. (1990) Wium and Qvist (1997) Dickinson and Goulding (1980)

Yang and Taranto (1982) Mpagana and Hardy (1986)

Emmentaler

5, 20, 80

15

16.4

17.5

1.07

Gouda

5, 10, 50

20–21

7.5–35

0.3–3.5

Gouda Mild Cheddar, Sharp Cheddar, Monterey Jack Process American cheese Mozzarella, Cheddar, Processed cheese spread Gouda Gruyere, processed Mozzarella

0.1–500 10

20 4

10, 20, 25 (also cubes of 10 and 20 mm) 15 20

20–30 7, 10, 13, 20

1.33–2 0.35–1

5

Room

10–21

2.5–10

0.12–1

0.5, 5, 50

7, 22

57

20, 30, 40

0.35–0.70

10 3.6, 5.8, 7.9, 10.8, 14.4

20 room

20 20

20 5, 8, 11, 15, 20

1 0.25–1

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Paraffin oil Mineral oil; emery paper Machine plates Machine plates

Machine plates; emery cloth (No.120) Paraffin oil; bonding with cyanoacrylate; machine plates Paraffin oil Machine plates; synthetic grease

Rohm and Lederer (1992) Culioli and Sherman (1976) Luyten et al. (1991a) Charalambides et al. (1995)

Chu and Peleg (1985)

Casiraghi et al. (1985)

Rohm et al. (1997) Charalambides et al. (2001)

Fracture stress (kPa)

200

150

100

50

0 0.0

0.5

1.0

1.5

2.0

2.5

Aspect ratio

FIGURE 2.22 Effect of aspect ratio (height-to-diameter ratio) on fracture stress of Gouda cheese in compression. (After Luyten et al., 1992.)

According to this procedure, measurements are made on specimens with a constant diameter and various heights. Then, results are plotted as true stress against 1/H for constant values of strain. The intercept of the resulting line (i.e., at 1/H = 0) gives the correction to be applied to the stress for that strain level. For uniaxial compression, Hencky strain can be written in terms of the deformation rate (or crosshead speed), Vz as below:  L (t )   Lo − ∆L   Lo − Vz t  ε H = ln   = ln   = ln    Lo   Lo   Lo 

(2.15)

where, L = current sample height, Lo = initial sample height, ∆L = deformation (= Vz t), and t = time. Since L ≤ Lo in uniaxial compression, εH will have a negative value, an appropriate sign for compressive strains. Most often the right-hand-side of Equation (2.15) is multiplied with –1 to make the resulting strain values positive for common use. In lubricated compression a cylindrical specimen of radius Ro and height Lo is deformed into a cylinder of radius R and height L. From the assumption of constantvolume deformation we can obtain radius at any time from the following relation: L  R = Ro  o   L

1/ 2

(2.16)

The true stress for lubricated compression is calculated from: σt =

[

F(t ) F(t ) L(t ) F(t ) Lo − Vz t = = A(t ) Ao Lo Ao Lo

]

(2.17)

where, F(t) = applied force at any time, A(t) = cross-sectional area at any time, Ao = initial cross-sectional area, Lo = initial length.

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In bonded compression, the cross-sectional area in contact with the compression platens remains constant, and the stress in bonded compression is given as (Casiraghi et al., 1985): σB =

F (t ) π Ro2

(2.18)

The stress is then corrected, σBC, for the shape changes using the following equation: σ BC =

σB R2 (1 + o 2 ) 2L

(2.19)

This corrected stress equation is shown to be effective to bring results in bonded compression into agreement with those in lubricated compression up to a strain level of 0.37 for Cheddar, 1.4 for Mozzarella, and 0.8 for processed cheese spread, where strain is defined as ∆L/L. This definition of strain is used since it relates directly to the extent of bulging (i.e., δo). For the bonded sample the relation is given by the following equation (Christianson et al., 1985): δo =

3 ∆L R 4 o L

(2.20)

Kamyab et al. (1998) and Charalambides et al. (2001) analyzed the uniaxial compression test with friction between the sample and the compression platens, which is quantified by the coefficient of friction. They provided a scheme that enables calculation of true stress–Hencky strain curve from uniaxial compression data influenced by friction. The resulting analytical equation in its simpler form is given as: FL µL  = σt + σt  o  ∀o 3 L

3/ 2

 Do  L   o

(2.21)

where, ∀o = initial sample volume (i.e., πRo2Lo), µ = coefficient of friction, and Do = initial sample diameter. The results from compression tests are analyzed by plotting [FL/∀o] as a function of [Do/Lo] at fixed values of [Lo/L]. The intercept gives the true stress, σt, and the slope can be used to calculate the coefficient of friction, µ. Thus, using this procedure one can construct true stress–Hencky strain curves and determine variation of µ with strain. More parameters, such as the modulus of deformability and fracture energy per volume or toughness per volume, can be extracted from stress–strain curves from uniaxial compression. To facilitate parameter calculations, Ak and Gunasekaran (1992) suggested using polynomial expressions to describe the stress–strain curves as:

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N

σ t = a1ε H + a2 ε 2H + a3ε 3H + ... =

∑a ε

i i H

(2.22)

i =1

where, i denotes an index for the coefficients (ai) and a power for the Hencky-strain term (εΗi ). The coefficients (ai) can readily be determined using a curve-fitting procedure. The modulus of deformability, ED, can be obtained from Equation 2.22 using the following definition:  dσ  ED =  t  = a1  dε H  ε H →0

(2.23)

The coefficient of the first term in Equation 2.22 becomes equal to the modulus of deformability, and this is why it is necessary to apply a constraint so that it has non-negative values in curve-fitting procedure. As an alternative approach, we shall mention that Wium et al. (1997) determined the deformability modulus of UF-Feta cheese as the maximum slope in the range 0 ≤ εΗ ≤ 0.05. The peak strain, εf, which may sometimes correspond to fracture strain, can be estimated by locating the strain at which the slope becomes zero. That is: dσ t =0= dε H

N

∑a ε

i −1 i H

(2.24)

i =1

The strain that makes the slope zero (or nearly zero with some tolerance) can be determined using a root-finding procedure with computation software. Once the peak strain is computed, then its value can be inserted back into Equation 2.22 to determine the corresponding peak stress, σf , which may sometimes correspond to fracture stress. Of course, in some cases, it may be easier to obtain the fracture stress and fracture strain values directly from the experimental data without using Equation 2.24. However, for cases where a distinct peak is not readily discernible, use of Equation 2.24 is a practical approach. It is important to restate that in compression tests the fracture usually starts in the interior of the specimen and often before the maximum stress is reached (Luyten et al., 1991a). One can obtain fracture work per unit volume (W) (or the total energy per unit volume, or modulus of toughness) from the area under the stress–strain curve (Figure 2.17): εf

W=

∫ σ dε t

H

(2.25)

0

The calculation of fracture work becomes simpler with the substitution of Equation 2.22 for stress in Equation 2.25. With this approach we can also easily

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True stress (kPa)

70

A

60 50 40 30 20 10 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

Hencky strain (-) 250 B Slope (kPa)

200 150 100 50 0 −50 0.00

0.50 Hencky strain (-)

1.00

1.50

FIGURE 2.23 Example showing extracting various parameters from stress–strain data (symbols) by fitting a polynomial equation ( σ = 214ε H − 695ε H2 + 1342ε H2 − 1158ε H4 + 355ε H5 ) to the true  dσ 

stress–Hencky strain curve (line) (A). From the plot of slope   vs. Hencky strain (B), the  dε H  modulus of deformability (= slope when Hencky strain approaches zero = 214 kPa) and fracture strain (εH,f = 0.95), and fracture stress (σf = 58 kPa) are calculated at zero slope. Integrating the true stress–Hencky strain polynomial equation between the limits εH = 0 and εH = 0.95, according to Equation (2.25), yields the value of fracture work or modulus of toughness as 35 kJ/m3. (After Ak and Gunasekaran, 1992.)

obtain the work up to any given strain or deformation by simply changing the upper limit of the integral. For instance, if we insert the proportional limit for the upper limit of integral the resulting area is termed the modulus of resilience and is the work done per unit volume to reach the proportional limit (Figure 2.17). The modulus of toughness is a measure of the ductility of a material. The larger the modulus of toughness relative to the modulus of resilience, the more ductile is the material (Fletcher, 1985). In Figure 2.23 we present a numerical example where the mechanical parameters mentioned above are extracted from the experimental data. As can be seen in Figure 2.23, there are more than one minimum and maximum points in the slope vs. strain curve. It is not clear if these points relate to some structural changes during the compression test.

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F

∆L

L0 L

∆D/2

D0

∆D/2

D

FIGURE 2.24 When a material is compressed by ∆L (from original length Lo to final L), its diameter increases by ∆D (from original Do to final D). The associated axial and lateral strains are used to calculate the Poisson’s ratio. (Equations 26a and 26b.)

Another important rheological parameter is the Poisson’s ratio (Figure 2.24). When a specimen of length Lo is compressed to final length L it experiences a concomitant increase in diameter from original value of Do to final D. That is, the imposed axial strain brings about a lateral strain. The Poisson’s ratio is the ratio of lateral strain to axial strain as given below: ν=−

ε ( D − D0 ) / Do lateral strain = − lateral = − axial strain ε axial ( L − Lo ) / Lo

(2.26a)

or, in terms of Hencky strains, it is given as:

ν=−

ε H lateral ε H axial

ln  D D    O =−  ln  L L   0 

(2.26b)

The negative sign indicates that the lateral dimensions decrease as the axial dimensions increase. It also makes ν a positive number since the lateral and axial strains are of opposite sign. The Poisson’s ratio is a material property and is based on the observation that when a material is subjected to an axial force, let us say tension, it will not only elongate but it will also contract laterally (Riley et al., 1995).

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FIGURE 2.25 Picture of compressed Mozzarella samples taken parallel and perpendicular to the fiber direction. (After Ak, 1993.)

Equations 26a and 26b are applicable only to homogeneous isotropic materials; that is, materials with the same properties in all directions. It assumes that the lateral expansion in uniaxial compression and lateral contraction in uniaxial tension is uniform in the radial direction. This may not be the case for some cheeses. For instance, Ak and Gunasekaran (1997) demonstrated that the kneading and stretching of the curd in hot water results in a Mozzarella cheese with anisotropic tensile and compressive properties. Anisotropy refers to the fact that material behavior is dependent on the direction in which stress is applied or on the direction in which sampling is done. As shown in Figure 2.25, the postdeformation appearances of compressed specimens taken parallel and perpendicular to the fiber orientation are clearly different. Thus, Poisson’s ratio calculations based on the lateral expansion of these two cases would certainly produce different values. For some cheeses, anisotropic mechanical properties may also be of commercial importance. For Gruyère de Comté, a Swiss-type hard cheese, it is reported that anisotropic rheological properties are important in the formation of eyes and slits (Grappin et al., 1993). The resistance to wire cutting of Cheddar cheese (4 months old) from different manufacturers is reported to vary with the cutting direction (Ney, 1985). Although allowable range of Poisson’s ratio is from –1 to 0.5, its value generally varies from 0 (totally compressible) to 0.5 (incompressible). For most metals it has a value between 0.25 and 0.35 (Riley et al., 1995). Rubber has a Poisson’s ratio about 0.5, making it nearly incompressible. On the other hand, cork has a Poisson’s ratio close to zero, which makes it a good bottle stopper. An axially loaded cork will not show a lateral expansion, thus making its insertion into a bottle easy. A negative value for Poisson’s ratio has been reported for polymeric and metallic foam structures (Lakes, 1987; Friis et al., 1988). Regarding cheese, experimental

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results indicate that the Poisson’s ratios of Cheddar and Gouda cheeses vary between 0.40 and 0.45; that is 20% and 10% lower than the theoretical value of 0.5 for incompressible materials (Calzada and Peleg, 1978; Luyten et al., 1991b; Rohm et al., 1997). The Poisson’s ratio is related to the elastic constants such as Young’s modulus (E), shear modulus (G), and bulk modulus (K) by the following formulas (Findley et al., 1989): E = 2(1 + ν)G K=

E 3(1 − 2V )

(2.27)

Bulk modulus describes the change in volume in response to hydrostatic pressure (i.e., equal pressures in all directions). From Equation 2.27, for an incompressible (ν = 0.5) linear elastic solid we can compute E = 3G and K = ∞.

UNIAXIAL TENSION As far as the direction of applied stress is concerned, uniaxial tension is simply the opposite of uniaxial compression. However, a more fundamental difference between tension and compression tests is in the strain rate. When a specimen is deformed at a constant speed, the strain rate decreases in tension but increases in compression. Various features of different fundamental methods are listed in Table 2.5. Uniaxial tension tests are considered not suitable for routine measurements since they are more difficult to execute due to lengthy sample preparation and difficulty of gripping (Luyten et al., 1992). Specially designed grips are often necessary in order to eliminate slippage and breakage of sample in the grips. Grip surfaces can be scored or serrated to enable better holding. It is generally assumed that the grip assembly and the specimen ends are nearly rigid and all of the deformation is taking place in the gage section of the specimen. A large number of grips are commercially available for different purposes and materials (Figure 2.26). The existence of many sophisticated grips designed for particular materials is sufficient to show that the tensile test is difficult to perform even for engineering materials. Therefore, it is not a commonly performed test for cheese, particularly at temperatures above melting point of fat in the cheese. The test specimen used in tensile testing may have either a circular or a rectangular cross-section. The latter shape is more suitable for cheese. The ends of tensile specimens are generally enlarged to provide extra area for gripping and to prevent sample prematurely breaking at the grips. A typical tension specimen described in ASTM Standards for plastics is illustrated in Figure 2.27. The specimen must be aligned as perfectly as possible with the direction of stretching so that the long axis of the test specimen will coincide with the direction of the grip assembly. Strictly speaking, data from only those tests that produce failure in the gage length should be used to obtain material properties. In practice, specimens may fail near the grips where there is stress concentration. Therefore, a small notch can be made in the central part of the test piece to ensure the location where the fracture will start (Luyten, 1988) (Figure 2.28).

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TABLE 2.5 Advantages and Drawbacks of Various Test Methods Used for Cheese Test Method I.

Test Type

Uniaxial Constant compression rate

Advantages

a) Difficult to obtain specimens with flat and perfectly parallel ends b) Friction affects the property calculations c) The strain rate increases during a test if a constant crosshead speed is applied (typical of Universal Testing Machines used in food studies) d) Rheological parameters depend on specimen size as a result of friction, varying strain rate, and the inhomogeneities in the cheese e) Start of fracture is often inside the test piece and does not correspond to the maximum stress in the stress–strain curve f) Assumptions of constant volume and perfect cylinder shape during deformation may not hold g) Test piece undergoes inhomogeneous straining Lubricated a) Biaxial extensional viscosity a) Difficult to separate elastic contribution squeeze may be determined relatively from viscous contribution to material’s flow easily when cheese response specimen is compressed b) Difficult to completely eliminate friction between lubricated plates c) Equations will not apply unless the b) Deformation rate can easily assumption of perfect cylinder shape holds be varied to obtain biaxial extensional viscosity as a function of strain rate Constant a) Constant force tests (creep a) Stress decreases during the test if the force tests) can be executed easily plate diameter is greater than specimen for long time scales provided diameter that necessary precautions are b) Strain rate varies during the test taken to avoid physical and c) Drawbacks mentioned above for the chemical changes constant rate case applies here as well b) The Young’s modulus and except that related to strain rate the compliance can be determined c) An apparent viscosity can be calculated from the so-called “secondary stage” where the strain rate is nearly constant d) Relevant to hole (eye) formation in cheese and sagging of cheese under its own mass

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a) Easy to prepare samples and to perform the test b) Young’s modulus can be obtained c) Fracture stress and strain can be obtained d) Easy to vary deformation rate e) Small samples with less chance of containing undesired inhomogeneities

Drawbacks

TABLE 2.5 (continued) Advantages and Drawbacks of Various Test Methods Used for Cheese Test Method

Test Type

II. Uniaxial tension

Constant rate or force

III. Bending

Constant rate or force

IV. Cutting (wire or wedge)

Constant rate

Advantages

Drawbacks

a) Fundamental rheological and fracture properties can be determined, such as Young’s modulus, fracture stress, fracture strain, toughness b) Friction effect is not present c) Fracture initiation and propagation can be controlled using notched samples a) Easy to perform the test b) No need to fix the specimen to an apparatus c) Fracture can be observed mostly on the outside (tension side) of the specimen d) Test imitates closely the sensory evaluation of cheese by graders a) b) c) d) e)

a) It is often difficult to grip the sample, thus requires specially designed grips to hold samples b) Fracture may occur at the grips, which is avoided using special sample shapes (e.g., dog-bone shape) c) Test piece must be long compared to other dimensions for deformation to be homogeneous and for reliable stress–strain calculations. d) Strain rate decreases during a tension test a) Test can be used only for cheese of some rigidity and fairly short texture b) Large test pieces increase the possibility of containing an undesired inhomogeneity c) Length of samples must be much larger than the other dimensions, which is sometimes not practical d) Deformation is far from being homogeneous as it varies from a compressive strain to a no strain at neutral axis, and to a tensile strain at the outside Easy to execute and no need a) Only fracture energy is determined from to clamp sample this test, and other tests are to be carried Small test piece out to obtain other rheological and fracture Useful for determination of properties fracture energy of cheese b) Additional cracks may be formed due to Similar to biting food with inhomogeneities in the structure of brittle teeth materials Fracture is in tension c) Friction between the wedge and the specimen may contribute to the measured force, which can be reduced by lubricating the wedge

Source: After van Vliet, 1991a; Luyten et al., 1992.

Parameter calculations in uniaxial tension are similar to those given earlier for uniaxial compression. Strain and stress in uniaxial tension can be calculated using the following expressions, respectively:  Lo + Vz t   L( t )   L o + ∆L  ε H = ln   = ln   = ln   = ln(1 + ε)  Lo   Lo   Lo 

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(2.28)

FIGURE 2.26 Various designs of commercial grips for tensile tests. (From www.itinscale.com/ grips.htm; www.dillon.fm/grip.htm#clevis; www.cscforce.com/gripping.htm. With permission.)

σt =

[

F(t ) F(t ) L(t ) F(t ) Lo + Vz t = = A(t ) Ao Lo Ao Lo

]

(2.29)

Here, Lo and L are initial and final gage lengths instead of total specimen lengths. In stress calculation it is assumed that the volume of specimen remains constant during extension (i.e., A(t) L(t) = Ao Lo). In strain calculation it is assumed that the deformation as a result of the crosshead movement is taking place in the gage length of the specimen. If this assumption is of suspect, one way to obtain strain values is

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D G W

R

WO

L LO

Recommended tensile specimen dimensions (in mm) for samples of the thickness (mm) listed below (after Swallowe, 1999). Sample thickness

Dimension W L WO (min) LO (min) G D R

7 to 14 19 57 29 246 50 115 76

4 to 7 13 57 19 165 50 115 76

<4 3.18 9.53 9.53 63.5 7.62 25.4 12.7

Tolerance ±0.5 ±0.5 +6.4 (3.18 for <4) No max ±0.25 ±5 ±1

FIGURE 2.27 Tensile specimen with recommended dimensions. Gage length

Notch

FIGURE 2.28 Tensile specimens with notches.

to draw marker lines on the specimen before testing and take photographs or videotape of the specimen during the deformation (Figure 2.29). Using the distance between the lines one can calculate the real strain values. Of course, more advanced techniques involving video recording and image analysis would yield quicker and more accurate results. There is an alternative technique to measure tensile properties while actually performing the test in compression. This technique is called the diametral compression (also known as the Brazilian test, indirect tension test, or compression splitting test), which is simpler to execute than the uniaxial tension test. It is a well-established method to measure the tensile strength of brittle materials such as concrete and ceramics (Fahad, 1996). Its application to determine the tensile strength of rice grains

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FIGURE 2.29 Pictures of a deforming cheese specimen at different times in the uniaxial horizontal extension experiment. (After Ak, 1993.)

has also been reported (Kamst et al., 1999). The diametral compression test is based on the fact that tensile stresses develop when a circular disc is compressed between two diametrically opposite faces (Fahad, 1996). For a specimen in the form of a right-circular cylinder of diameter D and thickness t undergoing diametral compression (Figure 2.30) the tensile strength value σΤ is calculated from: σT =

2F πDt

(2.30)

where, F is the applied force. This equation is derived for a Hookean solid for which the stress is proportional to the strain. Equation 2.30 is strictly valid for samples with a thickness-to-diameter ratio of 0.25 ≤ t/D ≤ 0.5 (Newton et al., 2000).

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F

R

t σT

FIGURE 2.30 Schematic drawing of diametral compression test (F = compressive force; R = sample radius; t = sample thickness; σT = tensile stress developed in the material).

BENDING TEST In sensory evaluation of cheese the panelist takes the ends of a cheese plug by the forefingers and thumbs of both hands and bends the plug slowly into a semicircle to observe when the sample breaks, as well as the nature of the break. This sensory evaluation sort of mimics the bending test. The bending test can be readily practiced with a rubber eraser or with a piece of string cheese. The major advantage of the bending test is that there is no need to fix the specimen to the measuring instrument. In this respect the bending test is easy to conduct, especially for brittle and other hard-to-grip materials. Typically, a cylindrical or rectangular cross-section sample is laid horizontally on a support with two (blunt or rounded) supporting edges, and the sample is pushed down at the center of the specimen (Figure 2.31) by means of a blunt (or rounded) plunger attached to the crosshead of a UTM. There are three points at which the material comes in contact with the test device. Thus, this test is also known as the three-point-bending test. The part of the sample on the side of the plunger experiences compressive stress (and compressive strain), and the opposite side experiences tensile stress (and tensile strain). The plane of transition from compressive to tensile stress (and strain) is known as the neutral axis. Fracture can often be observed on the side of the sample experiencing tensile stress (and strain). For a proper bending test, the test piece must have a large ratio of length to diameter or thickness, which is hard to obtain with cheese (van Vliet, 1991a). According to Luyten (1988), for Gouda cheese, this ratio should be 3.33 or greater

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F Plunger b (width) Neutral axis

h (height or thickness) -Side view-

-Front viewL F/2

F/2 compression

neutral

tension

FIGURE 2.31 Schematic drawing of three-point bending test.

in order to obtain reproducible results. Large specimen size implies higher probability of presence of inhomogeneities in the specimen (see Table 4.1 for various possible inhomogeneities in cheese). Luyten (1988) further noted that the bending test is good for mature and acid cheese with low fracture strain (i.e., short consistency), but not suitable for young cheese with high fracture strain where the test piece can slide from the supports before it fractures. For soft and deformable materials, penetration of the plunger used for bending complicates the situation as it introduces a significant compressive stress (Luyten, 1988). It can generally be stated that the bending test is most suitable for studying brittle materials. The equation for a linear elastic solid giving the bending stress can generally be expressed in the following form: σ=

Mc I

(2.31)

where, M is the bending moment, c the vertical distance between the neutral axis and the point at which the stress is sought, and I the area moment of the crosssection of the beam. The maximum deformation occurs at the center of the beam where the load is applied. We can write the following relations for stress and strain. Specimen with a Rectangular Cross-Section Maximum stress is given by: σ max = ±

3FL 2 b h2

(2.32)

where, F is the applied force, L the span or the distance between supports, b the width of test piece, and h the height or thickness of test piece.

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The corresponding strain at the base of the beam is given by:

ε=

6 h ∆y L2

(2.33)

where, ∆y is the (maximum) deflection at the center of the beam. We note that for the test piece with rectangular cross-section the maximum compressive stress (Equation 2.32 with negative sign) occurs at the top of the beam, whereas the maximum tensile (Equation 2.32 with positive sign) stress occurs at the bottom of the beam. The inherent assumption is that the elastic moduli of the material are the same in tension and compression. Specimen with a Circular Cross-Section Maximum stress is given by:

σ max =

8FL π D3

(2.34)

The corresponding strain is given by:

ε=

6 D ∆y L2

(2.35)

All of the equations given for bending are valid only for small strains and linear elastic materials (Luyten, 1988).

TORSION TEST Torsion test is applied by twisting a specimen about its longitudinal axis. Specimens used in torsion tests are usually circular in cross-section (Figure 2.32). The test piece can be fixed to the apparatus by gluing; for instance, by using cyanoacrylate adhesive. The torsion test produces pure shear, and hence does not change the specimen volume. Therefore, it is ideally suited for materials that may exude some of their contents (e.g., moisture, fat, etc.) under applied force. For a homogeneous and isotropic material exhibiting linearly elastic behavior (i.e., Hooke’s law applicable, τ = Gγ) the equations to calculate stress and strain are given below. Maximum shear stress at the surface of test piece:

τ max =

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2 Tmax π R3

(2.36)

γ T γ

θ R

r

L τ

R

r

FIGURE 2.32 Schematic drawing of torsion test (L = specimen length; R = specimen radius; T = torque applied during test; θ = angle of twist; γ = shear strain).

Maximum shear strain at the surface of test piece: γ max = R

θ L

(2.37)

where, Tmax is the torque on the surface, R the radius of the specimen, θ the total angle of twist in radians, and L the length of the specimen. The equations given above apply to solid, circular materials. Montejano et al. (1983) used capstan-shaped (i.e., narrow mid-section and enlarged ends) specimens to minimize undesirable stress concentrations at the locations where the twisting moments are applied (Figure 2.33). Since the diameter of the specimen is not uniform, a geometric correction factor, K, is to be applied to Equations 2.36 and 2.37 for calculating shear stress and shear strain (Hamann, 1983). The maximum shear stress is given by: τ max = K

2 Tmax 3 π Rmin

(2.38)

where, Rmin, is the specimen minimum radius, K the constant depending on the sample geometry. K is given by (Lanier, 2000): 1/ 2 2      31 +  Rmin + 1        Rc     K=  1/ 2    Rmin    4 1 + 2 + 1   Rc         

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(2.39)

D T

Rmin

Rc

T

FIGURE 2.33 Schematic drawing of a capstan-shaped test piece for torsion test (D = specimen diameter at ends; Rmin minimum radius at the specimen center, Rc = radius of curvature; T = torque applied during test). (After Montejano et al., 1983.)

and the maximum shear strain is obtained from: γ max =

2Kθ 3 Q π Rmin

(2.40)

Q is given by:

Q=

4 π

zo

∫ (R 0

[

min

dz

(

+ Rc ) − Rc2 − z 2

)

]

1/ 2 4

(2.41)

where, z varies from 0 (center of the groove) to zo (boundary of the groove and end section). For instance, Montejano et al. (1983) used cylindrical gel specimens with L = 28.7 mm, zo = 6.4 mm, D = 18.6 mm, Rmin = 5 mm, and Rc = 9.4 mm. Using these numerical values and Equations 2.39 and 2.41 we find that K = 1.08 and Q = 8.32 × 106 m–3.

VANE METHOD The vane geometry has been developed to eliminate slip effects frequently observed in yield stress measurements with the rotational viscometers (Barnes and Nguyen, 2001). It is simple but effective means of directly measuring the yield stress (Barnes and Nguyen, 2001; Nguyen and Boger, 1983; Nguyen and Boger, 1985). In a recent review, Barnes and Nguyen (2001) discuss the utility of the vane technique in measuring various rheological quantities such as (a) modulus of linear elastic solids and viscosity of Newtonian liquids; (b) yield stress; and (c) flow-curves of nonNewtonian fluids. In food rheology, the vane geometry is primarily used for direct measurement of yield stress (Table 2.6). © 2003 by CRC Press LLC

TABLE 2.6 Experimental Conditions in Food-Related Studies Using the Vane Method Vane Spindle Test Material Frozen ice cream Spreadable foods

Property Measured

Height (mm)

18 10

Stirred yogurt

Equilibrium stress

45

38 20 28 36 67.5

Set yogurt Processed cheese analogs Processed and natural cheese Cream cheese

Yield stress Yield stress

35 6

40–60 5.5

6–10

15–20

10b

20 25b 35 20 24 28 32

Protein foams

Yield stress Yield stress

Diameter (mm)

Fracture stress and equilibrium stress Yield stress and strain Yield stress

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10

Instrument Used Lab-made Brookfield HBTDV-I & 5X HBTDV-I Physica Rheolab MC100 Haake VT 550 Brookfield HBTDV-I Haake VT 550

Number of Blades

Thickness of Blades (mm)

Rotational Speed (rpm)

4

0.1

1

4

0.80

0.5

4

NAa

NA

6 4

NA NA

NA NA

4

NA

0.028–5

4

0.7

0.5

4

NA

0.3

Haake VT 550

Brookfield DV-I 25xLVTDV

References Briggs et al., 1996 Daubert et al., 1998

Geraghty and Butler, 1999 Dimonte et al., 1998 Mleko and Foegeding, 2000 Truong and Daubert, 2001 Breidinger and Steffe, 2001 Pernell et al., 2000

TABLE 2.6 (continued) Experimental Conditions in Food-Related Studies Using the Vane Method Vane Spindle Test Material

Property Measured

Molten chocolate

Yield stress

Food dispersions

Yield stress

a b c d

NA = Not Available Recommended dimensions CR = Controlled rate mode CS = Controlled stress mode

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Diameter (mm)

Height (mm)

15 20 25 40 (CRc mode) 21 (CSd mode)

40 55 70 60 (CR mode) 30 (CS mode)

Instrument Used Brabender Rheotron Haake RV2 Deer Rheometer III

Number of Blades

Thickness of Blades (mm)

4

0.55

6 (CR mode) 4 (CS mode)

NA NA

Rotational Speed (rpm) 0.064 0.120 0.224 0.4

References Wilson et al., 1993

Yoo et al., 1995

Although the existence of a yield stress as a physical reality has been debated in the literature (Barnes, 1999), the utility of this rheological parameter is recognized in food processing (Campanella and Peleg, 1987a; Steffe, 1996). Contributing to the discussion on yield stress, Schurz (1992) mentioned the critical role of this parameter in polymer processing and suggested the use of the term apparent yield stress as a resolution of the debate. Astarita (1990) stated that whether yield stress is or is not an engineering reality depends on the problem in consideration. Thus, from a processing point of view, the concept of yield stress is useful as long as the Deborah number (i.e., the ratio of a material’s characteristic relaxation time to the characteristic process time) is large (Zhu et al., 2001). Many reasons can be advanced to support usefulness of the concept of yield stress in food rheology. For instance, (a) for the short time scales encountered in food processing, consumption, and handling activities, a viscoplastic or elastoplastic material may demonstrate solid-like behavior (i.e., not flowing within the time available under a given stress); (b) rheological equations with a yield-stress term (e.g., Bingham, Casson, Herschel-Bulkley models) are successfully used in modeling behavior of several foods; (c) yield stress is considered a key parameter for quality control and evaluation of many products (e.g., ketchup, cream cheese, mayonnaise, various spreads) (Steffe, 1996). These commercially important products are formulated to display yield stress. The vane geometry is similar to the concentric cylinder system, except that the inner cylinder (i.e., the bob) is replaced by a vane spindle. The vane spindle is simply an attachment adapted to fit an existing rotational rheometer or viscometer (e.g., Brookefield viscometer) (Nijman and Chakrabarti, 1997). A vane consists of a number (2 to 8) of thin blades arranged at equal angles around a slender central shaft. A schematic drawing of a typical four-bladed vane rotor is presented in Figure 2.34. Several examples and dimensions of vane rotors used are listed in Table 2.6. The key assumptions in vane rheometry are that the shearing stress is uniform over the virtual cylindrical surface described by the outer edges of the blades, the material trapped between the blades of the vane is rotating as a rigid body, and there are no secondary flows between the blades (Barnes and Nguyen, 2001). These assumptions are valid if the vane consists of four or more blades and rotates at low speeds. There are experimental results on various nonfood and food systems such as shaving cream (Zhang et al., 1998), oil-in-water emulsions (Yoshimura et al., 1987), and applesauce (Qiu and Rao, 1988), as well as simulation data (Yan and James, 1997) to support validity of assumptions under stated conditions. In addition to eliminating the wall slip, the vane geometry offers other advantages over conventional rotational techniques (e.g., concentric cylinder): the sample preparation is simple and gentle, which enables measurements on weak materials inserting the vane spindle into the sample causing little disturbance to the material structure. This is important, particularly when working with thixotropic systems and delicate structures such as foams (Zhang et al., 1998). Multi-phase systems (e.g., suspensions, emulsions) have a tendency to form a low-viscosity, particle-depleted layer adjacent to the shearing surfaces of the traditional viscometer geometries. The velocity gradient in the low-viscosity layer at a fixed shear stress is larger than that in the bulk material, which then results in apparent slip. However, the vane geometry avoids

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Ω

H H

D

D

FIGURE 2.34 The vane rotor with four blades (H = vane height; D = vane diameter; Ω = angular velocity).

the wall-slip problem by using the test material contained between the vane blades as the virtual shearing surface. In a way, the vane acts like a solid cylinder (i.e., bob) without the wall-slip complications. It is also worth noting that the slip at the outer cylindrical boundary can be eliminated by inserting a slender gauze basket inside the outer cylinder (Barnes and Nguyen, 2001) or lining the inner wall with aluminum foil (Yoshimura et al., 1987). Another advantage of the vane method is that original product containers can be used as sample holders while measuring with the vane spindle. There is no need for a narrow gap (in contrast to concentric cylinder geometry), and the vane is less susceptible to artifacts arising from the presence of large particles. Breidinger and Steffe (2001) recommend the vane dimensions of 10 mm in length by 25 mm in diameter after considering the size of most commercial cream-cheese containers and maximum torque capacity of rotational viscometers. Nguyen and Boger (1983) studied the effect of rotational speed on the yield stress of bauxite residue suspensions (red mud) over a range of speeds from 0.1 rpm to 256 rpm. Their results, replotted in Figure 2.35, indicate a practically constant yield stress between 0.1 rpm to 8 rpm, followed by a rising yield stress with

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400

Yield stress (Pa)

300

200

100

0 0.1

1

10

100

1000

Rotational speed (rpm)

FIGURE 2.35 Effect of vane rotational speed on yield stress of red mud. Vane geometry: H/D = 1.923. (After Nguyen and Boger, 1983.)

increasing rotational speed. However, Nguyen and Boger (1983) used the lowest available speed of 0.1 rpm to minimize any unforeseen errors. As noticed in Table 2.6, in studies on foods, the vane is often rotated at a constant speed less than 1 rpm. There is experimental evidence indicating the effect of rotational speed on the yield stress values of molten chocolates and food dispersions (Wilson et al., 1993; Qiu and Rao, 1988) and TiO2 suspensions (Liddell and Boger, 1996). High vane speeds, particularly in low-viscosity liquids, are risky since secondary flows may develop between the blades (Barnes, 1999). A typical torque-time response for a material having a yield stress is illustrated in Figure 2.36. The initial elastic region is followed by a slightly curved part before reaching the peak torque. After a distinct maximum torque, a decline (rapid or

Torque

Tmax

tmax

Time

FIGURE 2.36 Typical torque-time response from the vane in a rate-controlled mode. Maximum torque (Tmax) occurs after a certain time (tmax) of rotation of the vane.

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Ω

Ω

Z1

H

D Z2 DT (a)

(b)

FIGURE 2.37 Schematic diagram of vane system (diameter, D; height, H, and container diameter, DT; Ω = angular velocity) in different positions: (a) immersed in the sample (Z1 and Z2 height of sample above and below the vane, respectively), (b) top surface in level with the sample.

gradual depending upon conditions) is observed towards an equilibrium torque value. In general, the peak torque is the only parameter derived from these curves to compute the yield stress. The peak torque is, of course, readily and unequivocally determined in comparison to other points of possible interest (e.g., departure from linearity, equilibrium level). When the vane blades are entirely immersed in a sample, as shown in Figure 2.37a, the following equation is used to calculate the yield stress (τy) from the measured maximum torque and vane dimensions:  2T  τ y =  max3  πD 

 H + 1  D 3 

−1

(2.42)

where Tmax is the maximum torque, D the vane diameter, H the vane height. When the top of the vane blades are aligned even with the top surface of the sample (Figure 2.37b), the stress contribution from the material above the vane is eliminated, and Equation 2.42 takes the form:  2T  τ y =  max3  πD 

H + 1  D 6 

−1

(2.43)

The following geometrical ratios have been proposed for accurate measurements with the vane method: H/D < 3.5; DT/D > 2.0; Z1/D > 1.0; Z2/D > 0.5 (Nguyen and Boger, 1985). Here, DT is the diameter of the container, Z1 and Z2 are height of © 2003 by CRC Press LLC

material above and below the vane, respectively. Typically, the blades are made of stainless steel with the thickness less than 1 mm. Recently, a new instrument called “slotted-plate device” has been developed to directly measure static yield stresses of suspensions (Zhu et al., 2001). The slottedplate device is reported to be more reliable for evaluating smaller yield stresses and avoids possible secondary flows between the blades and nonuniform stress distribution along a virtual cylindrical surface — the key assumptions in the vane geometry. The success with the vane method has resulted in new applications and designs of this geometry such as oscillatory testing and texture analysis (Junus and Briggs, 2001) and hand-held versions of the vane instrument (Keener et al., 1999).

STRESS-RELAXATION TEST One of the fundamental tests to study viscoelastic response is stress relaxation. This test can be performed in (uniaxial) tension, compression, shear, bending, torsion, etc. When a constant strain is applied to a viscoelastic material isothermally, the stress necessary to maintain that strain is not constant but decreases with time. Hence, the decrease of stress at constant strain is called stress relaxation. Two kinds of relaxation experiments can be conducted: stress relaxation after a sudden step strain, which is often applied to solids; and stress relaxation following a cessation of steady flow, which is often applied to liquids (Figure 2.38) (Dealy, 1995; Ferry, 1980; Whorlow, 1980). Stress-relaxation response permits rapid characterization of material behavior as shown in Figure 2.39. When a step strain is applied to ideal elastic solid, a finite and constant stress will be reached. Ideal elastic solids store all the energy charged during the straining step and would expend this energy upon removal of stress to return to its original size and shape. In a way, ideal elastic solids possess a perfect memory of the initial state. Thus, the same stress should be kept on the specimen at

Strain

Cessation of flow

Step strain

Time

FIGURE 2.38 Two types of stress relaxation test: step strain for solids and cessation of steady flow for liquids.

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Strain

Constant strain input

Time

Stress

Ideal elastic response

Stress

Time

Ideal viscous response

Time 2

Stress

Linear viscoelastic response

3

4

1

Time ε0

ε0

ε0

1

2

3

4

σ1=0

σ2

σ3

σ4

σ2 > σ3 > σ4

FIGURE 2.39 Step-strain input (A) and stress relaxation response of ideal elastic material (B), ideal viscous material (C), and viscoelastic material (D). The stress and strain on the viscoelastic material is schematically depicted at different times during the test at the bottom.

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all times for strain to remain constant. On the other hand, for ideal viscous liquids the stress decays to zero immediately after the cessation of strain application. Ideal viscous liquids do not store any energy and have no memory of the initial state. However, various materials, including foods, are viscoelastic and exhibit an intermediate response where stress relaxes at a finite rate characterized by the relaxation time (Peleg, 1987). Viscoelastic materials can be considered as materials with “fading memory.” If a viscoelastic material relaxes to zero stress within a certain period (e.g., experimental time) it is further characterized as “viscoelastic liquid.” In contrast, a viscoelastic material is considered as “viscoelastic solid” if a finite stress remains unrelaxed (i.e., residual stress) after a sufficiently long time. With most foods, however, the “sufficiently long time” is on the order of few minutes due to chemical, enzymatic, and physical changes that foods normally experience. The residual stress after an arbitrary time for test duration (e.g., 10 min) is suggested as a quantitative measure of the degree of “solidity” of foods (Peleg, 1987). The relaxation experiment can be viewed as composed of two steps: the straining step and the relaxation step. Ideally, the straining step is instantaneous, but in reality it takes finite time. The time it takes to apply the step strain is called the rise time. The rise time depends upon the capability of the instrument used and the magnitude of strain. For instance, if the highest crosshead speed of a UTM machine were 1000 mm/min, then it would require 0.09 s to apply 10% deformation on a sample of 15 mm height. Since stress relaxation of a viscoelastic material is affected by the history of deformation, the time taken for the straining step is important (Meissner, 1978). Accurate stress-relaxation tests require the rise time of the applied strain to be short in comparison with the relaxation times to be measured. With the advanced rheometers it is possible to apply a step strain within few seconds or milliseconds (e.g., 20 ms to 1000 ms) (Lauger and Huck, 2002). Obviously, for a proper test the applied strain, and consequently the resulting stress, should be lower than the corresponding fracture value. Although in nonfood applications stress-relaxation tests can be continued for a long time, the test duration for foods is limited (on the order of minutes, e.g., 10 min or less) because degradation of sample may occur before the test is completed as a result of physical changes (e.g., moisture exchange with environment), microbial activity, and chemical and biochemical changes (e.g., enzymatic browning in fruits, oxidation in oil-containing foods) (Peleg, 1987). For a linear viscoelastic material subjected to an instantaneous constant strain (εo),* the initial stress will be proportional to the applied strain and will decrease with time (Figure 2.40). By linearity it is meant that when the applied strain is multiplied by any factor (e.g., doubling), the stress it produces also changes by the same factor (e.g., doubling). The rate of stress decay is quantified by a material characteristic time known as relaxation time, λ. The relaxation time in practice is defined as the time for stress to decay to about 37% of the initial level. However, single-relaxation time is often insufficient to fully describe the relaxation curve of most food materials. A better representation of relaxation curve is possible by using more than one relaxation time or, ideally, by using a continuous relaxation-time spectrum (Peleg and Normand, 1983). * The symbol ε hereafter denotes Hencky strain unless stated otherwise.

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Stress

Straining stage Relaxation stage

σ0

0.37σ0

Rise time

Relaxation time, λ

Time

FIGURE 2.40 In actual relaxation test, the strain is applied over a finite time (rise time). The peak stress at the end of the straining stage is the inital stress (σo). Time taken for the stress to decay to 0.37σo during the relaxation stage is the relaxation time, λ.

For linear viscoelastic materials the stress decay with time t can be described, in tension or compression, by the following equation: σ(t ) = E (t ) ε o (2.44)

or E (t ) =

σ (t ) εo

where, the function E(t) is called the relaxation modulus. The relaxation modulus represents the change in stress per unit of applied strain and is a material property. For linear elastic solids the E(t) = E, the Young’s modulus. In shear configuration the corresponding equations are given as: τ( t ) = G( t ) γ o (2.45)

or G( t ) =

τ( t ) γo

where, τ(t) is the shear stress, G(t) the shear stress relaxation modulus, and γ the applied constant shear strain.

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o

Analysis of Relaxation Behavior Stress relaxation is a basic test providing information on the viscoelastic character of materials rapidly. Although in principle relaxation test can be done in any configuration (i.e., compression, tension, shear, torsion, bending, etc) the most common one in cheese studies is compression. To determine linear viscoelastic region of a material in relaxation, a series of relaxation curves is obtained by sequentially increasing the applied strain. When the resulting data is replotted in terms of modulus vs. time, the curves within the linear viscoelastic region will overlap. The strain level at which the curve does not overlap indicates that the linear viscoelastic region is exceeded. Alternately, the linear range of the isochronal — the plot of stress against strain at a specific time — will indicate the extent of strain level over which the material response can be considered linear (Ak and Gunasekaran, 2001). The process of obtaining isochronal plots is illustrated in Figure 2.41. The data obtained at two constant strains (ε1 and ε2) are represented in Figures 2.41A and 2.41B. From these, data points (for, e.g., a, b, c, d in Figure 2.41A and 2.41B) are gathered at different times (e.g., t1 and t2). Then the corresponding σ(t) vs. ε plot is constructed for each of the times at which the stress response is measured (Figure 2.41C). The strain value at which the isochronal begins to deviate from linearity (indicated by dotted line in Figure 2.41C) is the upper limit of the liner viscoelastic region for the material. The hatched region in Figure 2.41C indicates the nonlinear range of the material studied. The mechanical model most suitable for quantification of relaxation behavior of foods and a variety of polymeric materials has traditionally been the generalized Maxwell model (Figure 2.42) with a discrete number of elements (Peleg and Normand, 1983):

σ (t ) = E(t ) = Eo + εo



n



t 

∑ E exp − λ   i

i =1

(2.46)

i

where, Eo is the modulus of the single spring (λ = ∞) in parallel to Maxwell elements in Figure 2.42, t the time, Ei the modulus of each Maxwell element, and λi the relaxation time of each Maxwell element. It must be mentioned that for a true viscoelastic liquid the first term (i.e., Eo) will be zero and the material will eventually relax completely. For linear viscoelastic behavior, the relaxation parameters are a function of time only. However, for nonlinear viscoelastic behavior, the relaxation parameters will be a function of time as well as imposed strain and strain history. An alternative model to describe relaxation and creep curves of viscoelastic solids is suggested by Peleg (1979, 1980): t = k1 + k2 t Y (t )

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(2.47)

ε2 ε1 t

t

σ1(t)

σ2(t) c a

d

b

t1

t

t2

t1

t2

(a)

t

(b)

σ σ(t1)

Linear

c σ(t2)

a d Nonlinear b ε1

ε2

ε (c)

FIGURE 2.41 Plotting isochronals to determine linear viscoelastic range from stress relaxation data. (A) relaxation experiment at applied strain ε1; (B) relaxation experiment at applied strain ε2; and (C) isochronals plotted using data points a, b, c, and d from A and B at times t1 and t2 . (After Ak and Gunasekaran, 2001.)

and Y (t ) =

σ o − σ (t ) σo

(2.48)

where, σo is the initial stress and σ(t) the decaying stress. This linearization makes the calculation of model parameters easy as the slope gives k2 and the intercept gives the k1 . As it is also true for the parameters of the generalized Maxwell model,

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E0

E1

h1

E2

h2

E3

h3

En

hn

FIGURE 2.42 Generalized Maxwell element for stress relaxation (E0, E2, E3, … En are spring stiffnesses; η1, η2, η3, … ηn are dashpot viscosities).

the dependency of the constants k1 and k2 on the applied strain is an indication of nonlinear viscoelasticity related to the structural modifications that occur during deformation. Peleg (1980) further stated that 1/k1 represents the initial decay rate, while 1/k2 represents asymptotic level of Y(t) when t→∞.

CREEP TEST As with stress relaxation, a creep test can be performed in different configurations (i.e., compression, tension, shear, torsion, etc). In an isothermal creep test, a constant stress is applied to the material, and the resultant strain is recorded as a function of time (Figure 2.43). In an actual test the stress application is not instantaneous but can be rapid such as by dropping the weight on the specimen. Analysis of Creep Behavior In a creep test a constant step-stress is applied to a material and the resulting deformation or strain is measured as a function of time. The distinction between constant stress and constant force is necessary, especially for highly deformable foods, because of the progressive change in the cross-sectional area of the specimen. Hence, a constant force (i.e., dead weight) results in a progressively increasing stress in uniaxial tension and decreasing stress in uniaxial compression (Purkayastha et al., 1985). Although in principle creep tests can be done in any configuration (i.e., compression, tension, shear, torsion, bending, etc.), the most common one in cheese studies is compression. For linear materials, the time-dependent compliance, D(t), is given by (Findley et al., 1989): D(t ) ≡ ε(t ) σ o

(2.49)

where, ε(t) is the tensile or compressive strain. Symbol J(t) is used to represent the shear creep compliance, that is, J(t) = γ (t)/τo, where γ (t) is the shear strain, and

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Load removed Constant stress application

A

Stress

σo

0 B

t1

Time

t1

Time

Elastic solid response

Strain

εo quid

li cous

onse

resp

Vis

0

Recovery

Creep C 4

εi

Strain

3

5 2 Permanent strain

εi 1 t1

0 W

1

Time

Linear viscoelastic response

2

W

3

W W

4

5

FIGURE 2.43 Typical creep–recovery test. (A) application of instantaneous and constant stress (σo); (B) strain response of elastic solid and viscous liquid; (C) strain response of viscoelastic material. The application and removal of load (W) is shown at the bottom at various times along the creep–recovery curve for the viscoelastic material.

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D(t) Creep Curve ∑Di

Delayed creep Steady state flow slope = 1/η

Do

Instantaneous compliance

Time

FIGURE 2.44 Typical creep compliance D(t) vs. time response of a viscoelastic material comprises of instantaneous compliance, delayed creep, and steady state flow (of viscosity η).

σ3

Strain

σ1 σ3 > σ2 > σ1

Time (a)

σ3 Compliance, D (t)

σ2

σ2 & σ1

Time (b)

FIGURE 2.45 Determining linear viscoelastic region by creep tests. A. Creep curves at different stress levels σ1, σ2, and σ3; B. Compliance D(t) vs. time for the corresponding creep curves overlap within the linear viscoelastic region (σ1 to σ2). Stress level σ3 is outside of linear viscoelastic region. (After Anon, 2002.)

τo the applied shear stress. The objective of creep tests is to determine material properties D(t) and J(t) from the experimental strain vs. time data (Figure 2.44). To determine linear viscoelastic region of a material in creep, a series of creep curves is obtained by sequentially increasing the applied stress (Figure 2.45). When the resulting data is replotted in terms of creep compliance vs. time the curves within the linear viscoelastic region will overlap. A typical creep compliance curve is shown schematically in Figure 2.44. Unless the applied force or stress is carefully selected the test terminates with the failure of the specimen, especially in tension. Quantification of creep behavior of foods and a variety of biological and polymeric materials has been traditionally based on the © 2003 by CRC Press LLC

E2

E3

En η1

E0

η2

η3

ηn

FIGURE 2.46 Generalized Voigt-Kelvin element for creep (E0, E2, E3, … En are spring stiffnesses; η1, η2, η3, … ηn are dashpot viscosities).

generalized Kelvin-Voigt model (Figure 2.46) with a discrete number of elements (Purkayastha et al., 1984): ε (t ) t = D(t ) = Do + + σo η1



n



t 

∑ D 1 − exp − τ   i

i =2

(2.50)

i

where, Do is the instantaneous compliance (= 1/Eo), t the time, η1 the Newtonian viscosity while 1/η1 being the slope of the linear portion of the creep curve after sufficiently long time, Di the delayed compliance of each Kelvin-Voigt element (= 1/Ei), and τi the retardation time of each Kelvin-Voigt element. The last term in Equation 2.50 is called the creep function and denoted by ψ(t) (Purkayastha et al., 1984). It must be mentioned that for a true viscoelastic solid material the second term (i.e., t/η1) will be zero, and the material will eventually reach an equilibrium creep compliance. Equation 2.50 also reveals that a typical creep curve is composed of three components, as illustrated in Figure 2.44. For linear viscoelastic behaviors the creep parameters are a function of time only. However, for nonlinear viscoelastic behaviors the creep parameters will be a function of time as well as imposed stress and stress history. As for the relaxation case, the Peleg model (Purkayastha et al., 1984) can be used to linearize and represent the creep behavior of foods. For creep data, the Peleg model is used to represent the creep function using constants k1″ and k2″ as: ψ (t ) = D(t ) − Do −

t t = " η1 k1 + k2" t

(2.51)

SHEAR RHEOMETRY Polymer and food-processing applications involve a wide range of shear rates as shown in Figure 2.47. Thus, various rheometry measurements based on different geometries are essential and complementary to each other.

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Oscillatory/Vibrational Rotational Elongational Capillary Polymer Processing Food Processing 10−6

10−3

10−2

10−1

100

101

102

103

104

105

Shear rate (s−1)

FIGURE 2.47 Approximate shear rate ranges for different rheometry measurements and those involved in polymer processing and food processing applications. (After Riande et al., 2000.)

Rheological measurements based on shear flow are conveniently divided into two groups: (a) drag flows in which shear is generated between a moving and a fixed solid surface, and (b) pressure-driven flows in which shear is generated by a pressure difference over a closed channel (Macosko, 1994). Examples of shear-flow geometries belonging to the first group include sliding plates, concentric cylinders, parallel disks, and cone and plate. Examples of shear-flow geometries belonging to the second group include capillary or Poiseuille flow, slit flow, and axial annulus flow. The working equations for some of these measurement techniques are presented here. Interested readers are referred to other sources (Collyer and Clegg, 1988; Macosko, 1994; Steffe, 1996) for detailed discussions. The measurement systems described below can be used to conduct a variety of tests (e.g., steady shear, dynamic, relaxation, creep). In some tests, one system may be preferred over the others due to the shear-rate range or other advantages it offers. For instance, parallel-plate geometry is often preferred for measuring viscoelastic properties of solid cheese (e.g., relaxation modulus, creep compliance, dynamic moduli) since the sample handling is easier and the sensitivity to gap setting is less as compared to the cone-and-plate geometry. There are several companies manufacturing highly advanced rheometers and viscometers that will satisfy the measurement needs of researchers. Barnes et al. (1999) summarized the history of commercial viscometry and rheometry. Web sites of various companies offering rheological instruments are given in Table 2.7 for readers to have quick access.

SLIDING-PLATES GEOMETRY The schematic drawing of the sliding-plate geometry is shown in Figure 2.48. This relatively simple arrangement is generally used in defining shear viscosity. The

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TABLE 2.7 Some Major Manufacturers of Rheometers and Viscometers Company

Web Site

Alpha Technologies ATS RheoSystems Bohlin Instruments Brookfield Camtel Dynisco Polymer Test GBC Scientific Equipment Pty Ltd. Goettfert Inc. Haake Infra Scientific Kaltec Scientific Paar Physica Porpoise Viscometers Pressure Profile Systems, Inc. Reologica Instruments AB Research Equipment (London) Ltd. Rheometric Scientific TA Instruments Vilastic Scientific Inc.

http://www.alpha-technologies.com/ http://www.atsrheosystems.com http://www.bohlin.com/ http://www.brookfieldengineering.com/ http://www.camtel.co.uk/ http://www.dynisco.com/ http://www.gbcsci.com/ http://www.goettfert.com http://www.thermo.com/ http://www.infra.uk.com/ http://www.kaltecsci.com/ http://www.physica.de/ http://www.porpoise.co.uk/ http://www.pressure-profile.com/ http://www.reologica.se/ http://www.research-equipment.com/ http://www.rheosci.com/ http://www.tainst.com/ http://www.vilastic.com/

Source: The Society of Rheology Web site, http://www.rheology.org/sor.

Moving plate ∆X

y

Fx,Vx sample

H

sample

x Stationary plate

L Width of plate = W; Area of plate, A = L.W

FIGURE 2.48 Description of sliding plate geometry. Application of shear force Fx moves the top plate by ∆X at a velocity Vx.

sliding-plate rheometer can be operated in either strain-controlled or stress-controlled mode. The shear strain (γ), shear rate (γ˙), and shear stress (τ) can be calculated from the following equations (Dealy and Wissbrun, 1989; Macosko, 1994): γ=

∆X Vx t = H H

(2.52)

Vx H

(2.53)

γ˙ =

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τ=

Fx F = x A LW

(2.54)

where, L is the plate length, W the plate width, H the sample thickness, ∆X the sliding-plate displacement, Vx the velocity of sliding plate, Fx the shear force, and t the time. The shear viscosity is then computed from η = τ/ γ˙. The assumptions involved in the sliding-plates geometry include: (a) negligible inertial and edge effects to establish homogenous, simple shear flow, and (b) L and W are much greater than H, and H is as small as possible. The principal advantage of the sliding-plate geometry is that it is ideally suited for studying nonlinear viscoelasticity. The relative advantages and disadvantages of different rheometer geometries for studying nonlinear viscoelasticity are listed in Table 6.1. Further discussion on the theory and application of the sliding-plate rheometer for studying nonlinear viscoelasticity of cheese is presented in Chapter 6.

CONCENTRIC-CYLINDERS GEOMETRY The schematic views of different concentric-cylinder geometries are shown in Figure 2.49. The concentric-cylinder geometry has long been used in commercial viscometers. The concentric-cylinder system consists of an inner cylinder (called “bob”) positioned inside an outer cylinder (called “cup”). The sample is contained in the annular gap between the “infinitely” long bob and cup. In some cases the cup is rotated at a steady angular velocity while the bob is kept stationary, and in others, the bob is rotated at a constant angular velocity and the cup is fixed. The concentric-cylinder system is typically used with low-viscosity materials and mobile suspensions. The double-gap or double-Couette geometry (Figure 2.49) offers greater sensitivity than the other concentric-cylinder systems at low shear rates and viscosities as a result of its larger surface area. If sample drying (or skin formation) is likely to be an issue, which is a common problem in working with low-fat cheeses, it is better to use a solvent trap with the measuring system or alternatively a low-viscosity oil can be used as a barrier provided that the oil used does not interact with the sample to alter the sample properties. Working equations for shear strain γ, shear strain rate γ˙, and shear stress τ are given as (Macosko, 1994): Shear strain:

γ=

Ωi t R R (for narrow gaps; that is κ = i ≥ 0.99) Ro − Ri Ro (2.55)

and R=

( Ro + Ri )

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2

Bob

Cup

Wi

Wi

Ri

L Ro

L z

r

a

Lb

Lb

sample

Standard concentric cylinder

Coaxial cylinder with conic base

Wi

Wi

trapped air

Mooney cell (recessed bottom cylinder)

Double gap (double Couette)

FIGURE 2.49 Different concentric-cylinder measurement systems.

Shear strain rate: γ˙ ( Ri ) ≅ γ˙ ( Ro ) =

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Ωi R 2 Ωi = Ro − Ri 1 − κ 2

(for κ > 0.99)

and γ˙ ( Ri ) =

(

2 Ωi

n 1 − κ2/n

)

and γ˙ ( Ro ) =

(

−2 Ω i

n 1 − κ −2 / n

)

(for 0.5 < κ < 0.99) (2.56)

where n=

d ln Mi d ln Ω i

and

R=

Ro + Ri 2

Shear stress: τ( Ri ) =

Mi 2 π Ri2 L

(2.57)

where, Ri is the radius of bob, Ro the radius of cylinder, Mi the torque on bob and Ωi the angular velocity of bob, L the height of bob. Other alternative designs that are generally used to minimize end effects or make possible to account for the end effects are also depicted in Figure 2.49. The shear stress for the coaxial cylinder with conic base is given by: τ( Ri ) =

Mi 2 πR 2 L + 2 πR3  i 3 i  

(2.58)

With the Mooney cell or recessed bob the air is trapped underneath the bob and contributes practically no torque to the overall response. As can be seen from Equation (2.56), the shear rate changes across the gap for a wide-gap viscometer. This is a serious concern when using concentric-cylinder geometry with concentrated suspensions. Rotating the bob in a concentrated suspension causes particles to migrate away from higher shear-rate regions near the bob to lower shear-rate regions near to the cup (Abbott et al., 1991).

CONE-AND-PLATE GEOMETRY Sketches of different cone-and-plate (C&P) geometries are shown in Figure 2.50. The C&P system consists of a rotating (stationary) cone and a stationary (rotating) plate with a sample contained between them. The apex of the cone is essentially in contact with the plate. As seen in the following working equations the main advantage of using the C&P geometry is that the shear rate is approximately constant (i.e., independent of radial position) throughout the sample provided that the cone angle does not exceed a few degrees (e.g., ≤ 4°) (Macosko, 1994). This feature of constant shear rate is the reason why C&P geometry is particularly useful for studying nonNewtonian behavior.

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Ω, φ

θ

α

sample

Rt r

R

R

Normal cone-and-plate system

Truncated cone-and-plate system

R hc Rd

Double cone system

Extended cone-and-plate system Cone-and-dish system

FIGURE 2.50 Different cone-and-plate measurement systems.

Shear strain: γ=

φ tan α

(2.59)

where φ is the angle of rotation and α the cone angle. It is true that for a small cone angle tan(α) ≅ α*, for which the shear strain becomes: γ=

φ α

(2.60)

It is seen that for a given cone angle the strain is homogeneous and independent of position in the sample. Shear rate: dγ dφ 1 Ω = γ˙ = = dt dt sin α sin α

(2.61)

For small cone angles the shear rate can be simplified to:

* Maclaurin series for tan(α) is given as: tan(α) = α + (α3/3) + (2α5/15) + … where α in radian unit (Thomas and Finney, 1988).

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γ˙ =

Ω α

(2.62)

where, Ω = specified angular velocity. This equation shows that a uniform shear rate is realized experimentally with cone-and-plate system with small cone angles. According to the calculations of Adams and Lodge, reported in Lodge (1964), the errors involved in shear rate approximation by Equation 2.62 are 0.02, 0.18, 0.50, and 2% for cone angles of 1°, 3°, 5°, and 10°, respectively, for a material with a constant viscosity. Shear stress: τ=

3M 2 π R3

(2.63)

where, M = torque and R = radius of plate. This equation indicates that proper loading of the specimen is vital so that a full contact of the cone with the specimen is established since the torque measurement (and, consequently, the stress calculation) depends on R3. The C&P geometry is typically configured with cones having angles less than 4°. The cone angle shall be chosen with care since, for instance, for large cone angles the shear rate across the gap will vary; on the other hand, for the small cone angles there is higher chance for errors due to gap settings. For instance, for a cone angle of 10° the variation in shear rate across the gap is 3%, and the resulting error in calculated viscosity of Newtonian liquids is 2%. However, since the cone angles typically used is 4° or less the resulting error is quite small (Dealy, 1982). The C&P geometry cannot accommodate materials that contain particles since the particles can be subjected to grinding action near the tip of the cone. Therefore, quite often the tip of the cone is slightly truncated to allow measurements on particulate fluids. Cones are often slightly truncated, as shown in Figure 2.50, by removing the tip of the cone to make them more robust measurement tools. Errors due to cone truncation are generally negligible since the radius of truncation Rt is much smaller than R. The maximum error in torque associated with truncated cones can be calculated from the following equation:  R3 − Rt3  Maximum error = 1 −  100 R3  

(2.64)

For instance, if Rt = 0.2R then the maximum theoretical error in torque is 0.8%. Although C&P geometry is very simple and useful there are cases in which it shall not be preferred: (a) it is not recommended when conducting temperature sweeps unless the rheometer is equipped with an automatic system for thermal expansion compensation; and (b) it is not recommended for testing samples with particulate materials. The particles can jam the cone apex, giving erroneous data. Moreover, cone-and-plate system is not suitable for materials with a high concentration of solids, as the solids become expelled from the gap under high shear rates.

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In the extended C&P geometry the apex of the cone does not touch the plate, instead there is a finite distance between the apex and the plate, denoted by hc in Figure 2.50. The shear rate for this case is determined from (Powell, 1988): γ˙ ec =

RΩ hc + R tan α

(2.65)

It is sometimes essential to replace the flat plate with a dish to contain liquid materials as seen in Figure 2.50. Truncated and extended cones can also be utilized with a dish in place of a flat plate. Furthermore, double cone (or biconical) sensors (Figure 2.50) have been developed and employed for measuring very low viscosity liquids with small sample volume. This geometry eliminates the free surface and variation of its shape with rotational speed, and minimizes the sample exposure to the environment. On the other hand, it introduces a new type of edge effect (Dealy, 1982).

PARALLEL-PLATE GEOMETRY A schematic drawing of the parallel-plate geometry is shown in Figure 2.51. The parallel-plate system consists of a rotating (stationary) upper plate and a stationary (rotating) lower plate separated by the sample to be tested. Although similar in many ways to C&P system, the major difference between the parallel-plate and C&P systems is that the shear rate in the parallel-plate system is not constant but varies across the sample. Thus, if the objective is to subject the entire sample to a uniform shear, then the parallel-plate geometry is not appropriate. On the other hand, parallelplate geometry is not as sensitive to the gap-setting errors as the cone-and-plate system (Macosko, 1994). The working equations for the parallel-plate geometry is given as follows: Shear strain: γ=

φr h

(2.66)

It is clear that shear strain is not homogeneous and varies with radial position r. Shear rate at the edge (at r = R): γ˙ R =

R Ω h

(2.67)

It is seen that the shear rate can be varied in two ways: (a) by changing the rotational speed, Ω, and (b) by changing the gap between plates or sample thickness, h. Shear stress: τR =

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M 2 π R3

 d ln M  3 +  d ln γ˙ R  

(2.68)

Ω, φ

sample h R

Sample thickness or gap setting

R h

Rdish

FIGURE 2.51 Parallel-plate measurement systems.

where, M = torque on the rotating plate. The derivative term in the brackets makes the shear stress and viscosity calculations in the parallel-plate geometry more involved and difficult than those in cone-and-plate geometry. The accurate evaluation of the derivative term requires sufficient amount of torque versus edge shear rate data. For a Newtonian liquid the derivative term is equal to 1.0, and the equation reduces to: τR =

2M π R3

(2.69)

When the lower plate is replaced with a dish to contain the liquid sample there will be additional torque contribution caused by the increased frictional drag of the dish. Vrentas et al. (1991) presented an analysis of the dish effect (referred to as reservoir effect in their paper) for the flow of a Newtonian fluid in a parallel-plate rotational viscometer. According to their results, provided that the ratio of radius of

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dish, Rdish, to radius of upper plate, R, is greater than 1.10, the following equation can be used to calculate the torque: M=

Mmeasured h 1 + 1.9 R

(2.70)

The torque, M, from this equation can be used in Equation 2.69 to calculate shear stress τR for a Newtonian fluid.

CAPILLARY RHEOMETRY Capillary tube rheometry is a well-established technique for studying shear properties of materials. It has been applied to study viscosity of cheese (Smith et al., 1980), butter (Shukla and Rizvi, 1995), and many other food materials (Halliday and Smith, 1995; Sharma et al., 1993; White et al., 1993). Capillary viscometers are often used in laboratories and as an on-line instrument in process industries to measure viscosity (Roberts, 2001). The capillary rheometer consists of a small tube through which an incompressible fluid is forced to undergo steady axial laminar flow, either by means of an imposed pressure or a piston moving at a constant speed (Figure 2.52). The capillary rheometers can also be designed to have several capillary sections of different diameters in series so that non-Newtonian fluids can be characterized in a single pass of fluid (White et al., 1993). The quantities normally measured are the volumetric flow rate, Q, and the driving pressure, Pdriving. When a moving piston generates the flow, the driving pressure is related to the piston force (Fpiston) and reservoir radius (Rreservoir) as follows (Dealy and Wissbrun, 1989): Pdriving =

F piston 2 π Rreservoir

(2.71)

The important assumptions made in the analysis of capillary flow are (Macosko, 1994): (a) fully developed, steady, isothermal, laminar flow; and (b) fluid velocity is zero at wall — that is no slip at the wall. The total pressure drop (∆P) for flow of fluid from a reservoir, through a capillary and out to the ambient pressure consists of two components (Dealy and Wissbrun, 1989)*: Pdriving − Pambient = ∆P = ∆Pend + ∆Pcapillary

(2.72)

where, ∆Pend = excess pressure loss due to the entrance and exit flow (i.e., ∆Pend = ∆Pentrance + ∆Pexit), and Pambient = ambient pressure. The components of total pressure drop are schematically illustrated in Figure 2.53. * Although ∆ means “final-initial,” which makes ∆P a negative value; for convenience we consider the term ∆P as “Phigher – Plower” to make it a positive quantity.

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W (Dead weight) or Vz (Constant velocity) z Plunger r Rr

Sample Reservoir or barrel section

R

Capillary section

L

Q (Volumetric flow rate)

FIGURE 2.52 Schematic drawing of a piston-driven capillary rheometer.

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∆P

∆Pentrance

∆Pcapillary

∆Pexit In

Out

Reservoir section

Capillary section

FIGURE 2.53 The pressure profile in different sections of a capillary rheometer.

The working equations for capillary rheometry are given as (Macosko, 1994): Wall shear stress:

τw =

1 ∆Pcapillary 1 ∆P 1 ∆P − ∆Pend = = 2 ( L / R) 2 [( L / R) + CB ] 2 ( L / R)

(2.73)

where, CB (= ∆Pend /(2τw) is the Bagley correction, which takes into account the pressure losses in the entrance and exit of the capillary. The Bagley correction is either applied to capillary length-to-radius (L/R) term or to the pressure term, as written in Equation 2.73 The Bagley correction procedure involves measuring the pressure drop for a number of capillaries having different lengths (thus, different L/R ratios) at selected values of apparent wall shear rate. It is common practice to use at least three tubes of the same diameter but different lengths. The magnitudes of end corrections are determined from Bagley plots as shown schematically in Figure 2.54. It may be necessary to apply corrections to the measured volumetric flow rates (Qm ) if there is wall slippage. Wall slip is to be suspected when plots of τw vs. apparent shear rate at wall γ˙aw , (see below) for capillaries with the same L/R ratio but different diameters do not fall on a single curve. In accounting for slip, the slope of [Qm/(πR3τw)] versus [1/R2 ] is taken as the corrected slip coefficient, βc, and this parameter is used in the following equation to calculate the corrected volumetric flow rate (Qc): Qc = Qm − β c π R τ w

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(2.74)

∆P

. γaw3

. γaw2

. γaw1

∆Pend3 ∆Pend2 ∆Pend1

e3

e2

e1

L /R

FIGURE 2.54 Bagley plot for pressure corrections for the end effects. The measured pressure drop (∆P) for different length-to-radius ratio (L/R) of the pipe is obtained for different wall shear rates (γ˙ aw1, γ˙ aw2, γ˙aw3). The correction factors (∆Pend1, ∆Pend2, ∆P end3) are obtained from the intercepts.

Apparent or Newtonian shear rate at the wall is given by: γ˙ aw =

4 Qc π R3

(2.75)

For a non-Newtonian liquid the shear stress at the wall τw is unchanged while the shear rate at the wall is calculated from Weissenberg-Rabinowitsch-Mooney equation (Macosko, 1994):  3 1 d ln Qc  γ˙ w = γ˙ aw  +   4 4 d ln Pc 

(2.76)

The term in square brackets is called the Rabinowitsch correction. The slope (dlnQc/dlnPc) is equal to 1.0 for Newtonian fluids, and to (1/n) for power-law fluids with n being the flow-behavior index. Once shear rate and shear stress are known at the same location we can then calculate shear viscosity (η = τw /γ˙w) and construct either the flow curve (τw vs. γ˙w) or viscosity curve (η vs. γ˙w). The capillary rheometer can be operated in two modes: (a) controlled volume or displacement mode, where Q is controlled and ∆P is measured, and (b) controlled pressure mode, where ∆P is controlled and volumetric flow rate (Q) is measured. The first mode can be realized using a Universal Testing Machine with constant crosshead speeds. The second mode can be realized either by applying a dead weight on the plunger or by using gas pressure to move the plunger.

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EXTENSIONAL RHEOMETRY Extensional or elongational rheometry is a relatively new area of active research when compared to shear rheometry, and began to receive increased attention around 1970. (Macosko, 1994; Doraiswamy, 2002; Barnes et al., 1989). Its development stems from the observation that several industrially important polymer processing operations such as extrusion, molding, fiber spinning, calendaring, blowing, coating, and foam production involve significant extensional deformation in addition to shear deformation (Cogswell, 1981; Macosko, 1994; Baird, 1999). Currently, commercial elongational rheometers are available to measure extensional properties of polymer melts (Schulze et al., 2001; Meissner and Hostettler, 1994). Moreover, the filamentstretching rheometer has been developed to measure extensional properties of mobile polymer solutions (Tirtaatmadja and Sridhar, 1993; Sridhar, 2000). Extensional flows are more sensitive to variations in molecular structure of a polymeric material, and thus offer a powerful means of polymer characterization (Münstedt et al., 1998). It is possible for polymers to have identical shear flow properties while exhibiting extremely different extensional flow properties. Only for deformations that are either very small or very slow, the theory of linear viscoelasticity provides relationships between material functions determined using various kinds of deformations (Dealy and Wissbrun, 1989). For instance, the following limiting relation between extensional and shear properties is established (Barnes et al., 1989; Dealy, 1995): ηE (ε˙ ) ε˙ →0 = 3η( γ˙ ) γ˙ →0

(2.77)

where, ηE is the tensile or extensional viscosity and η is the shear viscosity. For Newtonian fluids ηE = 3η for all values of strain rates. This relationship is named as Trouton ratio, TR, defined as (Jones et al., 1987): TR =

η E (ε˙ ) η γ˙ = 3ε˙

(

)

(2.78)

For calculating TR, the shear viscosity should be evaluated at a shear rate numerically equal to 3ε˙ . Trouton ratio is exactly 3 for inelastic flows, and any departure from the value of 3 is associated with viscoelastic effects (Jones et al., 1987; Barnes et al., 1989). It is clear that when the relation given in Equation 2.77 is valid there is no need to make extensional tests since the extensional viscosity can be calculated from the shear viscosity function determined at small and slow shearing experiment (Dealy and Wissbrun, 1989). However, for large and rapid deformations the relation given in Equation 2.77 is not valid, except at small strains, and therefore it is essential to make extensional measurements. There are several kinds of extensional-flow geometries such as uniaxial extension, squeezing flow, sheet stretching, fiber spinning, bubble collapse, stagnation flows, and entrance flows (Macosko, 1994). Direct extensional-flow measurements have an advantage over shear measurements in that the measurement does not involve

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a sample–instrument interface, and thus there is no slip problem to consider (Cogswell, 1981). Some of these extensional methods are already applied to cheese with some success, as described in Chapter 9. Here we limit our attention to lubricated squeezing flow (LSF) technique, which is the most popular and promising method of studying extensional properties of (melted) cheese.

LUBRICATED SQUEEZING FLOW Squeeze flow or squeezing flow is often used to determine flow properties of highly viscous materials such as polymer melts and semiliquid or semisolid food products (e.g., cream cheese, peanut butter, melted cheese, tomato paste, butter, dough, etc). A schematic diagram of the squeezing-flow geometry is shown in Figure 2.55. Although it is a simple test to perform, the analysis of squeezing flow may not be straightforward, particularly if there is friction between the specimen ends and compression plates (i.e., unlubricated squeezing flow). In unlubricated squeezing flow, if a significant shearing component is present it alters the pattern of outward flow of material between the plates. Thus, it is necessary to lubricate the sample–platen contact surfaces in order to eliminate the shear in the sample and obtain purely shear-free or biaxial extensional flow. Lubricated or unlubricated squeezing flow can be conducted in constant volume or constant area configurations depicted in Figure 2.55. The material is squeezed out between two parallel plates at either controlled force (or stress) or controlled speed (or strain rate). Quite often the upper plate is moving at a constant speed while the lower plate is stationary. The squeezing-flow configuration represents one of the few cases where specimen loading and cleaning of equipment are fairly easy. The simple geometry of the lubricated squeezing flow (LSF) makes it also convenient for performing stress relaxation or creep experiments. Replacing the lower plate with a shallow dish results in a new configuration named as “imperfect squeezing flow” (Lee and Peleg, 1992) (Figure 2.55). LSF has been developed and used first by Chatraei and Macosko (1981) to measure biaxial extensional viscosity of polydimethyl siloxane and polyisobutylene melts under constant stress. The LSF technique was introduced to food rheology in the mid-1980s (Casiraghi et al., 1985) and has since been applied to various kinds of food products (Campanella et al., 1987; Campanella and Peleg, 1987b; Hoffner et al., 1997; Shukla et al., 1995; Huang and Kokini, 1993; Bagley et al., 1990; Corradini et al., 2000; Suwonsichon and Peleg, 1999; Wang et al., 1998; Ak and Gunasekaran, 1995). Recently, Campanella and Peleg (2002) reviewed LSF applications to semiliquid foods. A good example of application of LSF for cheese is the UW Meltmeter, the cheese meltability measurement device developed by Wang et al. (1998). In this, the fat melting from cheese at high temperature self-lubricates the compression plates, making it an ideal test method. The UW Meltmeter is discussed in detail in Chapter 8. The LSF geometry and velocity profile in the specimen and the lubricant layer are depicted in Figure 2.56. In an ideal situation, the lubricant undergoes shear deformation, and the sample undergoes biaxial extension. The working equations for LSF method are given as follows (Chatraei and Macosko, 1981; Macosko, 1994):

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R

R

Sample

H

r(t) Unlubricated constant volume squeezing flow

Unlubricated constant area squeezing flow

R

R

Sample

H

r(t) Lubricated constant volume squeezing flow

Lubricated constant area squeezing flow

R Sample Imperfect squeezing flow = Constant Load, W or = Constant Velocity, Vz

FIGURE 2.55 Configurations of unlubricated squeezing flow, lubricated squeezing flow, and imperfect squeezing flow tests.

Axial Hencky strain:  H ε H = ln   Ho 

(2.79)

Axial strain rate: ε˙ H =

1 dH Vz = H dt H

(2.80)

where Vz is the velocity in the vertical direction (e.g., crosshead speed of a universal testing machine).

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Upper plate (moving) δ/2

Lubricant layer

The ideal velocity profile

H

Specimen

Lubricant layer

δ/2

*Shear in the lubricant *Extension in the sample

Lower plate (fixed)

FIGURE 2.56 Lubricant and sample velocity profiles in ideal lubricated squeezing flow (the sample thickness H is much greater than the total lubricant layer thickness δ). (After Papanastasiou et al., 1986.)

Radial or biaxial strain:  R 1  H ε B = ln  = − ln  2  Ho   Ro 

(2.81)

where, the constant volume assumption, (R/R0) = (H0/H)1/2, is applied. Radial or biaxial strain rate: ε˙ B = −

1 dH 2 H dt

(2.82)

It is assumed that at any moment the lubricant film thickness, δ, is smaller than the specimen thickness, H, and therefore, H + δ ≅ H. This is justified at the start of the test, but may be questionable at later stages when the specimen thickness becomes small at large strains (e.g., when εΒ = 2.0, H/Ho = 0.018). Biaxial (compressive) stress when the gap is fully filled with sample: σB =

F π R2

(2.83)

In this case Rspeciman ≥ Rplate = R. Biaxial (compressive) stress when the gap is partially filled with sample: σB =

F π r(t) 2

In this case r(t) represents the instantaneous radius of the specimen.

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(2.84)

Biaxial stress growth coefficient (Dealy, 1995): η+B (t, ε˙ B ) ≡

σB ε˙ B

(2.85)

Biaxial extensional or elongational viscosity:

[

]

η B (ε˙ B ) = lim η+B (t, ε˙ B )

t →∞

(2.86)

For Newtonian fluids the biaxial elongational viscosity is six times the shear viscosity, ηB = 6η. One important consideration in LSF, which is often not addressed in food-related studies, is the loss of effective lubrication, which limits the maximum achievable strain. Macosko (1994) mentions that the strain in LSF is limited to 1.0–1.5 because of the loss of effective lubrication. It is experimentally demonstrated that lubrication is maintained up to a higher total strain if the lubricant has a higher zero-shear viscosity (Chatraei and Macosko, 1981). The optimum ratio of the zero-shear viscosities of the sample to the lubricant is reported to range from 500 Pa.s to 1000 Pa.s (Papanastasiou et al., 1986; Soskey and Winter, 1985). The criterion for good lubrication is given as (Macosko, 1994): 2δ η L R 2 < < 20 H ηS δ 2

(2.87)

where ηS is the sample viscosity, δ the lubricant thickness, H the sample thickness, ηL the lubricant viscosity, and R the plate radius.

EQUATIONS

FOR

DIFFERENT FLUIDS

IN

LUBRICATING SQUEEZING FLOW

Analytical solutions for lubricated-squeezing flow of Newtonian and non-Newtonian fluids are given in various publications in the rheology literature. We present below these equations describing the specimen thickness as a function of time under constant load, or the load as a function of time under constant velocity for Newtonian and non-Newtonian fluids. (1) Newtonian fluids (a) Flow under constant load–constant volume (Lee and Peleg, 1989): 1 1 W t = + H (t ) Ho 3ηΛ

(2.88)

where, W is the constant load, η the Newtonian viscosity, Λ the specimen volume, and t the time.

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(b) Flow under constant load–constant area:  Wt  H (t ) = Ho exp − π 3 R 2 η  

(2.89)

where, R is the radius of the plate (= radius of the sample). (c) Flow under constant velocity–constant volume: 3ηΛ V [H(t)]2 z

F (t ) =

(2.90)

where, Vz is the squeezing speed. (d) Flow under constant velocity–constant area: F (t ) =

3π η R 2 Vz H(t)

(2.91)

(2) Power-law fluids (a) Flow under constant load–constant volume (Campanella and Peleg, 1987b): 1/ n     t  W   1  1 = +    H (t )  Ho1 / n n  n2+1 K 3 Λ    

n

(2.92)

where, K is the consistency index, and n the flow behavior index. (b) Flow under constant velocity–constant volume: F (t ) = 3

n +1 2

ΛK

(Vz )n

(2.93)

[ H (t )]n+1

(c) Flow under constant load–constant area: 1/ n    W  t  H (t ) = Ho exp  − n+1   2 2  3 π R K  

(2.94)

(d) Flow under constant velocity–constant area: F (t ) = 3

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n +1 2

 V  πKR  z   H (t )  2

n

(2.95)

(3) Herschel-Bulkley fluids (a) Flow under constant load–constant volume (Ak and Gunasekaran, 2000):   1 1 −n 1 3 τo Λ  ,1 + , +  1 / n  Hypg2 F1 , n H (t ) W  n n  ( H (t ) W )  1/ n   1 1   −n 1 3 τo Λ  1   ,1 + , t  = − ( n +1)  1 / n Hypg2 F1 , n Ho W   ( Ho W )  K Λ 3  n n  

(2.96)

where, Hypg2F1[a,b,c,z] is the hypergeometric function 2F1[a,b;c;z] (Mathematica 3.0, Wolfram Research; Andrews, 1992). The validity of this hypergeometric solution, Equation 2.96, is verified by the fact that it reduces correctly to Equation 2.88 for n = 1 and τo = 0, and to Equation 2.92 for τo = 0 (Ak and Gunasekaran, 2000). (b) Flow under constant velocity–constant volume: V   Λ  F (t ) = 3 τ o + K  3 z   H(t)  H (t ) 

n

  

(2.97)

(c) Flow under constant load–constant area:   W − πR2 3 τ  1 / n  o H (t ) = Ho exp − n +1  t 2   πR 3 K  

(2.98)

(d) Flow under constant velocity–constant area: n  V    F (t ) = 3 π R 2  τ o + K  3 z    H (t )   

(2.99)

REFERENCES Abbott, J. et al. 1991. Experimental observations of particle migration in concentrated suspensions: Couette flow. Journal of Rheology 35(5):773–795. Ak, M.M. 1993. Rheological Measurements on Mozzarella Cheese. University of WisconsinMadison, Ph.D. thesis. Ak, M.M. and S. Gunasekaran. 1992. Stress–strain curve analysis of Cheddar cheese under uniaxial compression. Journal of Food Science 57(5):1078–1081. Ak, M.M. and S. Gunasekaran. 1995. Evaluating rheological properties of Mozzarella cheese by the squeezing flow method. Journal of Texture Studies 26:695–711.

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Ak, M.M. and S. Gunasekaran. 1997. Anisotropy in tensile properties of Mozzarella cheese. Journal of Food Science 62(5):1031–1033. Ak, M.M. and S. Gunasekaran. 2000. Simulation of lubricated squeezing flow of a HerschelBulkley fluid under constant force. Applied Rheology 10(6):274–279. Ak, M.M. and S. Gunasekaran. 2001. Linear viscoelastic methods, in Nondestructive Food Evaluation: Techniques to Analyze Properties and Quality, S. Gunasekaran, Ed., pp 287–334. New York: Marcel Dekker, Inc. Andrews, L.C. 1992. Special Functions of Mathematics for Engineers. New York: McGraw-Hill, Inc. Anon. 2002. Determining the linear viscoelastic region in polymers. Rheology Application Notes: RS-23 (TA Instruments), http://www.tainst.com. Astarita, G. 1990. Letter to the Editor: The engineering reality of the yield stress. Journal of Rheology 34(2):275–277. ASTM. 1995. Standard test method for tensile properties of plastics (Metric). 59–67. ASTM. 1996. Standard test methods for rubber properties in compression. 113–116. Bagley, E., D. Christianson, and D. Trebacz. 1990. The computation of viscosity and relaxation time of doughs from biaxial extension data. Journal of Texture Studies 21:339–354. Baird, D. 1999. The role of extensional rheology in polymer processing. Korea-Australia Rheology Journal 11(4):305–311. Barnes, H.A. 1999. The yield stress — a review or ‘παντα ρει — everything flows? Journal of Non-Newtonian Fluid Mechanics 81:133–178. Barnes H.A., J.F. Hutton, and K. Walters. 1989. An Introduction to Rheology. Amsterdam: Elsevier Science Publishers B.V. Barnes, H.A., H. Schimanski, and D. Bell. 1999. 30 Years of progress in viscometers and rheometers. Applied Rheology 9(2):69–76. Barnes, H.A. and Q.D. Nguyen. 2001. Rotating vane rheometry — a review. Journal of Non-Newtonian Fluid Mechanics 98(1):1–14. Bourne, M.C. 1977. Compression rates in the mouth. Journal of Texture Studies 8:373–376. Bourne, M.C. 1982. Food Texture and Viscosity: Concept and Measurement. New York: Academic Press. Breidinger, S.L. and J.F. Steffe. 2001. Texture map of cream cheese. Journal of Food Science 66(3):453–456. Briggs, J.L., J.F. Steffe, and Z. Ustunol. 1996. Vane method to evaluate the yield stress of frozen ice cream. Journal of Dairy Science 79(4):527–531. Calzada, J.F. and M. Peleg, 1978. Mechanical interpretation of compressive stress-strain relationships of solid foods. Journal of Food Science 43:1087–1092. Campanella, O.H. and M. Peleg, 1987a. Determination of the yield stress of semi-liquid foods from squeezing flow data. Journal of Food Science 52(1):214–215, 217. Campanella, O.H. and M. Peleg, 1987b. Squeezing flow viscosimetry of peanut butter. Journal of Food Science 52(1):180–184. Campanella, O.H., L. Popplewell, J. Rosenau and M. Peleg, 1987. Elongational viscosity measurements of melting American process cheese. Journal of Food Science 52(5):1249–1251. Campanella, O.H. and M. Peleg, 2002. Squeezing flow viscometry for nonelastic semiliquid foods — Theory and applications. Critical Reviews in Food Science & Nutrition 42(3):241–264. Casiraghi, E.M., E.B. Bagley, and D.D. Christianson. 1985. Behavior of Mozzarella, Cheddar and processed cheese spread in lubricated and bonded uniaxial compression. Journal of Texture Studies 16:281–301. Charalambides, M.N. et al. 2001. The analysis of the frictional effect on stress–strain data from uniaxial compression of cheese. Journal of Materials Science 36(9):2313–2321.

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Hamann, D.D. 1983. Structural failure in solid foods, in Physical Properties of Foods, M. Peleg and E.B. Bagley, Eds., pp 351–383. Westport, CT: AVI Publishing Company, Inc. Hoffner, B., C. Gerhards, and M. Peleg, 1997. Imperfect lubricated squeezing flow viscometry for foods. Rheologica Acta 36:686–693. Huang, H. and J. Kokini. 1993. Measurement of biaxial extensional viscosity of wheat flour doughs. Journal of Rheology 37(5):879–891. Jones, D.M., K. Walters, and P.R. Williams. 1987. On the extensional viscosity of mobile polymer solutions. Rheologica Acta 26:20–30. Junus, S. and J.L. Briggs. 2001. Vane sensor system in small strain oscillatory testing. Applied Rheology 11(5):264–270. Kamst, G.F. et al. 1999. A new method for the measurement of the tensile strength of rice grains by using the diametral compression test. Journal of Food Engineering 40:227–232. Kamyab, I., S. Chakrabarti, and J. G. Williams. 1998. Cutting cheese with wire. Journal of Materials Science 33(11):2763–2770. Keener, K.M., C.R. Daubert, and T.A. Glenn. 1999. Development and evaluation of a hand vane device for rapid quality measurement during food processing. Abstracts, IFT Annual Meeting, Chicago, IL. Konstance, R.P. and V.H. Holsinger. 1992. Development of rheological test methods for cheese. Food Technology 46:105–109. Lakes, R.S. 1987. Foam structure with a negative Poisson’s ratio. Science 235:1038–1040. Langley, K.R. and R.J. Marshall. 1993. Jaw movement during mastication of fibrous and nonfibrous composite foods by adult subjects. Journal of Texture Studies 24:11–25. Lanier, T.C. 2000. Measurement of fracture of solid and semi-solid foods with the Hamann torsion gelometer, in Proceedings of the 2nd International Symposium on Food Rheology and Structure, P. Fischer, I. Marti, and E.J. Windhab, Eds., pp 121–125. Zürich, Switzerland. Lauger, J. and S. Huck. 2002. Real controlled stress and controlled strain experiments with the same rheometer. www.physica.de. Lee, S. and M. Peleg, 1989. Squeezing flow of a double layered array of two Newtonian liquids. Chemical Engineering Science 44(12):2979–2986. Lee, S. and M. Peleg, 1992. Imperfect squeezing flow viscosimetry with a wide plate and a shallow container. Journal of Texture Studies 23:267–278. Liddell, P.V. and D.V. Boger. 1996. Yield stress measurements with the vane. Journal of Non-Newtonian Fluid Mechanics 63:235–261. Lodge A.S. 1964. Elastic Solids: An Introductory Vector Treatment of Finite-Strain Polymer Rheology. New York: Academic Press. Luyten H. 1988. The Rheological and Fracture Properties of Gouda Cheese. Wageningen Agricultural University, The Netherlands, Ph.D. thesis. Luyten, H., T. van Vliet, and P. Walstra. 1991a. Characterization of the consistency of Gouda cheese: Fracture properties. Netherlands Milk and Dairy Journal 45:55–80. Luyten, H., T. van Vliet, and P. Walstra. 1991b. Characterization of the consistency of Gouda cheese: Rheological properties. Netherlands Milk and Dairy Journal 45:33–53. Luyten, H., T. van Vliet, and P. Walstra. 1992. Comparison of various methods to evaluate fracture phenomena in food materials. Journal of Texture Studies 23:245–266. Macosko C.W. 1994. Rheology: Principles, Measurements, and Applications. New York: VCH Publishers, Inc. Meissner, J. 1978. Combined constant strain rate and stress relaxation test for linear viscoelastic studies. Journal of Polymer Science 16:915–919.

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Meissner, J. and J. Hostettler. 1994. A new elongational rheometer for polymer melts and other highly viscoelastic liquids. Rheologica Acta 33:1–21. Mitchell, J.R. 1984. Rheological Techniques, in Food Analysis: Principles and Techniques Volume 1. Physical Characterization, D.W. Gruenwedel and J. R. Whitaker, Eds., pp 151–220. New York: Marcel Dekker, Inc. Mleko, S. and E.A. Foegeding. 2000. Physical properties of rennet casein gels and processed cheese analogs containing whey proteins. Milchwissenschaft 55(9):513–516. Mohsenin, N. and J. Mittal. 1977. Use of rheological terms and correlation of compatible measurements in food texture research. Journal of Texture Studies 8:395–408. Molander, E., K.R. Kristiansen and H. Werner. 1990. Instrumental and sensoric measurement of Brie texture. Milchwissenschaft 45(9):589–593. Montejano, J.G., H.H. Hamann, and T.C. Lanier. 1983. Final strengths and rheological changes during processing of thermally induced fish muscle gels. Journal of Rheology 27(6):557–579. Mpagana, M. and J. Hardy. 1986. Effect of salting on some rheological properties of fresh Camembert cheese as measured by uniaxial compression. Milchwissenschaft 41(4):210–213. Münstedt, H., S. Kurzbeck, and L. Egersdörfer. 1998. Influence of molecular structure on rheological properties of polyethylenes. II. Elongational behavior. Rheologica Acta 37:21–29. Newton, J.M., I. Haririan, and F. Podczeck. 2000. The influence of punch curvature on the mechanical properties of compacted powders. Powder Technology 107:79–83. Ney, K.H. 1985. Rheology of foods. Anisotropy in Cheddar cheese. Gordian 85(9):172, 174. Nguyen, Q.D. and D.V. Boger. 1983. Yield stress measurement for concentrated suspensions. Journal of Rheology 27(4):321–349. Nguyen, Q.D. and D.V. Boger. 1985. Direct yield stress measurement with the vane method. Journal of Rheology 29(3):335–347. Nijman, J. and S. Chakrabarti. 1997. A rotational rheometer for material characterization by the rheologist and the nonrheologist. American Laboratory 29(16):17–18, 20. Papanastasiou, A., C. Macosko, and L. Scriven. 1986. Analysis of lubricated squeezing flow. International Journal of Numerical Methods in Fluids 6:816–839. Peleg, M. 1979. Characterization of the stress relaxation curves of solid foods. Journal of Food Science 44(1):277–281. Peleg, M. 1980. Linearization of relaxation and creep curves of solid biological materials. Journal of Rheology 24(4):451–463. Peleg, M. 1984. A note on the various strain measures at large compressive deformations. Journal of Texture Studies 15:317–326. Peleg, M. 1987. The basics of solid foods rheology, in Food Texture: Instrumental and Sensory Measurement, H.R. Moskowitz, Ed., pp 3–33. New York: Marcel Dekker. Peleg, M. and M.D. Normand. 1983. Comparison of two methods for stress relaxation data presentation of solid foods. Rheologica Acta 22:108–113. Pernell, C.W., E.A. Foegeding, and C.R. Daubert. 2000. Measurement of the yield stress of protein foams by vane rheometry. Journal of Food Science 65(1):110–114. Powell, R.L. 1988. Rotational viscometry, in Rheological Measurement, A.A. Collyer and D.W. Clegg, Eds., pp 247–296. London: Elsevier Applied Science. Purkayastha, S. et al. 1985. A computer aided characterization of the compressive creep behavior of potato and cheddar cheese. Journal of Food Science 50:45–50, 55. Purkayastha, S., M. Peleg, and M. Normand. 1984. Presentation of the creep curves of solid biological materials by a simplified mathematical version of the generalized KelvinVoigt model. Rheologica Acta 23:556–563.

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Qiu, C.G. and M.A. Rao. 1988. Role of pulp content and particle size in yield stress of apple sauce. Journal of Food Science 53(4):1165–1170. Reiner, M. 1964. The Deborah number. Physics Today 17(1):62. Riande E. et al. 2000. Polymer Viscoelasticity — Stress and Strain in Practice. New York: Marcel Dekker, Inc. Riley W.F., L.D. Sturges, and D.H. Morris. 1995. Statics and Mechanics of Materials: An Integrated Approach. New York: John Wiley & Sons. Roberts, I. 2001. In-line and on-line rheology measurement, in Instrumentation and Sensors for the Food Industry, E. Kress-Rogers and C.J.B. Brimelow, Eds., pp 403–422. Cambridge: Woodhead Publishing Ltd. Rohm, H., D. Jaros, and M. deHaan. 1997. A video-based method for determination of average stress–strain relations in uniaxial compression of selected foods. Journal of Texture Studies 28:245–255. Rohm, H. and H. Lederer. 1992. Uniaxial compression of Swiss-type cheese at different strain rates. International Dairy Journal 2:331–343. Schulze, J. et al. 2001. A comparison of extensional viscosity measurements from various RME rheometers. Rheologica Acta 40:457–466. Schurz, J. 1992. Letter to the editor: A yield value in a true solution. Journal of Rheology 36(7):1319–1321. Shama, F. and P. Sherman. 1973. Evaluation of some textural properties of foods with the Instron universal testing machine. Journal of Texture Studies 4:344–352. Sharma, N., M.A. Hanna, and Y.R. Chen. 1993. Flow behavior of wheat flour-water dough using a capillary rheometer. I. Effect of capillary geometry. Cereal Chemistry 70(1):59–63. Sherman, P. 1975. Factors influencing the instrumental and sensory evaluation of food emulsions, in Theory, Determination and Control of Physical Properties of Food Materials, C.-K. Rha, Ed., pp 251–266. Dordrecht-Holland: D. Reidel. Shoemaker, C., J. Lewis, and M. Tamura. 1987. Instrumentation for rheological measurements of food. Food Technology (3):80–84. Shukla, A. and S. Rizvi. 1995. Measurement of flowability of butter by capillary rheometry. Journal of Texture Studies 26:299–311. Shukla, A., S. Rizvi, and J. Bartsch. 1995. Rheological characterization of butter using lubricated squeezing flow. Journal of Texture Studies 26:313–323. Smith, C., J. Rosenau, and M. Peleg, 1980. Evaluation of the flowability of melted Mozzarella cheese by capillary rheometry. Journal of Food Science 45:1142–1145. Soskey, P. and H. Winter. 1985. Equibiaxial extension of two polymer melts: polystyrene and low density polyethylene. Journal of Rheology 29(5):493–517. Sridhar, T. 2000. From rheometry to rheology. Korea-Australia Rheology Journal 12(1):39–53. Steffe J.F. 1996. Rheological Methods in Food Process Engineering. Michigan: Freeman Press. Suwonsichon, T. and M. Peleg, 1999. Imperfect squeezing flow viscometry of mustards with suspended particles. Journal of Food Engineering 39:217–226. Swallowe, G.M. 1999. Tensile and Compressive Testing, in Mechanical Properties and Testing of Polymers: An A-Z Reference, G.M. Swallowe, Ed., pp 242–243. AH Dordrecht, The Netherlands: Kluwer Academic Publishers. Thomas, G.B. Jr. and R.L. Finney. 1988. Calculus and Analytic Geometry. 7th edition. New York: Addison-Wesley Publishing Company. Tirtaatmadja, V. and T. Sridhar. 1993. A filament stretching device for measurement of extensional viscosity. Journal of Rheology 37(6):1081–1102. Truong, V.D. and C.R. Daubert. 2001. Textural characterization of cheeses using vane rheometry and torsion analysis. Journal of Food Science 66(5):716–721.

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3

Uniaxial Testing of Cheese

Uniaxial testing is the most popular configuration for evaluating mechanical and rheological properties of cheeses. In this chapter, we attempt to summarize the extensive literature on different cheeses. The available data are diverse and are often collected by various testing modes, which can be grouped under the word “uniaxial.” Uniaxial testing is also the most popular method for instrumental evaluation of cheese texture (see Chapter 7). One way to handle such diverse literature on properties of different cheeses would be to present the available data according to the type of cheese. However, we organized the information according to the specific test method (e.g., uniaxial compression, tension, relaxation, etc.), since effects of many experimental factors (e.g., deformation rate, cheese age, etc.) on rheological properties of different cheeses bear some similarities. Rigorous analysis of the literature data is seriously hampered by the lack of standardization in terms of sample preparation, measurement conditions, parameter evaluations, and reporting style. It may not be feasible to specify particular requirements for each of these issues since the objectives of measurements can be totally different (e.g., quality control, correlations with sensory results, etc.), and the prevailing conditions under which the tests are made may also vary. However, minimum requirements in data reporting may be (and perhaps should be) universally agreed upon, which would greatly facilitate comparison of results from different sources. Masi (1987) reported a major attempt to improve the comparability of results from different laboratories and to identify the most suitable measurement conditions for generating reproducible mechanical data on cheese. Even in this collaborative work the participating laboratories used different experimental conditions (i.e., sample size and shape, test temperature, sample handling, sample age at testing, number of samples tested, etc.). The recommendations based on the results of this extensive study are given in Table 3.1 for cheese, as well as general recommendations for reporting compression results. Some of these suggestions are no longer relevant due to advances in the instrumentation. For instance, the recommended crosshead speeds are naturally based on the characteristics of uniaxial testing machines available at that time and the capabilities of the strip-chart recorders, which are practically obsolete now. A group at the International Dairy Federation (IDF) also formed a working team (IDF E703) to develop standards for testing and reporting uniaxial test results on cheese. Though a draft was prepared, it was never officially published.* Nevertheless, the special bulletin of IDF (1991) includes expert opinions on important issues related to cheese rheology and texture measurements, and recommendations on test methods. * Philip Watkinson, Fonterra Research Center, New Zealand, personal communication.

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TABLE 3.1A Recommendations for Compression Testing of Cheese Measurement Conditions

Data to Be Reported

a. Shape: vertical cylinder or prism b. Size: aspect ratio > 1 (aspect ratio = sample height/sample width or diameter) c. Crosshead speed: 5 cm/min and two other speeds in the range 0–20 cm/min d. Boundaries: Both bonded and lubricated platens

a. Rupturea (or yield) stress b. Rupture (or yield) strain c. Elastic modulus d. Rupture (or yield) work per unit of volume e. Failure mode

a

If the cheese does not show rupture or yield, then the stress and the work per unit of volume should correspond to 80% deformation. Source: After Masi, 1987. With permission.

TABLE 3.1B Information to be Included in Compression-Test Reports Contextual Information

Measurement Conditions

Results

a. Detailed description of sample b. Sample dimensions c. Sample history (including preparation and conditioning)

a. Temperature of environment b. Relative humidity of environment c. Sample temperature d. Interface between sample and compression surfaces I. Material II. Roughness III. Dimensions e. Compression rate f. Machine details Accuracy of (1) compression rate, and (2) force measurement g. Initial position of crosshead in relation to the sample h. Response time

a. All original and derived results b. Complete force–deformation curve

Source: After McKenna, 1987. With permission.

The theory of fracture mechanics and the methods specially designed to study fracture properties of materials are discussed in Chapter 4. Fracture properties reported in this chapter are those that are often routinely determined even though the primary objective of the research is not to study fracture behavior. For instance, work-to-fracture (or area under stress–strain curve) values are given in this chapter, whereas the specific fracture energy data are reported in Chapter 4.

UNIAXIAL COMPRESSION MEASUREMENTS Mechanical properties commonly determined from uniaxial compression tests on cheese include modulus of deformability ED, fracture stress σf , fracture strain εf , and work to fracture Wf . All these variables are defined in Chapter 2 (see Figure 2.23). © 2003 by CRC Press LLC

The numerical results for these properties extracted from many publications on different cheeses are listed in Tables 3.2 to 3.5. In the following sections, we will frequently refer to these compilations. For viscoelastic materials, Mohsenin and Mittal (1977) suggested the term “modulus of deformability” instead of Young’s modulus, which is reserved for engineering materials obeying the Hooke’s law. The modulus of deformability is the slope of the “initial linear” part of the stress–strain curve. There are several methods for getting a representative value of the slope. One of these methods is to fit the stress–strain data to a polynomial equation (see Chapter 2, Equation 2.22) and to determine properties from the resulting fit equation (Ak and Gunasekaran, 1992). The other approach is to take the maximum slope within the strain range from 0 to 0.05 (Wium et al., 1997). Another method is to take the slope at a particular strain level (e.g., 5%) as the modulus of deformability (i.e., secant modulus described in Chapter 2). Linear regression on the data pertaining to the initial part of the stress–strain curve is yet another option to calculate the modulus of deformability. Watkinson and Jackson (1999) suggested a new procedure to calculate the modulus of deformability using the gradient of the inflection at the lowest strain in a stress vs. strain curve. This new procedure was used to calculate modulus of deformability ED for three cheeses and compared with the results from three alternative procedures, including the simple polynomial fitting suggested by Ak and Gunasekaran (1992). As shown in Table 3.6, the ranking of ED for each cheese was the same for each procedure, and the relative magnitude of ED for each cheese along with the coefficient of variation was similar for each procedure. Watkinson and Jackson (1999) discussed some special features of their procedure. The usual practice in uniaxial compression of foods is to run the crosshead at constant speed, since Universal Testing Machines (UTMs) machines are normally designed to do that. It is quite unusual, but perhaps highly necessary, to see compression tests made on cheese at constant true strain rate. The true strain rate continuously increases in uniaxial compression at a constant crosshead speed as the specimen height decreases, and this has a great effect in uniaxial compression of foods (Peleg, 1977a; 1977b). We are not aware of any such studies on cheese except that of Jaros and Rohm (1994). A simple device has been described earlier by Luton et al. (1974) for use with Instron testing machines to produce a constant true strain rate in compression or tension tests. Jaros and Rohm (1994) described a method to conduct uniaxial compression tests at constant strain rate using an Instron testing machine. Based on the analysis of rheological data on 136 Swiss cheese samples, it was shown that stress and strain at fracture are significantly lower in constant strain rate compression than in constant speed compression, due to the differences in strain history of the two modes. The modulus of deformability, obtained at 0.04 strain level, is, however, not affected by the test setup. The authors reported the following equations relating fracture stress σf and fracture strain εf from the two modes of deformation: σ f (constant strain rate) = 1.27 σ f (constant speed)0.917

(3.1)

ε f (constant strain rate) = 1.01 ε f (constant speed)0.867

(3.2)

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TABLE 3.2 Values of Modulus of Deformability from Uniaxial Testing of Several Cheesesa

Cheese Variety Apericube processed Bel, France Appenzell Arzua-Ulloa Spanish soft cheese — type I Arzua-Ulloa Spanish soft cheese — type II Blue Brick UF-Feta 8–10 weeks Blue Brick UF-Feta 8–10 weeks Blue Brick UF-Feta 8–10 weeks Blue Brick UF-Feta 8–10 weeks Caciocavallo Caerphilly Camembert 1-d before brining Camembert 1-d after brining Camembert 8-d-old Camembert 15-d-old Camembert 22-d-old Camembert 29-d-old Cheddar Cheddar Cheddar 20 days Cheddar 8 weeks old Cheddar 64 weeks old Cracker Barrel Tasty: Kraft, USA Danbo cheese with 45% fat Danish Feta Double Gloucester Double Gloucester Edam Edam Emmental Emmental Emmentaler 4 months Emmentaler 4 months Emmentaler 4 months Emmentaler 4 months English Mature Cheddar Galbanino Galbanino Galbanino Galbanino Garrotxa-type goat milk cheese Gouda Gouda

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Initial Strain Rate s–1b

Modulus kPa

— — 46 46 110 220 330 440 4.2 — 5.56 5.56 5.56 5.56 5.56 5.56 — — 1.4–110 32 32 — 833 — — — — — — — 4.76 19 76.2 19 — 0.556 11 28 56 500 — —

70 22 84 44 229 221 225 176 687 8 357 429 749 1070 251 0 48 180 242 640 290 580 189 470 1000 850 ~500 290 18 470 139 182 234 182 890 600 1000 1400 1800 343 405 390

Ref. Agrawal et al., 1997 Prentice et al., 1993 Almena et al., 1998 Almena et al., 1998 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Masi and Addeo, 1986 Prentice et al., 1993 Schlesser et al., 1992 Schlesser et al., 1992 Schlesser et al., 1992 Schlesser et al., 1992 Schlesser et al., 1992 Schlesser et al., 1992 Prentice et al., 1993 Prentice et al., 1993 Ak and Gunasekaran, 1992 Hort and Le Grys, 2001 Hort and Le Grys, 2001 Agrawal et al., 1997 Madsen and Ardö, 2001 Agrawal et al., 1997 Prentice et al., 1993 Agrawal et al., 1997 Prentice et al., 1993 Agrawal et al., 1997 Prentice et al., 1993 Agrawal et al., 1997 Rohm and Lederer, 1992 Rohm and Lederer, 1992 Rohm and Lederer, 1992 Rohm et al., 1992 Agrawal et al., 1997 Masi, 1989 Masi, 1989 Masi, 1989 Masi, 1989 Saldo et al., 2000 Prentice et al., 1993 Prentice et al., 1993

TABLE 3.2 (continued) Values of Modulus of Deformability from Uniaxial Testing of Several Cheesesa

Cheese Variety Gouda Gruyère Gruyère Gruyère-type strong cohesion Gruyère-type strong cohesion — Tension Gruyère-type weak cohesion Gruyère-type weak cohesion — Tension Jarlsberg La Serena 2 days old, with lactic starter La Serena 2 days old, without lactic starter La Serena 60 days old, with lactic starter La Serena 60 days old, without lactic starter Lancashire Lancashire Leicester Mahon >150 days Mahon <60 days Mahon from 60 to 150 days Mild Cheddar Mild Cheddar 37 days old Mild Cheddar 182 days old Mild Cheddar — Tension Montasio Monterey Jack 46 days old Monterey Jack 185 days old Mozzarella Mozzarella Mozzarella Münster Parmesan Parmesan Parmigiano Reggiano 12 months old Parmigiano Reggiano 18 months old Parmigiano Reggiano 28 months old Pecorino Romano Process cheese loaf, light Process cheese loaf, regular Process cheese slice, American 1 Process cheese slice, American 1 — Tension Process cheese slice, American 2 Process cheese slice, American 2 — Tension

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Initial Strain Rate s–1b

Modulus kPa

Ref.

— — — 55.5 11 55.5 11 — — — — — — — — 8.33 8.33 8.33 3 8.3–24 8.3–24 3 — 8.3–24 8.3–24 — — 4.2 — — — 42 42 42 — 3 3 3 3 3 3

410 690 77 479 111 468 93 350 61 32 348 104 ~1250 710 650 2487 497 1426 349 1176 1050 747 470 1008 652 15 150 49 6 1980 2260 1340 1530 2280 2840 154 107 318 374 138 162

Agrawal et al., 1997 Agrawal et al., 1997 Prentice et al., 1993 Pesenti and Luginbühl, 1999 Pesenti and Luginbühl, 1999 Pesenti and Luginbühl, 1999 Pesenti and Luginbühl, 1999 Agrawal et al., 1997 Medina et al., 1991 Medina et al., 1991 Medina et al., 1991 Medina et al., 1991 Prentice et al., 1993 Agrawal et al., 1997 Agrawal et al., 1997 Benedito et al., 2000 Benedito et al., 2000 Benedito et al., 2000 Kamyab et al., 1998 Charalambides et al., 1995 Charalambides et al., 1995 Kamyab et al., 1998 Prentice et al., 1993 Charalambides et al., 1995 Charalambides et al., 1995 Prentice et al., 1993 Agrawal et al., 1997 Masi and Addeo, 1986 Prentice et al., 1993 Prentice et al., 1993 Agrawal et al., 1997 Noel et al., 1996 Noel et al., 1996 Noel et al., 1996 Prentice et al., 1993 Kamyab et al., 1998 Kamyab et al., 1998 Kamyab et al., 1998 Kamyab et al., 1998 Kamyab et al., 1998 Kamyab et al., 1998

TABLE 3.2 (continued) Values of Modulus of Deformability from Uniaxial Testing of Several Cheesesa

Cheese Variety Processed cheese analogs high fat, high moisture Processed cheese analogs high fat, high moisture Processed cheese analogs high fat, high moisture Processed cheese analogs low fat, low moisture Processed cheese analogs low fat, low moisture Processed cheese analogs low fat, low moisture Provolone Provolone Raclette Red Brick UF-Feta 8–10 weeks Red Brick UF-Feta 8–10 weeks Red Brick UF-Feta 8–10 weeks Red Brick UF-Feta 8–10 weeks Reduced Fat Cheddar Mainland, New Zealand Sbrinz Sharp Cheddar Sharp Cheddar 1 month old Sharp Cheddar 6 months old Sharp Cheddar — Tension Silano Smoked Cheddar King Island, Australia String Swiss Appenzeller type — rapeseed-added diet Swiss Appenzeller type — regular diet Teleme 1 month old Tilsit Tin UF-Feta 8–10 weeks Tin UF-Feta 8–10 weeks Tin UF-Feta 8–10 weeks Tin UF-Feta 8–10 weeks Vorarlberger Bergkase White Cheshire a b

Initial Strain Rate s–1b

Modulus kPa

5.56

27

Marshall, 1990

55.6

48

Marshall, 1990

556

50

Marshall, 1990

5.56

223

Marshall, 1990

55.6

231

Marshall, 1990

556

276

Marshall, 1990

— 4.2 — 110 220 330 440 — — 3 8.3–24 8.3–24 3 4.2 — 11 17 17 36

240 559 210 301 256 260 190 940 195 198 1580 1938 220 137 990 100 401 490 175

— 110 220 330 440 16.7 —

30 465 387 404 407 600 470

Prentice et al., 1993 Masi and Addeo, 1986 Agrawal et al., 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Agrawal et al., 1997 Prentice et al., 1993 Kamyab et al., 1998 Charalambides et al., 1995 Charalambides et al., 1995 Kamyab et al., 1998 Masi and Addeo 1986 Agrawal et al., 1997 Taneya et al., 1992 Jaros et al., 2001 Jaros et al., 2001 Raphaelides and Antoniou, 1996 Prentice et al., 1993 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Jaros and Rohm, 1997 Agrawal et al., 1997

Ref.

Data are from uniaxial compression test unless indicated otherwise by a remark next to the variety name. Values in this column are already multiplied by a factor of 1000 to avoid small numbers.

© 2003 by CRC Press LLC

TABLE 3.3 Values of Strain at Fracture from Uniaxial Testing of Several Cheesesa

Cheese Variety

Initial Strain Rate s–1b

Peak Strain

American Light — Shear American — Shear Appenzell Arzua-Ulloa Spanish soft cheese — type I Arzua-Ulloa Spanish soft cheese — type II Blue Brick UF-Feta 8–10 weeks Blue Brick UF-Feta 8–10 weeks Blue Brick UF-Feta 8–10 weeks Blue Brick UF-Feta 8–10 weeks Caciocavallo Caerphilly Cheddar Cheddar Cheddar Cheddar Cheddar Cheddar Cheddar 225 d old Cheddar 8 weeks old Cheddar 64 weeks old Cheddar 5-mo-old, full-fat: 32% Cheddar 5-mo-old, low-fat: 5% Cheshire Danbo Double Gloucester Edam Emmental Emmental 16 weeks Emmental 16 weeks Emmental 16 weeks Emmental 7-d-old Emmental 28-d-old Emmental 70-d old Emmental 112-d-old Emmentaler 4 months Emmentaler 4 months Emmentaler 4 months Emmentaler 4-mo-old Garrotxa-type goat milk cheese Gouda Gouda Gouda 1 week, pH = 4.94 Gouda 1 week, pH = 4.94

261 261 — 46 46 110 220 330 440 — — — — — 1.4–110 11 110 29 32 32 440 440 — 833 — — — 16.7 16.7 16.7 16.7 16.7 16.7 16.7 4.8 19 76.2 19 500 — — 2.8 28

1.05 1.01 0.63 0.37 0.71 0.31 0.32 0.34 0.34 0.80 0.17 0.20 0.21 0.21 0.81–0.91 0.85 0.97 0.37 0.73 0.27 0.42 0.13 0.33 1.10 0.24 0.63 1.05 1.19 1.21 1.27 1.47 1.63 1.43 1.25 1.08 1.17 1.15 1.12 0.24 0.72 0.37 0.55 0.60

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Ref. Gwartney et al. 2002 Gwartney et al., 2002 Prentice et al., 1993 Almena et al., 1998 Almena et al., 1998 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Masi and Addeo, 1986 Prentice et al., 1993 Prentice et al., 1993 Prentice et al., 1993 Prentice et al., 1993 Ak and Gunasekaran, 1992 Rosenau et al., 1978 Rosenau et al., 1978 Fenelon and Guinee, 2000 Hort and Le Grys, 2001 Hort and Le Grys, 2001 Kucukoner et al., 1998 Kucukoner et al., 1998 Prentice et al., 1993 Madsen and Ardö, 2001 Prentice et al., 1993 Prentice et al., 1993 Prentice et al., 1993 Rohm et al., 1996 Rohm et al., 1996 Rohm et al., 1996 Jaros et al., 1997 Jaros et al., 1997 Jaros et al., 1997 Jaros et al., 1997 Rohm and Lederer, 1992 Rohm and Lederer, 1992 Rohm and Lederer, 1992 Rohm et al., 1992 Saldo et al., 2000 Prentice et al., 1993 Prentice et al., 1993 Luyten, 1988 Luyten, 1988

TABLE 3.3 (continued) Values of Strain at Fracture from Uniaxial Testing of Several Cheesesa

Cheese Variety Gouda 1 week, pH = 4.94 Gouda 2 week, pH = 5.24 Gouda 2 week, pH = 5.24 Gouda 2 week, pH = 5.24 Gouda 2 week, pH = 5.24 Gouda 6 months Gouda 6 months Gouda 6 months Gouda 6 months Gruyère Gruyère-type strong cohesion Gruyère-type strong cohesion — Tension Gruyère-type weak cohesion Gruyère-type weak cohesion — Tension Lancashire Leicester Mild Cheddar — A Reduced Fat — Shear Mild Cheddar — A — Shear Mild Cheddar — B Light — Shear Mild Cheddar — B — Shear Montasio Monterey Jack Light — Shear Monterey Jack — Shear Mozzarella Mozzarella Münster Parmesan Parmigiano Reggiano 12 months old Parmigiano Reggiano 18 months old Parmigiano Reggiano 28 months old Pecorino Romano Processed American Processed American Processed cheese analogs high fat, high moisture Processed cheese analogs high fat, high moisture Processed cheese analogs high fat, high moisture Processed cheese analogs low fat, low moisture Processed cheese analogs low fat, low moisture

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Initial Strain Rate s–1b

Peak Strain

140 0.67 2.7 50 250 0.28 2.8 28 170 — 55.5 11 55.5 11 — — 261 261 261 261 — 261 261 — — — — 42 42 42 — 11 110 5.56

0.61 1.48 1.39 1.31 1.07 0.29 0.31 0.30 0.32 0.51 0.75 1.30 0.73 0.46 0.20 0.30 1.28 1.13 1.47 0.95 0.58 1.36 1.41 0.55 1.08 0.10 0.14 0.22 0.18 0.12 0.25 0.86 0.79 1.20

Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Prentice et al., 1993 Pesenti and Luginbühl, Pesenti and Luginbühl, Pesenti and Luginbühl, Pesenti and Luginbühl, Prentice et al., 1993 Prentice et al., 1993 Gwartney et al., 2002 Gwartney et al., 2002 Gwartney et al., 2002 Gwartney et al., 2002 Prentice et al., 1993 Gwartney et al., 2002 Gwartney et al., 2002 Prentice et al., 1993 Masi and Addeo, 1986 Prentice et al., 1993 Prentice et al., 1993 Noel et al., 1996 Noel et al., 1996 Noel et al., 1996 Prentice et al., 1993 Rosenau et al., 1978 Rosenau et al.,1978 Marshall, 1990

55.6

1.43

Marshall, 1990

556

1.47

Marshall, 1990

5.56

0.92

Marshall, 1990

55.6

1.02

Marshall, 1990

Ref.

1999 1999 1999 1999

TABLE 3.3 (continued) Values of Strain at Fracture from Uniaxial Testing of Several Cheesesa

Cheese Variety Processed cheese analogs low fat, low moisture Provolone Provolone Red Brick UF-Feta 8–10 weeks Red Brick UF-Feta 8–10 weeks Red Brick UF-Feta 8–10 weeks Red Brick UF-Feta 8–10 weeks Sbrinz Sharp Cheddar Light — Shear Sharp Cheddar — Shear Silano Tilsit Tin UF-Feta 8–10 weeks Tin UF-Feta 8-10 weeks Tin UF-Feta 8-10 weeks Tin UF-Feta 8-10 weeks Tybo Argentino up to 114 days Vorarlberger Bergkase a b

Initial Strain Rate s–1b

Peak Strain

556

1.02

Marshall, 1990

— — 110 220 330 440 — 261 261 — — 110 220 330 440 42 16.7

0.53 0.80 0.30 0.33 0.34 0.35 0.41 1.26 0.94 0.99 0.78 0.21 0.20 0.20 0.22 1.20 0.55

Prentice et al., 1993 Masi and Addeo, 1986 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Prentice et al., 1993 Gwartney et al., 2002 Gwartney et al., 2002 Masi and Addeo, 1986 Prentice et al., 1993 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Bertola et al., 1992 Jaros and Rohm, 1997

Ref.

Data are from uniaxial compression test unless indicated otherwise by a remark next to the variety name. Values in this column are already multiplied by a factor of 1000 to avoid small numbers.

The constant strain rate compression has also been applied to biopolymer gels (Rohm, et al., 1995). Prentice (1992) discussed main issues related to the measurement and data interpretation. Prentice (1992)* also listed the mechanical properties for a number of cheeses, which are included in Tables 3.2 to 3.5. These properties are zero-strain modulus, Eo, which we can take as modulus of deformability, peak stress, and peak strain, which we can identify, as often done by many authors, as fracture stress and fracture strain. The zero-strain modulus is based on the following expression: σ = Eo ε − c ε 2

(3.3)

Where, σ is the true stress, ε is the Hencky strain below some critical level, and c is a constant. * The mechanical properties presented in Table 8.1 of Prentice (1992) were, however, different than those reported by the same author and coworkers in a later publication (Prentice et al., 1993). Since our calculations based on data from the few original papers agreed better with the results of Prentice et al. (1993), these values are included in our Tables 3.2 to 3.5.

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TABLE 3.4 Values of Stress at Fracture from Uniaxial Testing of Several Cheesesa

Cheese Variety

Initial Strain Rate s–1b

Peak Stress kPa

American Light — Shear American — Shear Appenzell Arzua-Ulloa Spanish soft cheese — type I Arzua-Ulloa Spanish soft cheese — type II Blue Brick UF-Feta 8–10 weeks Blue Brick UF-Feta 8–10 weeks Blue Brick UF-Feta 8–10 weeks Blue Brick UF-Feta 8–10 weeks Caciocavallo Caerphilly Cheddar Cheddar Cheddar Cheddar Cheddar Cheddar Cheddar 32.5% fat, 225 d old Cheddar 6.3% fat, 225 d old Cheddar 64 weeks old Cheddar 8 weeks old Cheddar 20-d-old Cheddar 20-d-old Cheddar 20-d-old Cheddar 20-d-old Cheddar 20-d-old Cheddar 20-d-old Cheddar 20-d-old Cheddar 20-d-old Cheddar 20-d-old Cheddar 20-d-old Cheddar 20-d-old Cheddar 20-d-old Cheddar 5-mo-old, full-fat: 32% Cheddar 5-mo-old, low-fat: 5% Cheshire Danbo Double Gloucester Edam Emmental Emmental 16 weeks Emmental 16 weeks Emmental 16 weeks

261 261 — 46 46 110 220 330 440 4.2 — — — — — 11.1 110 29 29 32 32 1.4 2.2 3.7 5.6 7.2 11 14.5 22.2 29.2 44.6 72.9 111 440 440 — 833 — — — 16.7 16.7 16.7

38 29 7 39 220 20 22 23 22 383 64 8 44 23 108 44 59 220 740 30 60 39 45 50 57 50 68 59 72 62 82 75 100 94 525 44 94 94 146 12 165 126 91

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Ref. Gwartney et al., 2002 Gwartney et al., 2002 Prentice et al., 1993 Almena et al., 1998 Almena et al., 1998 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Masi and Addeo, 1986 Prentice et al., 1993 Prentice et al., 1993 Prentice et al., 1993 Prentice et al., 1993 Prentice et al., 1993 Rosenau et al., 1978 Rosenau et al., 1978 Fenelon and Guinee, 2000 Fenelon and Guinee, 2000 Hort and Le Grys, 2001 Hort and Le Grys 2001 Ak and Gunasekaran 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Kucukoner et al., 1998 Kucukoner et al., 1998 Prentice et al., 1993 Madsen and Ardö, 2001 Prentice et al., 1993 Prentice et al., 1993 Prentice et al., 1993 Rohm et al., 1996 Rohm et al., 1996 Rohm et al., 1996

TABLE 3.4 (continued) Values of Stress at Fracture from Uniaxial Testing of Several Cheesesa

Cheese Variety

Initial Strain Rate s–1b

Peak Stress kPa

Ref.

Emmental 112-d-old Emmental 28-d-old Emmental 70-d-old Emmental 7-day-old Emmentaler 4 months Emmentaler 4 months Emmentaler 4 months Emmentaler 4-mo-old Garrotxa-type goat milk cheese Gouda Gouda Gouda 1 week, pH = 4.94 Gouda 1 week, pH = 4.94 Gouda 1 week, pH = 4.94 Gouda 2 week, pH = 5.24 Gouda 2 week, pH = 5.24 Gouda 2 week, pH = 5.24 Gouda 2 week, pH = 5.24 Gouda 6 months Gouda 6 months Gouda 6 months Gouda 6 months Gruyère Gruyère-type strong cohesion Gruyère-type strong cohesion — Tension Gruyère-type weak cohesion Gruyère-type weak cohesion — Tension Lancashire Leicester Leicester Mild Cheddar 37 days old Mild Cheddar 182 days old Mild Cheddar — A Reduced Fat — Shear Mild Cheddar — A — Shear Mild Cheddar — B Light — Shear Mild Cheddar — B — Shear Montasio Monterey Jack 46 days old Monterey Jack 185 days old Monterey Jack Light — Shear Monterey Jack — Shear Mozzarella Mozzarella

16.7 16.7 16.7 16.7 4.8 19 76.2 19 500 — — 2.8 28 140 0.67 2.7 50 250 0.28 2.8 28 170 — 55.5 11.1 55.5 11.1 — — — 8.3–24 8.3–24 261 261 261 261 — 8.3–24 8.3–24 261 261 — 4.2

170 265 205 280 78 95 121 96 65 69 68 27 41 66 35 55 108 182 42 64 82 108 15 1338 70 909 32 87 48 50 170 140 43 37 50 33 125 110 80 50 25 3 147

Jaros et al., 1997 Jaros et al., 1997 Jaros et al., 1997 Jaros et al., 1997 Rohm and Lederer, 1992 Rohm and Lederer, 1992 Rohm and Lederer, 1992 Rohm et al., 1992 Saldo et al., 2000 Prentice et al., 1993 Prentice et al., 1993 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Luyten, 1988 Prentice et al., 1993 Pesenti and Luginbühl, 1999 Pesenti and Luginbühl, 1999 Pesenti and Luginbühl, 1999 Pesenti and Luginbühl, 1999 Prentice et al., 1993 Prentice et al., 1993 Prentice et al., 1993 Charalambides et al., 1995 Charalambides et al., 1995 Gwartney et al., 2002 Gwartney et al., 2002 Gwartney et al., 2002 Gwartney et al., 2002 Prentice et al., 1993 Charalambides et al., 1995 Charalambides et al., 1995 Gwartney et al., 2002 Gwartney et al., 2002 Prentice et al., 1993 Masi and Addeo, 1986

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TABLE 3.4 (continued) Values of Stress at Fracture from Uniaxial Testing of Several Cheesesa

Cheese Variety Münster Parmesan Parmigiano Reggiano 12 months old Parmigiano Reggiano 18 months old Parmigiano Reggiano 28 months old Pecorino Romano Processed American Processed American Processed cheese analogs high fat, high moisture Processed cheese analogs high fat, high moisture Processed cheese analogs high fat, high moisture Processed cheese analogs low fat, low moisture Processed cheese analogs low fat, low moisture Processed cheese analogs low fat, low moisture Provolone Provolone Red Brick UF-Feta 8–10 weeks Red Brick UF-Feta 8–10 weeks Red Brick UF-Feta 8–10 weeks Red Brick UF-Feta 8–10 weeks Sbrinz Sharp Cheddar 1 month old Sharp Cheddar 6 months old Sharp Cheddar Light — Shear Sharp Cheddar — Shear Silano Swiss Appenzeller type — rapeseed diet Swiss Appenzeller type — regular diet Tilsit Tin UF-Feta 8–10 weeks Tin UF-Feta 8–10 weeks Tin UF-Feta 8–10 weeks Tin UF-Feta 8–10 weeks Vorarlberger Bergkase a b

Initial Strain Rate s–1b

Peak Stress kPa

— — 42 42 42 — 11.1 110 5.56

3 112 211 199 186 187 20 31 48

Prentice et al., 1993 Prentice et al., 1993 Noel et al., 1996 Noel et al., 1996 Noel et al., 1996 Prentice et al., 1993 Rosenau et al., 1978 Rosenau et al., 1978 Marshall, 1990

55.6

79

Marshall, 1990

556

102

Marshall, 1990

5.56

368

Marshall, 1990

55.6

424

Marshall, 1990

556

453

Marshall,1990

— 4.2 110 220 330 440 — 8.3–24 8.3–24 261 261 4.2 17 17 — 110 220 330 440 17

57 314 25 27 27 27 22 120 155 51 44 157 104 135 7 33 39 40 46 123

Prentice et al., 1993 Masi and Addeo, 1986 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Prentice et al., 1993 Charalambides et al., 1995 Charalambides et al., 1995 Gwartney et al., 2002 Gwartney et al., 2002 Masi and Addeo, 1986 Jaros et al., 2001 Jaros et al., 2001 Prentice et al., 1993 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Jaros and Rohm, 1997

Ref.

Data are from uniaxial compression test unless indicated otherwise by a remark next to the variety name. Values in this column are already multiplied by a factor of 1000 to avoid small numbers.

© 2003 by CRC Press LLC

TABLE 3.5 Values of Work-to-Fracture from Uniaxial Testing of Several Cheesesa

Cheese Variety Arzua-Ulloa Spanish soft cheese — type I Arzua-Ulloa Spanish soft cheese — type II Blue Brick UF-Feta Blue Brick UF-Feta Blue Brick UF-Feta Blue Brick UF-Feta Caciocavallo Cheddar 8 weeks old Cheddar 64 weeks old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Cheddar cheese 20-d-old Danbo Garrotxa-type goat milk cheese Gruyere-type strong cohesion Gruyere-type strong cohesion — Tension Gruyere-type weak cohesion Gruyere-type weak cohesion — Tension Mozzarella Parmigiano Reggiano 12 months old Parmigiano Reggiano 18 months old Parmigiano Reggiano 28 months old Provolone Red Brick UF-Feta Red Brick UF-Feta Red Brick UF-Feta Red Brick UF-Feta Silano Tin UF-Feta Tin UF-Feta Tin UF-Feta Tin UF-Feta a b c

Initial Strain Rate s–1b

Toughness kJ/m3c

46 46

7.1 31.7

Almena et al., 1998 Almena et al., 1998

110 220 330 440 4.2 32 32 1.4 2.2 3.7 5.6 7.2 11 14.5 22.2 29.2 44.6 72.9 111 833 500 55.5 11.1 55.5 11.1 4.2 42 42 42 4.2 110 220 330 440 4.2 110 220 330 440

4.4 5.2 5.5 5.5 8 42.3 7 23 27 26 32 34 42 30 35 40 47 51 61 61 6.5 210 57 152 8 2 30.6 23.8 18.4 6.4 5.5 6.4 6.7 6.7 3.3 5 5.4 5.5 6.2

Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist,1997 Wium and Qvist, 1997 Masi and Addeo, 1986 Hort and Le Grys, 2001 Hort and Le Grys, 2001 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Ak and Gunasekaran, 1992 Madsen and Ardö, 2001 Saldo et al., 2000 Pesenti and Luginbühl, 1999 Pesenti and Luginbühl, 1999 Pesenti and Luginbühl, 1999 Pesenti and Luginbühl, 1999 Masi and Addeo, 1986 Noel et al., 1996 Noel et al., 1996 Noel et al., 1996 Masi and Addeo, 1986 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Masi and Addeo, 1986 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997 Wium and Qvist, 1997

Ref.

Data are from uniaxial compression test unless indicated otherwise by a remark next to the variety name. Values in this column are already multiplied by a factor of 1000 to avoid small numbers. Obtained from area under the stress–strain curve up to peak location.

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TABLE 3.6 Comparison of Modulus of Deformability Values Obtained Through Different Procedures for Three Cheeses at 20°C Procedure

Standard Cheddar (18-week-old)

Granular Cheddar (34-week-old)

Standard Mozzarella (7-week-old)

A B C D

1210 (10)a 1150 (11) 934 (13) 996 (13)

958 (8) 946 (10) 694 (3) 685 (4)

144 (21) 133 (27) 115 (21) 93 (22)

A: Gradient at inflection (Inf.) method. B: Gradient at strain range Inf./2 to 1.5 Inf. C: Gradient at strain range 0 to 0.04. D: Linear term of the polynomial fit (Equation 2.22, Chapter 2). a

Numbers in parentheses are coefficients of variation (100*Std.Dev./Mean).

Source: After Watkinson and Jackson, 1999.

As stated in Chapter 2, it is not sure at which stage and where the fracture actually starts in compression testing of cheese (Luyten et al., 1991b). Nevertheless, in the literature it is common to identify the maximum point on the true stress–Hencky strain curve as the fracture point in order to extract fracture stress and fracture strain data. Fracture properties determined by this practical method are likely to be related to the actual stress and strain at fracture. Luginbühl (1996) contested the use of true stress–Hencky strain curve for determination of fracture parameters. He stated that the true stress calculation at large deformation is based on incorrect assumptions. Two of these assumptions are the constancy of volume and the retention of cylindrical shape. He also stated that the shift of the apparent fracture strain towards smaller values is merely due to a mathematical effect. He advocated that the fracture parameters of hard and semihard cheeses should be determined from the coordinates of the apparent fracture point in the engineering stress–engineering strain curve. If need arises, Equations 2.7 and 2.12 can be used to convert fracture parameters from one set of coordinates to the other. Following the criticisms of Luginbühl (1996), Rohm et al. (1997) conducted compression tests on various foods, including Gouda cheese, where the contact surfaces were generously lubricated with paraffin oil. The compression tests were recorded, and the resulting video frames were analyzed using image-processing software. Their results showed that the shape of Gouda cheese specimen remained nearly cylindrical even at a relative deformation of 60% or Hencky strain of 0.92. Furthermore, for Gouda cheese, the true stress calculated by Equation 2.17, was shown to be in close agreement with the average stress based on the actual crosssectional area obtained from the video image analysis. In addition to the previous findings of other researchers (Culioli and Sherman, 1976; Calzada and Peleg, 1978; Luyten et al., 1991a), these results confirmed the assumptions of constant volume

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and shape retention during uniaxial compression with lubrication, at least for Gouda cheese. Taneya et al. (1992) calculated, using Equation 2.27, Poisson’s ratio of 0.493 for string cheese, signifying that it is practically incompressible, and thus the constant volume assumption is valid. Moreover, Brennan and Bourne (1994) and Charalambides et al. (2001) presented photographic evidence illustrating that cylindrical shapes in lubricated compression of mild Provolone, Gruyere, and Mozzarella cheeses were maintained. On the other hand, compression between molar teeth in the mouth followed the nonlubricated pattern (i.e., barreling), although some lubrication was provided by the saliva (Brennan and Bourne, 1994). For truly elastic solids or Hookean solids, the Young’s modulus will not be affected by the deformation rate. Cheese, however, is a viscoelastic material, and, consequently, the rate of loading or deformation is expected to have a significant impact on its rheological properties. Many researchers have actually observed the rate effect for a variety of cheeses (Shama and Sherman, 1973; Culioli and Sherman, 1976; Vernon-Carter and Sherman, 1978; Dickinson and Goulding, 1980). The results of Shama and Sherman (1973) on double Gloucester cheese clearly demonstrate the effect of deformation rate on cheese properties. The modulus of deformability and the stress at fracture are usually more influenced by the deformation rate than the strain at fracture. For instance, the fracture stress of 20-day-old Cheddar cheese almost doubled upon increasing the initial strain rate (i.e., crosshead speed/original specimen height) by fiftyfold during the lubricated compression; meanwhile, only a small change in the fracture strain was observed (Ak and Gunasekaran, 1992). In a similar fashion, the modulus of deformability for 4-month-old Emmentaler cheese increased by 1.7 times when the initial strain rate was increased by sixteenfold. For this change in the rate of deformation the fracture strain increased only by 1.07 times (Rohm and Lederer, 1992). A quick look at the data in Tables 3.2 to 3.5 will confirm the effect of deformation rate on the mechanical properties of various cheeses. Generally speaking, as the deformation rate of deformation is increased, the stress at fracture and the modulus of deformability increase, whereas the strain at fracture may increase, decrease, or remain unchanged. The common explanation for the rate effect is that at higher deformation rates the viscoelastic cheese has less time to relax some of the stress during the loading stage and therefore attains higher values of stress. In other words, Deborah number, which is the ratio of the characteristic time of the material to the time-scale of the experiment, determines the way a viscoelastic material responds to mechanical perturbations. The rate dependence of stress–strain relationship as a result of viscoelasticity of cheese can be represented by a power-law relationship: σ = Cε˙ n or ln σ = ln C + n ln ε˙

(3.4)

Where, C is a constant and n is the exponent signifying the relative contributions of viscous and elastic components. The n value is zero for an ideally elastic material (i.e., no viscous part) and increases with the extent of the viscous contribution. According to the analysis of Luyten et al. (1991a) the relation between n and the tan δ at the same time scale is given by:

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TABLE 3.7 Values for the Exponent n in Equation 3.4 for Different Types of Cheese

Cheese

Range of Initial Strain Rate s–1a

n

Ref.

Double Gloucester Gouda Cream cheese American Cheddar Cheddar Leicester Cheshire Cheddar Processed cheese Provolone Gouda-type 1 Cheddar Emmentaler Tin Feta Red Brick Feta Blue Brick Feta

20 fold 20–300 2–500 2–500 2–500 3–600 3–600 3–600 2–400 0.2–400 4–200 0.2–200 1.4–110 4.8–76 110–440 110–440 110–440

0.23 0.19 0.18 0.14 0.22 0.22 0.21 0.14 0.19 0.15 0.19 0.15–0.20 0.19 0.16 0.21 0.06 0.09

Luyten et al., (1991a) Luyten et al., (1991a) Luyten et al., (1991a) Luyten et al., (1991a) Luyten et al., (1991a) Luyten et al., (1991a) Luyten et al., (1991a) Luyten et al., (1991a) Luyten et al., (1991a) Luyten et al., (1991a) Luyten et al., (1991a) Luyten et al., (1991a) Ak and Gunasekaran, (1992) Rohm and Lederer, (1992) Wium and Qvist, (1997) Wium and Qvist, (1997) Wium and Qvist, (1997)

a

Values in this column are already multiplied with a factor of 1000 to avoid small numbers.

tan δ =

π n 2

(3.5)

This equation forms a bridge between nonlinear property n from the static experiments and the linear property tan δ from the dynamic experiments (see Chapter 5). The n values for a variety of cheeses are listed in Table 3.7. Luyten and van Vliet (1996) offered two mechanisms to explain the relation between fracture strain and rate of deformation or time-scale of deformation. The first mechanism is related to energy dissipation due to viscous flow. As the viscouslike character of a material increases with decreasing deformation rate (or increasing time-scale of deformation), the energy dissipation due to viscous flow becomes relatively more important (e.g., in cheese with high water content). Therefore, the amount of elastically-stored energy available for fracture at a given deformation (see Chapter 4) decreases so that fracture will not take place before the cheese is deformed further. Hence, the fracture strain will attain a larger value. Accordingly, a truly viscous liquid will not fracture at all, and a truly elastic solid will store all mechanical energy until fracture. The second mechanism is related to another dissipative effect in cheese, which is internal friction due to relative motion of different components. The energy dissipation through friction, however, increases with increasing rate of

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deformation. Thus, this mechanism lowers more of the energy available for fracture at higher deformation rates, resulting in a larger fracture strain. There may also be cheeses for which the fracture strain seems independent of the deformation rate due to the balance between these two mechanisms. The instrumental texture measurements often seek to obtain high correlations with the sensory evaluations, so that the sensory panel can be replaced with instrumental tests (Bourne, 1982; Peleg, 1983). The instrumental texture determinations are discussed in Chapter 7. It is usually hoped that when instrumental tests are made under conditions similar to those prevailing during sensory evaluations, one can obtain good correlations. There are, however, many theoretical and practical issues that need to be addressed in order to obtain satisfactory and accurate correlations (Peleg, 1983). In addition, poor correlations may sometimes stem from other reasons; for instance, the difference in fracture mechanisms of Cheddar cheese and Cheshire cheese in the mouth and in compression testing (Green et al., 1985). Often the deformation rates employed in instrumental measurements are smaller than the rates estimated during the sensory evaluations (e.g., chewing rate). This discrepancy has long been considered to exert a negative effect on the correlation between instrumental and sensory measurements. However, a recent study on UF-Feta cheese indicated that the correlation between oral firmness and stress at fracture was independent of deformation rate (Wium et al., 1997). Whether this is a rule or exception is yet to be established with other cheeses. For instance, the effects of deformation level and deformation rate on the maximum compression force, which is related to sensory hardness, were recently investigated for 26 commercial cheeses (Xiong et al., 2002). The highest correlation was obtained at a combination of compression level between 70 and 90% and deformation rate of 1.0 mm/s, which was not the highest rate used in the study (i.e., 10 mm/s). As for many other cheese varieties, the compression force increased with the initial strain rate in log-linear fashion (Figure 3.1).

Maximum compression force (N)

400 Deli-Provolone Farmer’s

300

Edam Gouda

200

100 0 0.01

0.1

1

Initial strain rate (1/s)

FIGURE 3.1 Relationship between maximum compression force and strain rate in uniaxial compression of various cheeses. (After Xiong et al., 2002.)

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TENSION

PARALLEL PERPENDICULAR

CHEESE BLOCK

COMPRESSION Parallel

Perpendicular

FIGURE 3.2 Sample preparations for parallel and perpendicular orientations.

STRUCTURE AND COMPOSITION EFFECTS When cylindrical samples of cheese with oriented fibrous structure are evaluated by uniaxial compression, according to Prentice et al. (1993), the values of Young’s modulus and maximum stress may be the same whether they are deformed along or across the direction of the internal fibers. Prentice et al. (1993) commented that during uniaxial compression of cheese cylinders the stresses are distributed radially throughout the sample such that stresses will be both along and across the direction of the internal fibers. Quantitative results for the effect of sampling direction on compression properties of Mozzarella cheese have been presented in Ak (1993). The schematic drawing of compression test is given in Figure 3.2, and the experimental conditions are given in Table 3.8. The deformability modulus ED of samples with perpendicular orientation was initially higher than those of parallel orientation. As the cheese matured, the difference in ED values first diminished at day 14, and later reversed (Figure 3.3). Examining the compression forces at three deformation levels (i.e., 25%, 50%, 75%), we see no definite trend emerging (Table 3.9) (Ak, 1993). Nevertheless, especially at 50% and 75% deformations, the force was usually higher when the fibers in the sample were perpendicular to the compression direction. This is consistent with the findings of Cervantes et al. (1983) with Mozzarella cheese, where force at 50%

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TABLE 3.8 Details of Experimental Conditions in Uniaxial Compression of Mozzarella Cheese with Different Sampling Directions Explanation Cheese Ambient temperature Specimen temperature

Crosshead speed Storage time Compression level Replication

Commercial low-moisture, part-skim Mozzarella. Tests were conducted at room temperature (~23°C). Specimens were thermally conditioned in an incubator at 15°C. This temperature was selected to reduce complications that may arise from melting of cheese fat. It was measured that the specimen temperature increased at most by 0.5°C during 40 s of testing It was set to 50 mm/min in order to reduce the time a specimen was exposed to ambient conditions during testing. Tests were made 7, 14, 21, and 28 days after the production date. Samples stored at refrigeration temperature 25, 50, and 75% compression level was applied separately on different days Sixteen specimens were tested for each orientation at each storage time

Source: After Ak, 1993.

170 Deformability modulus (kPa)

Parallel Perpendicular 150

130

110

90 7

14

21

28

Storage time (day)

FIGURE 3.3 Effect of aging on deformability modulus of cheese with parallel and perpendicular orientations. (After Ak, 1993.)

compression was used for comparison. On the other hand, Pompei et al. (1987) examined whether the anisotropy of Provolone cheese, due to stretching of hot curd, affected its rheological behavior. For that purpose they applied force in direction parallel and normal to the run of the macroscopic fibers. The hardness, energy, and cohesiveness values from the texture profile analysis (TPA, see Chapter 7) tests did not reveal sufficient evidence to claim the existence of anisotropic behavior in Provolone cheese of 5–6 mo old.

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TABLE 3.9 Force Values at Different Compression Levels for Samples Taken Parallel and Perpendicular to the Fiber Orientation in Mozzarella Cheese During Refrigerated Storage Mean Compressive Force (N) 25% Compression Cheese Age (day) 7 14 21 28 a

50% Compression

Parallel

Perpendicular

Sig. Levela

8.1 12.3 10.6 10.2

8.3 11.9 9.4 9.1

0.73 0.36 0.009 0.005

75% Compression

Parallel

Perpendicular

Sig. Level

Parallel

Perpendicular

Sig. Level

21.2 29.2 25.0 26.0

23.5 31.1 25.1 23.7

0.013 0.050 0.93 0.027

51.5 65.1 51.4 57.7

61.1 73.7 57.8 54.0

0.0001 0.003 0.015 0.124

Significance level

Source: After Ak, 1993.

TABLE 3.10 Effect of Sampling Direction on Compression Properties of Gruyère de Comté Cheese Rheological Parameter Modulus (kPa) Fracture stress (kPa) Fracture strain (%)

Axial Compression

Perpendicular Compression

Significance Level

367 184 43

429 142 38

** ** **

Note: ** = significant p<0.01; comparison of the means by t-test. Source: After Grappin et al., 1993. With permission.

For some cheeses (e.g., Gruyère de Comté, a Swiss-type, hard cheese), anisotropy in the rheological properties is of commercial importance. As an example, we cite the study of Grappin et al. (1993), where significantly different rheological properties were reported for samples taken according to the direction of pressing (axial) or perpendicular to it (Table 3.10). The authors established that the formation of slits favors large differences in stress and strain values at fracture for axial and perpendicular directions. They further established clearly that the difference in fracture strains between the two directions is chiefly responsible for the formation of slits — a quality defect that downgrades commercial value of Comté cheese (Grappin et al., 1993). It is known that rheological properties of cheeses vary with the composition (i.e., the amounts and states of constituents, namely casein, fat, water, salt, pH, etc.) and the degree of maturation. However, it may not be easy to establish sound relations between composition and rheological properties of the cheeses. The reason for this, © 2003 by CRC Press LLC

Penetration stress (kPa)

1600 y = 73 x − 1256 R2 = 0.76 1200

800

400

0 10

20

30

40

Protein content (%)

FIGURE 3.4 Relationship between penetration force and protein content of 11 different cheeses. (After Chen et al., 1979.)

as already acknowledged by many researchers (Creamer and Olson, 1982; Luyten et al., 1982; Marshall, 1990; Wium et al., 1998), is the difficulty of making cheese that differs only in one constituent (e.g., fat content), while keeping others (e.g., water content, salt content, pH, etc.) constant. In some cases, statistical methods are used to analyze the simultaneous variations in more than one variable. Rohm et al. (1992) evaluated chief compositional and maturation parameters affecting uniaxial compression properties of Swiss-type cheese (4-month-old Emmental) by multiple regression analysis. The mean values for rheological and fracture parameters of this work are presented in Tables 3.2 to 3.5. Casein is the main constituent in cheese that builds the structure and gives, when intact, the elastic or solid character. Based on the data of Chen et al. (1979), the relation between penetration stress (required pushing the plunger, D = 0.64 cm, into the sample for 1.91 cm) and protein content of different cheeses is shown in Figure 3.4. Based on the same study (excluding processed Cheddar cheese), Prentice (1992) concluded that about 25%* of the cheese by weight must be casein in order to provide a rigid framework. A similar procedure is applied to the compression data taken from Lee et al. (1978), and the resulting plot is given in Figure 3.5. It is seen that the compression stress at 80% deformation increases with the protein content of different cheeses (protein values taken from Bassette and Acosta, 1988). In the study by Chen et al. (1979) the penetration tests were made at 12.2 to 13.3°C, while the compression tests by Lee et al. (1978) were made at room temperature. We shall remark that the composition of cheeses tested in these studies differed not only in protein content but also in all other constituents (i.e., moisture, fat, salt, pH). However, the results of Chen et al. and Lee et al. indicated that maximum compression force for cheese varieties with widely differing composition correlate most closely with protein content and was not related to fat content. Other protein-containing * Protein contents (%) in the original study and those that appear in Figure 8.6 of Prentice (1992) appear to be different.

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Stress at 80% compression (kPa)

12

y = 0.41x − 2.95 R2 = 0.57

10 8 6 4 2 0 5

10

15 20 Protein content (%)

25

30

FIGURE 3.5 Relationship between compression stress and protein content of different cheeses. (After Lee et al., 1978.)

foods also exhibit similar relations (e.g., Hsieh and Regenstein, 1993). Therefore, although it may not be entirely correct to attribute the changes in rheological properties fully to the protein content, the data presented in Figures 3.4 and 3.5 demonstrate, however, that firmness is largely related to the protein content. Another clear evidence of a strong relation between protein content and properties by penetration method has been reported for heat-induced skim-milk gels (Kalab and Harwalkar, 1974; Holcomb et al., 1992). Besides, since hydrolysis of protein (i.e., casein fractions) during maturation weakens the structure and reduces the magnitude of cheese strength, it is therefore consistent to observe an increase in strength of cheese with an increase in protein content, irrespective of the type of cheese. Perhaps more compelling findings on the relation between protein content and firmness of cheese are the results of de Jong (1978) for Meshanger cheese (old Dutch cheese). The relation between protein content and firmness (i.e., force by extrusion method) is shown in Figure 3.6. The firmness was determined by an extrusion method involving a close-fitting cylinder and piston, which is set to move at a constant speed (de Jong, 1976). de Jong (1978) did not anticipate much contribution from the discontinuous fat to the overall firmness of Meshanger cheese. The classification of cheese according to water content testifies for the importance of this constituent. Chen et al. (1979) analyzed the relation between texture and composition (in relative unit of percent) of eleven cheeses to suggest the following sequence of decreasing contribution to the texture parameters: protein > NaCl > water > pH > fat. However, in another investigation, the sequence obtained was different (Rüegg, 1985): water > fat > pH > Ca > (Nsol-NPN), where Nsol means soluble nitrogen and NPN nonprotein nitrogen. Regardless of its position in such ranking, it is well established that a strong relation exists between water content and mechanical and textural properties for several cheeses (Amantea et al., 1986; Luyten, 1988; Tunick et al., 1993; Prentice, 1992; Visser, 1991; Taranto et al., 1979; Rohm et al., 1992; Tunick et al., 1991). As the moisture content increases, the resistance of cheese to deformation, and hence its modulus of deformability, decreases. The stress at

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Firmness (empirical units)

250 200 150 100 50 0 0.20

0.30

0.40

0.50

0.60

Volume fraction of protein

FIGURE 3.6 Strong contribution of protein content to the overall firmness of cheese. (After de Jong, 1978. With permission.)

fracture also decreases with increasing water content. The strain at fracture, however, either remains unaffected or increases with the moisture content, depending on the age of cheese (Visser, 1991; Rohm et al., 1992). The effect of water content on the modulus is usually explained by following reasons: (a) a high water content means a low protein content, which is the stress-carrying component; (b) water is a low-viscosity liquid that occupies the space between the fat and protein, and acts as a good lubricant; and (c) more swollen protein particles due to high water content offers less resistance to deformation (Luyten, 1988; Prentice, 1992). There can be significant variation in rheological properties within a single cheese block as a result of various reasons: (a) presence or absence of a rind; (b) frequency of turning during ripening; (c) development of moisture gradient; and (d) nonuniform proteolytic activity (Prentice et al., 1993). It is likely that not only the magnitudes but also the trends for a particular property (e.g., deformability modulus) can vary with the position in a cheese block, from surface (where moisture loss may dominate) to center (where proteolytic activities may dominate). Based on the data of Steffen (1976) reported by Prentice et al. (1993), there can be a variation of about 50% in firmness with distance from the surface in an otherwise uniform cheese. Recently, few studies have been conducted where hydrocolloid-based edible coatings were applied to semihard and brined cheeses for different purposes (e.g., moisture regulation, appearance, protection against microbial contamination) while still maintaining their desirable textural properties (Kampf and Nussinovitch, 2000). In terms of mechanical properties, the outcome of such coatings was promising, especially for semihard cheese (Kampf and Nussinovitch, 2000). Fat is one of the primary constituents contributing greatly to rheology, texture, and organoleptic characteristics (e.g., imparting a desirable mouthfeel to cheese) of cheeses (Marshall, 1990). It is also considered important in transport and packaging (Green et al., 1990). The contribution of fat to cheese quality is better appreciated when it is removed or reduced in manufacturing low-fat varieties. A reduction in fat content often adversely affects texture and flavor of cheese (Olson and Johnson,

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1990; Jameson, 1990). The level of intact casein in 225-day-old Cheddar cheese was twice higher in the reduced-fat cheese than that in the full-fat cheese. But the rate of decrease in the levels of intact casein was practically independent of the fat content (Fenelon and Guinee, 2000). The technological strategies for coping with the challenges in making of reduced-fat cheese and low-fat cheese and some regulatory issues have been discussed in recent reviews (Olson and Johnson, 1990; Drake and Swanson, 1995; Mistry, 2001). Reduction in fat content of hard cheeses (e.g., Cheddar) affects not only the flavor development but also the texture. It is well known that the texture of a reduced fat cheese is firmer and more elastic than that with full-fat content. Marshall (1990) conducted a thorough study to determine effects of changing fat and moisture [as moisture in nonfat solids (MNFS)] contents on the sensory, rheological, and structural properties of the processed cheese analogs. Numerical results from this work are presented in Tables 3.2 to 3.5. As can be seen from the data in these tables, the rheological parameters tended to decrease with an increase in MNFS, probably because of moisture acting as a plasticizer in the protein network. The fat content affects the microstructure of cheese. Full-fat cheeses of all varieties (i.e., Cheddar, Mozzarella, processed, and Swiss cheeses) are characterized by a protein matrix interspersed with fat globules existing in various sizes and shapes. Low-fat cheeses, however, have fewer and smaller fat globules within the dense protein network. The consequence of the protein-dominated structure of lowfat cheeses, is a firm and rubbery body and texture (Mistry and Anderson, 1993). In an earlier work, Green et al. (1981) examined, by different microscopic techniques, the structure development in Cheddar cheese from concentrated milks throughout cheese making and maturation. As the milk used in cheesemaking became more concentrated, the protein network became progressively coarser and this, in addition to large loss of fat into whey, led to higher resistance to compression (i.e., higher firmness). The role of fat in rheology of cheese was occasionally treated in terms of composite material behavior (Prentice, 1992; Luyten and van Vliet, 1990). The cheese is viewed as a composite material with casein-water forming the matrix and fat globules acting like fillers or inclusions. The mechanical properties of a composite material therefore depend on the properties of the matrix, the volume fraction and properties of the filler, and the mechanical interaction between the filler and matrix. According to Prentice (1992) the only interaction between fat and casein is friction. Green et al. (1990) studied the composite behavior of cheese analogs containing fat globules in a protein matrix. They varied fat concentration and fat hardness, and they either emulsified the fat with a neutral detergent (minimizing interaction between fat globules and the matrix) or emulsified with sodium caseinate (increasing interaction between fat globules and the matrix). The higher fat content at room temperature (70 to 80% liquid form) increased the lubrication effect of fat and reduced the fracture properties in compression and in wire cutting. Using different amounts of sunflower oil (completely liquid at room temperature) instead of butterfat decreased the maximum stress from 304 kPa at 6.2% oil to 165 kPa at 20.7% oil, and Young’s modulus from 115 kPa at 6.2% oil to 77 kPa at 20.7% oil. On the other

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hand, substituting partially hydrogenated oil (50% solid) for butterfat decreased the maximum stress from 349 kPa at 6.8% fat to 282 at 21.5% fat, but increased enormously the Young’s modulus from 152 kPa at 6.8% fat to 2061 kPa at 21.5% fat. Moreover, butterfat contributed more to the composite behavior when it was emulsified with sodium caseinate (i.e., more interaction with the matrix). It seems that simple substitution of fat by protein, water, and fat replacers results in a low-fat cheese that is inferior in many respects to its full-fat counterpart (Aryana and Haque, 2001). Several characteristics of fat or lack of it in low-fat cheeses can contribute to this result. Mechanical properties of fats, and their contribution to cheese and probably to perception of texture by consumers, are influenced by their chemical composition and temperature. The solid fraction of fat changes sharply in a relatively narrow temperature range (e.g., 10 to 35°C). However, water, for instance, within this temperature range, will have more or less constant properties. The interaction between fat and protein is hard (if not impossible) to mimic by the interaction between water and protein, or between fat replacers and protein. Commercially available fat replacers, of which none can yet fully duplicate functional and sensory attributes of fat, are one of three types: lipid based, carbohydrate based and protein based (Akoh, 1998). Interaction between water and fat replacers, in contrast to water binding of casein (Geurts et al., 1974), can also have a large impact on the properties of the final cheese. Another point worth mentioning is that during ripening of traditional cheeses, the fat globules can aggregate (and possibly coalesce) to increase in size and decrease in number, and this has an impact on the sensory properties of the cheese. The clumping of fat globules was observed in Cheddar cheese (Kimber et al., 1974) and Mozzarella cheese of varying fat contents and aged for 6 weeks (Tunick et al., 1993) and 50 days (Kiely et al., 1993), as well as in Cheddar-type cheese (Guinee et al., 2000). Kiely et al. (1993) suggested that fat aggregates are formed due to proteolytic destruction of the casein network. They also suggested that aggregation of fat globules could be the reason for the age-related increase in freeoil formation observed in low-moisture, part-skim Mozzarella cheese by Kiely et al. (1991). Tunick (1994) also reported that free-oil formation in Mozzarella cheese increased with the percentage of fat and protein breakdown. However, homogenization of cheese milk and cream greatly reduced free-oil due to the reduction of fat droplet size, while homogenization of skim milk had no effect (Tunick, 1994; Oommen, et al., 2000). Agglomeration of fat globules into larger particles was microscopically observed in both stirred-curd and stretched-curd Mozzarella cheeses after baking in a conventional oven (Paquet and Kalab, 1988). The agglomeration of fat globules is difficult to occur in low-fat cheese where the massive protein matrix keeps the small fat droplets well dispersed. This contributes to the rubbery texture and mouthfeel of the low-fat cheeses. Lastly, the contribution of free fatty acids and fat-soluble flavors to the taste of traditional cheese must be mentioned. Even after aging for 12 months, sensory panelists noted a flat flavor and lack of Cheddar flavor in reduced fat (50%) cheese (Olson and Johnson, 1990). The physical state of the fat globules (i.e., proportion of solid fat) determines its relative rigidity or stiffness in comparison to the casein matrix. Thus, the relative contribution of milk fat to the overall cheese properties is highly temperature

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Modulus of elasticity (kPa)

40

y = -34.4 x + 57.9 R2 = 0.96

30

20

10 0.7

0.8

0.9

1.0

1.1

1.2

Fat/SNF

Modulus of elasticity (kPa)

40 y = -21.5 x + 66.9 R2 = 0.90 30

20

10 1.5

1.7

1.9

2.1

2.3

Water/SNF

FIGURE 3.7 Effects of fat and moisture contents on the elasticity modulus of different cheese varieties. (Masi and Addeo, 1986.)

dependent. Melting of milk-fat globules occurs over a large temperature range from –30 to 40°C due to varying melting points of triglycerides (Dufour et al., 2000). It is entirely liquid above 40°C and completely solid below –30°C. Between these extremes it is a mixture of crystals and oil, where the latter is a continuous phase. Masi and Addeo (1986) reported a clear relation between the fat content (expressed as the ratio of fat to solids-nonfat, SNF) and the modulus of elasticity for Mozzarella cheese (Figure 3.7). However, it may be incorrect to attribute the decrease in the modulus entirely to the increase in fat content since moisture contents of these experimental cheeses also changed. The size of variation in the fat content was 4.7 units, whereas that in the water content was 3.2 units; that is, rather comparable numbers. As shown in Figure 3.7, we can also plot the modulus against the water content (as water/SNF ratio) for the same cheeses and still obtain a good correlation. A recent study by Madsen and Ardö (2001) on Danbo cheese with three fat contents provides further results regarding effects of fat and water on rheological properties (Table 3.11). On one hand, when the fat content of Danbo cheese is

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TABLE 3.11 Uniaxial Compression Properties of Low-Fat, Reduced-Fat, and Normal-Fat Danbo Cheese Parameter

Low-Fat

Reduced-Fat

Normal-Fat

Deformability modulus (kPa) Fracture stress (kPa) Fracture strain (–) Work to fracture (kJ/m3)

208 194 1.3 127

143 92 1.1 55

189 94 1.1 61

Fat (%,w/w) Moisture (%,w/w)

13.6 52.9

16.7 53.3

25.0 47.4

Source: After Madsen and Ardö, 2001. With permission.

reduced from 25 to 16.7% (a change of 33%), there was no change in the rheological parameters except the modulus. On the other hand, when the fat content is further reduced from 16.7 to 13.6% (a change of 19%), all parameters increased dramatically. It was concluded that water is not an adequate substitute for fat in order to obtain good quality, low-fat Danbo cheese (Madsen and Ardö, 2001). Considering Gouda cheese as a composite material, Luyten (1988) and Luyten and van Vliet (1990) determined the effect of temperature on the compression properties of the cheese. They pointed out that at 10°C the fat is stiffer than the matrix, and therefore the E for high-fat (60%) cheese is greater than the E for lowfat (10%) cheese. By the same token, the opposite is true at high temperature (26°C) where fat is nearly entirely liquid and contributes little to the modulus of the cheese. At the middle temperature (20°C), there was no influence of volume fraction of fat, indicating that the modulus of the fat is equal to the modulus of the protein matrix and is about 100 kPa (Luyten and van Vliet, 1990). The authors estimated that the modulus of the fat particles at 14°C to be 460 to 880 kPa. This is comparable to the modulus of deformability of a variety of cheeses listed in Table 3.2. It is also important to note that part of the temperature effect is due to the changes in rheological properties of the protein matrix. The theory of composite materials predicts a decrease in fracture strain with an increase in volume fraction of the filler. Since this was not observed in Gouda cheese, Luyten and van Vliet (1990) concluded that the milk-fat globules are relatively small (0.1–10 µm, Mulder and Walstra, 1974) and do not create stress concentrations to cause crack initiation. The fracture stress of Gouda cheese is, however, affected by the fat content and test temperature. The fracture stress decreased with the increasing fat content, and the temperature effect was stronger in high-fat cheese than in lowfat cheese. The importance of pH for a variety of cheese has been discussed from the cheesemanufacturing point of view (e.g., Lawrence et al., 1983; Lawrence et al., 1984; Chapter 1). The apparent effect of pH is more striking for Mozzarella and string cheeses. It is known that the kneading and stretching process of Mozzarella cheese curd is best performed at about pH 5.2 to 5.4 (Kosikowski, 1982). Kimura et al. (1992)

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reported on the structure and properties of string cheese at different pH and demineralization levels. Their results indicated that stringiness is limited by the calcium/phosphate (Ca/P) ratio in curd and not specifically by the curd pH. However, curd pH is an operational parameter that is associated with the Ca/P ratio. It is known that cheese has a “short” consistency (i.e., small fracture strain) if it has a low pH or a high salt content (Luyten et al., 1982). The effect of salt content on rheological properties of unripened Camembert (Mpagana and Hardy, 1986) and Gouda (Luyten, 1988) cheeses has been reported. Mpagana and Hardy (1986) adjusted the salt content of Camembert cheese by first keeping small, cylindrical pieces (2.4 cm diameter, 3.0 cm height) in saturated NaCl solution (pH = 5.0) at 15°C and then storing the brined pieces at 15°C and relative humidity of 95% for three days to assure homogeneous salt distribution within the samples. The test pieces (1.38 cm diameter, 1.0 cm height) were compressed to 20% of their original height (i.e., 80% deformation) at an initial strain rate 0.017 s–1. Although only the salt content was intentionally altered by applying different brining times, the water content of cheese would have decreased as well due to brining. Nevertheless, the modulus of deformability and fracture stress of Camembert increased exponentially, while the fracture strain decreased linearly with the salt content of the cheese (Figure 3.8). These findings are consistent with the results on other cheeses, such as Mozzarella cheese (Cervantes et al., 1983), Gouda (Luyten, 1988), and Feta cheese (Katsiari et al., 1997). Watkinson et al. (2001) preferred to work with a model cheese system, obtained by direct acidification, in order to study effects of pH on rheological properties during ripening with minimal confounding from other variables. It is observed that at a given ripening time, the fracture strain increased with pH in the range of 5.2 to 6.2, except there was a distinct maximum at pH 5.8 for the 87-day data. At a given pH value, the fracture strain increased with ripening time, with the exception of a constant value after seven days for the pH 6.2 cheeses. It shall be recalled that the local maximum in fracture strain of young Gouda cheese (1-week-old) was positioned at a lower pH 5.2 (Luyten et al., 1982). Further results from Watkinson et al. (2001) demonstrate that, in general, fracture stress increases with pH (e.g., at day 7 from about 160 kPa at pH 5.2 to about 270 kPa at pH 6.2) and modulus of deformability decreases with pH (e.g., at day 2 from about 1200 kPa at pH 5.2 to about 825 kPa at pH 6.2). Changes in rheological properties of cheese curd during the initial stages of ripening were studied at 20°C as a function of pH (5.45–6.05) and storage time (2–14 days) using a specially developed extrusion-flow technique (Ramkumar et al., 1998). The maximum force exerted on the grated curd during extrusion testing tended to increase with pH, reaching the maximum at pH 5.90. Increasing solid-like behavior with pH was also observed in oscillatory shear results for the cheese curd, indicating that the effect of pH is persistent in both small and large deformation regimes. Moreover, the tendency to exhibit more solid-like response is in accordance with the pH effect on the fracture stress (Watkinson et al., 2001). Perhaps the most important factor affecting rheological and other properties of cheese is proteolysis during maturation. The proteolytic activity that contributes

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Modulus of deformability (kPa)

1000

100

y = 109.3e0.09x R2 = 0.91 10 0

5

10

15

20

25

Salt content (g NaCl/100 H2O)

Engineering fracture stress (kPa)

1000

100

y = 37.6e0.10x R2 = 0.91 10 0

5

10

15

20

25

Salt content (g NaCl/100 g H2O) 1.2

Fracture strain (-)

1.0 0.8 0.6 0.4 y = -0.016 x + 0.85 R2 = 0.56

0.2 0.0 0

5

10

15

20

25

Salt content (g NaCl/100 g H2O)

FIGURE 3.8 Effect of salt content on the mechanical properties of Camembert cheese. (After Mpagana and Hardy, 1986.)

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greatly to the rheological and textural properties of cheeses basically means a reduction in the levels of intact casein (i.e., αs1-casein and β-casein). It is usually observed that αs1-casein fraction is hydrolyzed to a greater extent than β-casein, although the extent may depend on the cheese variety and the type of proteolytic enzyme (Fox, 1989; Trujillo et al., 1999; Dervisoglu and Yazici, 2001; Katsiari et al., 2000). Many ripening agents from different sources are responsible at different stages for the hydrolysis of caseins into small peptides and eventually to free amino acids, thus contributing to changes in both the texture and flavor during ripening (Fox et al., 1993; Farkye and Fox, 1990). It is of great importance to the cheese industry to be able to predict and control, and particularly accelerate, the ripening process (Fox et al., 1996; Fedrick, 1987; van den Berg and Exterkate, 1993; Folkertsma et al., 1996; Law, 1987; Saldo et al., 2000). Degradation of αs1-casein and β-casein during ripening of various cheeses is shown in Figure 3.9. We must note that only the trends should be considered and no comparison shall be made between different cheeses since the percent values are based on different reference quantities (e.g., expressed as % of levels in milk, or % of levels in fresh curd, % of levels in 1-day-old cheese, etc). An interesting example for effect of hydrolysis of para-casein on properties of cheese was reported for Camembert cheese (Schlesser et al., 1992). During early stages of ripening (up to 15 days) there was an increase in deformability modulus (called elasticity in the original paper) of Camembert cheese, which later on decreased with further aging until zero. After aging for more than 29 days the samples became semifluid (Schlesser et al., 1992). Consistent with the expectations based on previous findings, mechanical properties of Tybo Argentino cheese (semihard variety) decreased with ripening at 10°C and 60% relative humidity (Bertola et al., 1992). Although there was much scatter in the results, the deformability modulus of this cheese decreased from about 65 to 15 kPa during 120 days of ripening. Assuming a linear dependency, this means a decrease of 0.4 kPa/day. Ak and Gunasekaran (1995) reported a similar change for Mozzarella cheese over one month of aging. The strain at fracture did not vary with ripening time, and the average value was reported as 70% or εf = 1.20 (Bertola et al., 1992). Noël et al. (1996) determined rheological properties of Parmigiano Reggiano aged for up to 28 months and established relationships with the sensory properties. These authors reported not only standard rheological parameters, such as apparent elastic modulus and fracture parameters, but also the proportional limit and the modulus of resilience (see Chapter 2). The strain at apparent elastic limit of Parmigiano Reggiano cheese was about 7.6%, regardless of its age, while the stress limit increased from 117 kPa at 12 months to 191 kPa at 28 months. The apparent elastic modulus of the cheese increased with the age almost linearly with a rate of 60 kPa/month during maturation from 12 months to 28 months. The fracture strain and fracture stress values decreased linearly with the age of the cheese at a rate 0.006 units/month and 1.5 kPa/month, respectively. Raphaelides and Antoniou (1996) reported that for both traditional and UF-Teleme cheeses, the main changes in cheese structure, as reflected in mechanical properties, took place within the first month of ripening (Figure 3.10). Wium and Qvist (1997)

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Mild Cheddar

100 Alpha (s1)-casein (%)

Monterey Jack Sharp Cheddar

80

Cheddar

60

La Serena Kulek

40

Feta

20 0 0

10

20

30

40

50

60

Maturation time (week)

Mild Cheddar

120

Monterey Jack Sharp Cheddar

Beta-casein (%)

100

Cheddar

80

La Serena Kulek

60

Feta

40 20 0 0

10

20 30 40 Maturation time (week)

50

60

FIGURE 3.9 Proteolysis in numerous cheeses as measured by the decrease in intact αs1casein and β-casein. (Data from different sources referenced in text.)

reported on the fracture properties of three types of UF-Feta determined by uniaxial compression and dynamic tests. As can be seen in Table 3.4 the stress at fracture for these cheeses varied between 20 to 46 kPa, with the Tin Feta cheese always having higher values than the Red Brick Feta cheese and the Blue Brick Feta cheese. Moreover, when these cheeses were evaluated by sensory means (i.e., nonoral firmness: the resistance of a cube of cheese to moderate squeezing between thumb and forefinger; and oral firmness: the resistance of a cube of cheese during normal mastication), the Tin Feta cheese was selected as the firmest cheese, followed by the Red Brick Feta cheese and the Blue Brick Feta cheese (Wium and Qvist, 1997). On the other hand, the Tin Feta cheese also had the highest n value (Table 3.7), as well as tan δ, both signifying the more viscous character of this cheese. It seems that the parameters n and tan δ do not play a significant role in sensory evaluation of cheese. The modulus of deformability (ED) values (Table 3.2) in uniaxial compression of three UF-Feta cheeses ranged from 176 to 465 kPa (Wium and Qvist, 1997). It can © 2003 by CRC Press LLC

Deformability modulus (kPa)

200 160 120 80 Traditional

40

UF-unheated UF-heated

0 0

1

2

3

4

5

Maturation time (month)

FIGURE 3.10 Effect of maturation time on the deformability modulus of different kinds of Feta cheese. (After Raphaelides and Antoniou, 1996. With permission.)

be seen that the Tin Feta* had higher ED values at all rates than the Red Brick Feta cheese and the Blue Brick Feta cheese, indicating that the Tin Feta cheese is the stiffest. Wium and Qvist (1998) and Wium et al. (1998) reported on changes in rheological properties of UF Feta cheese made by acidification using glucono-δ-lactone (GDL). In these studies, the gross chemical composition (e.g., moisture, salt, pH, total N, and fat) of the cheeses was kept essentially constant while studying the effects of rennet concentration, coagulation method, and storage time. Measurement of proteolysis by capillary electrophoresis showed that αs1-casein was degraded more than β-casein due to the relatively faster action of chymosin on the former casein fraction, and also, the greater inhibitory influence of NaCl on the hydrolysis of β-casein by enzymes (Fox and Walley, 1971). Similarly, the ripening of Meshanger cheese was characterized by a very rapid and complete hydrolysis of αs1-casein, while the β-casein remaining essentially unattacked (de Jong, 1976). Substantial amounts of αs1-casein and β-casein were hydrolyzed by the high level of residual rennet in Feta cheese having salt-in-moisture concentrations from 3.99 to 4.32 and pH from 4.65 to 4.71 (Samal et al., 1993). The compression variables (ED, σf , εf , Wf) for UF-Feta cheese generally decreased with storage time, and that was ascribed purely to the proteolysis since the gross chemical composition remained essentially constant. It was further observed that stress at fracture, modulus of deformability, and work to fracture all increased significantly with rennet concentration, more so in the young cheese, with some showing a maximum at some intermediate levels (Figure 3.11). This was associated with the formation of a coarser network at higher rennet concentrations and viewed as a potential way of making soft variants of UF-Feta cheese with a smooth texture by using less rennet. On the other hand, strain at fracture decreased with increasing rennet concentration, again consistent with coarser * The Tin Feta is packed in tins containing brine and the Red Brick Feta and Blue Brick Feta are packed in Tetra-Brick packages without brine.

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80

0.5

0.3 40 0.2 20

Fracture strain (-)

Fracture stress (kPa)

0.4 60

0.1

stress strain 0 0.001

0 0.01

0.1

1

10

Rennet concentration (g/kg)

FIGURE 3.11 Effect of rennet concentration on fracture stress and fracture strain of Feta cheese made from ultrafiltered milk. (After Wium and Qvist, 1998.)

structure explanation. Luyten and van Vliet (1996) stated that the strain at fracture is rather low for very young Gouda cheeses (e.g., 1-day- or 2-day-old) due to the large inherent defects (e.g., incomplete fusing of curd particles) present in such cheeses (Luyten, 1988). A recent interesting work on the fracture stress of fused curd grains (Lodaite et al., 2002) indicated that the applied compressive stress, the degree of syneresis prior to fusion, and the fusion time exerted significant positive effects on the quality of fusion and the magnitude of fracture stress. A low fracture strain implies a short texture and possibly a crumbly behavior (Luyten et al., 1982). In general, the shortness of cheese increases with maturation. Watkinson et al. (1997) has shown that the strain at fracture of New Zealand Cheddar cheese initially increased in the first 28 days, and thereafter it decreased with further aging. Their results, combined with those from Creamer and Olson (1982), are plotted in Figure 3.12, which shows a large decrease in fracture strain during maturation of Cheddar cheese. Similar trends have been reported for several other cheeses (Luyten, 1988; Ak et al., 1993; Luyten and van Vliet, 1996). The initial increase in εf is attributed to the process of fusion until the proteolysis dominates and causes a decrease in εf or an increase in shortness. However, we must note that the relation between fracture strain and ripening time depends on other factors, such as pH. A fresh but acid cheese can have a fracture-strain value similar to that of a mature cheese (Luyten et al., 1982; Luyten and van Vliet, 1996; Rohm et al., 1992). Moreover, for 7-week-old Gouda cheese, a maximum in the strain at fracture was found at around pH 5.2 to 5.25 (Luyten et al., 1982). It is common to see that effects of one compositional variable are confounded with another compositional variable and with ripening time. Rohm et al. (1996) determined the impact of seasonal variations in raw-milk quality on the composition and fracture properties of Emmental cheeses. Regarding the composition, the iodine value (IV), which is an indicator of the softness of the © 2003 by CRC Press LLC

1.6 Strain at fracture (-)

Watkinson et al. (1997) Creamer and Olson (1982)

1.2

0.8

0.4

0.0 0

100

200

300

400

500

Maturation time (day)

FIGURE 3.12 Variation of strain at fracture for Cheddar cheese as a function of maturation time. (After Creamer and Olson, 1982; Watkinson et al., 1997.)

Strain at fracture (-)

1.8

1.6

1.4

1.2

1.0 0

20

40

60

80

100

120

Age of cheese (day)

FIGURE 3.13 Fracture strain of Emmental cheese as affected by maturation. (After Rohm et al., 1996.)

milk fat, and thus cheese, increased, as expected, from 34.3 in winter cheeses to 41.5 in summer cheeses. Moreover, Emmental cheeses produced during winter showed accelerated lactic-acid degradation and propionic-acid generation, and reduced secondary proteolysis than those produced during summer. It is observed that the fracture strain of Emmental cheese is not affected by the seasonal variations, but decreased with the maturation time (Figure 3.13). Emmental cheese made in different seasons exhibited considerably different fracture stress (Figure 3.14), most probably due to the seasonal variations in fattyacid composition of the milk fat (Rohm et al., 1996). The mean values of fracture stress, which correlates well with sensory firmness, are about 165, 126, and 91 kPa for mature cheeses (16 weeks) made in winter, spring, and summer, respectively. This is in line with the increase in iodine value of milk fat as the season changes from winter to summer. The iodine value is associated with the number of double

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350

Fracture stress (kPa)

summer cheese 300

spring cheese

250

winter cheese

200 150 100 50 0 0

20

40

60

80

100

120

Age of cheese (day)

FIGURE 3.14 Fracture stress of Emmental cheese as affected by maturation time and production season. (After Rohm et al., 1996.)

Stress at fracture (kPa)

160

120

80

40 0

1

2

3

4 5 6 7 Production month

8

9

10

11

12

FIGURE 3.15 Seasonal variations in fracture stress of Vorarlberger Bergkäse. (After Jaros and Rohm, 1997.)

bonds in fat. As the number of double bonds increases, the solid fraction of milk fat at a given temperature decreases (Jaros et al. 2001). Therefore, the iodine value of the milk fat serves as an indicator of the firmness of fat, and in turn, of cheese. Jaros and Rohm (1997) reported on the seasonal variations in mechanical properties of Vorarlberger Bergkäse (a smear-ripened, Gruyère-type, raw-milk hard cheese). Figure 3.15 shows apparent fracture stress for Bergkäse as a function of the production month. The mean values of fracture stress for summer and winter cheeses are reported to be 107 and 133 kPa, respectively. The corresponding fracture strain values for summer and winter cheeses are found to be 0.48 and 0.61, respectively (Jaros and Rohm, 1997).

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Without altering the gross chemical composition of the cheese (Swiss Appenzeller), Jaros et al. (2001) increased the amount of unsaturated fatty acids in milk fat by adding shredded rapeseed to the cattle diet. Those cheeses made with milk from the modified diet exhibited significantly lower values for the modulus of deformability and the fracture strain. The property values of the cheese with and without the rapeseed are given in Tables 3.2 to 3.5. It is shown that the rapeseed feeding can be utilized advantageously to eliminate the firmness differences in cheeses of summer and winter periods, and therefore provide the consumer with more consistent products (Jaros et al., 2001). Ohashi et al. (1982) demonstrated by wire-cutting tests the effect of seasonal variations on mechanical properties of milk-rennet curd in connection with the composition of milk. In agreement with results of the other studies cited above, the elastic moduli of the curd were as follows for the spring, summer, autumn, and winter seasons: 55.3, 37.1, 44.4, and 50.1 kPa, respectively.

STRESS-RELAXATION MEASUREMENTS Stress-relaxation properties are very important in many industrial operations, as they control the materials’ response to external mechanical forces. Generally speaking, stress relaxation can be due to physical events or chemical processes (Ferry, 1980; Grosberg and Khokhlov, 1997). In any case, the relaxation process is regulated by the ratio of two variables: the characteristic time of a material (λ) to the characteristic time of observation (t), hence the Deborah number, De = λ/t. A high De (De>>1) corresponds to solid-like behavior (i.e., no relaxation), whereas a low De (De<<1) corresponds to a liquid-like behavior (i.e., instantaneous relaxation). The material behavior is called viscoelastic when the relaxation time and the observation time (e.g., experimentation time) are similar (i.e., De ≈ 1.0). The characteristic time of a material is often represented by its relaxation time. The relaxation time of materials varies in a wide range: for instance, at 20°C it is ~10–12 s for water, and at 27°C it is greater than 105 s for glass (Tanner, 1985). Thus, water will not exhibit an elastic response unless it is subjected to a deformation on a time scale less than 10–12 s. Due to various constituents present, single relaxation time is usually not sufficient to describe the relaxation behavior of foods. There is a fundamental issue that needs attention, and it is related to the time it takes to deform the sample (i.e., rise time mentioned in Chapter 2). If the rise time is t1 seconds, then the rule-of-ten (Meissner, 1978) requires that only relaxation data at times greater than 10t1 seconds should be used in analyzing the results. However, as pointed out by Masi (1989), if this rule is strictly obeyed, the relaxation process is very likely to be completed before starting the collection of “actual” data. The situation is, in fact, better with the advances in rheological instruments. In principle and practice, it is now possible to make t1 fairly short by using high-speed loading (e.g., 2500 mm/min), but the drawback of this is that at high-speed deformation, material may break before reaching the preset strain. In any case, the effect of deformation time or rise time on the subsequent relaxation behavior must be taken into consideration. Theoretically, a viscoelastic solid deformed at a very slow rate completes its relaxation during the deformation stage, and the stress remains almost © 2003 by CRC Press LLC

Stress Relaxation stage Deformation stage

High speed Low speed Very low speed Asymptotic stress 0

Time

Rise time

FIGURE 3.16 Schematic illustration of the deformation and relaxation stages of a stressrelaxation test. (After Purkayastha and Peleg, 1986.) 1000

Relaxation time (s)

1st relaxation time 2nd relaxation time 100

10

1 0.1

1

10

Rise time (s)

FIGURE 3.17 Effect of rise time or deformation time on the time constants of the twoelement Maxwell model. (After Masi, 1989. With permission.)

the same during the relaxation stage, Figure 3.16 (Purkayastha and Peleg, 1986). In Figure 3.17 the relaxation time constants of Galbanino cheese obtained through fitting the rheological data to the two-term Maxwell model (Masi, 1989) are presented. The relaxation time of the second Maxwell element is considerably longer than that of the first element. The apparent relaxation times (i.e., the time required for the stress to relax to 1/e, or ~37%, of its initial value) of many cheeses obtained from published reports are listed in Table 3.12, whereas the values of Maxwell model parameters are listed in Table 3.13. Nolan (1987) studied stress relaxation of commercial-stirred curd Cheddar cheese aged up to 14 months at a storage temperature of –2 to 0°C. Different © 2003 by CRC Press LLC

TABLE 3.12 Calculated Apparent Relaxation Timesa for Some Cheeses Cheese

Rise Time (s)

Temperature (°C)

Relaxation Time (s)

Reference No.

24 0.5 0.09

23 15 21 30 40 50 60

47.5 60.8 290 7.4 1.7 0.8 0.6

A B C

0.9–1.6

20

375 280 50 25

E

0.20

24

189 183 219

F

2.4

20

38 40 50 55 60

G

1.8

15

H

0.5

19–21

141 133 140

Mozzarella Emmentaler Processed cheese Mozzarella

0.43–0.72

Stirred curd Cheddar Fresh 2 mo old 7 mo old 14 mo old Gouda Normal Lubricated Emery paper Mozzarella I II III IV V. Gruyere-type Weak cohesion Strong cohesion Garrotxa-type

D

I

A: Masi and Addeo, 1986. At less than 10% compression. Maximum load 150 g. Since crosshead speed for relaxation tests is not explicitly specified it is taken to be 5 mm/min, which is the rate used in compression tests. B: Rohm and Lederer, 1992. 5% deformation. C: Atkin, 1990: Fit parameters given in the original paper are used to regenerate the stress–time plot and then the apparent relaxation time is obtained as defined above. 10% deformation. D: Ak and Gunasekaran, 1995: Compression levels varied from 30 to 50%. E: Nolan, 1987. Average relaxation times are given at maturation of 2, 7, and 14 months. The level of deformation varied from 4 to 7%. F: Goh and Sherman, 1987. Commercial Gouda cheese. 10% deformation. G: Diefes et al., 1993. 20% compression. I: control cheese refrigerated (5°C) for only 14 days. II: cheese refrigerated 90 days. III: cheese frozen (–20°C) for 90 days and tempered at 5°C for 21 days. IV: cheese frozen for 30 days and thawed at 5°C for 24 h. V: cheese frozen for 90 days and thawed at 5°C for 24 h. H: Pesenti and Luginbühl, 1999. 10% deformation. I: Saldo et al., 2000. Goat’s milk cheese in Catalunya (Spain). 5% deformation. a

Unless stated otherwise, apparent relaxation time is defined as the time for initial force or stress to relax to 37% of its initial value.

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TABLE 3.13 Parameters of Maxwella Model Used to Describe Relaxation Curves of Cheeses in Compression Cheese Gouda Normal Lubricated Emery Processed cheese Cheddar cheese

Processed cheese Tybo Argentinob Day 3 Day 114 Gruyere-type Weak-cohesion Strong-cohesion Cheddar 8 weeks old 64 weeks old Garrotxa-type (goat’s milk)

Deformation (%)

No. of Elements

Eo (kPa)

E1 (kPa)

E2 (kPa)

E3 (kPa)

E4 (kPa)

λ1 (s)

λ2 (s)

λ3 (s)

λ4 (s)

Temp (°C)

10

3

—

3400 200 200 95 6900

600 30 30 4.2 —

Goh and Sherman, 1987

— —

3200 2900 2700 1534 156

24

— —

40 26 54 29 —

—

3 2

48 30 54 9.3 80

—

10 —

58 47 88 30 160

— —

21 —

10

3

—

84

42

41

—

2794

140

20

—

18–19

Atkin, 1990 Mohsenin and Morrow, 1967, cited in Peleg and Normand, 1983 Robert and Sherman, 1988

40

2

0.24 0.16

0.35 0.51

0.40 0.32

—

—

4.1 4.7

104 58

—

—

20

10

3

48 52

65 72

48 55

49 58

—

2.3 2.1

26 25

267 262

—

15

<10

2

50 40

80 40

60 30

—

—

18.2 16.6

388 347

—

—

20

5

2

156

215

192

—

—

9.2

105

—

—

19–21

Ref.

Bertola et al., 1992 Pesenti and Luginbühl, 1999

a

Hort and Le Grys, 2001

Saldo et al., 2000

For Maxwell model, see Equation 2.46. In the original article the data are fitted to a dimensionless force equation: F(t)/F(0) = A∞ + A1 exp (–t/λ1) + A2 exp(–t/λ2), and therefore quantities A∞, A1, and A2 are dimensionless even though they are listed in this table for Ei′s, which have units of kPa.

b

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Apparent relaxation time (s)

400

300

200

100

0 0

3

6

9

12

15

Cheese age (month)

FIGURE 3.18 Variation in apparent relaxation time of Cheddar cheese as a function of maturation time. (After Nolan, 1987.)

empirical models, including the two forms of the Peleg model, Equation 2.47, have been evaluated for their ability to describe relaxation curves of aging Cheddar cheese. Here, we utilize Nolan’s data to regenerate the relaxation curves in terms of true stress vs. time for calculating apparent relaxation time as a function of cheese age. The resulting values are plotted in Figure 3.18. From this graph, it is evident that the relaxation time decreases with the age of stirred-curd Cheddar cheese, especially during the first six months (Nolan, 1987). Similar trends have been reported for Mozzarella cheese during one month of refrigerated storage (Ak and Gunasekaran, 1995). The rheological changes occurring during cheese aging are due to changes in pH, moisture, and salt content, and mainly due to the degradation of different casein fractions by residual rennet, indigenous milk proteinases, and starter enzymes (Desmazeaud and Gripon, 1997; Fox, 1989; Visser, 1993). Goh and Sherman (1987) studied stress relaxation of commercial Gouda cheese under reduced (by lubrication) and intensified (by inserting emery paper) friction at several compression levels (10 to 60%). The crosshead speed was set to a relatively high value, 100 cm/min, except few cases where it was 5 cm/min. The relaxation tests were conducted at room temperature on samples taken from the central region of the cheese. The apparent relaxation times for different friction conditions are plotted against the compression level in Figure 3.19. It is clear that at each crosshead speed and surface condition the relaxation time decreases with increasing percent compression. It is interesting to note that lubrication resulted in lower relaxation times as compared to normal and high friction conditions only when the compression was 20% or less. This was thought to be due to cracks developing, for instance, in Gouda cheese at compressions exceeding 20%. Hence, lubrication and compression less than 20% were suggested as test conditions to obtain true stress-relaxation behavior of Gouda cheese. In the same figure, the relaxation time of processed cheese (Atkin, 1990) at different compression levels is also shown. It is seen that the relaxation time for processed cheese drops nearly to zero at compressions above 30%, probably due to cracking (Atkin, 1990). The other factor that may affect the results for lubricated case, particularly at large compressions, is the loss or depletion of lubricant to a different extent at different compression levels (Atkin, 1990). More © 2003 by CRC Press LLC

Apparent relaxation time (s)

350 Gouda Normal-100

300

Gouda Lubricated-100

Gouda Emery-100

250

Gouda Normal-5 Gouda Lubricated-5

200

Gouda Emery-5

150

Proc. cheese-100

100 50 0 0

25 50 Compression level (%)

75

FIGURE 3.19 Apparent relaxation times of Gouda cheese (after Goh and Sherman, 1987) and processed cheese (after Robert and Sherman, 1988) under different surface conditions (5 and 100 means the initial compression was imposed at a crosshead speed of 5 cm/min and 100 cm/min, respectively).

detailed analyses of the data in terms of multiple-element Maxwell model (without the asymptotic parameter corresponding to the single spring — see Equation 2.46 and Figure 2.42) resulted in parameter values given in Table 3.13. We must, however, state here that the interpretation of model parameters is difficult and often not meaningful since they depend on the number of Maxwell (or Kelvin-Voigt in creep) elements included in the model. Robert and Sherman (1988) determined the influence of friction on stressrelaxation parameters of commercial processed cheese tested at ambient temperature (18°C to 19°C) and compression levels from 5 to 20%. The researchers used a rather novel approach and compressed simultaneously from one to four specimens in order to determine the components of the total force, FT: a) the force to compress the cheese, FC, and b) the force to overcome the surface friction, FF. Only the former component relaxes. By plotting the compression results as FT/N versus 1/N, where N is the number of specimens tested simultaneously, it was possible to determine the FC from the intercept and FF from the slope of the linear relation. The results suggested that cracks develop in processed cheese somewhere between 15 and 20% compression, which is in good agreement with the conclusions of Atkin (1990) discussed above. Maxwell model parameters for processed cheese obtained in the two investigations were however considerably different (Table 3.13). For Emmentaler cheese, a significant relationship was reported between apparent fracture strain and apparent relaxation time at any deformation rate between 0.5 and 80 mm/min. An inverse relation was observed between the relaxation time and the fracture strain. For instance, Emmentaler cheese that fractured at a strain of 0.84 had a longer relaxation time (~90 s) than that fractured at a strain of 1.28 (~35 s) (Rohm and Lederer, 1992). Low-moisture, part-skim (LMPS) Mozzarella cheese was subjected to several storage treatments (e.g., freezing, thawing, refrigeration) before measuring its

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250

1000

200

100

150 10 100 1

50 0

0.1 0

20

40

60

Initial relaxation modulus (kPa)

Apparent relaxation time (s)

Relx time-tension Relx time-comp Relx modulus-tension Relx modulus-comp

80

Temperature (°C)

FIGURE 3.20 Stress-relaxation parameters of Mozzarella cheese as a function of temperature. (After Ak and Gunasekaran, 1995.)

properties by stress-relaxation tests made at 20°C and 20% compression (Diefes et al., 1993). The reasons for changes in mechanical properties observed in freezing and refrigeration were considered to be different. In refrigerated storage, the proteolysis was the main factor for progressive softening of cheese. During freezing and subsequent frozen storage, local dehydration, compaction, and disulfidebond formation as well as modified water-binding ability after thawing were considered to be possible causes for the observed changes in mechanical properties (Diefes et al., 1993). The apparent relaxation time of Mozzarella subjected to different storage treatments was highest for cheese frozen for 90 days and thawed in a refrigerator over 24 h, and lowest for control cheese that was only refrigerated for 14 days before measurements. Ak and Gunasekaran (1995) reported on temperature effect on rheological properties of Mozzarella cheese during one month of refrigerated storage. Figure 3.20 shows that both the apparent relaxation time and the initial relaxation modulus decrease significantly with temperature; more steeply in the range from 10 to 40°C. Korolczuk (1996) analyzed stress-relaxation curves for five types of commercial acid-fresh cheeses (7 to 12% protein, 0 to 58% fat) using different models, such as two-parameter Maxwell model, power-law model, Peleg model, and kinetic (Avrami) model. Based on the average coefficients of variation for these equations, the Avrami model was decided to best represent the stress-relaxation data of the cheeses. The behavior of acid-type fresh cheese was characterized more like a viscoelastic liquid since the residual stress after relaxation was fairly low and independent of the applied strain (Korolczuk, 1996). Stress-relaxation behavior of Gouda cheese packed in plastic films of low gaseous permeability was studied at 10 and 20°C during ripening up to 70 days (Bertola et al., 2000). The packaging did not offer any advantage in terms of textural properties of Gouda cheese. The asymptotic (residual) modulus, an indicator of the degree of solidity (Peleg, 1987), was independent of ripening temperature, but increased from

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1.4 Hort & Le Grys Creamer & Olson

Fracture strain (-)

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

20

40

60

80

100

120

Cheese age (week)

FIGURE 3.21 Variation in fracture strain of Cheddar cheese as a function of ripening time. (After Creamer and Olson, 1982; Hort and Le Grys, 2001.)

44 kPa at day 15 to 54 kPa at day 70. The changes in mechanical properties were related to the decrease in the water content and increase in the proteolytic activity. Although relaxation behavior was modeled using a Maxwell model, the values of model parameters were not reported completely. It is no doubt that acceleration of ripening, especially in long-ripened varieties, is highly desirable for both economical and safety reasons. One of the relatively new ways being investigated for accelerating cheese ripening is to apply high pressure. Under high pressure, ripening is accelerated due to increased water retention, releasing bacterial enzymes, and increased enzyme activity (Saldo et al., 2000). It was shown that the values of the elastic constants in the Maxwell model were greater and the relaxation times were longer for the high-pressure-treated (≥400 MPa), Garrotxa-type cheese (Spanish cheese made from goat milk) than for the control and the cheese treated with 50 MPa pressure (Saldo et al., 2000). According to Trujillo et al. (1999), goat cheeses made with high-pressure-treated milk matured more quickly than the control cheeses. Thus, high-pressure treatment may be an alternative way of accelerating cheese ripening. Hort and Le Grys (2001) examined the effect of ripening time at 8°C on compression and relaxation parameters of commercial English Cheddar cheese. Plotted in Figure 3.21 are the progressive changes in fracture strain of Cheddar cheese from Hort and Le Grys (2001) and Creamer and Olson (1982). It is observed that there is a clear negative relation between fracture strain and maturation time. The overall agreement between the values from the two studies is satisfactory.

TORSION MEASUREMENTS Torsion test was used by Wodecki et al. (1984) to study mechanical properties of Edam cheese in relation to its moisture content at different stages (i.e., after pressing, during ripening, and as marketed). The authors found no significant correlation between modulus determined from torsion test and water content for fresh cheese

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TABLE 3.14 Equations Relating Hardness of Edam Cheese to Its Moisture Contenta Equation

Descriptions

H1 ( Pa) = 64059 − 3.1 ⋅ 10 −7 exp(0.55 W1 )

W1: water content after pressing (%) H1: Hardness modulusb after pressing (Pa) R2 = 0.886 W2: water content at marketing time (%) H2: Hardness modulus at marketing time (Pa) R2 = 0.773 ∆W: Change in water content through maturation

H2 ( Pa) = 1.15 ⋅ 10 6 exp( −0.0685 W2 )

[

]

W1 (%) = 4.185 log 10.3 + ∆W − 16.4 ⋅ 10 −5 H2 + 43.1 (*)c a

Authors emphasize that “the coefficients throughout this analysis refer only to that milk and those processing conditions which were used in this particular study; they should not be regarded as general for all Edam cheese.” b Hardness modulus “measured as the pressure to impress a test sphere to a particular depth.” c This equation is applicable for: 41 ≤ W (%) ≤ 46; 2.2 ≤ ∆W (%) ≤ 6.6; 45 × 103 ≤ H (Pa) ≤ 10.5 1 2 Source: After Wodecki et al., 1984.

(i.e., after pressing). However, once the cheese was matured for 12 weeks before marketing, its modulus as a function of water content varied according to the following equation: Ms ( Pa) = 8219 − 174W2

(3.6)

where, W2 is the water content of the marketed cheese (Wodecki et al., 1984). They further developed other equations relating modulus of Edam cheese (determined by impressing a sphere to a particular depth) to the moisture content as described in Table 3.14. Based on this study, they suggested that the modulus of Edam cheese can be controlled by adjusting the moisture content of freshly made cheese according to the equation given in Table 3.14, indicated as (*). Bowland and Foegeding (1999) showed that fracture stress of a model processed cheese, formulated to contain 20% protein, 27% fat, and 1.5% NaCl as fixed ingredients, can be varied from about 25 to 80 kPa by manipulating processing variables and usual ingredients (e.g., processing time, solution pH, percentage of disodium phosphate). The fracture strain of the model cheeses varied from 0.66 to 1.88. It was found that the model processed cheese fractured in tension regardless of changes in processing variables. Moreover, the results of this work suggest that a wide variety of textures from soft and ductile to firm and brittle can be obtained by carefully controlling compositional and processing factors. Recently, casein hydrolysate fractions were shown to have potential to replace traditional emulsifiers (e.g., sodium phosphates) in process cheese (Kwak et al., 2002).

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60 Monterey Jack

Change in fracture stress (%)

50

Mild Cheddar-A Sharp Cheddar

40

Mild Cheddar-B

30

American

20 10 0 30

40

50

60

Change in fat (%)

FIGURE 3.22 Effect of fat reduction on fracture stress of different kinds of natural and processed cheeses. (After Gwartney et al., 1999.)

Gwartney et al. (2002) carried out torsion tests on capstan-shaped specimens (see Chapter 2) of various commercial cheese products to determine their fracture properties at 20°C. As expected, full-fat cheeses are characterized by lower fracturestress values than their reduced-fat counterparts. The impact of fat reduction on the fracture stress is highly dependent on the cheese type (e.g., Monterey Jack vs. Sharp Cheddar), as well as the processing factors (e.g., Mild Cheddar-A vs. Mild Cheddar-B), as shown in Figure 3.22.

TENSION MEASUREMENTS Tension tests are considered particularly good for determining fracture properties (van Vliet and Luyten, 1995). The rheological information collected by tension test is also free of serious complications, such as friction, and thus easier, in general, to interpret correctly. The main obstacle preventing a broader use of tension tests in cheese rheology (or in food rheology, for that matter) is the problem and difficulty of proper gripping. Nevertheless, several research reports on tensile properties of various foods have been published (Gillett et al., 1978; Schoorl and Holt, 1983; Nussinovitch et al., 1990; Lelievre et al., 1992; Tang et al., 1997; Teratsubo et al., 2001). Tensile measurements on foods and cheeses are expected to increase since special and creative grips and testing machines are designed particularly for measurements on foods. There are few investigations on the tensile properties of cheeses. Luyten et al. (1992) provided an in-depth analysis and comparison of tension, compression, and bending methods for cheese and potato-starch gels. Fracture data reported by Luyten (1988) and Luyten et al. (1992) for Gouda cheese are included in Chapter 4. Moreover, we utilized quite heavily in Chapter 2 the information on the merits of each specific method as presented in detail by Luyten et al. (1992). Tensile properties of low-moisture, part-skim Mozzarella cheese have been determined as a function of age (up to one month), temperature (10 to 40°C), and deformation rate (5 to 50 cm/min) using a uniaxial horizontal extension apparatus

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modulus

90

0.4

60 0.2

30 0 5

10 15 20 Maturation time (day)

modulus

0 30

strain 0.8

200 0.6

150

0.4

100

0.2

50

0 40

0 0

10

20 Temperature (°C)

Stress

Modulus

Fracture strain (-)

Fracture stress (kPa) Deformability modulus (kPa)

stress

25

Fracture strain (-)

0.6

0

Fracture stress (kPa) Deformability modulus (kPa)

strain

30

Strain 0.6

200 150

0.4

100 0.2 50 0 0

0.05

0.1

Fracture strain (-)

Fracture stress (kPa) Deformability modulus (kPa)

stress 120

0 0.15

Initial strain rate (1/s)

FIGURE 3.23 Tensile properties of Mozzarella cheese as affected by as a function of age, temperature, and initial strain rate. (After Ak et al., 1993.)

by Ak et al. (1993). For Mozzarella cheese, which is one of the main ingredients of pizza, the tensile properties (though at higher temperatures than could be realized in this particular study) are of practical and commercial importance, since it will undergo stretching during consumption. The mean values of tensile properties are shown in Figure 3.23 as a function of age, temperature, and initial strain rate. Among the three rheological parameters, the modulus of deformability exhibited a simple dependency on the independent variables: it decreased with aging at a rate 2.2 kPa/day,

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it decreased with temperature at a rate about 8.9 kPa/°C, and it increased with initial strain rate at a rate 453 kPa/s–1. Ak and Gunasekaran (1995) reported the corresponding average values from the squeezing flow of Mozzarella cheese as: 0.4 kPa/day (one month aging), 0.5 kPa/°C (in the range 30 to 60°C), and 48 kPa/s–1. Thus, the tensile properties appear to be more sensitive to changes in the experimental variables than the compressive properties (of course, for a moment we are neglecting the large differences between the two experimental setups). Kamyab et al. (1998) determined the rheological and fracture properties of several cheeses by using various methods, including the tension test with singleedge-notched specimens. The modulus of deformability values for Cheddar (sharp and mild) and two American processed cheese varieties are given in Table 3.2. A comparison of the tensile and compression moduli indicated that in general, an acceptable difference from 10 to 20% between tensile and compression moduli was observed, with the exception for mild Cheddar where there was a difference by factor of 2. Major results of this study concerning fracture properties of various cheeses are given in Chapter 4. In a majority of rheological studies on cheese, it is accepted that cheese is an isotropic material, meaning that if test pieces are taken at various directions from a cheese block, they will all yield essentially the same stress–strain curve. Although this may practically be true for many cheeses, it is worth investigating for pasta filata cheeses since the curd-stretching step during their manufacture induces orientation of the structural components. Scanning electron micrographs of Mozzarella cheese curd after it passed through the stretcher clearly showed the formation of a fibrous, oriented structure of the cheese (Kalab, 1977; Oberg et al., 1993; Kalab, 1993; Kiely et al., 1993; Paquet and Kalab, 1988), as shown in Figure 3.24. The protein matrix is largely modified by the stretching process to form a bundle of long, parallel casein strands interspersed with channels containing serum, fat globules, and starter culture. In reduced-fat cheeses, fewer channels exist between the protein strands. This means more interaction of proteins and a firmer and rubbery cheese body (McMahon et al., 1996; McMahon and Oberg, 1999). In fact, scanning electron micrographs revealed

FIGURE 3.24 Scanning electron micrograph of 2-day-old Mozzarella cheese showing that stretching the curd results in longitudinally directed fibers (scale bar = 8 µm). (After Kuo, 2001.)

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TABLE 3.15 Mean Tensile Properties of 14-Day-Old Mozzarella Cheese Fracture Strain (–)

Fracture Stress (kPa)

Fracture Toughness (kJ/m3)

Sampling direction Parallel Perpendicular

0.46 0.32

70.7 33.5

16.2 5.8

Cheese type Reduced-fata Low-moisture part-skimb

0.43 0.34

112.5 21.0

23.6 4.0

Deformation rate 25.0 cm/min 5.0 cm/min

0.39 0.38

59.3 39.8

12.4 7.6

Variables

a b

Composition: 57.2% moisture, 31.7% protein, 7% fat, 3.5% carbohydrate, 0.6% sodium. Composition: 50% moisture, 28.2% protein, 17.6% fat, 3.5% carbohydrate, 0.7% sodium.

Source: After Ak and Gunasekaran, 1997.

that the size of casein aggregates increased as the fat content of Feta cheese was reduced. Furthermore, the addition of tapioca starch and lecithin as fat mimetics improved overall acceptability of the reduced-fat (16.4% fat) and low-fat (12.5% fat) Feta cheeses to the level not too far from the full-fat (19.8% fat) sample (Sipahioglu et al., 1999). Although substantial improvements in the textural quality of low-fat Cheddar cheese (5% fat) were realized by incorporating commercial fat replacers, neither the microstructure nor the stress–strain behavior of full-fat cheese (32% fat) could be satisfactorily duplicated (Kucukoner et al., 1998). The microscopic observations mentioned above and the theoretical notion that almost no material is truly uniform and isotropic, led Ak and Gunasekaran (1997) to measure fracture properties of Mozzarella cheese by taking samples parallel and perpendicular to the long axis (Figure 3.2) of the cheese block (i.e., presumably representing protein orientation). The mean tensile fracture properties are presented in Table 3.15. The results indicated that the fracture toughness, fracture stress, and fracture strain of Mozzarella cheese were 2.8, 2.1, and 1.4 times greater in parallel direction than in perpendicular direction. This considerable variation in properties indicated anisotropic nature of the cheese. Orientation of protein strands in a particular direction in the cheese block appears to enhance fracture properties significantly in that direction. Furthermore, reduced-fat variety had significantly higher fracture values than the regular LMPS Mozzarella cheese, consistent with the expectations. Pesenti and Luginbühl (1999) determined rheological properties of Gruyere-type cheese using tensile test, among others. The numerical property data from this research for the weak-cohesion and strong-cohesion types of cheese are listed in Tables 3.2 to 3.5. The authors remarked that the tension test, in accord with theoretical expectations, proved to be the most powerful test also in practice.

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CREEP MEASUREMENTS Creep is another characteristic behavior of a viscoelastic material. Most often, the creep response of cheese is described by the Kelvin–Voigt model with a varying number of elements. This model has been described in Chapter 2; see Equation 2.50 and Figure 2.46. The analysis of creep behavior of cheese, or any foods for that matter, involves determination of model constants (individual elasticities Ei, Newtonian viscosity η, and individual viscosities ηi) from creep data (i.e., strain vs. time or compliance vs. time data). The tedious task of parameter determination is made easy and faster by using computers and optimized calculation procedures (Balaban et al., 1988). As mentioned in Chapter 2, the alternative method to analyze creep curves is to employ the Peleg model (Purkayastha et al., 1984), which is simpler to apply* as demonstrated for various foods (e.g., apple, pectin gel, orange, potato, cheese) (Peleg, 1980; Purkayastha, et al., 1984; Purkayastha et al., 1985). Using parameters of the Peleg model, one can also estimate an asymptotic compliance (Purkayastha and Peleg, 1986), which is of practical importance, since conducting long duration tests (i.e., creep and relaxation) on foods is not feasible due to physical, biological, and chemical alterations. Purkayastha et al. (1985) represented creep curves of potato and Cheddar cheese using a four-parameter Peleg model [i.e., D(t) = ko + k1t + t/(k2 + k3t), where, D is compliance, t time and ko, k1, k2, and k3 are constants] and the discrete Kelvin–Voigt model with 4 to 6 constants. The values of parameters for corrected compliance of mild Cheddar cheese are tabulated in Table 3.16 along with those for many other cheeses. Purkayastha et al. (1985) stated that the yielding nature of the cheese was evident in the values of k1 and its dependency on the initial stress. Kuo et al. (2000) used the viscoelastic parameters derived from analysis of creep curves to successfully predict meltability of Cheddar cheese with two fat contents. This procedure is further described in Chapter 8. Creep tests are used to study effects of formulation changes on properties of white, fresh cheese by adding different levels of sodium caseinate up to 13.92 g/L (LobatoCalleros et al., 2000). These authors also represented the creep curves of white, fresh cheese with a 6 parameter Kelvin–Voigt model. The parameter values for the standard white cheese (59.7% moisture, 19% fat, 17.3% protein, pH = 5.7) are given in Table 3.16. The effects of some factors on the creep parameters are summarized in Table 3.17. The authors also reported that white cheese with sodium caseinate addition showed higher yield and lower syneresis compared to the standard cheese. Creep measurements were made to determine effects of milk fat and lecithin (Ma et al., 1996) and commercial fat mimetics (Ma et al., 1997) on viscoelastic * Nolan (1987) expressed concerns regarding one form of the Peleg model, Equation 2.47, where the same variable (i.e., time) appears in both ordinate and abscissa. As stated by Nolan (1987), this kind of plotting, according to Mickley et al. (1957), may cause misleading correlations and is a poor test of the experimental data. Moreover, Hunston (1974) compared three linear forms of the model and found that when a variable appears only in abscissa, the model does not provide as good a representation of the data as when it appears in both ordinate and abscissa. Nevertheless, the Peleg model is frequently used not only in rheological studies but also in diffusion studies (e.g., Abu-Ghannam and McKenna, 1997; Sopade et al., 1992).

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TABLE 3.16 Values of Parameters of Kelvin–Voigta Model Used to Describe Creep Curves of Cheeses Cheese Mild Cheddar White fresh (6-d-old) Velveeta Velveeta Cheddar full fat (3-mo-old) Cheddar reduced fat Cheddar full fat (3-mo- old) Cheddar low-fat (3-mo- old) Gruyere-type (weak cohesion) Gruyere-type (strong cohesion) Cheesef

Initial Stress (kPa) 18.5 40.0 76.6 2.0

No. of Elements 2 — 2 Four-element modelc

Ko (MPa)-1

K1 (MPa s)–1

K2 (MPa)–1

τ2 (s)

K3 (MPa)-1

τ3 (s)

K4 (MPa)–1

τ4 (s)

Temp. Type of (°C) testb

1.32 1.31 310 20.5

4.54 × 10 8.17 × 10–3 1.96 1 × 10–2

5.39 0.85 440 36

9.42 5.04 131 540

0.95 1.36 410 —

82.2 54.6 21.1 —

— — — —

— — — —

Room Room 20 Room

C C S C

Purkayastha et al., 1985 Purkayastha et al., 1985 Lobato-Calleros et al., 2000 Chang et al., 1986

–3

Ref.

2.9 2e

2

19.3 7.54

8.3 × 10–3 9.3 × 10–2

24 13.4

420 32.9

— 9.9

— 3.0

—

— —

Room 20

C S

Chang et al., 1986 Ma et al., 1996

2d 1e

2 2

12 6.9

0.24 9.0 × 10–2

23.5 11.3

23.3 25.3

15.6 8.2

2.5 2

— —

— —

20 20

S S

Ma et al., 1996 Ma et al., 1997

1e

2

11.8

0.2

21.7

24.3

15.3

1.8

—

—

20

S

Ma et al., 1997

43.3

3

3.4

8.8 × 10–3

4.1

119.9

1.8

16.4

1.0

1.16

15

C

43.3

3

3.8

9.2 × 10–3

4.4

119.5

2.0

15.8

1.0

1.12

15

C

—

1

1.89

3.23 × 10–4

0.88

152

—

—

—

—

—

—

Pesenti and Luginbühl, 1999 Pesenti and Luginbühl, 1999 Purkayastha et al., 1984

For Kelvin–Voigt model, see Equation 2.50: Kη = 1/η = 1/ηN; K1: first retarded compliance; τ1: first retardation time; K2: second retarded compliance; τ2: second retardation time; Kn: nth retarded compliance; τn: nth retardation time. Although we use the same symbol Ko to represent Do in compression and Jo in shear, Do and Jo are not equal, but related to each other as D(t) = J(t)/3 in the linear viscoelastic region of an incompressible material. b C: compression; S: shear. For shear creep the letter J is normally used (i.e., J , η, J , J , τ , τ , etc.). o 1 2 1 2 c Combination of a Maxwell and a Kelvin element in series. d The initial applied stress is not explicitly specified, but 2 kPa was reported to be limit of linear viscoelasticity. e The initial applied stress is not explicitly specified, but 1 kPa was reported to be limit of linear viscoelasticity. f The type of cheese is not specified in the original article by Datta and Morrow, 1983. It is probably Cheddar. a

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TABLE 3.17 Effect of Experimental Factors on Different Creep Parameters of White Fresh Cheese Creep Parameter Instantaneous compliance, Jo Retarded compliance (1st), J1

Retarded compliance (2nd), J2 Newtonian viscosity, ηN Retardation time (1st), τ1

Main Variable Moisture Na-caseinate Moisture Na-caseinate pH Aging Na-caseinate Aging Na-caseinate pH Aging

Nature of Effect (+) (+) (+) (+) (–) (+) (+) (+) (–) (+) (–)

Note: (+): Parameter value increases with increasing value of the variable; (–): Paremeter value decreases with increasing value of the variable. Source: After Lobato-Calleros et al., 2000.

properties of Cheddar cheese. The values of six-parameter Kelvin–Voigt model are presented in Table 3.16 for full-fat (35.6%), reduced-fat (21%, estimated), and low-fat (13.5%) varieties. Addition of lecithin at a rate of 0.2–0.5% apparently improved the protein matrix of reduced-fat cheese, but not enough to simulate the behavior of full-fat Cheddar cheese (Ma et al., 1996). In a similar fashion, addition of carbohydrate-based fat mimetic improved rheological properties of low-fat cheese, but not enough to simulate the behavior of the full-fat Cheddar cheese. It was also found that both granular lecithin at concentrations of 0.05% and higher and hydrogenated lecithin at concentration of 0.2% decreased creep recovery* of reduced-fat processed cheeses (Drake et al., 1999b). These results were consistent with the sensory evaluations by trained panelists. A number of different cheeses containing varying amounts fat all exhibited creep recovery to some extent upon releasing the applied stress (Drake et al., 1999a). The cheeses that were evaluated as firm (e.g., Parmesan, Feta, Cheddar cheeses) responded in a more elastic manner (74 to 80% recovery) than the soft cheeses (e.g., Velveeta™ and Brie) that recovered less (52 to 64%). In a recent study on viscoelastic properties of Tetilla cheese (soft-paste, washedrind Spanish cheese), creep response was modeled by the generalized Burgers model (Equation 2.50 with n = 9), but only the instantaneous compliance and Newtonian viscosity were reported (Tovar et al., 2002). There was a significant variation in the creep behavior of this cheese collected from several factories complying with the regulations of Tetilla cheese denominations. A positive relation was obtained * Creep recovery test involves removal of stress at a time during creep test and measuring the height of sample after allowing sufficiently long time for recovery. © 2003 by CRC Press LLC

60

Instantaneous shear compliance (MPa−1)

50 40 30 20 10 0 40

45

50 Dry extract (%)

55

60

FIGURE 3.25 Relationship between instantaneous creep compliance and dry-matter content of Tetilla cheese from Spain. (After Tovar et al., 2002.)

between the instantaneous creep compliance in shear and the dry extract of the cheese (Figure 3.25).

BENDING MEASUREMENTS The three-point bending test is considered to mimic the way cheese graders evaluate body and texture by bending a plug of cheese until it breaks (Pesenti and Luginbühl, 1999; van Vliet, 1991a). One of the key requirements for a proper bending test is to assure sufficiently high length-to-diameter (or thickness) ratio of the test piece. This ratio seems to vary with the material being tested: it is required to be 8 and 24 for metal beams and rectangular timber beams, respectively (van Vliet and Luyten; 1995). For paperboard, a span-to-thickness ratio greater than 100 was used (Fellers and Carlsson, 1979). For cheese, at least for Gouda, a length-to-diameter ratio of 3.3 or more was observed to be sufficient (Luyten, 1988; van Vliet and Luyten, 1995). This ratio was higher than 3.5 in other studies on different cheeses: Mozzarella (Cervantes et al., 1983), Gruyere-type (Pesenti and Luginbühl, 1999), and Cheddar (Charalambides et al., 1995). Cervantes et al. (1983) reported that increasing the salt content of Mozzarella cheese from 0.24 to 2.40% caused an increase in sensory firmness, which was detected by compression and beam-bending tests. A nonlinear strong interaction existed between salt content and age of the cheese affecting textural and mechanical properties. However, no effect of the freeze–thaw cycle and frozen storage (–15°C) was detected on mechanical properties and textural characteristics of Mozzarella aged up to 39 days. Results of Charalambides et al. (1995) on fracture properties of sharp Cheddar, mild Cheddar, and Monterey Jack by bending test are presented in Chapter 4. In general, the fracture toughness of the cheeses decreased with aging, indicating more brittle behavior with maturation. This is associated with the breakdown of αs1-casein during maturation.

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TABLE 3.18 Rheological Properties of Gruyere-Type Cheese in Bending and Tension Type

Parameter

Bending

Tension

Ratio (B/T)

Weak cohesion

Deformability modulus (kPa) Fracture strain (–) Fracture stress (kPa) Work to fracture (kJ/m3) Deformability modulus (kPa) Fracture strain (–) Fracture stress (kPa) Work to fracture (kJ/m3)

193 0.34 41 0.9 204 1.01 130 8.7

93 0.46 32 8 111 1.30 70 57

2.10 0.74 1.28 0.11 1.84 0.78 1.86 0.15

Strong cohesion

Source: After Pesenti and Luginbühl, 1999. With permission.

The quantitative assessment of cohesion in Gruyere-type (unripened hard) cheese has been done using a number of static and transient methods, including three-point bending (Pesenti and Luginbühl, 1999). Although all static methods were able to differentiate different levels of cohesion in Gruyere-type cheese, the uniaxial tension test has been selected as the most powerful test for quantitative measurements of cohesive properties of the cheese. Rheological properties of the cheese from bending tests are given in Table 3.18. Also given in this table are the tensile properties, since in a bending test the fracture is expected to occur on the outer surface (tensile side) of the samples. The fracture parameters are affected by the level of cohesion and the type of test. For Gouda cheese, no significant difference was found for deformability modulus from tension, bending, and compression tests (Luyten et al., 1992) (see Table 4.3).

VANE MEASUREMENTS Whey protein concentrates (WPC) and whey protein isolates (WPI) are finding more use as food ingredients in various applications due to their nutritional quality and functional properties, such as water binding, viscosity, gelation, etc. (de Wit, 1984; Harper, 1991). Mleko and Foegeding (2000) investigated physical properties of processed cheese analogs containing various amounts of WPI and whey protein polymers obtained by heating WPI solutions. They used a four-blade vane attached to a rotational viscometer to measure the yield stress of processed cheese analogs. Both addition of WPI and substitution of casein with WPI increased the yield stress of the processed cheese analogs, more effectively when whey proteins are formed into polymers before addition. In the same study, yield-stress values of commercialprocessed cheeses are reported to vary between 2 and 4 kPa; values that are very close to those obtained for the cheese analogs. The addition of whey protein polymers to replace a portion of rennet casein in processed cheese analogs also increased the yield stress of the cheese, the effect being stronger with the double-heated whey protein polymers (Mleko and Foegeding, 2001).

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DeMartine and Cussler (1975) proposed the following reciprocal relation between the subjective spreadability, which is evaluated by spreading the samples along the plate with the index finger:  subjective  1  ~ τ   spreadability spread

(3.7)

This relation is shown to hold true for both Newtonian and non-Newtonian (shear thinning without yield stress) fluids with a high correlation coefficient of 0.95 (log–log scale) (DeMartine and Cussler, 1975). Later, Kokini and Cussler (1987) demonstrated that the same kind of relation is valid for numerous foods (e.g., ketchup, mustard, margarine, whipped cream cheese, peanut butter, etc.) where the sensory assessment of spreadability is made using a knife (hence, τspread is replaced with τknife. In these studies, the stress on the index finger or the knife is predicted using psychophysical models and fluid mechanics analysis. Spreadability is certainly one of the key textural attributes of semisolid foods affecting their quality and acceptance (van Vliet, 1991b). Consumers have come to expect and demand such foods (e.g., margarine, butter, peanut butter) to spread easily even at low temperatures (e.g., refrigeration temperature). A strong link between sensory spreadability and yield stress has already been established for butter by Mortensen and Danmark (1982) and Rohm and Weidinger (1991), where the yield stress is measured by penetrometers and sectilometer. Mortensen and Danmark (1982) concluded that the yield stress alone is a sufficient measure for the spreadability of butter. Thus, the accurate measurement of yield stress becomes crucial for quantitative evaluation of the quality of semisolid products. In this respect, the vane method stands out as a simple and powerful tool for direct and accurate measurement of the yield stress. Daubert et al. (1998) found that not only yield stress but also yield strain, perhaps to a lesser degree, plays an important role in the spreadability of foods. They prepared a plot of yield stress vs. yield strain (more correctly the angular rotation at the yield point) and named the resulting graph as a “spreadability map.” They calculated yield strain γo using the following approximate equation: γ o = t max Ω − Cs R

(3.8)

where, tmax is the time (s) to the peak torque, Ω the rotational speed (rad/s), Cs the spring constant for the viscometer (rad/torque reading), and R the viscometer torque reading.* These researchers established three categories of spreadability by sensory analysis as easy, mild and hard, and associated them with the yield stress and yield strain results from the vane measurements. It is seen that materials with a combination of high yield stress and yield strain will be most difficult to spread. The spreadability map is considered to be a simple tool for direct comparison of * It must be noted that differences in the wind-up characteristics of rotational viscometers are to be taken into account when evaluating yield stresses determined using the vane method (see Steffe, 1992, for a numerical example).

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similar materials, as well as for quantifying the impact of changes in processing and composition variables on the spreadability of products. Breidinger and Steffe (2001) used the vane method in the controlled rate mode to construct a texture map by plotting yield stress vs. apparent yield strain for various regular and light cream cheeses. They determined yield stress using Equation 2.43 and apparent yield strain γo (rad) using the following equation: γo =

t max Ω 2π

(3.9)

where, the vane rotational speed Ω is given in (rev/s). No attempt was made to develop sensory spreadability categories in order to correlate with the instrumental data. Their results and those from Daubert et al. (1998) are presented in Figure 3.26 in the form of yield stress vs. angular rotation. Some trends can be noticed in these plots: (a) a decrease in yield stress corresponds to an increase in apparent yield strain; (b) at refrigeration temperature, cream cheese with regular fat level is generally less spreadable than its reduced-fat counterparts; (c) variations in temperature (from 5 to 22°C) caused relatively small changes in rheological behavior of fat-free samples; (d) fat-free varieties from different manufacturers show significantly different results at both temperatures (i.e., 1-FF vs. 6-FF in Figure 3.26); and (e) differences in properties of the regular varieties from different manufacturers are less at 22°C than at 5°C. Many factors can contribute to the differences observed among cream cheeses: ingredients and exact compositions of products; total fat content and percent of solid and liquid fractions at a specific temperature; type and level of stabilizers in fat-free types; emulsion characteristics of the products; and processing conditions. Commercially acceptable spreadability of cream cheese is given in terms of yield stress and apparent yield strain in Table 3.19 (Breidinger and Steffe, 2001). These values may be useful as a guide in quality-control and product-development efforts. There is, however, a need for more thorough sensory analysis and correlations between sensory and instrumental results, since we note that values in Table 3.19 would fall all over the three parts (i.e., easy, mild, and hard) of the spreadability map developed by Daubert et al. (1998).* The vane technique has also been employed to study the characteristics of cheeses with different textures such as firm (Cheddar), rubbery (Mozzarella), and soft (Processed cheese) (Truong and Daubert, 2001). In these types of cheeses it is the fracture, rather than flow, that ensues the peak stress. The fracture is likely to start at the tips of vane blades, where stress is concentrated, and propagates outward (Truong and Daubert, 2001; Yan and James, 1997). The shear stress at the peak point is calculated from Equation 2.43, and the corresponding strain is computed from: γ=

t⋅ Ω d  f  − 1   d 

(3.10)

* We must, of course, state that the spreadability map of Daubert et al. (1998) is made not for cream cheese but for elastoplastic foods, including a few cream cheese samples. It may be more helpful if such maps are made for individual foods at a constant temperature.

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22°C

5°C

6

7 6 Yield stress (kPa)

Yield stress (kPa)

4

PCS 6-FF

3

CC 5-R

2

2-R 3-L

1

4-R 9-N 8-N

7-L

3-L

5

4-R

6-FF 5-R

4

FCC

7-L 8-N 9-N

3 2

CC 10-W

1

10-W 0 0.0

2-R

1-FF

1-FF

5

0 0.1

ABBREVIATION 1-FF 6-FF 2-R 4-R 5-R 3-L 7-L 8-N 9-N 10-W

0.2 0.3 0.4 0.5 Angular rotation (rad)

DESCRIPTION Kraft Philly Fat Free Store Brand Fat Free Bruegger’s Regular Store Brand Regular Kraft Philly Regular Kraft Philly Light Bruegger’s Light Store Brand Neufchatel Kraft Philly Neufchatel Kraft Philly Whipped

0.6

0.7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Angular rotation (rad)

REFERENCE

ABBREVIATION PCS CC FCC

DESCRIPTION Processed Cheese Spread Cream Cheese Free Cream Cheese

REFERENCE Daubert et al., 1998

Breidinger and Steffe, 2001.

FIGURE 3.26 Texture map for various cheeses at two temperatures. (5 and 22°C). (After Daubert et al., 1998; Breidinger and Steffe, 2001.)

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TABLE 3.19 Acceptable Yield Stress and Yield Strain Ranges for Commercial Cream Cheeses Temperature (°C)

Stress Range (Pa)

Strain Range (rad)

5 22

3500–6100 1200–2000

0.23–0.46 0.23–0.42

Source: After Breidinger and Steffe, 2001.

where df is the diameter of the fractured surface measured with a caliper (Truong and Daubert, 2001). Both the maximum shear stress and the parameter quantifying subsequent structural breakdown (i.e., maximum stress–final stress) are found useful to monitor textural characteristics of these cheeses. At low strain-rate range, the peak stress is dependent on the shear rate (Figure 3.27). The slopes of the individual lines for each cheese show that extra-sharp Cheddar (firm) cheese is the most sensitive, and American yellow type processed cheese (soft, elastic) is the least sensitive to the increases in shear rate (Figure 3.27). Therefore, the concept of texture map based on vane data provides a rapid and useful way to compare textural characteristics of a wide range of cheeses (see Chapter 7 for more on texture map of cheeses). It is clear that vane method is convenient to determine yield stresses of a variety of materials, including numerous cheeses. Vanes can, however, be used also for the measurement of steady-state flow curves of Newtonian and non-Newtonian fluids (Barnes and Nguyen, 2001). Additional details on procedures for shear rate estimations for vane attachments and examples of flow-curves for Newtonian and nonNewtonian fluids obtained with the vane method have been published (Steffe, 1996; Barnes and Carnali, 1990; Glenn III et al., 2000).

SHEAR MEASUREMENTS Experiments based on shear deformation have often been utilized to study viscoelastic properties of solid cheeses, and part of these studies has been discussed in other chapters. For instance, in Chapter 5 we present the small amplitude oscillatory shear properties, and in Chapter 6 the large amplitude oscillatory shear properties. Moreover, flow curves of melted Mozzarella cheese obtained by the capillary pistondriven rheometer have been discussed in Chapter 8. The rheometers based on the Poiseuille flow, for instance, capillary and slit rheometers, make it possible to study material properties at velocities (or shear rates) comparable to those found in most processing operations (Pérez-Trejo et al., 2001). Shukla and Rizvi (1995) used the capillary rheometry to study and compare the rheological behaviors of butters made from supercritically-fractionated, high-melting triglyceride and anhydrous milk fat at different temperatures (17°C, 22°C, 27°C). They also showed the application of correction procedures (i.e., Bagley pressure correction and wall slip correction; see Chapter 2) to the capillary rheometry data on butter.

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20

16 Peak stress (kPa)

P3-CP P2-Light 12

P1-Full P4-Amer Mozzarella

8

Ched-2 Ched-1 4

0 0

0.01

0.02

0.03

0.04

Shear rate (1/s)

Cheese type

Symbol

Slope Textural Characteristics (kPa.s)

Extra sharp Cheddar Deluxe Cheddar Mozzarella Processed cheese low-fat

Ched-1 Ched-2 Mozzarella P2-Light

Firm Firm Rubbery Soft, Elastic, Sticky

Processed cheese American white Processed cheese full-fat

P4-Amer P1-full

Processed cheese American yellow

P3-CP

R2

182 90 54 46

0.986 0.984 0.984 0.971

Firm Soft, Sticky

42 36

0.725 0.966

Soft, Elastic

23

1.000

FIGURE 3.27 Peak stress dependency on the shear rate for a number of cheeses. (After Truong and Daubert, 2001.)

Flow properties of string cheese were measured at temperatures from 45 to 70°C using a piston-driven capillary rheometer (Taneya et al., 1992). The resulting rheological data were analyzed with the power-law equation: τ = Kγ˙ n

(3.11)

The end effects are corrected according to the Bagley procedure. Both the flow index n and the consistency index K decreased expectedly with temperature. Similar to the increase in the maximum extrusion force with pH of grated cheese curd (Ramkumar et al., 1998), the K value of the string cheese curd was highest (~180 kPa sn) for the highest pH = 5.9 (Taneya et al., 1992).

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TABLE 3.20 Parameter Values for the Viscosity Equation of Enzyme Modified Cheese Shear Rate Range Up curve: 1.92–384 s-1 Down curve: 384–1.92 s-1

A1

a

b

c

56.3 18.4

–0.72 –0.61

94.6 88.5

–0.076 –0.064

Note: Temperature range: 24–72°C; moisture range: 42.3–59.3% Source: After Jao et al., 1981. With permission.

Rheology of enzyme-modified cheese (EMC) has been studied with a cone-andplate viscometer equipped with a temperature control unit (Jao et al., 1981). The rheological properties of EMC were essential for development of a manufacturing process and selection of proper equipment for processing. The shear viscosity vs. shear rate curves in the range from 1.92 s–1 to 384 s–1 showed hysteresis, which disappeared after two cycles of up and down shearing. The authors also examined the effect of temperature and moisture content on the rheology of EMC to provide the following equations describing viscosity of the cheese in terms of significant technological variables: η = A1 γ˙ a e b / T e c M

(3.12)

where, η the apparent viscosity (mPa.s), γ˙ the shear rate (s–1), T the temperature (°C), M the moisture content (%), a, b, and c are constants. The rheological behavior of EMC was characterized as thixotropic shear thinning. Table 3.20 lists the values of the model coefficients and the applicability ranges for temperature and moisture. Massaguer-Roig et al. (1984) modeled shear-dependent and time-dependent behavior of experimental cheese spreads and two commercial Neufchatel cheeses (plain and chocolate flavored) using the following rheological equation proposed by Tiu and Boger (1974): k1 γ˙ t 1 1 = + η − ηe ηo − ηe τ y + Kγ˙ n

(3.13)

where, k1 is the rate constant for structural decay, γ˙ the shear rate, η the apparent viscosity at time t, ηo the initial apparent viscosity, ηe the apparent viscosity at equilibrium, K the flow-consistency index and n the flow-behavior index. The loading of a small volume of sample (0.5 mL) on a cone-and-plate viscometer was made using a modified plastic syringe with maximum care in order not to damage the sample before actual testing. The model parameters accounting for the shear dependency of cheeses are presented in Table 3.21. It is evident from the table that experimental cheeses have at least three times higher yield stress than the reference

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TABLE 3.21 Values of Rheological Model Parameters for Neufchatel and Experimental Cheeses Neufchatel Cheese

Experimental Cheese Spreads

Model Parameter

Plain

Chocolate Flavored

A

B

K (Pa.sn) n (–) τy (Pa)

142 0.37 72

435 0.22 114

1001 0.07 334

787 0.12 350

Source: After Massaguer-Roig et al., 1984. With permission.

Neufchatel cheeses. The other point deserving a mention is that two, instead of one as suggested in the model, structural decay constants (k ′1 and k ″1) is needed to adequately describe the 1/(η – ηe) vs. time plots. Other studies reporting time-dependent rheological behavior are Sanchez et al. (1996) for double cream cheese and Korolczuk and Mahaut (1990) for two types of fresh-acid cheese. In the former study, a coaxial cylinder rheometer with a cup-tobob diameter ratio of 1.08 was used while obtaining flow curves at 20°C and in the shear rate up to 300 s–1. Korolczuk and Mahaut (1990) employed a coaxial cylinder viscometer with a cup-to-bob diameter ratio from 1.08 to 4 at temperatures from 5 to 40°C in two different shear rate range: (a) lower shear rate from 1.7 × 10–4 s–1 and 2.0 × 10–3 s–1, and (b) high shear rate from 9 s–1 to 482 s–1. The flow curves (i.e., shear stress vs. shear rate) of double cream cheese at 20°C exhibited hysteresis loops that did not disappear even after seven to nine days of storage at 5°C, signifying only a partial recovery of the original structure or permanent damage to the structure. The hysteresis loops also contained at least two stress peaks generally below the shear rate of 100 s–1. In spite of all precautions, the damage to sample during preparation could not be eliminated, making us think that for such materials the lubricated squeezing flow (see below) may be a better method for rheological characterization. The apparent viscosity of the fresh cheese was found to depend more on the shear rate than on the time of shearing, but the latter factor was not negligible. Thus, the authors developed the following equation to describe the thixotropic behavior of fresh cheeses: log ηt ,γ˙ = 4.32 − 0.569 log γ˙ − 0.0529 log t + 0.0169 log γ˙ log t

(3.14)

where, ηt,γ˙ is the apparent viscosity (mPa.s) at a given time and shear rate. It was also determined that the temperature effect on the apparent viscosity could be described by an Arrhenius-type expression with the activation energy of flow increasing from 13.4 kJ/mol for nonfat cheese to about 48 kJ/mol for the cheese containing 20% fat in dry matter and for the temperature range between 15 and 20°C. Such

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equations relating shear viscosity to shear rate and time are expected to be useful for process designers and technologists.

LUBRICATED SQUEEZING FLOW MEASUREMENTS Chatraei et al. (1981) developed and used the lubricated squeezing flow (LSF) technique to obtain biaxial viscosity data on polymer melts. Casiraghi et al. (1985) introduced the LSF technique to food research in the mid-1980s. We must also recognize the fundamental contributions of Peleg and his coworkers, which widened the use of the LSF method in food rheology. Recent review by Campanella and Peleg (2002) provides a detailed account of the theory and application of the LSF technique to semiliquid foods. We will limit our discussion in this section to the LSF studies on cheese. Casiraghi et al. (1985) conducted LSF measurements on processed cheese spread (at 7 and 22°C) and Mozzarella cheese (at 22°C). It may seem unusual to talk about “flow” at such temperatures, but one must remember that cheese in general is a viscoelastic material and will normally have a viscous component, which may be small for some varieties at low temperatures. In many respects, the LSF technique is similar to the uniaxial compression under lubrication, but it focuses on the determination of viscous properties of the materials. Plots of apparent elongational viscosity (or biaxial stress-growth coefficient as defined in Chapter 2, Equation 2.85) as a function of biaxial extension rates (Equation 2.82) approached asymptotically a straight line, as schematically shown in Figure 3.28. This is a fairly typical response observed for cheeses. For example, Ak and Gunasekaran (1992) reported the same type of behavior for Cheddar cheese,

Apparent elongational viscosity

log-log scale

Asymptotic line V1

V2

V3 V3 > V2 > V1

Biaxial extension rate

FIGURE 3.28 Schematic drawing of elongational viscosity vs. biaxial strain-rate relationship for fluids in lubricated squeezing flow. V: deformation rate. (After Ak and Gunasekaran, 1992.)

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Apparent elongational viscosity (kPa.s)

10000

Mozzarella: 0.015 1/s Mozzarella: 0.15 1/s Process American-N: 0.015 1/s Process American-S: 0.015 1/s

1000

100

10

1 25

35 45 55 Temperature (°C)

65

FIGURE 3.29 Elongational viscosity of two cheeses as a function of temperature at slow strain rates. (After Companella et al., 1987; Ak and Gunasekaran, 1995.))

although at 22°C. In fact, the slope of the apparent elongational viscosity vs. strainrate curve was similar: –0.85 and –0.88 for processed cheese spread at 7 and 22°C (Casiraghi et al., 1985); –0.85 for 20-day-old Cheddar cheese (Ak and Gunasekaran, 1992); and ranged from –0.80 to –0.85 for Gouda and a number of other cheeses (Luyten et al., 1991a). The slope corresponds to the flow-behavior index of powerlaw model, which is widely used in modeling of steady-shear behavior of liquid and semisolid foods (e.g., Barbosa-Canovas and Peleg, 1983). The elongational viscosity against temperature at two extension rates (0.15 s–1 and 0.015 s–1) for two kinds of process American cheeses (national and supermarket brands) and low-moisture part-skim Mozzarella cheese are shown in Figure 3.29. As expected, the viscosity decreases almost linearly with the temperature on semilog coordinates. The biaxial extension rates experienced by a melting cheese in a sandwich or on a pizza pie are expected to be very low (Campanella et al., 1987), perhaps similar to those reported in the figure. Ak and Gunasekaran (1995) and later Wang et al. (1998) suggested that the apparent elongational viscosity, as determined by LSF technique, might be used as a quantitative measure of the cheese meltability, since its variations with maturation (i.e., decreasing with age of cheese) and temperature are consistent with practice. However, in order to relate this parameter to cheese meltability, the approximate extension rates during melting of cheese over pizza pie and other surfaces must be estimated. Based on the LSF technique, Wang et al. (1998) developed and used an instrument called “UW-meltmeter” (see Chapter 8) to determine apparent elongational viscosity of full-fat (43%) and reduced-fat (14%) Mozzarella cheeses. The behavior of melted Mozzarella cheese was characterized as strain-rate thinning at 40 and 60°C and covering the strain rate 10–4 s–1 to 10–1 s–1. The elongational viscosity vs. extensionrate curves for all conditions appeared to fall within a relatively narrow band (see Figure 8.19), which might be divided into a few regions of different meltability from the upper-left corner to the lower-right corner. Cheese meltability measurements with the UW-meltmeter and other methods are discussed in detail in Chapter 8.

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The LSF technique was employed by Suwonsichon and Peleg (1999b) to study rheological properties of Ricotta cheeses (whole-milk, part-skim, and fat-free kinds) of different brands. The imperfect squeezing-flow (see Chapter 2) method enables characterization of rheological behavior of the cheese without causing structural damage. It was observed that the Ricotta cheeses had a significant yield stress on the time scale of the experiments (i.e., 3 min). The results, for instance the residual stresses at t = 60 s and t = 120 s, were sufficiently sensitive to variations in consistency of the cheese so that the different brands and fat contents of ricotta cheeses could be distinguished on the basis of yield stress. Thus, the LSF technique, in either perfect or imperfect geometry, is expected to find increased applications in food research, since it offers a practical solution to serious problems encountered in coaxial and capillary viscometry, namely the slip and the partial destruction of the specimen’s microstructure during sample loading (Hoffner et al., 1998; Suwonsichon and Peleg, 1999a). An additional benefit may be the relatively low cost of an LSF instrument as compared to that of commercial rheometers.

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van Vliet, T. 1991a. Inventory of test methods, in Rheological and Fracture Properties of Cheese, IDF Bulletin No. 268: pp 16–25. Brussels, Belgium: International Dairy Federation. van Vliet, T. 1991b. Spreadability of (low-fat) spreads; some rheological aspects. IFI 2:36–39. van Vliet, T. and H. Luyten. 1995. Fracture mechanics of solid foods, in New Physico-Chemical Techniques for the Characterization of Complex Food Systems, E. Dickinson, Ed., pp 157–176. New York: Blackie Academic & Professional. Vernon-Carter, E.J. and P. Sherman. 1978. Evaluation of the firmness of Leicester cheese by compression tests with the Instron universal testing machine. Journal of Texture Studies 9:311–324. Visser, J. 1991. Factors affecting the rheological and fracture properties of hard and semihard cheese, in Rheological and Fracture Properties of Cheese, Anon, Ed., IDF Bulletin No. 268: pp49–61. Brussels, Belgium: International Dairy Federation. Visser, S. 1993. Proteolytic enzymes and their relation to cheese ripening and flavor: an overview. Journal of Dairy Science 76:329–350. Wang, Y.-C. et al. 1998. A device for evaluating melt/flow characteristics of cheeses. Journal of Texture Studies 29:43–55. Watkinson, P. et al. 2001. Effect of cheese pH and ripening time on model cheese textural properties and proteolysis. International Dairy Journal 11:455–464. Watkinson, P. et al. 1997. Rheological properties and maturation of New Zealand Cheddar cheese. Lait 77:109–120. Watkinson, P. and L. Jackson. 1999. New procedure for estimating the modulus of deformability of cheese from uniaxial compression tests. Journal of Texture Studies 30:563–580. Wium, H., K. Kristiansen, and K. Qvist. 1998. Proteolysis and its role in relation to texture of Feta cheese made from ultrafiltered milk with different amounts of rennet. Journal of Dairy Research 65:665–674. Wium, H., M. Gross, and K.B. Qvist. 1997. Uniaxial compression of UF-Feta cheese related to sensory texture analysis. Journal of Texture Studies 28:455–476. Wium, H. and K. Qvist. 1997. Rheological properties of UF-Feta cheese determined by uniaxial compression and dynamic testing. Journal of Texture Studies 28:435–454. Wium, H. and K. Qvist. 1998. Effect of rennet concentration and method of coagulation on the texture of Feta cheeses made from ultrafiltered bovine milk. Journal of Dairy Research 65:653–663. Wodecki, E. et al. 1984. Effect of water content on the hardness of Edam cheese. Journal of Food Engineering 3:295–305. Xiong, R. et al. 2002. Relationship between sensory and instrumental hardness of commercial cheeses. Journal of Food Science 67(2):877–883. Yan, J. and A E. James. 1997. The yield surface of viscoelastic and plastic fluids in a vane viscometer. Journal of Non-Newtonian Fluid Mechanics 70:237–253.

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4

Fracture Properties of Cheese

Fractures, cracks, or damage may originate from different aspects: debonding of atoms, nucleation, or growth and coalescence of microcracks and microcavities (Lemaitre, 2001). From an engineering materials point of view, the following damage categories can be defined: 1. Brittle or quasi-brittle failure — fracture occurs without significant irreversible strain 2. Ductile failure — failure at large plastic strain at low temperature (~1/4 of the melting temperature) 3. Creep failure — failure at large plastic strain at high temperature (>1/3 of the melting temperature) 4. Fatigue failure — failure due to repetitious loading either above or below yield stress; may be further classified into low-cycle, high-cycle, and gigacycle fatigue damage It must be emphasized that any fracture or crack mechanism is closely related to the material’s microstructure. In polymers, these mechanisms are dominated by the long and flexible macromolecules (Schirrer, 2001). Macromolecules are long series of monomers whose backbones are composed of linked carbon atoms. The cone angle of carbon atoms is fixed at about 70º (Figure 4.1). Therefore, the relative position of the linked carbon atom chain, i.e., the macromolecular backbone, is limited to some extent. The stiffness of the monomer and the space it occupies dictate the stiffness of the macromolecule. A large condensed assembly of macromolecules is the polymer. It may exist in either amorphous or crystalline structure, depending on its temperature. At material temperatures below its glass transition temperature, Tg, the macromolecules assume a glassy or amorphous disordered structure in which the smallest elementary volume of the material is about the size of the monomer. At temperatures above Tg, the material is said to be in the “rubbery” state. Figure 4.2 shows a typical modulus vs. temperature relationship for a polymer. In the glassy state, interactions between nonlinked atoms are strong, and any applied load is distributed atom to atom. When a small elastic load is applied, all carbon–carbon bonds are stressed, and their cone angles are strained. Larger loads lead to nonrecoverable plastic deformations. In the rubbery state, molecular interaction at the atomic level does not exist. Under applied loads, the entanglements deform about each other, and the atoms are free to twist on the carbon–carbon cone. The elastic properties are due primarily to the entropy variations of the entanglement positions, which are nearly proportional to the macroscopic strain (Schirrer, 2001). True rubbery materials may exhibit linearity between applied stress and strain up to strain levels of 10.

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70° Cone Linked carbon atoms

FIGURE 4.1 Schematic representation of a macromolecule as a string of monomers whose backbone is comprised of linked carbon atoms with limited movement (within the cone angle of 70°) about each other. (After Schirrer, 2001.)

Glassy

Iog (Modulus)

Leathery

Rubbery

Viscous Flow

Tg Temperature

FIGURE 4.2 Modulus vs. temperature relation for a typical polymer. Glass transition temperature, Tg, is identified at the transition from glassy to leathery state.

Sometimes a third state, semicrystalline, can be defined when the material temperature is close to Tg. The semicrystalline state is characterized by a more or less regular small rigid lamellar arrangement of macromolecules with flexible amorphous macromolecules connecting the crystalline states.

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Material

Environment

Loading Rate

Fatigue

Material Resistance

Crack Driving Force

Applied Stress

Crack Size

Crack Geometry

Loading Rate/Cycles

FIGURE 4.3 Various factors contributing to material resistance to fracture and crack driving force.

When strained, a network of entanglements in both glassy and rubbery states deform with increasing (in tension) or decreasing (in compression) distance between the entanglements. In the glassy state, the elongation is irreversible due to the atomic interactions, and the energy input is converted to heat. In some cases, a few molecules may break, creating a crack or cavity. Such an event entirely changes the material microstructure.

FRACTURE MECHANICS A fracture in a material is a failure mechanism that involves stable or unstable propagation of a flaw (e.g., a crack) within the material structure. Often the purpose of fracture-mechanics analysis is to prevent fracture (or propagation of an existing flaw). This criterion also applies to undesirable fracture in cheeses that will lower the overall quality and consumer appeal. However, the eye (slit) formation in some cheeses is not only desirable but is facilitated. In such cases, the focus is to limit the extent of crack growth. Regardless, it is useful to consider various factors that contribute to crack growth and those factors that tend to resist it. These factors are (Figure 4.3): (1) crack driving force – applied stress, crack size, crack geometry, and loading rate/cycles; and (2) material resistance factors — type of material, environment (temperature, chemical/physicochemical factors), loading rate, and fatigue. Naturally, when the driving force exceeds the material resistance, the crack will propagate. Under a specific set of conditions, the crack size that balances the driving force and resistance is known as the critical flaw size. These forces can be considered to act in one of three basic modes schematically illustrated in Figure 4.4. They are: Mode I — opening; Mode II — sliding; and Mode III — tearing. In the case of cheese and many other materials, Mode I, the opening mode, is most relevant. It represents the crack pulling open due to forces

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Mode I (Opening)

Mode II (Sliding)

Mode III (Tearing)

FIGURE 4.4 Typical failure modes in engineering materials.

acting perpendicular to the crack. Mode III is relevant when forces are applied perpendicular to a crack, causing the material to tear and slide along itself, and thus move out of its original plane. Separating strings from string cheese (Izutsu et al., 1991) is as an extreme example of Mode III behavior. In Mode II, the forces are acting parallel to the crack, causing an in-plane shear. There are three broad regimes to analyze the fracture mechanics of materials: linear elastic, elastic–plastic, and limit load. These regimes are illustrated in Figure 4.5. In linear elastic fracture mechanics (LEFM), only localized yielding around the crack tip is considered. A stress intensity factor, KI , represents the crack driving force. This is defined as:

K I = Yσ πa

(4.1)

where σ = applied stress, a = crack size, and Y = a dimensionless constant depending on material geometry and loading mode (more on this later under Determination of KI). The subscript I refers to Mode I described above (Figure 4.4). Since Mode I is the most common, the subscript I is sometimes omitted. The material resistance is measured by fracture toughness KIc. Fracture occurs when KI = KIc. Fracture toughness is a material property, i.e., it is independent of material geometry and test procedure. It is a measure of the energy per unit area necessary to give a new crack surface (Williams, 1984). In elastic–plastic fracture mechanics (EPFM) analysis, a large section around the crack tip is considered yielding. Depending of the extent of yielding, it may be termed “contained” or “full.” The crack driving force represents the work done under applied stress in the area around the crack tip. It is a function of crack and material geometry, applied stress, and elastic–plastic stress–strain relationship of the material. The limit load analysis or diffuse dissipation assumes that the entire cross-section of the material becomes fully plastic before it begins to fail. This is appropriate for highly ductile materials. It is possible to have this regime in conjunction with one of the other regimes (Williams, 1984).

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σ

σ

1

2

w a Crack

Crack

td

σ

σ

LEFM

EPFM (contained yielding)

σ

σ

3

4

Crack

Crack

σ

σ

EPFM (fully yielded)

Limit Load (diffuse dissipation)

FIGURE 4.5 Failure mechanisms: 1. LEFM — Linear elastic fracture mechanism, td<w-a; 4. Limit load or diffuse dissipation. (After Williams, 1984.)

The effect of fracture toughness on the governing failure mechanism is depicted in Figure 4.6. As can be noticed, within LEFM (for material with low KIc) brittle fracture is the governing failure mechanism. As KIc increases, LEFM is no longer valid, the failure mechanism is dominated by material flow properties, and EPFM will be prevalent. At extremely high KIc, fracture mechanics is no longer valid

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Br

itt le

Fr

ac

tu r

e

Failure Stress

Collapse

LEFM

EPFM

Limit Load Analysis

Fracture Toughness

FIGURE 4.6 Effect of fracture toughness on governing failure mechanism. (After Anderson, 1995.)

1.0

0.8

Kr 0.6

0.4

0.2

0.2

0.4

0.6 σr

0.8

1.0

FIGURE 4.7 Failure assessment diagram. (After BSI, 1991.)

because the failure stress is insensitive to toughness. In such cases, limit load analysis is sufficient to predict failure (Anderson, 1995). In most materials, plasticity effects precede failure, gross yielding effects predominate, and failure occurs by plastic collapse. To account for elastic fracture and plastic collapse, a two-parameter approach to failure has been developed. This is represented by a failure assessment diagram (Figure 4.7) with the following ratios:

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Kr =

KI K Ic

and

σr =

σ σf

(4.2)

where σ = applied stress and σf = flow stress. If Kr = 1, failure will occur by brittle fracture. If σf = 1, failure will occur by plastic collapse. In the failure assessment diagram, the region under the curve represents insignificant risk of failure, and the region outside the line represents a potential for failure.

BRITTLE FRACTURE A material is considered brittle if it breaks at small strains (and has small fracture toughness). Therefore, it is possible to study brittle failure using the theory of LEFM. An existing microcrack propagates when the stresses and strains at a critical distance ahead of the crack tip reach the fracture criterion of a fictitious tiny specimen (Francois, 2001). Consider an average stress σ applied to a plane of dimensions width w and thickness B of ideal isotropic, elastic material. Consider also a through-the-thickness crack of elliptical geometry (major and minor axes are 2a and 2b units, respectively) as shown in Figure 4.8. The stress distribution around the crack can be indicated by the stress σxx measured along the x-direction and the stress σyy along the ydirection. As shown, σxx is zero at the crack tip, reaching the maximum at a short distance away and falling back to zero again. However, σyy increases exponentially from σ at a distance away from the crack and reaches a maximum of σm at the crack tip. The maximum stress amplification or stress concentration (σm/σ) is measured as below (Riande et al., 2000):

σm 2a =1+ =1+ 2 a ρ σ b

(4.3)

where, ρ = radius of curvature of the crack tip = b2/a. The same σm can be considered to be present at the other end of the crack when present centrally within the material. For a circle (a = b) the stress concentration factor is 3 and for narrow cracks (a>>b) the stress concentration increases to a large value and can be approximated as:

σm =2 aρ σ

(4.4)

Therefore, even at an acceptably low applied stress the maximum stress can exceed that of the material fracture stress. If the material cannot relieve this stress concentration by plastic flow around the crack tip, the crack will grow, thereby lowering the total energy of the system. Bui and Ehrlacher (1981) described the damaged zone around a crack propagating in a brittle material. If the material was elastic and fails when the maximum

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σ

y σm

σyy σ

σxx

2b

x 2a

σ

FIGURE 4.8 Distribution of local stresses around an elliptical crack inside an elastic plane subjected to stress σ (After Riande et al., 2000.)

principal stress reaches a critical value σc, the thickness of this damaged zone td is given by:

⎛ k ⎞ td = ⎜ ⎟ ⎝ σc ⎠

2

(4.5)

where k = initial stiffness. The theoretical failure stress is the stress needed to break atomic bonds. This is on the order of E/10, where E = Young’s modulus of the material. However, the actual fracture stresses are several orders of magnitude lower. This is due to the heterogeneous distribution of the stresses in the material. For example, in a material containing several microcracks scattered within the entire volume, stress concentrations easily approach the fracture stress. In materials without such microcracks, inclusions or impurities contribute to the lowering of fracture stress. Given the high stress concentration at local flaws in a material, fracture is always considered to originate from such locations (Gordon, 1968). Various inhomogeneities and flaws in cheese may range from 10–5 mm to 10 mm or larger (Table 4.1). The practical problem with the stress-concentration approach is that σm approaches infinity as ρ approaches zero, as would be the case for an infinitely sharp © 2003 by CRC Press LLC

TABLE 4.1 Estimated Size of Various Inhomogeneities and Flaws in Cheese Type of Inhomogeneity/Flaw

Estimated Size (mm)

Casein sub-micelle Paracasein micelle Protein network strands Fat globule Unevenness of network Precipitates of salts, amino acids Curd grains Acid spots Holes Curd pieces (in Cheddar cheese) Difference rind-center

10–5 10–4 10–3 10–3 to 10–2 0.01 to 0.1 1 1 to 10 10 10 20 10 to 100

Source: After Walstra and van Vliet, 1982; Luyten, 1988.

crack. Since all materials are considered to contain infinitely small flaws, they all should fail upon application of an infinitesimal stress.

GRIFFITH CRITERION To overcome problems due to the local stress concentration approach, Griffith (1920) proposed an energy balance approach. According to this, an existing crack can grow or a new crack can form if and only if such a process would result in net decrease or, at best, no change in total energy of the system. The energy needed for the process is given in terms of specific surface energy (γs, J/m2) of the two new surfaces created (Williams, 1984):

γs =

σ f 2 πa 2E

(4.6)

where σf = failure stress; E = Young’s modulus; and a = flaw size. For a typical elastic system where applied energy is absorbed locally around the tip of a sharp crack the energy balance may be written as (Williams, 1984):

∆U1 = ∆U2 + ∆U3 + ∆U 4

(4.7)

where U1 = energy input; U2 = stored energy; U3 = energy dissipated (around the crack tip); and U4 = kinetic energy. If we further consider that the crack is growing such that increase in crack area is given as ∆a, then we can write:

⎛ ∆U1 ∆U2 ⎞ ∆U3 ∆U 4 − + ⎜ ⎟= ∆a ⎠ ∆a ∆a ⎝ ∆a © 2003 by CRC Press LLC

(4.8)

It is important to note that the changes in energy occur not due to crack displacement in the material, but due to increase in area. The left hand side of Equation 4.8 ∆U3 is known as the energy release rate (G) and on the right hand side, is the ∆a fracture resistance (R). The fracture resistance represents the work required to fracture a material. For crack initiation, U4 = 0. Therefore, we can write the following differential form for incremental values of the variables:

⎡ dU1 dU2 ⎤ dU3 ⎢⎣ da − da ⎥⎦ = da

or

G=R

(4.9)

Incidentally, the symbol G is used in fracture mechanics after Griffith, who introduced the energy-balance approach. Williams (1984) provides a detailed account of evaluating G for different test configurations. It can be assumed that the energy required to produce a crack is the same for each increment (i.e., R = a constant). Therefore, G = GIc where GIc is known as the critical energy release rate. It can be shown that:

⎛ 1 − ν2 ⎞ 2 for plane (biaxial) strain GIc = ⎜ ⎟K ⎝ E ⎠ I GIc =

K12 for plane (biaxial) stress E

(4.10)

(4.11)

where ν = Poisson’s ratio and E = Young’s modulus. When Equation 4.9 is first satisfied, the crack propagates in a stable manner. However, uncontrolled fracture occurs when (Williams, 1984):

dG dR ≥ da da

(4.12)

The material’s resistance to fracture R can be determined by knowing σf , fracture stress of a sample with a crack of size a in a fracture test (Broek, 2001). Typically, a residual strength vs. crack size diagram can be drawn. Such a plot can be used advantageously when combined with a crack growth curve (Figure 4.9) to determine the permissible crack size ap corresponding to permissible residual strength pp and the time taken for the crack to grow to that limit (tp). The surface-energy approach helps to understand fracture mechanics without having to assume infinitely sharp cracks and infinitely high stress concentrations within the material. It should be emphasized, however, that in LEFM only the elastic deformation (stored) energy is available for fracture. The energy dissipated due to material flow does not contribute to creating new surfaces, and hence is not available for crack propagation. The EPFM considers plastic flow around the crack

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Residual Strength, Pres

Crack Growth Time, t

tp

Pp

ap

a=0

Crack size, a

FIGURE 4.9 Residual strength and crack growth curve. (After Broek, 2001.)

tip (see Figure 4.5). For the EPFM the resistance to crack propagation R is GIc plus the energy dissipation in the flow region beyond the vicinity of crack tip. Thus, R is denoted by J (or JR) to account for this additional component. We should note that for the limiting elastic case J + R = GIc. It is worth pointing out that G is the energy release rate of the entire system and can include energy stored, whereas, R and J describe material behavior. Williams (1984) presents additional discussion on fracture mechanics of polymeric systems that exhibit such energy dissipation. Cheese being a viscoelastic material, strictly speaking, the LEFM is not directly applicable. However, unfortunately, theories suitable for evaluating combined fracture and flow in cheese are not available, and reasonable predictions can be made using the theory of LEFM. This is especially true if the flow region around the crack tip is small compared to the size of the crack (case 1 in Figure 4.5). In engineering materials, cracks usually occur rapidly. For cheese, crack propagation is a slow and prolonged process. For example, formation of eyes or holes in Gouda cheese takes about one week (Luyten, 1988). Based on the LEPM concept, the slow crack growth rate a˙ is measured as a function of KI or GI. That is,

a˙ =

da = A KI n dt

(4.13)

where A = material constant and n = exponent. As a˙ tends to zero, KI reduces towards a low threshold value Kth, and as a˙ tends to infinity, KI tends to approach KIc, the fracture toughness. Near Kth the crack growth is slow, and at Kc the crack growth is rapid. The material constant A varies, depending on the material and environmental conditions (e.g., temperature).

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DETERMINATION OF KI The stress-intensity factor KI is normally determined experimentally by “v-notch” test or other similar tests. As shown earlier for the case of a through-the-thickness crack of length 2a in an infinite plate subjected to a tensile stress σ, the stressintensity factor is given by

K I = σ πa

(4.14)

The Equation 4.14 is the same as Equation 4.1 given Y = 1. However, for finite specimens Y¦1 and alternate expressions have been developed (Williams, 1984; Anderson, 1995):

πa ⎞ ⎤ ⎡ 2w K I = σ πa ⎢ tan⎛ ⎝ 2 w ⎠ ⎥⎦ ⎣ πa

1

2

(4.15)

where w = width of the plate. Note that as a/w approaches zero (i.e., for a large plate), KI approaches that of infinite plate value. Therefore, for all geometries, KI is written as:

KI =

P φ( a w) B w

(4.16)

where, P = applied force, B = thickness of the plate and φ(a/w) is a calibration factor. Some common test specimen and notch geometries and the corresponding solutions for KI based on finite element analysis are presented in Table 4.2. The American Society for Testing and Materials (ASTM) has defined a certain specimen size to obtain valid results for KIc in metals. Recommendations are also available for plastics. Such recommendations do not exist for food and biological materials. Therefore, even if the experiments were performed carefully, the test results of cheese should be treated with this fact in mind — i.e., test geometry does affect the validity of the LEFM theories. Moreover, for viscoelastic materials, even though the testing and data analysis procedure are the same, the validity of K and J are not guaranteed (Anderson, 1995).

FRACTURE TESTS ON CHEESE Fracture properties of cheese can be determined by any of the fundamental materials testing methods discussed in Chapters 2 and 3. These methods include compression, tension, shear, torsion, and bending. Details of these methods and accompanying results have been presented in previous chapters. Here we will briefly discuss some results that are directly relevant to determining fracture of cheese using notchedtension and notched-bending tests. In general, tension or bending is best suited for determining fracture properties because it is easy to observe the crack initiation and propagation. However, tension tests are difficult to perform with soft materials such

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TABLE 4.2 Stress Intensity (KI) Factors (φ(a/w) in Equation [4.16]) for Different Test Geometries φ(a/w)1

Crack Geometry

[

2 tan m 0.752 + 2.02n + 0.37(1 − sin m)3 cos m

]

S n w 1.99 − n(1 − n)(2.15 − 3.93n + 2.7n 2 ) 2(1 + 2n)(1 − n)1.5 3

[

m (1.122 − 0.561n − 0.205n 2 + 0.471n 3 + 0.190n 4 ) 1− n

1

m = πa/2w; n = a/w

Source: After Anderson, 1995.

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]

30

Stress (kPa)

50 37

20

25 10

12.5 0

0 0

0.1

0.2

0.3 0.4 Strain (-) A

0.5

0.6

0

0.2

0.4

0.6 0.8

1.0

Strain (-) B

FIGURE 4.10 Stress–strain curves of A: six-week-old and B: 10-week-old Gouda cheese in compression (____), tension (— — -), and bending (-.-.-.-). (After Luyten, 1988. With permission.)

as cheese and other food and biological materials. Therefore, bending is the preferred fracture-test mode. The fracture properties can be determined using compression tests, and a good set of data may be obtained due to the small sample size used and small effect of sample inhomogeneities (Luyten, 1988). We shall note that compression tests are often carried out until sample failure even when the object of the test is not to determine the fracture properties. Luyten (1988) evaluated fracture properties of Gouda cheese in tension, compression, and bending. The stress–strain curves in all three modes agree well for small strains (Figure 4.10). However, large differences are noticed in fracture stress and strain values (normally estimated at the peak of stress–strain curve). As presented in Table 4.3, the results indicate the modulus values are fairly similar because they correspond to linear (initial) part of the curve (measured as the initial slope). The fracture stress and strain values in tension, bending, and compression are low, intermediate, and high, respectively. With some corrections (Luyten, 1988), the fracture stress values from three testing modes may agree better than the fracture strain values.

NOTCH TESTS Testing of specimens in tension and bending with known crack size by means of a notch is perhaps the most popular fracture test for engineering materials. In fact, the tension test results presented in Figure 4.10 and Table 4.3 for Gouda cheese are for notched specimens. For a proper notch test, the initial crack should be sharp (so that the stress concentration is high). Therefore, the notch is made by pressing a razor blade into the material to a measured distance (the crack length). Luyten (1988) performed notched tension tests on Gouda cheese of different ages with different notch lengths (0 mm to 5 mm) to determine the notch sensitivity for crack initiation and propagation. The aged Gouda cheese is less notch-sensitive than the young cheese for crack initiation, and once initiated the crack propagates more rapidly in mature cheese than in the young cheese (Figure 4.11). The perceived “brittleness” of mature cheese is thought to be due to its propensity for higher crack propagation rate compared to the younger cheese. © 2003 by CRC Press LLC

TABLE 4.3 Comparison of Modulus (E) Fracture Stress (σf) and Strain (εf) of 6-week-old Gouda Cheese at 21°C Measured in Compression, Tension, and Bending Tests

Test Mode

Applied Strain Rate (1/s)

E (kPa)

σf (kPa)

εf

Tension

0.0139

189 201 221 230

30.5 26.4 28.9 22.4

0.33 0.31 0.31 0.28

Bending

0.0181

188 173 169 188 165

41.3 40.8 37.6 43.6 44.1

0.48 0.43 0.47 0.62 0.54

Compression

0.0167

202 203 173 154 244

49.7 45.7 45.8 45.3 53.3

0.87 0.80 0.89 0.96 0.82

Source: After Luyten, 1988.

FIGURE 4.11 Results of notch sensitivity tests on young (A) and mature (B) Gouda cheese samples in tension. The dotted lines connecting solid circles (•) and open circles (o) indicate decreasing stress with increase in notch length for crack initiation and crack propagation, respectively. Some points (x) are calculated values. (After van Vliet et al., 1991. With permission.)

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FIGURE 4.12 Force–deflection curves from single-edge notched bending tests at a loading rate of 10 mm/min. (After Charalambides et al. 1995. With permission.)

Charalambides et al. (1995) and Kamyab et al. (1998) performed single-edge notched bending (SENB) tests on cheese. They followed the LEFM test protocol of the European Structural Integrity Society for testing of polymers (Williams and Cawood, 1990) using the test geometry for SENB as given in Table 4.2. This protocol has also been used for a model food system (Langley et al., 1994). For sufficiently large samples, the bending test specimen is prepared such that width (w) is twice the thickness (B), and the ratio of span (S = distance between supports) to B is four (Kamyab et al., 1998). Accordingly, samples of length, L = 88 mm, w = 18.5 mm, B = 9.3 mm, S = 74 mm, were used. Five-millimeter- to 6-millimeter-long notches were made using a razor blade at the center such that 0.45
Gc =

A Bwφ(a w )

where, φ(a/w) is the calibration factor. © 2003 by CRC Press LLC

(4.17)

TABLE 4.4 Fracture Toughness of Different Cheeses Measured by Single-Edge Notched Bending (SENB) and Single-Edge Notched Tension (SENT) Tests

Age (day)

Fracture Toughness (J/m2)

Test Modea

Sharp Cheddar

30 60 90 120 150 180 —

31.2 23.6 21.5 19.8 15.7 16.5 2.7

SENB SENB SENB SENB SENB SENB SENT

Mild Cheddar

37 89 155 182 —

41 29.3 17.9 30.6 13.8

SENB SENB SENB SENB SENB

Monterey Jack

46 102 152 185

26.5 24.6 20.4 17.5

SENB SENB SENB SENB

Process cheese, regular

4.1

SENT

Process cheese, light

2.4

SENT

Process American 1 Process American 2

5.6 3.8

SENT SENT

Cheese

a

SENB test results are from Charalambides et al. (1995); SENT test results are from Kamyab et al. (1998).

The measured fracture toughness values for sharp and mild Cheddar and Monterery Jack cheeses at 4°C are summarized in Table 4.4. These results show, as Luyten (1988) observed (Figure 4.11), that cheeses tend to be more brittle with age, i.e., fracture toughness decreases with maturation, which correlated well with the αs1casein breakdown during storage. Kamyab et al. (1998) reported also performing single-edge notch tension tests, SENT (see Table 4.2) with rigid clamps to avoid any rotation at the sample-test grip interface. Several samples of different a/w ratios were used. The tensile stress–strain curves are shown in Figure 4.13. The arrows on this figure indicate the fracture stress (σf) of the corresponding cheese obtained

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FIGURE 4.13 Stress–strain curves from tension tests of different cheeses. 1- mild Cheddar cheese; 2- sharp Cheddar cheese; 3- American process cheese1; 4- American process cheese 2. Arrows indicate fracture stress obtained in single-edge notched tension tests. (After Kamyab et al., 1998. With permission.)

in SENT tests. As in the case of SENB (Figure 4.12), the nonlinearity is also apparent in tensile tests. The fracture toughness is calculated as:

Gc =

Kc 2 E

(4.18)

where, E = tensile modulus obtained from the curves in Figure 4.13, and Kc = stress intensity factor for the rigid clamp case (Williams, 1984):

Kc = 1.12σ f πa

(4.19)

Luyten and van Vliet (1996) reported results of notched-tension tests on Gouda cheese at different ages. The relative values of fracture stress and strain (with respect to samples without notch) as a function of notch length are plotted in Figure 4.14. The fracture strain is small initially for the cheese as it is rather brittle before the curd particles fuse together. Fracture strain increased as the cheese matured. The same was true for other cheeses such as Gruyere, Appenzeller, and Cheddar. Further, due to viscoelastic effects the fracture strain decreased with strain rate. At low strain rates, a significant part of the energy is lost as viscous dissipation due to the material flow and the energy available for fracture is small. Therefore, for fracture to occur at lower strain rates the materials have to be deformed to a larger extent. This strain rate effect is rather large for young (2-week-old) Gouda cheese. For the 9-month-old

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Relative σf or εf

1.0

0.75

0.5

0.25

0 0

1

2

3

4

5

6

Notch length (mm)

FIGURE 4.14 Relative change (with respect to corresponding values of unnotched specimens) in fracture stress (circles) and fracture strain (squares) as a function of notch length in 2-week-old (open symbols) and 6-month-old (closed symbols) Gouda cheese. (After Luyten and van Vliet, 1996.) 1.5

Fracture strain (-)

Gouda cheese

1.0

2-week-old

0.5

9-month-old 10−4

10−3

10−2

10−1

100

Strain rate (1/s)

FIGURE 4.15 Fracture strain as a function of strain rate. (After Luyten and van Vliet, 1996.)

Gouda cheese, though the fracture strain is considerably smaller than that for the young cheese, the strain-rate effect is not observable (Figure 4.15). Luyten (1988) also reported fracture energy for crack initiation and propagation estimated from SENT experiments (Table 4.5). These values were obtained assuming negligible energy dissipation, and thus are lower than the actual energy available for fracture. It has been estimated perhaps only 20 to 40% of the energies reported in Table 4.5 are actually available for fracture. Though not consistent, it can be observed that, in general, the energy for crack initiation and propagation decrease with age.

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TABLE 4.5 Fracture Energy for Gouda Cheese at 20°C in Notched Tension Tests Performed at a Strain Rate of 0.0028 s–1 Fracture Energy (J/m2)

Cheese Age (months)

Crack Initiation

Crack Propagation

0.5 1 2 4 6 10 12

6.3–9.2 4.5–8.1 2.9–7.8 5.3–6.8 6.6–9.1 1.3–3.1 0.6–3.1

11.0–12.5 — — — — — 0.8–1.5

Source: From Luyten, 1988.

FIGURE 4.16 Sliced, cubed, and shredded cheese samples. (After DMI, 2002.)

CUTTING, SLICING, AND SHREDDING Cutting, slicing, and shredding are routine for both natural and process cheeses in retail marketing. Natural cheeses are made in huge blocks as large as 640 pounds. For supermarket sale, these blocks are cut into bricks ranging from one-half to two pounds and shrink-wrapped, or cut into small cubes or thin strips and packaged in plastic bags (Figure 4.16). Sliced and shredded cheeses are also popular for food service, restaurants, and other ready-to-eat end uses. These products represent a huge share of the cheese market. Shredded cheese has captured nearly 25% of the cheese market, and its share is still growing, obviously due to increased use in the readyto-eat and heat-and-serve food categories. The top 10 vendors of natural shredded cheese had sales of more than $1.7 billion (U.S.) in 2001, a 7% increase from the previous year (www.dairyfoods.com).

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Much of the shredded cheese market is based on the integrity and uniformity of the shreds. In addition to being appealing to the eyes, the shreds that retain their integrity melt uniformly, and are easier to sprinkle on foods (Dubuy, 1980). These attributes enhance sales and use of shredded cheese as a food ingredient. Machined cheeses make portion control and fill-weight control easy (Andres, 1983). However, the shreds often crumble, stick, or mat. Special processes are used to maintain the length of each shred so that breakage or crumbling is held to a minimum. Microcrystalline cellulose is used to prevent caking or stickiness. Consequently, the cheese will not mat together on storage and can be easily sprinkled onto formulated food. The consistency of the shreds, plus the fact that it does not mat together, makes better portion control possible (Andres, 1983). Use of the cellulose additive must be done carefully, because if used improperly, it shows up as a white dusting, which is mistaken for mold, hurting cheese sales. Therefore, to take full advantage of the growing shredded-cheese market, it is essential to offer cheese shreds that do not mat or fragment. However, cheese processors often find it difficult to maintain the integrity of cheese shreds, especially when composition and manufacturing parameters vary widely. The lower-fat cheeses are especially hard to cut satisfactorily. The other major problems are “stickiness,” primarily due to high moisture content, and the inability to increase the speed of cutting without compromising product quality. These problems are encountered in the industry due to, in part, lack of adequate understanding of the relationships between shredding process and cheese properties. Computer-vision techniques have been proposed to examine cheese shreds individually (Apostopoulos and Marshall, 1994) or en masse (Ni and Gunasekaran, 1998 and 2002) to quantify shred integrity and uniformity. Machining of cheeses, as with most other foods and biological materials, is still largely performed empirically. The design and operation of food-cutting equipment are mostly adapted from equipment used in the lumber and metal industries (Pomerantz and Feeney, 1985; Antonissen, 1986). Little published information is available about fracture properties of cheeses, which are undoubtedly affected by several physicochemical properties (moisture content, temperature, composition, pH, etc.), rheological properties (modulus, toughness, failure stress and strain, etc.), and operating parameters (cutting speed, blade type, contact angle, etc.) Typical commercial shredders take precut cheese cubes and pass them over a series of cutting blades or cutting heads by centrifugal action. Shred shape is controlled by the form of the cutting heads (Barritt, 1985). Conventional shredded cheese has a diameter of 1/8" while a new line of cheese shreds, called fancy shreds, has shred diameters ranging from 1/32" and 1/64". Several designs for shredding and application of cheese shreds have been described (Dubuy, 1980). The fancy shreds give the appearance of significant increase in volume of cheese per given weight — the volume of cheese is increased by as much as 50% (Andres, 1983).

CUTTING WITH WIRE AND BLADE Cutting cheese with wire and blade is very popular. Wire cutters range from small tabletop units to large-scale cutters at the factory level. Cutting with wire and blade comprise fracture, plastic deformation, and friction. They can be schematically represented as shown in Figure 4.17. The elastic–plastic fracture mechanics theory deems that the material flows only in a small area around the crack tip. Therefore, © 2003 by CRC Press LLC

Cutting Blade Cheese Plastic Deformation Fracture

2d Cheese

d Fc

Cutting wire

Plastic Deformation B Fracture

FIGURE 4.17 Schematic of cutting cheese with a blade (left) and wire of diameter d (right). (After Luyten, 1988; Kamyab et al., 1998.)

the stored and flow energies are limited. During wire cutting, it can be assumed that only the material in the vicinity of the wire undergoes plastic deformation. The total energy during cutting may be considered to comprise of three major components (Atkins and Vincent, 1984): friction, flow, and fracture. The net energy balance during slicing or cutting may be written following the form of Equation (4.7) (Atkins and Mai, 1985; Luyten, 1988; van Vliet et al., 1991):

U1 = U2 + U3 + U f + U d

(4.20)

where U1 = total energy; U2 = stored energy; U3 = dissipated energy; Uf = dissipated energy due to fracture; and Ud = dissipated energy due to plastic deformation, curling, etc. When cutting a sample of width B, with a wire diameter of d at a cutting speed v, the total energy input to the sample during time t is:

U1 = Fc vt

(4.21)

where Fc = cutting force, the constant force obtained on the force–time curve (Figure 4.18). This energy is used primarily for fracture and plastic deformation. Therefore,

Fc vt = γ s vtB + (U2 + U3 )2 dBvt

(4.22)

where γs = specific fracture energy (J/m2) and B = sample width. The surface energy γs can be replaced by Gc, the energy release rate (Williams, 1984). Therefore, when d = 0,

Gc =

( Fc ) d = 0 B

(4.23)

which can be obtained by extrapolating the Fc /B vs. d curve to d = 0 (Figure 4.19). Luyten (1988) and Kamyab et al. (1998) performed wire-cutting tests on natural

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FIGURE 4.18 Force–deflection diagram during wire-cutting of process cheese. Cutting force Fc is the constant force developed during the test. (After Kamyab et al., 1998.) 80 100 mm/min 70

Fc /B (J/m2)

60 10 mm/min

50 40

1 mm/min

30 20 10 0 0

0.1

0.2

0.3 0.4 0.5 Wire diameter (mm)

0.6

0.7

0.8

FIGURE 4.19 Effect of wire diameter and rate of cutting on cutting force for process cheese. The intercept of each line represent the fracture toughness of the cheese. (After Kamyab et al., 1998.)

and process cheeses. Their data are summarized in Table 4.6. The cheese type and cutting speed appear to have significant effect on the specific fracture energy, which is in the range of about 3 J/m2 to 10 J/m2. Luyten (1988) also reported a decrease in fracture energy as Gouda cheese matured, apparently due to casein breakdown as it aged. The value of fracture energy is considered to be on the order of the theoretical energy needed to break all chemical bonds in one plane, which is estimated to be 1 J/m2 (Gordon, 1978). For most materials, © 2003 by CRC Press LLC

TABLE 4.6 Specific Fracture Energy of Some Natural and Processes Cheeses Determined By Wire Cutting Tests Cheese Type

Cutting Speed (mm/min)

Gouda

Regular Processb

Light Processb

Mild Cheddarb

1 10 20 100

4.9 6.7 9.6 —

2.9 4.6 — 8.1

— 3.44 — —

— 5.3 — —

a b

a

From Luyten, 1988. From Kanyab et al., 1998.

the fracture energy is higher than this theoretical limit because of plastic deformation in the vicinity of fractured surfaces. The low fracture energy for cheeses is believed to be due to rather incomplete network throughout the cheese (Luyten, 1988). Brown et al. (2000) studied the effect of cutting speed and cheese temperature while cutting a mature Cheddar cheese using a knife blade mounted at a 45° angle to the sample. Their results of peak average cutting force (Figure 4.20) indicate expected trends — higher forces at higher cutting speeds and at lower temperatures. The effect of temperature is greater than that of the cutting speed. Atkins and Vincent (1984) remark that the angle the blade makes with the cutting surface is critical. At angles greater than optimum, the forces are higher due to energy expended in curling of the cut section. The cutting studies also allow measuring friction forces. Brown et al. (2000) measured the friction forces of the knife blade slicing the cheese. The trends of the friction forces are the same as that of the cutting force, i.e., friction force increases with cutting speed and decreases with cheese temperature (Figure 4.21). Kamyab et al. (1998) determined the coefficient of friction µ from the wirecutting force vs. deformation curve. This is based on the fact that the cutting force Fc should also sustain yield stress σy normal to the surface and frictional force µσy. Therefore,

Fc = Gc + (1 + µ ) σ y d B

(4.24)

where d = diameter of cutting wire. Therefore, the slope of Fc /B vs. d curve (Figure 4.19) is (1 + µ)σy. If σy is determined from another test (e.g., compression test), µ can be determined from wire-cutting data. The µ determined from friction tests, wire-cutting tests, and compression tests are comparable for different cheeses (Table 4.7). The friction force for slicing cheese with a blade (Brown et al., 2000) is higher than for cutting with a wire (Kamyab et al., 1998) by about an order of magnitude, mainly due to larger blade-to-cheese contact area during slicing. Of course, the © 2003 by CRC Press LLC

60

Cutting force (N)

50 40 30 20 10 0

−5

239 Cu ttin g s 105 pe ed (m

)

5

e tur

(°C

ra

pe

15

26

m/

s)

se

tem

ee

Ch

20

Friction force (N

30

)

FIGURE 4.20 Maximum cutting force as a function of cutting speed and cheese temperature during blade cutting of mature Cheddar cheese. (After Brown et al., 2000.)

10

Ch -5 ee se

0 239

te

5

m

pe

ra

/s)

m

105

re

d

ee

tu

( oC

15 )

26

ing

(m

sp

tt

Cu

FIGURE 4.21 Maximum friction force as a function of cutting speed and cheese temperature during blade cutting of mature Cheddar cheese. (After Brown et al., 2000.)

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TABLE 4.7 Comparison of Friction Coefficient of Different Cheeses Determined By Different Tests Cheese Type

Friction Test

Cutting Test

Compression Test

Regular process cheese Light process cheese Sharp Cheddar Mild Cheddar Process American 1 Process American 2

0.77–0.85 0.82–0.93 0.97–1.04 0.61–0.65 0.98–1.06 1.13–1.28

0.75 0.86 1.07 0.52 1.13 1.25

0.69 0.39 0.54 0.54 0.57 0.53

Source: From Kamyab et al., 1998.

differences are further exacerbated by cheese temperatures and composition (e.g., moisture content).

EYE/SLIT FORMATION AND GROWTH Small, round holes distributed throughout a cheese mass is a characteristic and desirable feature of Emmentaler (e.g., Swiss), Gouda, and Edam cheeses. These holes, known as eyes, are formed primarily from CO2 produced as propionic and citric acids are fermented by the starter organisms and from N2 dissolved in the cheese milk (Akkerman et al., 1989; Polychroniadou, 2001). Holes formed in other cheeses (e.g., Tilsit and Havarti) are not called eyes but still are considered typical of these varieties (Polychroniadou, 2001). However, holes present in Cheddar-type cheeses caused by some spoilage organisms producing CO2, H2, or H2S are an indication of a quality defect (Table 4.8). Even in cheeses where eyes or holes are expected and accepted, slits or cracks are formed under certain conditions. This is a quality defect. Biochemical and microbiological aspects of hole formation has been well researched (Zoon and Allersma, 1996; Akkerman et al., 1989; Polychroniadou, 2001). A nucleus is required in order for a hole to form. Small air bubbles (N2 in milk) attached to curd particles may form as nuclei along with some impurities and small mechanical openings. The nuclei grow into eyes due to diffusion of CO2. The size, number and distribution of eyes can be related to the time, quantity, intensity, and rate of CO2 production in cheese (Polychroniadou, 2001). Akkerman et al. (1989) discussed the mechanism of eye formation and growth in detail. From a fracture mechanics viewpoint, the formation of holes, slits, and cracks in cheese can be considered as controlled by the rheological and fracture properties of the cheese. Walstra (1991) presented a succinct discussion on the rheological foundation of eyes and slits. The driving force for hole growth is the differential gas pressure ∆P between the inside and outside of the hole. In Gouda-type cheeses, this is estimated to be on the order of 5 kPa to 10 kPa (Walstra, 1991). The hole growth, which can be measured in terms of the biaxial elongational strain rate (BESR), is dictated by the biaxial elongational viscosity (BEV). Therefore, © 2003 by CRC Press LLC

TABLE 4.8 Eyes in Different Cheese Types Cheese Type Dutch

Emmental

Havarti

Blue-veined

Cheddar

Appearance of Eyes

Cause (Organism)

Small and round Citrate fermentation (φ < 1 cm); (mesophilic lactococci and leuconostocs) smooth and shiny internal surface Lactate fermentation Large and round (thermophilic and meso(φ = 1–3 cm); smooth and shiny philic lactic acid and internal surface propionic acid bacteria) Small and irregular Mechanical and citrate fermentation (mesophilic lactococci and leuconostocs) Open structure; Mechanical and possibly irregular slits citrate fermentation (mesophilic lactococci and leuconostocs) Normally no holes; Mechanical and citrate fermentation (gas slits and cracks in defective cheeses forming starters and nonstarter lactic acid bacteria, e.g., lactococci)

Stage of Formation

Curd pH

Cheese Texture

Over-long ripening period

5.4

Flexible, pliable body

Over-long ripening period

5.4

Firm, flexible body

During manufacture and first weeks of ripening Mainly during manufacture

5.2

Firm, flexible body

4.7

Firm (friable) body

During manufacture and ripening

5.0

Short texture

Source: After Polychroniadou, 2001.

BEV =

BESR =

∆P BER

(4.25)

d (ln r ) dt

(4.26)

where r = radius of the hole at time t. If the rate of gas diffusion into the hole is higher, for a cheese of certain BEV, the hole growth will be faster. Due to the strain rate thinning nature of the cheese, at higher BESR, the BEV is lower, leading to a faster hole growth. However, the faster the growth of the hole, the faster the decrease in ∆P. It has been estimated that the BESR is on the order of 10–6 s–1 and rapidly decreases during the hole growth (Akkerman et al, 1989). In the event that ∆P is greater than the fracture stress of the cheese, a slit will form and progress until the slit area grows sufficiently to lower the ∆P below the fracture stress. Luyten (1988) estimated a fracture stress of about 6 kPa at a strain rate of 10–6 s–1 based on compression tests on Gouda cheese in the strain rate range of 0.001 to 0.1 (Figure 4.22). Walstra (1991) questioned such an estimate because hole growth © 2003 by CRC Press LLC

1-week-old, pH=4.94

Fracture stress (kPa)

100

2-week-old, pH= 5.24

10

10−6

10−5

10−4

10−3 10−2 Strain rate (1/s)

10−1

100

FIGURE 4.22 Fracture stress as a function of strain rate for Gouda cheese. Dotted line extrapolates fracture stress to a strain rate of 10–6 s–1 prevalent during eye or slit formation. (After Walstra 1991. With permission.)

is an elongational property, the linear extrapolation may not hold in the low strain rate range, and the temperature at which the testing was done (20°C) was higher than the refrigerator conditions at which the cheese is normally aged. Nonetheless, the estimated fracture stress is well within the ∆P estimated by Walstra (1991). There are indications that low cheese pH (<5.2) may be the key factor in determining the tendency for cheese to develop eyes or slits. Walstra (1991) also points out that there may be a pH optimum around which conditions are detrimental with respect to eye formation.

REFERENCES Akkerman, J.C., P. Walstra, and H.J.M. van Dijk. 1989. Holes in Dutch-type cheese. 1. Conditions allowing eye formation. Netherlands Milk and Dairy Journal 43:453–476. Anderson, T.L. 1995. Fracture Mechanics — Fundamental and Applications, 2nd ed. Boca Raton, FL: CRC Press. Andres, C. 1983. Natural cheese in new form provides improved aesthetic and functional qualities. Food Processing 44(12):64,66. Antonissen, P. 1986. Method and apparatus for slicing a product in accordance with its anticipated weight distribution. Patent No. US4572044. Apostopoulos, C. and Marshall, R.J. (1994). A Quantitative method for determination of shred quality of cheese. Journal of Food Quality 17:115–128. Atkins, A.G. and Y.-M. Mai. 1985. Elastic and Plastic Fracture. Chichester, U.K.: Horwood Publishers. Atkins, A.G. and J.F.V. Vincent. 1984. An instrumented microtome for improved histological sections and the measurement of fracture toughness. Journal of Materials Science Letters 3:310–312. Barritt, S. 1985. Slicing up the cheese market. Food Manufacture 60(6):41.

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Broek, D. 2001. Practical application of fracture mechanics — fracture control, in Handbook of Materials Behavior Models 2, J. Lemaitre, Ed., San Diego: Academic Press, pp. 661–671. Brown, T. et al. 2000. Improving food cutting systems. Food and Drink 2000: Processing Solutions for Innovative Products. Warwickshire, U.K.: Institution of Chemical Engineers. BSI. 1991. Guidance on methods for assessing the acceptability of flaws in fusion welded structures. PD6493. London: British Standards Institution. Bui, H.D. and A. Ehrlacher. 1981. Propagation of damage in elastic and plastic solids, in Advances in Fracture Mechanic, Vol. 3, D. Francois, Ed., New York: Pergamon Press, p. 533. Charalambides, M.N., J.G. Williams, and S. Chakrabarti. 1995. A study of the influence of aging on the mechanical properties of Cheddar cheese. Journal of Material Science 30(16):3959–3967. DMI. 2002. Putting the flavor back in reduced-fat cheese. Dairy Dimensions 5(1):1. Dubuy, M.M. 1980. The French art of shredding cheese. Food Processing Industry 49:52–53. Francois, D. 2001. Brittle fracture, in Handbook of Materials Behavior Models 2, J. Lemaitre, Ed., San Diego: Academic Press, pp. 566–576. Gordon, J.E. 1978. Structures, or Why Things Don’t Fall Down. London: Penguin Books. Gordon, J.E. 1968. The New Science of Strong Materials. London: Penguin Books. Griffith, A.A. 1920. The phenomena of rupture and flow in solids. Philosophical Transactions, Series A 221:163–198. Izutsu, T. et al. 1991. Rheological properties of fibrous structured cheese. Nippon Kagaku Kaishi 8:1059–1065. Kamyab, I., S. Chakrabarti, and J.G. Williams. 1998. Cutting cheese with wire. Journal of Materials Science 33:2763–2770. Langley, K.R., A. Martin, and S.L. Ogin. 1994. The effect of filler volume fraction on the fracture–toughness of a model food composite. Composites Science and Technology 50(2):259–264. Lemaitre, J. 2001. Handbook of Materials Behavior Models, Vol. II, Failures of Materials. New York: Academic Press. Luyten, H. 1988. The Rheological and Fracture Properties of Gouda Cheese. Ph.D. thesis, Wageningen Agricultural University, Wageningen, The Netherlands. Luyten, H. and T. van Vliet. 1996. Effect of maturation on large deformation and fracture properties of (semi-)hard cheeses. Netherlands Milk and Dairy Journal 50:295–307. Ni, H. and S. Gunasekaran. 1998. Computer vision method for determining length of shredded cheese. Artificial Intelligence Review. 12:27–37. Ni, H. and S. Gunasekaran. 2002. Image Processing Algorithm for Cheese Shred Evaluation. Journal of Food Engineering (submitted). Polychroniadou, A. 2001. Eyes in cheese: a concise review. Milchwissenschaft 56(2):74–77. Pomerantz, J. and P. Feeney. 1985. Slicing device for food stuffs [e.g., cheese]. Patent No. US4516458. Riande, E. et al. 2000. Polymer Viscoelasticity — Stress and Strain in Parctice. Marcell Dekker, Inc., New York. pp. 616–638. Schirrer, R. 2001. Damage mechanisms in amorphous glassy polymers, in Handbook of Materials Behavior Models 2, J. Lemaitre, Ed., San Diego: Academic Press, pp. 488–499. Van Vliet, T., H. Luyten, and P. Walstra. 1991. Fracture and yielding of gels, in Food Polymers, Gels and Colloids, E. Dickinson, Ed., Cambridge, England: The Royal Society of Chemistry, pp. 392–403. Walstra, P. 1991. Rheological foundation of eye or slit formation, in Bulletin of the IDF, No. 268, Rheological and Fracture Properties of Cheese, Brussels, Belgium: International Dairy Federation.

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Walstra, P. and van Vliet, T. 1982. Rheology of cheese. Bulletin of the IDF, No. 153. Brussels, Belgium: International Dairy Federation. Williams, J.G. 1984. Fracture Mechanics of Polymers. Chichester, England: Ellis Harwood Limited Publishers. Williams, J.G. and M.J. Cawood. 1990. European group on fracture-kc and Gc method for polymers. Polymer Testing 9(1):15–20. Zoon, P. and D. Allersma. 1996. Eye and crack formation in cheese by carbon dioxide from decarboxylation of gluconic acid. Netherlands Milk and Dairy Journal 50(2):309–318.

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5

Linear Viscoelasticity of Cheese

The rheological behavior of cheese is viscoelastic. A viscoelastic material exhibits both elastic solid and viscous liquid behavior simultaneously under a wide range of conditions. An elastic solid stores mechanical energy during deformation and reverts to its original form (shape and size) upon removal of external forces; a viscous liquid dissipates such energy. Though no material is a “true solid” or a “true liquid,” a steel spring or rubber band is a good example of an elastic solid, and water is an ubiquitous example of a viscous liquid. The simplest type of viscoelastic behavior is linear viscoelasticity, where the measured properties are independent of magnitude of the input variable (Ferry, 1980). This type of behavior is observed when the deformation is so small that the structure of a material is disturbed only to a negligible extent. The small amplitude oscillatory shear (SAOS) measurements are commonly used to study the linear viscoelasticity of cheese and other foods. SAOS is a special subset of the dynamic mechanical analysis (DMA). DMA is used to measure mechanical properties of materials while they are subjected to an oscillating strain (or stress), usually applied sinusoidally. When DMA accounts for temperature effects, it is termed “dynamic mechanical thermal analysis” (DMTA). DMA and DMTA are extremely useful material characterization techniques. The main feature of SAOS tests is that, due to small strain (and stress) used, they can be considered as objective and nondestructive tests suitable for probing material structure and structure development during different processes. We have recently reviewed the use of SAOS technique in food and dairy research (Gunasekaran and Ak, 2000; Ak and Gunasekaran, 2001). SAOS measurements allow determination of shear moduli, (i) storage modulus (or elastic modulus) and (ii) loss modulus (or viscous modulus) as a function of test frequency (ω) in the linear viscoelastic (LVE) region of the test material. The storage modulus G′(ω) is a measure of the energy stored and recovered per cycle, and the loss modulus G″(ω) is a measure of the energy dissipated or lost as heat per cycle of imposed deformation (Ferry, 1980). In addition, phase angle (or mechanical loss angle) δ and loss tangent tan δ, relative measures of the ratio of viscous to elastic component, can be determined.

MATHEMATICAL RELATIONS IN LINEAR VISCOELASTICITY In dynamic testing, a sample is subjected to an alternating strain, and the resulting stress is measured. Most often the form of the alternating strain is sinusoidal, and the deformation is usually in shear mode. In food rheology, dynamic measurements

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are rarely made in compression mode (e.g., Weipert, 1997). The amplitude of strain is usually chosen to be small (often less than 1% for cheese) so that the stress response is proportional to the input strain amplitude, or, in other words, the response is in the LVE region. Then the material properties, G′(ω), G″(ω), and tan δ are determined. Applying a sinusoidal stress and measuring the resulting strain is another way to conduct dynamic measurements. In principle, measurements in an LVE region will yield the same result regardless of how it is performed. In actuality, there may be some differences due to the accuracy of measurements with strain-controlled vs. stresscontrolled instruments. This aspect will be briefly discussed later in this chapter. In SAOS experiments, the material is subjected to a sinusoidal shear strain of constant amplitude γο and frequency ω so that the shear strain varies with time as: γ (t ) = γ o sin(ω t )

(5.1)

When the strain amplitude is sufficiently small the stress response will also be sinusoidal: σ(t ) = σ o sin(ω t + δ)

(5.2)

where, σο is the stress amplitude. Using a trigonometric identity* Equation 5.2 can alternatively be written as:

[

]

σ(t ) = σ o sin(ω t) cos(δ) + cos(ω t ) sin(δ)

(5.3)

Multiplying the right hand side of Equation (5.3)by (γο /γο) and using the following relations G ′( ω ) =

σo cos(δ) γo

(5.4)

G ′′(ω ) =

σo sin(δ ) γo

(5.5)

Equation 5.3 can be rewritten as: σ(t ) = γ o [G ′(ω ) sin(ωt ) + G ′′(ω ) cos(ωt )]

* sin(A + B) = sin(A) cos(B) + cos(A) sin(B)

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(5.6)

The ratio (σo /γo) in Equations 5.4 and 5.5 is the magnitude of the complex modulus (G*) and it is related to the storage (G′) and loss (G″ ) moduli by the following expression: G * = (G ′) 2 + (G ′′) 2

(5.7)

Quite often the dynamic response of materials is expressed in terms of the loss tangent defined as: tan δ(ω ) =

G′′(ω ) G ′(ω )

(5.8)

For a Hookean (ideal elastic) solid the loss angle δ = 0, so all the energy is stored (i.e., recoverable). For a Newtonian (ideal viscous) liquid δ = π/2, so all the energy is dissipated (i.e., lost) during deformation. The corresponding values for tan δ are 0 and ∞. For a viscoelastic material, 0<δ<π/2, and thus the relative amount of energy stored or dissipated is determined from the magnitude of phase angle. The typical SAOS responses for these materials are illustrated in Figure 5.1. An increase in tan δ indicates that the material is reacting to an external stress in a relatively more viscous and less elastic manner. For instance, tan δ is used as a measure of the dynamic character (life–time) of protein–protein bonds in rennet Hookean Solid

γ0

Newtonian Liquid

σ0

ωt

ωt

δ = π/2 Strain input Stress output

Strain input Stress output

Viscoelastic Material

ωt

0< δ < π/2 Strain input Stress output

FIGURE 5.1 Sinusoidal strain input and typical stress–strain responses of elastic solid, viscous liquid and viscoelastic materials.

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casein gels (van Vliet et al., 1989). When, G′ = G″, tan δ = 1 and the modulus value at this point is called the “crossover modulus.” At tan δ = 1, the material is equally liquid and solid. When tan δ<1, the material is more solid-like, and when tan δ>1, the material is more liquid-like. Hence, change in tan δ value around 1 signifies that the state of the material is crossing over from predominantly solid to liquid or vice versa. Another way to present results of oscillatory experiments is to use complex viscosity η*, which is related to its viscous and elastic components, η′ and η″, as follows: η* =

(η′)2 + ( η′′)2

(5.9)

The real part of the complex viscosity (i.e., η′) is called the dynamic viscosity, and for a Newtonian fluid, it corresponds to shear viscosity. The complex viscosity is also related to the complex modulus as given below: η* =

1 G* ω

(5.10)

Furthermore, we can write the loss tangent in terms of the components of complex viscosity: tan δ(ω ) =

η′ η′′

(5.11)

The physical significance of these dynamic quantities may be appreciated better in terms of energy stored and dissipated during sinusoidal deformation. The energy, or work, is given by (Ward and Hadley, 1993): W = ∆E =

∫ σ dγ = ∫ σ γ˙ dt

(5.12)

It has been shown (Ferry, 1980; Tschoegl, 1989) that the average energy per unit volume stored in a cycle is given by: Estored (ω ) =

1 2 γ G ′(ω ) 4 o

(5.13)

The energy dissipated in a complete cycle is given by: Edissipated (ω ) = π γ o 2 G ′′(ω )

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(5.14)

In a similar fashion, the stored energy is proportional to η″, and dissipated energy is proportional to η′ as shown in Equations (5.15) and (5.16): 1 2 γ ω η′′ 4 o

(5.15)

Edissipated (ω ) = π γ o 2 ω η′

(5.16)

Estored (ω ) = and

TYPES OF SAOS MEASUREMENTS There are four major experimental variables in any dynamic test: strain (or stress), frequency, temperature, and time. Thus, different types of dynamic tests can be set up changing one or more of these experimental variables. The commonly performed tests are: strain (or stress) sweep; frequency sweep; temperature sweep, and time sweep (gel cure). Each of these tests serves to fulfill a certain objective. Depending on the input variable, two types of rheometers are commercially available: “controlled strain” (or controlled strain rate) with torque measurement and “controlled stress” with angular motion measurement. Detailed discussion of such rheometers is outside the scope of this book, but interested readers can find additional information elsewhere (Macosko, 1994). We shall only mention here that with most of the commercial rheometers it is possible, through the versatility of the operating software, to conduct measurements in either the constant stress or the constant strain mode. This, however, may have some problems related to the precision of dynamic measurements. Bafna (1996) examined the precision of complex viscosity measurements in the constant stress and constant strain modes. One of the important findings of Bafna’s work is that constant stress measurements provide improved precision at lower frequencies, whereas constant strain measurements are more precise at higher frequencies.

STRAIN (OR STRESS) SWEEP In this type of oscillatory tests the moduli are measured as a function of increasing strain while the frequency is fixed, for instance, at 1 Hz (Figure 5.2). Usually, the objective of a strain sweep test is to determine the critical point beyond which the dynamic shear moduli (G*, G′, G″) become dependent on the input variable, strain. In other words, it is carried out to determine the limits of linear viscoelasticity. The strain sweep test is the first step in dynamic mechanical analysis and always performed prior to a frequency sweep test in order to specify the strain level for frequency sweeps. In case of controlled stress dynamic rheometers, a stress sweep is performed and serves the same purpose of identifying the limit of LVE region.

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0.024

−0.024

0

0.2

0.4

0.6

0.8

0

−0.024

1

Strain (-)

0

0.024

amplitude: 1%

amplitude: 0.5% Strain (-)

Strain (-)

0.024

0

0.2

0.4

0.6

0.8

1

0

−0.024

Time (s)

Time (s)

amplitude: 2%

0

0.2

0.4

0.6

0.8

1

Time (s)

Complex modulus (kPa)

90 80 70 60

LVE limit

50 40 0

0.5

1

1.5

2

Strain amplitude (%)

FIGURE 5.2 Schematic representation of a strain sweep test at constant frequency (e.g., 1 Hz) with an example of response in terms of complex modulus. (LVE stands for linear viscoelasticity.) (After Ak and Gunasekaran, 1996.)

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FREQUENCY SWEEP The frequency sweep is probably the most versatile rheological test to characterize viscoelastic behavior of materials. In this test, a sinusoidal strain (or stress) of fixed amplitude is imposed on the material and the dynamic moduli are determined over a wide range of frequencies (Figure 5.3). The resultant plot is also known as the “mechanical spectrum” of the material. The strain amplitude must be selected with care and, under all conditions, should be less than the strain limit of linear viscoelasticity. Contemporary rheometers are capable of measuring dynamic properties at a wide range of frequencies, typically from 0.01 Hz to 100 Hz. With advanced rheometers one can even conduct oscillatory measurements at frequencies as low as 10–5 Hz. With such instruments, the low frequency selection is dictated mainly by the stability of the sample and the researcher’s patience in performing long dynamic measurements. For instance, it takes nearly 28 h to complete one oscillation cycle at 10–5 Hz. An efficient way to shorten the total experimental time is to use, whenever applicable, the time–temperature superposition (TTS) procedure, which will be discussed later. In the high-frequency range, the measurements have been limited due to inertia effects. However, performance improvements at high frequencies are reported for new rheometers (Eidam et al., 2001). When using a controlled stress instrument, test software allows setting a “target strain,” which should be below the strain amplitude limit of LVE region. One of the enhancements in rheometry is the introduction of multiwave oscillation mode, where the sample is exposed simultaneously to oscillations at two or more frequencies (Holly et al., 1988; Anon, 2002a; Anon, 2002b). Multiwave oscillation mode reduces experimental time, as compared to running several experiments each at a different frequency, while providing the same standard dynamic parameters. This is a significant advantage especially when large numbers of tests must be done in a limited time (e.g., quality-control testing). It is important that the sum of strain amplitudes, which are additive in multiwave oscillation, remains within the LVE region of the material (Holly et al., 1988). Multiwave oscillation is particularly useful for materials with transient structure, and therefore it may be suitable for studying milk gelation.

TEMPERATURE SWEEP The temperature-sweep test involves measurement of dynamic moduli over a temperature range at constant frequency and constant strain (or stress) amplitude. Temperature sweeps can be carried out in a ramp or stepwise fashion (Figure 5.4). If the ramp mode is employed, then the rate of temperature change and frequency of oscillation must be selected carefully. For instance, if one conducts the test at 1 Hz and 1°C/min, then the temperature change per cycle (0.017°C) can be considered insignificant. Temperature sweeps are essential to investigate phase transitions. For example, during a temperature sweep, the temperature at crossover modulus (G′ = G″) is considered to signify the beginning of gel forming (or gel melting) temperature (Gunasekaran and Ak, 2000). During cheese melting, the temperature at crossover modulus is an indication of the “softening point” of cheese, the onset

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5 Hz

2 Hz

Strain

Strain

Strain

1 Hz

0

0.5

1

0

0.5

Time (s)

1

0

Time (s)

0.5 Time (s)

1

Complex modulus (kPa)

1000

100 0.1

1

10 Frequency (rad/s)

100

1000

FIGURE 5.3 Schematic representation of a frequency sweep test at constant strain amplitude (e.g., 0.5%) with an example of response in terms of complex modulus. (After Ak and Gunasekaran, 1996.)

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Step change

Example: Ramp rate = 5°C/min

Temperature

Temperature

Ramp change

log Storage modulus (Pa)

Time

Time

7 6 5 4 3 2 1 0 0

20

40 60 Temperature (°C)

80

100

FIGURE 5.4 Schematic representation of a temperature sweep test (in ramps or steps) with an example of response in terms of storage modulus. (After Wetton and Marsh, 1990.)

temperature of rapid melt and flow (Gunasekaran et al., 2002) (see Chapter 8 for details). This is illustrated in Figure 5.5 for Mozzarella cheese. The temperature sweep test is also helpful to detect changes that would occur at rather high, and possibly inaccessible, frequencies if measurements were made at room temperature.

TIME SWEEP Time-sweep measurements are often made isothermally at constant strain (or stress) amplitude and frequency (Figure 5.6). It is also known as a “gel cure” test, and may be performed along with a temperature-sweep program to examine changes in rheological behavior due to combined effects of time and temperature. It is common practice to set the oscillation frequency at 1 Hz. Time-sweep measurements are very useful in monitoring the build-up or breakdown of structure. For instance, the evolution of milk gel (i.e., firming) after the addition of rennet or another coagulant is usually monitored by time-sweep measurements of viscoelastic parameters, G′, G″, and tan δ (Gunasekaran and Ak, 2000; Renault et al., 2000; Singh and Waungana, 2001). The time at which crossover modulus is observed during gel cure can indicate gelation time in systems that gel at isothermal conditions. An example of this is presented in Figure 1.4 (Chapter 1) for determining the gelation time of rennetted milk gel.

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100 Mozzarella cheese (10-day-old) G¢ Modulus (kPa)

10

1

G¢¢

Crossover modulus

Softening point 0.1 20

30

40

50

60

70

80

Temperature (°C)

FIGURE 5.5 Temperature at crossover modulus correspond to cheese softening point. (After Gunasekaran et al., 2002.)

TIME-TEMPERATURE SUPERPOSITION Rheological properties of cheese are strongly dependent on temperature. Thus, measurements at different temperatures are made for full characterization of the cheese behavior. For some materials it is well known that the linear viscoelastic properties measured at several temperatures can be represented on one curve, called the “master curve,” at a reference temperature by means of time–temperature superposition (TTS) procedure (Ferry, 1980; Dealy and Wissbrun, 1989; Honerkamp and Weese, 1993). The resulting master curve will have a largely expanded time or frequency scale, which is very valuable for characterization of material behavior at times or frequencies that are not directly accessible with a single instrument or measurement technique. Materials for which TTS procedure is applicable are termed “thermorheologically simple.” Although cheese is less likely to be a thermorheologically simple material due to its multi-component nature and thermal phase changes, there have been successful applications of TTS (or more correctly frequency–temperature superposition) to cheese (Taneya et al., 1979; Subramanian and Gunasekaran, 1997b). Whenever TTS is applicable to foods it makes it possible to estimate long-term viscoelastic properties from the short-term data. This is significant considering that lengthy experiments with foods are hampered due to considerations for sample stability (i.e., physical, chemical, and enzymatic alterations). Time–temperature or frequency–temperature equivalence simply implies that the viscoelastic properties at one temperature are related by a constant ratio (i.e., the

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Strain (-)

Time (h)

Storage modulus, G′ (Pa)

1000

100

Unheated Heated (80°C, 30 min)

10

1

0

2

4

6

8

10

12

14

16

Time (h) after GDL addition

FIGURE 5.6 Schematic representation of an isothermal time-sweep test at constant frequency and amplitude with an example of response for milk gelation at 40°C by glucono-δ-lactone. (After Lucey and Singh, 1998.)

shift factor) to the corresponding property at the reference temperature. Ferry (1980) gives three criteria for the applicability of TTS procedure: 1. The shapes of adjacent curves should match closely. 2. The same values of empirical shift factors (aT) must superpose all the viscoelastic functions. 3. The temperature dependence of aT must have a reasonable form consistent with experience (e.g., Arrhenius-type or WLF type relation). If viscoelastic data are not superposable, it is often taken as an indication of two-phase behavior or a phase change caused by the changing temperature. Such materials are termed “thermorheologically complex,” for which the shift factor becomes a function of time in addition to temperature. Furthermore, chemical changes can also interfere with the superposition procedure (Gordon and Shaw, 1994). Several companies are making different rheometers of varying sophistication (and cost) to be used in routine quality control applications, or in advanced researchand-development activities. In most cases, these instruments are furnished with

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user-friendly software to control the operation of the instrument, and to collect and analyze the data. In advanced systems, the TTS module will be integrated into the software package so that the user can readily carry out the superposition of transient or dynamic rheological data. We must mention, for the readers who are savvy computer programmers, the book by Gordon and Shaw (1994) that gives the full source code of computer algorithms for performing rheological computational tasks such as TTS. In the example in the section on Mozzarella chesse, we will illustrate the TTS procedure using a spreadsheet program.

APPLICATION OF SAOS IN CHEESE RHEOLOGY The viscoelastic behavior of cheese is mostly dictated by the properties of the principal component forming the continuous network, that is the protein network. The other main constituents are fat and moisture, which contribute to the overall behavior by modifying the properties of the protein network. There are, of course, numerous other factors (e.g., proteolysis, temperature, pH, salt content) that greatly influence the viscoelastic behavior of cheeses (Walstra et al., 1987a; Luyten, 1988). As described earlier, SAOS measurements enable quantification of elastic and viscous effects simultaneously. Elastic response in cheese is primarily due to the protein–protein bonds. The viscous dissipation in cheese may be due to flow of the matrix material (i.e., protein), flow of liquid through the matrix, and movement of other structural elements relative to each other, causing friction (Luyten et al., 1991b).

LINEAR VISCOELASTIC REGION

OF

CHEESES

Measurements in LVE region are most useful in enhancing our understanding of cheese structure (bond formation and subsequent alterations). It is therefore important to correctly determine the LVE region of the sample. The SAOS strain (or stress) sweep test offers a rapid and accurate way to determine the critical limits of strain (or stress) for the LVE region. Shown in Figure 5.7 is an example of a strain-sweep test made on Mozzarella cheese to determine the LVE strain limit. It is evident that the critical strain of low-moisture, part-skim Mozzarella cheese is about 0.5%. It is further seen that a higher strain limit is observed at 0.1 Hz than at 1 Hz test frequency. Tchir and Saucier (1991) reported a strong dependence of the linear viscoelastic strain limit for a polymeric material on the test frequency. The linear range for this material ended at approximately 10% strain for 100 rad/s (15.9 Hz), but it extended much beyond 100% strain for 0.1 rad/s (0.0159 Hz). It is worth remarking that these strain limits of linear viscoelasticity are much higher than those observed for cheese and other foods. Taking advantage of the inverse relation between the linear strain limit and frequency, Tchir and Saucier (1991) suggested the variable strain technique to improve the quality of data, particularly at low frequencies where the torque noise may dominate. In this technique, the strain amplitude is manually adjusted so that a measurable torque is obtained while remaining in the domain of linear viscoelasticity.

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Complex modulus G* (kPa)

120 0.1 Hz 1 Hz

100 80 60

LVE

40 20 0

critical strains 0

0.5

1 1.5 Shear strain (%)

2

2.5

FIGURE 5.7 Linear viscoelastic region (LVE) for Mozzarella cheese determined at room temperature for two frequencies. (After Ak and Gunasekaran, 1996.)

Storage modulus (kPa)

1000 10°C 20°C 30°C 40°C 50°C 60°C 70°C

100

10

1 0.01

0.1 Shear strain (%)

1

FIGURE 5.8 Shear strain dispersion of storage modulus for 1-week-old low-moisture, partskim Mozzarella cheese tested at 1.5 Hz. (After Subramanian and Gunasekaran, 1997a.)

Subramanian and Gunasekaran (1997a) have conducted a detailed study on the variation of linear viscoelastic range of Mozzarella with age and temperature. They found that the region of linear viscoelasticity decreased with increasing cheese age and test temperature (Figure 5.8). A critical strain of 0.05% was determined for 12-week-old, low-fat, part-skim Mozzarella cheese at 70°C. A compilation of the critical strain values for the linear viscoelastic region of various cheeses is presented in Table 5.1. As evident from this table, for the majority of cheeses the linear viscoelastic strain limit is 1% or less. The exception is the range given by Luyten et al. (1991b) as 3–5% for Gouda cheese. The table serves only as a guide and does not eliminate the need to determine LVE region for the cheese according to the experimental conditions. It is important to recall that the limits of LVE vary with factors like temperature. Therefore, if tests are to be performed over a range of experimental conditions, one should use the smallest critical strain limit for all tests so that the results can be analyzed together.

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TABLE 5.1 Strain Limits of Linear Viscoelastic Region for Various Cheeses Cheese

Critical Straina (%)

Cheddar Cheddar-type Cheese curd Feta Gouda Gouda Imitation Mozzarella Mozzarella Mozzarella Mozzarella Mozzarella Mozzarella Process Process Quarg Several cheeses

0.55 0.6 0.1–0.3 <1 1 1 1 1 0.5 0.5 0.05–1 0.5 1 0.35–0.7 0.70 1 0.4

Reference Nolan et al., 1989a Guinee et al., 2000 Ramkumar et al., 1998 Wium and Qvist, 1997 Dewettinck et al., 1999 Messens et al., 2000 Mounsey and O’Riordan, 1999 Hsieh et al., 1993 Nolan et al., 1989b Ak and Gunasekaran, 1996 Subramanian and Gunasekaran, 1997a Diefes et al., 1993 Yun et al., 1994 Sutheerawattananonda and Bastian, 1998 Nolan et al., 1989a Kelly and O’Donnell, 1998 Drake et al., 1999

a

In some occasions, the value given in this column represents the strain actually used in the experiment rather than the true limit of linear viscoelasticity.

CHEDDAR CHEESE There is considerable interest in the properties of cheese as a function of temperature since the amount of cheese used as an ingredient in prepared foods has been rising, especially in the U.S. (Mann, 2000). Since prepared foods often undergo thermal processing before consumption, it is important to know how cheese behavior changes with heating. The properties of cheeses during refrigerated and frozen storage may be studied by cooling or freezing the sample. Initial investigation of dynamic properties of cheese as a function of temperature appears to be made by Taneya et al. (1979). They measured viscoelastic properties of Cheddar, Gouda, and processed cheese. Experimental conditions are given in Table 5.2 and chemical composition in Table 5.3. We note at this point that experimental conditions of each pertinent report examined in this chapter are presented in Table 5.2 with no further reference at the actual point of discussion. The temperature dispersion of the loss tangent for Cheddar cheese is plotted in Figure 5.9. One or more peaks are discernible in these plots for Cheddar cheese. The loss tangent peak locations for Cheddar cheese are dependent on the maturation period. It is worth to note that the dynamic response of cheese is both qualitatively and quantitatively different below and above 35°C. For example, the loss tangent of 5-month-old Cheddar cheese is the highest and lowest below and above 35°C, respectively. A few important points not addressed by Taneya et al. are (a) influence

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TABLE 5.2 Experimental Conditions Used in Small Amplitude Oscillatory Shear Measurements on Cheese

Cheese

Equipment

Sample Dimensions (mm)a

Storage Conditions

Test Temperature (°C)

Gouda: 1, 3, 5 Sanki Eng. Co. Sample Natural From –5 to 95 mo old; Ltd. IRCLcontainer: cheeses Cheddar: 1, SL type: 15 mm in matured at 3, 5 mo old; vertical diameter and 13°C and Process: hard oscillation depth; tempered at and soft types oscillating 5°C for rod: 3 mm 2 weeks; diameter process penetrating cheese stored 12.5 mm into at 5°C the specimen Cheddar: mild Polymer — — 0–100 and mature LaboratoriesDMTA Cheddar Rheometrics D = 25 — ~22–60 Pasteurized Dynamics H = 4 or 8 Process Analyzer 700 American Parallel Plate Cheese

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Test Frequency (Hz)

Strain Amplitude (%)

Contact Surface

Notes

Ref.

3, 10, 30, 100

Vertical amplitude: 0.1 mm

No mention of Samples taken from sample bonding central part of or serrated natural cheeses to surface avoid moisture variation

Taneya et al., 1979

1

—

—

—

Wetton and Marsh, 1990

0.0159–15.9

0.55–0.70

Specimens bonded to pitted plates with cyanoacrylate

Initial force of 100 g Nolan et al., applied to ensure 1989a bonding

TABLE 5.2 (continued) Experimental Conditions Used in Small Amplitude Oscillatory Shear Measurements on Cheese

Cheese

Equipment

20-wk-old Cheshire 60-wk-old Cheshire 60-wk-old Cheddar

Cheddar from pasteurized or raw milk

Cheddar

Rheometrics Dynamics Analyzer 700, 0–200 g–cm torque transducer, Parallel Plate TA Instruments Carri-Med CSL100, Parallel Plate

Sample Dimensions (mm)a D = 25 mm H = 4 mm

Commercial, Tempered 5 h prior to tests

D = 20 mm Pasteurized: H = 2, 5, and 19, 240, and 10 m (10 mm 470 days; was selected) raw: 246 and 475 days, both at 5°C

Rheometrics D = 60 mm 8400 fluid H = 1–2 mm spectrometer, Parallel Plate

Cheddar Haake CV20, (2- and Parallel Plate 24-week-old)

Storage Conditions

D = 20.4 H = 3.6

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Ripened at 7°C for 4 months in packages vacuumed —

Test Temperature (°C)

Test Frequency (Hz)

Strain Amplitude (%)

20, except for η* Strain and Strain sweep: measurements temperature 0–20; between sweeps:0.159 temperature 20 and 40 sweep: 2.5

Contact Surface Cheese samples bonded to the plates with cyanoacrylate

Notes Heating rate: 2°C/min

Ref. Tunick et al., 1990

25 for torque Torque sweep: Torque sweep: A special rough sweep; 10, 15, 4; frequency 0–1000 µN m; upper plate 25, 35 for sweep: frequency with 80 µm frequency 0.1–10 sweep: teeth sweep 700 µN m

25–90

25–60 on heating; 60–25 on cooling

0.159

0.1

1

0.5

A custom-made Rosenberg plastic et al., 1995 compartment was used to prevent drying and maintain consistent sample temperature No mention of Heating rate: Ustunol et al., sample bonding 2°C/min; fat 1994 or serrated content: from <1% surface to 34.3% —

Heating and cooling Venugopal and rate:1°C/min; gap Muthukumarsetting: 3.5 mm; fat appan, 2001 content: 8.2–28.4%

Cheddar type

TA Instruments Carri-Med CSL500, Parallel Plate

Cheddar

D = 40 H=2

20–90

1

0.6

Serrated plates

Tempering 15 min and equilibration 3 min at 20°C; heating rate: 3°C/min; fat content:1.3–30.6%

Physica D = 30 MC20/UM H=3 Parallel Plate, Stresscontrolled mode

Vacuum wrapped and stored first at 4°C 30 days and then at 7°C up to 190 days Vacuumsealed in plastic bags and stored 3 months at 7.2°C

20

0.05–20

—

Normal plates

Cheddar

Physica MC20/UM Parallel Plate, Stress controlled mode

D = 30 H=3

Vacuumsealed in plastic bags and stored 3 months at 7.2°C

20

0.05–20

—

Normal plates

Cremoso Argentino

Haake RV20, Parallel Plate

—

Ripened 20 days at 5°C and 80% relative humidity

30

0.1–9.6

5

Normal plates

Full fat, reduced fat Ma et al., 1996 with or without lecithin; 5-min relaxation after sample loading; for frequency sweeps: 2 kPa 1 carbohydrate- and Ma et al., 1997 2 whey-based fat mimetics are used; 5-min relaxation after sample loading; for frequency sweeps: 1 kPa Sample dimensions Zalazar et al., are not specified 2002

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Guinee et al., 2000

TABLE 5.2 (continued) Experimental Conditions Used in Small Amplitude Oscillatory Shear Measurements on Cheese

Cheese

Equipment

Sample Dimensions (mm)a

Storage Conditions

Test Temperature (°C)

Test Frequency (Hz)

Strain Amplitude (%)

Contact Surface

Gouda

Deer D = 15 Rheometer H = 9–10 PDR 81, Parallel plate

Ripening at 13–14°C; tempering 1.5 h in a closed tube

20

0.005–0.05

3–5

Plates covered with emery paper

Gouda

Bohlin CVO, D = 25 Parallel Plate H = 5

—

20

1

1

Serrated plates

Gouda

Bohlin CVO, D = 25 Parallel Plate H = 5

Salted 6 h at 14°C in brine, and vacuumpacked and stored 3 days at 14°C

14

1

1

Serrated plates

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Notes

Ref.

Upper plate made of Luyten et al., Perspex; wet cotton 1991b wool around sample to limit maximum weight loss in 45 min was 0.4%; cheese age: 1 week and 1, 3, and 6 months Stress amplitude Dewettinck sweep: 0–4000 Pa; et al., 1999 frequency sweep: 0.001–20; cheese: young (1–2 months), medium (6 months), old (12 months) Gap setting 4.5 mm Messens et al., (thus compression 2000 of 0.5 mm)

Natural LMPS Rheometrics Mozzarella Dynamics and Imitation Analyzer Mozzarella 700, Parallel Plate Part-skim Carri-Med Mozzarella Am. Inc. with protein Carri-Med fillers CSL100 Cone and Plate (4 cm diameter, 2° angle) LMPS Rheometrics Mozzarella RDS 7700 for 20°C tests; Bohlin Rheometer for 60°C; Parallel Plate LMPS Bohlin VOR Mozzarella Melt Rheometer, Parallel Plate LMPS and LFPS Mozzarella

Bohlin VOR, Parallel Plate

D = 25 H = 4 or 8

Stored at 4.4°C

25–70

0.0159–15.9

—

Refrigeration: 8–10°C

60–10

1

For 20°C: D = 25 H=4 For 60 °C: D = 25 H=2

Frozen: –20°C; Refrigerated: 5°C

20 and 60

Frequency 0.5 in 20 °C Serrated plates in Mineral-oil coating sweep: tests; 2.5% in 60°C tests of the exposed 0.0159–15.9 60°C tests. sample surfaces; for 20°C water activity tests; 0.1–20 controlled for 60°C tests

D = 30 H = 3.7

6–8°C up to 1 mo

10 and 20

D = 30 H = 3.5

4°C; 1 week to 12 week

Frequency sweep: 0.005–20; strain sweep: 0.1 and 1 Frequency sweep:0.314 and 125.6 rad/s

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10–70

0.5

1

Bonding sample 5-min relaxation to pitted after sample aluminum loading plates with cyanoacrylate Normal cone and Sample dimensions plate not specified; cooling from 60 to 10°C in 10 min

Strain sweep: up to 2.5; frequency sweep: 0.5

Normal plates

Strain sweep: 0.0001–0.01

Coarse sand paper glued to upper plate

Nolan et al., 1989b

Hsieh et al., 1993

Diefes et al., 1993

Mineral-oil coating Ak and of the exposed Gunasekaran, sample surfaces; 1996 wet paper towel to minimize drying Rheometer housed in Subramanian an environmental and chamber Guansekaran, 1997a, b

TABLE 5.2 (continued) Experimental Conditions Used in Small Amplitude Oscillatory Shear Measurements on Cheese

Cheese

Equipment

Sample Dimensions (mm)a D = 25 H = 2–2.5

Storage Conditions

Test Temperature (°C)

Test Frequency (Hz)

Strain Amplitude (%)

3 weeks at 4°C

22

Strain sweep: 1.59; frequency sweep: 0.0159–15.9 Strain sweep: 0.15; frequency sweep: .009–7

Strain sweep:0–20; frequency sweep: 1

Serrated plates

Strain sweep: 0.5–45, frequency sweep:0.9

Serrated plates

LMPS Mozzarella

Rheometrics RDA-II, Parallel Plate

UF-Feta

Bohlin VOR D = 30 Rheometer, H = 4.2 Parallel Plate

8–10 weeks old at reception and stored at 5°C

13

Deli-style Cheddar and pre-sliced Mozzarella Several commercial and experimental varieties

TA Instruments TA-1000 N

D = 40 H=?

Stored at 4°C

25

11

Stress sweep: 0.1–1000 Pa

Bohlin VOR, Parallel plates

D = 35 H = 3.5

Tempering 1 h at room temperature

23

Frequency sweep: 0.01–15

0.4

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Contact Surface

Notes

Ref.

Fiber direction in Yun et al., cheese ⊥ to parallel 1993 plated

Samples conditioned Wium and at 13°C for 16 h Qvist, 1997 before testing; specimens with weights within 1% of mean value are tested Smooth ss plates 5 or 20 N loading Pearce and and serrated normal force Bellmer, plates applied 2002 Normal plates

Gap setting: 3.2 mm; Drake et al., 5-min relaxation 1999 after loading; petroleum jelly applied to the exposed sample surfaces

Imitation cheese

Rheometrics SR 2000, Parallel plate

D = 24 H = 2.4

Quarg cheese

TA Not explicitly Instruments given CSL 100, Parallel Plate Process cheese Rheometrics D = 25 DSR, H = 2, 3, or 4 Parallel Plate Model processed cheese spreads a

TA Instruments Carri-Med CSL100, Parallel Plate

D = 20 H=1

D: diameter, H: thickness

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4°C

4–5°C, maximum 3 days

Strain sweep:22; temperature sweep: 22–100

1

<1

Normal plates

5

1

0.2–0.8

Normal plates

Stress sweep: 63–6300 Pa

Serrated plates and bonding with cyanoacrylate Normal plates

1 week at 4°C Frequency sweep: 23; temperature sweep: 25–90 Stored 3 weeks 20 at 20°C

Temperature sweep: 0.8; stress sweep: 0.8 Frequency sweep: 0.01–10

—

Imitation cheeses contained up to 9% pregelatinized starch; samples are compressed 0.2 mm before testing Samples compressed before testing; 15min rest for relaxation Sample edges lubricated with silicone oil; heating rate: 10°C/min Moist filter paper used to prevent drying

Mounsey and O’Riordan, 1999, 2001

Kelly and O’Donnell, 1998 Sutheerawattananonda and Bastian, 1998 Lee and Klostermeyer, 2001

TABLE 5.3 Chemical Composition of Cheeses Tested by Taneya et al. (1979) Cheese

Maturation Period (mo)

Moisture (%)

Fat (%)

pH

Caseinous Nitrogen

Gouda Cheddar Processed — hard Processed — soft

1/3/5 1/3/5 — —

39.9/33.7/32.7 42.4/37.9/35.8 44.5 42.5

26.4/31.3/31.5 23.6/28.6/30.2 26.0 27.5

5.89/5.78/5.80 6.92/5.81/5.77 6.00 5.75

80/70/70 87/80/73 77 77

Source: After Tanya et al., 1979. With permission. 2 1-mo 3-mo 5-mo

tan d (-)

1.5

1

0.5

0 -5

10

25

40

55

70

85

Temperature (°C)

FIGURE 5.9 Dynamic loss tangent of Cheddar cheese at different maturation stages. (After Taneya et al., 1979. With permission.)

of fat separation at high temperatures and potential for sample slippage; (b) effect rod insertion on structure; and (c) assertion that strain amplitude is in LVE region. Wetton and Marsh (1990) applied DMTA technique to a series of products including Cheddar cheese of different maturation grades to determine transition temperatures. The plots of loss tangent against temperature for mild and mature Cheddar cheeses are shown in Figure 5.10. Two peaks of loss tangent are evident at around 25 and 75°C. The first transition is thought to be associated with the melting of fat phase in the cheese and the second one with the mobilization of protein matrix. It is also seen that the peak temperatures for Cheddar cheese decreased with maturation, which is contrary to the results of Taneya et al. (1979). Wetton and Marsh (1990) proposed that the reason for this conflict might be the higher moisture content of the mature cheese as compared to that of the mild cheese in their work; however, the moisture contents of the cheeses are not specified. It is known that water can act as a plasticizer and modify certain properties (e.g., glass transition temperature, Tg) of food polymers (Slade and Levine, 1995; Roos, 1995; Noel et al., 1990). Moreover, the primary effect of plasticizers (i.e., low molecular weight diluents) is to reduce, for instance, the stiffness of polymers. However, it is also shown that an opposite

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1 mild mature

tan d (-)

0.8

0.6

protein phase

fat melting

0.4

0.2

0 0

20

40 60 Temperature (°C)

80

100

FIGURE 5.10 Temperature dispersion of the loss tangent for Cheddar cheese at two maturation stages. (After Wetton and Marsh, 1990.) 0.5

hot press molded extruded

tan d (-)

0.4 0.3 25% moisture 0.2 10% moisture 0.1 0 -50

-25

0

25

50

75

100

125

150

Temperature (°C)

FIGURE 5.11 The loss tangent of casein samples with different moisture contents from two alternative manufacturing methods. (After Wetton and Marsh, 1990.)

effect (“antiplasticization”) is possible, depending on the nature and amount of the plasticizer (Peleg, 1996; Seow et al., 1999). Wetton and Marsh (1990) in fact demonstrated the plasticization effect of water on the casein samples manufactured by two processes. The loss tangent peaks for casein samples with 10 and 25% moisture content are at about 55 and 98°C, respectively (Figure 5.11). Nolan et al. (1989a) determined dynamic properties of Cheddar and pasteurized process American cheeses using SAOS measurements, expecting that the data would aid in establishing quality criteria for purchase of cheese to be used in the school lunch program and other food donation programs. The loss tangent values of Cheddar cheese are essentially independent of frequency in the range 10 to 100 rad/s for all temperatures except 60°C and seen to exceed unity only at 60°C (Figure 5.12). The

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26°C

1.3

35°C 45°C

tan d (-)

1.0

60°C

0.7

0.4

0.1 10

100 Frequency (rad/s)

FIGURE 5.12 Variation of loss tangent with frequency for Cheddar cheese tested at different temperatures. (After Nolan et al., 1989a.)

TABLE 5.4 Equation of Complex Viscosity at Different Frequencies for Cheddar Cheese Frequency (rad/s)

Complex Viscosity Equation (kPa.s)

Evisc (cal/g mol)

1 10 100

η* = 1.06 × 10–25 exp(Evisc/RT) η* = 1.84 × 10–23 exp(Evisc/RT) η* = 3.37 × 10–21 exp(Evisc/RT)

36700 32600 28300

Note: These equations are valid between 22 and 50°C. Source: After Nolan et al., 1989a.

complex viscosity of Cheddar cheese is highly dependent on both temperature and frequency (Table 5.4) and decreases, for instance, at 40°C by a factor of 40 for increasing frequency from 1 to 100 rad/s, signifying a shear thinning character for melting cheese. Cheddar and Cheshire cheeses are quite similar in composition but significantly different in texture. The curd manipulation of Cheddar cheese results in matting of the curd particles into a close texture and firm body; while that in Cheshire cheese keeps the individual curd particles separate to obtain a crumbly texture. Expecting that this large difference in texture will be reflected in the rheological properties, Tunick et al. (1990) applied oscillatory shear tests to distinguish between Cheddar and Cheshire cheeses. The strain-sweep tests up to 20% shear strain did not reveal a clear linear region, but below 2.5% strain the complex modulus (G*) was practically constant for both cheeses. The complex viscosity (η*) values of Cheshire and Cheddar cheeses against

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5.5

log η* (Pa.s)

5 4.5 20-wk Cheshire 60-wk Cheshire 60-wk Cheddar

4 3.5 3 15

20

25

30

35

40

45

Temperature (°C)

FIGURE 5.13 Dynamic viscosities of Cheshire and Cheddar cheeses at 2.5% strain amplitude and 1 rad/s frequency. (After Tunick et al., 1990.)

TABLE 5.5 Arrhenius Equation with Fitting Parameters for Cheddar and Cheshire Cheeses Cheese

Maturation (week)

Arrhenius Equationa

Activation Energy (kJ/mol)

Cheddar Cheshire Cheshire

60 20 60

Y = 7195 X – 19.4 Y = 5380 X – 13.2 Y = 4475 X – 10.3

137 103 86

1

Y = log η*; X = 1/T; the unit of dynamic viscosity is Pa.s.

Source: After Tunick et al., 1990.

temperature at 2.5% strain and 1 rad/s are presented in Figure 5.13. The temperature dependence of η* is well described by an Arrhenius-type equation: E  1 ln η* = ln Avisc +  visc   R  T

(5.17)

where, Avisc preexponential factor, Evisc activation energy, R gas constant, and T absolute temperature. The resulting equations with numerical values of fitting parameters are listed in Table 5.5. It is shown that the complex viscosity and activation energy of Cheshire cheese decrease 17% during aging from 20 to 60 weeks, which is ascribed to the proteolysis. The activation energy of Cheddar cheese is significantly higher than that of Cheshire cheese. Thus, these authors concluded that the SAOS measurements provide an objective way of distinguishing between Cheddar and Cheshire cheeses and can be used for detecting mislabeled cheese. The majority of the rennet-coagulated cheeses are ripened, often under carefully controlled conditions, for periods ranging from four weeks to more than two years.

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log G′ (Pa)

6.5

5.5

PS-10 PM-10 PS-25 PM-25 PS-35 PM-35

4.5

3.5 0.1

1

10

100

10

100

Frequency (rad/s)

log G′ (Pa)

6.5 RS-10 RM-10 RS-25 RM-25 RS-35 RM-35

5.5

4.5

3.5 0.1

1 Frequency (rad/s)

FIGURE 5.14 The dynamic storage modulus of Cheddar cheese as a function of frequency and test temperature. Numbers 10, 25, and 35 represent test temperatures in °C; PS: Cheese made from pasteurized milk and aged 470 days; PM: Cheese made from pasteurized milk and aged 240 days; RS: Cheese made from raw milk and aged 475 days; RM: Cheese made from raw milk and aged 246 days. (After Rosenberg et al., 1995. With permission.)

For Cheddar cheese, the ripening time varies depending upon the flavor profile desired: Mild Cheddar is aged three months, medium Cheddar is aged four to nine months, and strong or sharp (old, extra old) Cheddars are aged from nine months to several years. During ripening, a series of physical and chemical/biochemical changes take place in the principal constituents of the cheese (i.e., drying, proteolysis, lipolysis, and glycolysis) (Fox, 1989). For most cheese varieties the primary proteolysis during ripening (Grappin et al., 1985; Rank et al., 1985) is the major biochemical event responsible for the changes in texture. Rosenberg et al. (1995) studied the linear viscoelastic properties of pasteurized (P-) and raw milk (R-) Cheddar cheese during ripening using SAOS technique. These researchers used a custom-made upper plate with a rough surface to prevent sample slippage during the oscillation tests. For P-Cheddar cheese, higher G′ values are reported for samples aged longer (PS vs. PM in Figure 5.14). On the other hand, for the same ripening, an opposite trend is observed for R-Cheddar cheese, where © 2003 by CRC Press LLC

PS PM RS RM

log G* (Pa)

6

5

4 0

10

20

30

40

Temperature (°C)

FIGURE 5.15 Effect of test temperature on dynamic modulus of Cheddar cheese made from pasteurized and raw milks. PS: Cheese made from pasteurized milk and aged 470 days; PM: Cheese made from pasteurized milk and aged 240 days; RS: Cheese made from raw milk and aged 475 days; RM: Cheese made from raw milk and aged 246 days. (After Rosenberg et al., 1995.)

the G′ values decreased with aging (RS vs. RM in Figure 5.14). The levels of soluble nitrogen in different cheese extracts are lower in R-cheese than in P-cheese. Likewise, as expected, the magnitudes of G′ values in P-cheese are smaller than those in R-cheese. These authors attributed the disparity in G′ trends to the differences in peptide profiles between pasteurized and raw milk cheeses. They suggested that the increase in the elastic character of P-Cheddar cheese is related to decrease in the amount of water previously available for solvation of the protein chains. As more ionic groups are formed due to cleavage of peptide bonds, and these groups bind water, then less water is available to provide lubrication and solvation. We shall note here that Creamer and Olson (1982) previously used this argument to explain the brittleness of maturing (up to 109 week) Cheddar cheese, as measured by the decrease in percent compression at the yield point. The effect of temperature on complex modulus (G*) is graphed in Figure 5.15. This figure shows that the change in complex modulus for each cheese is a gradual process, as pointed out by Rüegg et al. (1991). Rosenberg et al. (1995) stated that the inverse relation between dynamic properties and temperature is an indication of the thermal softening of the matrix. At this temperature range (10 to 35°C) melting of milk fat is likely to influence G′ and G″ of Cheddar cheese (Wetton and Marsh, 1990; Visser, 1991). Meltability is the key functional property of cheese when used as an ingredient (e.g., pizza, toasts, hamburgers, sauces). As discussed in Chapter 8, several empirical and fundamental methods exist to quantify cheese meltability. The definition proposed for meltability has two aspects that need to be quantified: (a) ease of melting, and (b) extent of flow. In terms of dynamic testing, the first aspect may be quantified with the temperature at which the viscous contribution becomes equal to the elastic contribution (i.e., transition temperature where tan δ = 1), and the second aspect may be quantified with the magnitude of the complex modulus, or more preferably © 2003 by CRC Press LLC

TABLE 5.6 Description of Terms Used to Classify Cheese with Reduced-Fat Content In United States Fat-free: Less than 0.5 g fat per reference amount and per labeled serving size and no added fat or oil ingredient Low fat: Maximum 3 g total fat per serving for serving size of more than 30 g or more than 2 tablespoons. 3 g or less of fat per 50 g product if serving size is 30 g or less or 2 tablespoons or less Light or Lite: If less than 50% of calories come from fat: minimum 33 1/3% reduction in calories per reference amount or minimum 50% reduction in fat per reference. If more than 50% of the calories come from fat: minimum 50% reduction in fat per reference amount. Reduced fat: Minimum 25% reduction in total fat per reference amount

In Codex High fat: >60% fat on dry basis Full fat: 45–60% fat on dry basis

Medium fat: 25–45% fat on dry basis

Low fat: 10–25% fat on dry basis Skim: <10% fat on dry basis

Source: After Mistry, 2001. With permission.

with the complex viscosity, at that transition temperature as well as the temperature dependence of the complex viscosity. The relationship between complex viscosity and complex modulus is given above by Equation (5.10). Figure 8.38 (Chapter 8) compares the softening point of cheeses measured by different tests, including using SAOS crossover modulus (Figure 5.5). As an objective method for meltability, Ustunol et al. (1994) applied SAOS to Cheddar cheese of different fat contents and correlated the complex modulus with meltability measurements from the traditional empirical test (i.e., Arnott test). Except for the very low-fat Cheddar cheeses (12.6 and <1% fat) that did not melt upon heating, the meltability of Cheddar cheese decreased with decrease in fat content. More results from this study are given in Chapter 8. Ustunol et al. (1994) pointed out that the G′ is greater than the G″ prior to melting, and the opposite is valid after melting. This observation gives support to the proposal of using tan δ = 1 as a criterion for detection of the transition temperature in meltability. Reduction in the fat content of cheese has a direct impact on texture, flavor profile, functional properties, and thus overall acceptability (Olson and Johnson, 1990; Fife et al., 1996). During the past two decades, the demand for reduced-fat and low-fat dairy products and other foods has been rising due to consumer concerns for health and dietary fat intake (Mistry, 2001). As a result, the legal standards of identity for cheeses containing a reduced amount of fat have also developed (Table 5.6). Meanwhile, the cheese industry has been dealing with the challenge of producing good-quality, reduced-fat cheeses that meet the consumer expectations. The consumers expect reduced-fat cheeses to have the functional and organoleptic characteristics of their traditional regular-fat counterparts. This challenge has prompted many investigations to understand and improve rheological properties of

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reduced-fat cheeses (Tunick et al., 1993; Tunick et al., 1995; Bryant et al., 1995; Ma et al., 1996; Ma et al., 1997; Rudan et al., 1998; Guinee et al., 2000). Venugopal and Muthukumarappan (2001) conducted SAOS measurements in time-sweep mode while heating and cooling Cheddar cheese to simulate conditions during preparation and consumption of foods containing cheese, for instance, pizza. Dynamic moduli of Cheddar cheese with 8.2 and 28.4% fat contents are measured as a function of temperature during melting and subsequent solidification. It is seen that a temperature hysteresis forms between heating (melting) and cooling (solidifying) curves. For Cheddar cheese with 8.2% fat content the moduli values during cooling are always higher than those during heating. The response is different, however, for Cheddar cheese with high-fat content (28.4%). In this case, G′ and G″ during cooling are greater than those during heating only at temperatures above ~43°C. Furthermore, it is observed that the slopes of G′ and G″ vs. temperature of higher-fat cheeses (22.8 and 28.4% fat) are steeper than those of lower-fat cheeses (8.2 and 16.5% fat). This is consistent with the results of Ustunol et al. (1995) where the fat content varied from 13 to 34%. The rheological differences of low-fat and high-fat Cheddar cheeses (i.e., more elastic character of low-fat type) certainly affect functionality and consumer acceptance of these products, in a negative way for reduced-fat cheese. Heating causes the cheese to melt and release fat, and therefore alter the original structure. Melted fat may coalesce and result in separation of fat from the protein matrix. This causes the undesirable effect of oiling-off or fat leakage. The resolidifying of fat during cooling may cause a less homogeneous distribution of fat and significant alteration in the cheese structure. It was also reported that both G′ and G″ decreased, as expected, with aging. The decrease in G′ is linked to proteolysis and that in G″ to water binding by ionic groups liberated in proteolysis, which presumably reduces availability of water to act as a lubricant (Venugopal and Muthukumarappan, 2001). The heat-induced changes on viscoelasticity of 5-day-old Cheddar-type cheeses of different fat contents have been recently reported (Guinee et al., 2000). As expected, increasing the temperature causes a large decrease in G′ and thus an increase in the phase angle (δ) of Cheddar cheese at different fat levels. This means that temperature effect on G″ is not as severe as that on G′. Much of the changes take place within the temperature range from 20 to 45°C. The factors that may affect the heat-induced softening of cheese, as evidenced by the reduction in G′, can be (a) melting of milk fat and (b) an increase in para-casein solvation or hydration (Guinee et al., 2000). It is known that milk fat is fully liquid above 40°C and completely solid below –40°C (Mulder and Walstra, 1974). Prentice (1992) commented that at low temperatures the fat globules are mainly solid and contribute to the rigidity of the casein matrix. At intermediate temperatures the fat is plastic and contributes to the rheological properties in a complex way. At 20°C and above most of the fat (nearly 80% of fat in milk) is already liquid, and it adds little to the firmness. It is interesting, however, to note that very low-fat cheese (1.3% fat) made from skim milk exhibited a greater decrease in G′ within this temperature range as compared to those with higher fat contents. This result indicates that between 20 and 40°C, more than the melting of fat, other factors such as solvation of protein are likely to govern the thermal softening of the cheese. Results of Guinee et al. (2000)

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further indicate that effect of fat reduction on rheological properties is better monitored via G′ at temperatures less than 50°C, and via the phase angle (δ) at temperatures greater than 50°C. Ma et al. (1996) compared viscoelastic properties of Cheddar cheeses of full fat, reduced fat, and reduced fat with added lecithin. The full-fat Cheddar cheese at 20°C possessed greater G′ and G″ than the reduced-fat kind with or without lecithin addition. These authors did not specify the fat contents of the samples. However, if we assume that the fat content of cheese is about 10 times the amount of fat in milk, we can estimate full-fat samples to contain 32%, and reduced-fat samples to contain 21% fat. Addition of lecithin, irrespective of the level (0.2 or 0.5%), contributes to the elastic part of the reduced-fat Cheddar cheese but not sufficient to fully simulate the full-fat kind. Results of Ma et al. (1996) regarding the effect of fat reduction on dynamic moduli are not in agreement with the other studies. For instance, an examination of the data of Ustunol et al. (1995) reveals that at 30°C (lowest in that study) the values G′ and G″ for 34%-fat cheese is smaller than those for 20%-fat cheese. Similarly, at 20°C, Guinee et al. (2000) reported nearly twice the G′ values for very low-fat (1.3%) cheese than full-fat (30%) cheese. The discrepancies in results of different studies are probably due to the difference in fat content (32% vs. 21% and 30% to 1.3%), the exact ratio of solid-to-liquid fat at respective temperatures (20 vs. 30°C), and thermal history before testing (Guinee et al., 2000). Another means of reducing the fat in natural and processed cheeses is to use fat replacers — a group of compounds developed to perform the functions of fat in reduced-fat foods (Drake and Swanson, 1995; Drake et al., 1996). Fat replacers are divided into two categories as fat substitutes and fat mimetics. Fat substitutes are nonpolar substances with physical and functional properties of fats and oils, except taste. They can be used to fully replace the fat for texture and mouthfeel. Fat mimetics are water-soluble substances that are used to partially replace the sensory and functional characteristics of fat (Drake and Swanson, 1995). Both protein-based (e.g., whey protein-based) and carbohydrate-based (e.g., starch-based) fat mimetics are commercially available. Ma et al. (1997) compared effects of three types of fat mimetics (dosage: 0.125 to 0.5%) on dynamic moduli of Cheddar cheese aged for three months at 7.2°C. The carbohydrate-based fat mimetic (consisting of microcrystalline cellulose, guar gum, and carrageenan) better mimics the functions of fat, as judged by the pairwise statistical comparison of G′ and G″ values for the resulting cheeses. Despite the contributions from the carbohydrate-based mimetic, the textural characteristics of reduced-fat cheeses are still inferior when compared to those of the full-fat cheeses. A recent report shows that attempts to replicate textural characteristics of fullfat Cremoso Argentino soft cheese with elevated moisture content or by addition of a fat replacer are not successful (Zalazar et al., 2002). Dynamic parameters of G′ and G″ are similar for the low-fat cheeses with and without Dairy-Lo fat replacer. But the moduli, particularly G′, for low-fat kind are significantly higher than those for full-fat version. It is seen that the sensory panel did not detect the textural differences manifested in the dynamic properties. It is concluded that, good-quality, low-fat Cremoso cheese can be made without fat replacers if 60% final moisture content is attained by technological means.

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1-mo

2

tan d (-)

3-mo 5-mo

1.5

1

0.5

0 0

10

20

30

40

50

60

70

80

Temperature (°C)

FIGURE 5.16 Dynamic loss tangent of Gouda cheese at different maturation stages. (After Taneya et al., 1979. With permission.)

GOUDA CHEESE Gouda cheese is one of the traditional and most popular Dutch-type cheeses with a classic shape of flat cylinder with bulging sides. It is produced today in several countries around the world (Scott, 1986). The cheese usually contains 49% fat (as FDM*) and 59 to 62% water (as WFFC**), and is matured for one to 20 months in the Netherlands (Walstra et al., 1987b; Visser, 1991). Gouda cheese is expected to contain some round holes evenly distributed over the body, and the number, size and shape of these holes are important aspects of its quality (Polychroniadou, 2001). Since Gouda cheese is produced and consumed worldwide, it is an active subject of rheological investigations (Culioli and Sherman, 1976; Goh and Sherman, 1987; Luyten, 1988; Luyten et al., 1991a; Luyten et al., 1991b; Dewettinck et al., 1999). The temperature dispersion of loss tangent for Gouda cheese matured for one month had a small peak at around 10°C and a large peak at about 45°C, as seen in Figure 5.16 (Taneya et al., 1979). Moreover, for Gouda cheese aged longer (i.e., three or five months) the locations of loss tangent peaks occur at higher temperatures. The data also indicate that 1-month-old Gouda cheese assumes a more viscous character (i.e., tan δ>1) at above 30°C. On the other hand, this character is observed only after 50°C for 3-month-old and 5-month-old cheeses. This is probably related to the higher moisture content (39.9% vs. 32.7 and 33.7%, Table 5.3) of young Gouda cheese. Luyten et al. (1991b) conducted a comprehensive rheological study on maturing Gouda cheese, including its dynamic properties. The tan δ values of Gouda cheese at different maturation stages varied between 0.3 and 0.4 for frequencies ranging from 0.005 and 0.05 Hz. This indicates strong viscoelastic solid character of the cheese. Furthermore, the loss tangent is higher at lower frequencies, showing that effective bonds in Gouda cheese have a more viscous character at longer time scales. A comparison of the loss tangent between Gouda and Feta cheeses indicates that Feta (tan δ = 0.17 – 0.25) is less viscous than Gouda cheese (tan δ = 0.32 – 0.4) (Wium and * FDM: fat content in the dry matter. ** WFFC: water content of fat-free cheese, when young.

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Qvist, 1997). Wium and Qvist (1997) suggest that the lower pH of Feta (4.5–4.7) as compared to that of Gouda (5.2 or higher) is probably the main reason for dominant elastic character of the Feta cheese. It is known that high pH milk gels exhibit significantly higher tan δ values as compared to those with low pH values, while a maximum in tan δ may appear at pH 5.2 (van Vliet et al., 1989; Roefs et al., 1990). Dewettinck et al. (1999) investigated dependence of dynamic rheological properties of commercial Gouda cheese on the sampling location using SAOS technique. The four sampling locations are 2.5, 6.5, 10.5, and 14.5 cm away from the crust. The dry matter content of Gouda increased with the position from 57.09% at the center to 58.75% at the crust, and with the cheese age from 58.75% for young (1 to 2 mo) and 67.41 for old (12 mo). The linear viscoelastic strain limit of the cheese with different ages was determined to be 1%. This value is lower than the range reported by Luyten et al. (1991b). The storage and loss moduli both changed during ripening in such a way that tan δ remained constant. This result is explained by the simultaneous and opposing effects of decrease in water and increase in proteolyis (Dewettinck et al., 1999). The high inventory cost associated with controlled storage during ripening has stimulated interest in accelerated ripening and resulted in several approaches, each with some advantages and disadvantages (Folkertsma et al., 1996). The major event of ripening is proteolysis that has direct and important influences on the texture and flavor of cheese (Law, 1987). One of the recent applications to accelerate ripening in cheese is the use of highpressure treatment. Isostatic high-pressure treatment (up to 1000 MPa) can influence protein conformation, and thus alter its functional properties (Messens et al., 1997). It is reported that the ripening time of Cheddar cheese could be reduced from six months to three days using continuous pressures of 50 and 250 MPa at 25°C (Messens et al., 1997). On the contrary, for Gouda cheese, the pressure treatment (50 to 400 MPa) did not influence the extent of proteolysis assessed by means of various nonspecific methods. Even the steady application of 50 MPa pressure for three days did not accelerate ripening of this cheese (Messens et al., 1999). Nevertheless, some textural differences detected manually have prompted a further study of rheological changes in Gouda cheese as a result of pressure treatment (Messens et al., 2000). The dynamic properties of high-pressure-treated (50 to 400 MPa, one hour) and untreated Gouda cheese indicate that pressure treatment leads to a decrease in both G′ and G″, more so in G′. Since proteolysis and other parameters presumably play no part immediately after pressure release, the changes in dynamic properties are attributed to weakening of hydrophobic interactions by pressure treatment (Messens et al., 1997; Messens et al., 2000). As the ripening progressed, the differences in rheological (dynamic and creep) and textural properties of treated and untreated samples become smaller and eventually not statistically significant at the end of 42-d ripening, indicating almost complete fading of pressure effects, or full restoration of hydrophobic interactions (Messens et al., 2000). It is interesting to note that the pressure treatment at 400 MPa for one hour brought about a reduction of about 150 kPa in G′ of Gouda cheese.* * Units of G′ and G″ in Figure 1 of the original paper must be kPa instead of Pa (Dewettinck, personal communication).

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TABLE 5.7 USDA Specifications for Mozzarella Cheeses Type Mozzarella cheese Low-moisture Mozzarella cheese Part-skim Mozzarella cheese Low-moisture, part-skim Mozzarella cheese a

Moisture Content (%) >52 but >45 but >52 but >45 but

≤60 ≤52 ≤60 ≤52

Fat Content (FDMa) (%) ≥45 ≥45 ≥30 but <45 ≥30 but <45

FDM: fat in the dry matter.

Source: After Anon, 1980.

MOZZARELLA CHEESE Mozzarella cheese is the famous member of pasta filata cheese family. Pasta filata cheeses are characterized by a unique texturization process where the curd is continually kneaded and stretched in hot water until a smooth, fibrous structure is obtained (Reinbold, 1963; Casiraghi and Lucisano, 1991). Traditional Mozzarella cheese, made from high-fat water-buffalo milk, is consumed as a dessert or appetizer in combination with fresh vegetables and cured meat. On the other hand, today Mozzarella cheese is made from cow’s milk and primarily used as an ingredient in various prepared foods. Introduction of Mozzarella into the United States at the start of 20th century by Italian immigrants greatly changed the fate of this traditional cheese (Bruno, 1999). Standards of identity in the U.S. specify four types of Mozzarella cheese according to moisture and fat contents, as shown in Table 5.7. The low-moisture, part-skim Mozzarella cheese makes the greatest proportion and is mainly used as a topping on pizza. Reports indicate that about 69 and 26% of all cheese manufactured in the U.S. and European Union, respectively, is used as an ingredient (Mann, 2000). More than 70% of Mozzarella cheese produced in the U.S. was used for pizza in 1986 (Alvarez, 1986; Kindstedt, 1993), and 96% of all American households eat pizza about 30 times a year, whether it is frozen, delivered, made-from-scratch, or eaten at pizzerias, (Anon, 1986; Sauber, 1990). Mozzarella cheese must have certain characteristics for use on pizzas and other foods. The desirable characteristics of the cheese in the solid and melted states are collectively referred to as “functional properties,” which, in a way, express consumer expectations of how the cheese should perform when used as an ingredient. The functional properties of Mozzarella cheese include shreddability for the solid cheese, and meltability, stretchability, elasticity, free oil formation, and browning for the melted cheese (Kindstedt, 1991; Kindstedt, 1993; McMahon et al., 1993). Clearly, a majority of these functional properties are associated with the rheology of the solid and melted cheese. Hence, there have been many studies on rheological properties of Mozzarella cheese and many attempts to relate them to the so-called functional properties, as discussed in other chapters.

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TABLE 5.8 Dynamic Shear Moduli (20°C) and Complex Viscosity of Natural LMPS Mozzarella and Imitation Cheeses Cheese Natural Mozzarella Imitation with 1% Ca caseinate Imitation with 2% Ca caseinate

G′′ (Pa)

G″″ (Pa)

η* (Pa.s)

2.27 × 104 ω0.17 5.92 × 104 ω0.20 1.59 × 104 ω0.21

1.03 × 104 ω0.19 1.98 × 104 ω0.14 1.98 × 104 ω0.16

3.2 × 10–3 e4100/T — 5.0 × 10–4 e4750/T

Note: T: absolute temperature (K). Source: After Nolan et al., 1989b.

Dynamic rheological properties of low-moisture, part-skim (LMPS) Mozzarella cheese appear to be first reported by Nolan et al. (1989a; 1989b), where they are used as an objective basis to distinguish between natural and imitation Mozzarella cheeses for purchasing purposes. The specimen slippage due to the lubrication of contact surfaces by melting milk fat was of serious concern for proper measurements. For this reason, Nolan et al. (1989b) have taken two critical precautions: (a) bonding of cheese sample directly to the pitted aluminum plates by cyanoacrylate ester adhesive, and (b) checking presence of slippage by following the analytical procedure suggested by Yoshimura and Prud’homme (1988). This procedure requires measurements of stress waveforms with at least two gap separations at the same strain and frequency. Identical stress waveforms from the two gap settings indicate that no slip is occurring. On the other hand, if the waveforms differ, then slip is occurring (Yoshimura and Prud’homme, 1988). The data obtained under a different set of conditions demonstrated that repeatable results with no evidence of slip could be obtained with Mozzarella (as well as Cheddar) samples bonded to the aluminum plates of the rheometer with cyanoacrylate resin adhesive. Moreover, it is shown that up to a 0.5% shear strain amplitude the G* values are almost constant, indicating linear behavior in the frequency range 0.1 to 100 rad/s. Further results from Nolan et al. (1989b) are given in the form of equations in Table 5.8. The sensitivity of the complex viscosity to added calcium caseinate is significant and used to differentiate between natural and imitation LMPS Mozzarella cheeses. Sutheerawattananonda and Bastian (1998) investigated the sample slippage during SAOS experiments for process cheeses by varying the gap setting. Their observations are discussed later in the Processed Cheese section. Hsieh et al. (1993) investigated changes in dynamic properties of Mozzarella cheese to which various protein fillers are either mixed with the shredded cheese and then heated, or added during cheesemaking. Figure 5.17 shows variation of tan δ with temperature for Mozzarella cheese mixed with 3% egg white. Among all the protein-filled Mozzarella cheeses, this one had the highest G′ and G″ values. The significant changes in tan δ occurred between 10 and 25°C and 40 to 60°C, and a nearly constant region in between. The addition of egg white seemed to contribute more to the elastic character than viscous character of Mozzarella cheese, and thereby reducing the tan δ in comparison with the control cheese. © 2003 by CRC Press LLC

0.7 0.6

tan δ (-)

0.5 0.4 0.3 0.2 0.1 0

0

10

20

30

40

50

60

Temperature (°C)

FIGURE 5.17 Temperature dependence of loss tangent for Mozzarella cheese containing 3% egg white. (After Hsieh et al., 1993.)

Freezing and frozen storage of cheese is practiced to arrest the changes in cheese during ripening, to preserve flavor and physical properties, and thus extend shelflife during marketing, especially those varieties of high-moisture contents (Olson, 1982). There are a number of research reports on the effects of freezing and frozen storage on various functional properties of cheese (Cervantes et al., 1983; Tunick et al., 1991; Viotto and Grosso, 1999). It seems that the effects of freezing on cheese quality are determined by the cheese type and conditions of freezing, frozen storage, and subsequent thawing. Unless frozen rapidly, the cheese may require some tempering time to regain desired flavor and, more importantly, functional attributes of unfrozen cheese (Olson, 1982). It is worth indicating here that a survey of pizza restaurants in the state of Vermont (U.S.) revealed that nearly all of the pizza restaurants (96% of 22 respondents) stored cheese in refrigerated condition rather than frozen condition (Pilcher and Kindstedt, 1990). Diefes et al. (1993) investigated the rheological changes in LMPS Mozzarella during a commercially usable freeze-thaw protocol. Data from Diefes et al. (1993) are plotted in Figure 5.18 as the loss tangent against frequency. Since the loss tangent represents the ratio of energy lost (viscous effects) to energy stored (elastic effects) in a cyclic deformation, it provides an overall picture of changes. The loss tangent at 20°C is always less than unity regardless of the storage treatment. Furthermore, there is a slight decrease in tan δ as the cheese aged either in refrigerated or frozen storage for 90 days. The difference in tan δ of cheese refrigerated or frozen during storage is minimal and seemed to vary with frequency; at low frequencies it is slightly lower for the refrigerated sample than for the frozen sample and opposite at higher frequencies. It is interesting to note that for similar ages of LMPS Mozzarella, the results from two studies (Diefes et al., 1993; Nolan et al., 1989b) differ much more than the difference due to the storage effect. Another point to highlight is that at 20°C the LMPS Mozzarella has a more viscous character at shorter time scales (higher frequencies). An opposite trend has been reported, for instance, by Zoon et al. (1989) for rennet-induced skim milk gels of different pH at 30°C and 0.00159 to 0.159 Hz;

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0.6

tan δ (-)

0.5

Control: 14-d refrigerated 90-d refrigerated 90-d frozen, 1-d tempered 90-d frozen, 21-d Nolan et al. tempered Nolan et al.

0.4

0.3

0.2 0.01

0.1

1

10

100

Frequency (Hz) 3 Control: 14-d refrigerated 90-d refrigerated 90-d frozen

2.5

tan δ (-)

2 1.5 1 0.5 0 0.1

1

10

100

Frequency (Hz)

FIGURE 5.18 Loss tangent profiles at 20°C (upper plot) and 60°C (lower plot) of LMPS Mozzarella cheese subjected to different storage treatments. (After Diefes et al., 1993; Nolan et al., 1989b.)

by Luyten et al. (1991) for Gouda cheese (1 week old to 6 months old) at 20°C and 0.005 to 0.05 Hz; and by Ak and Gunasekaran (1996) for LMPS Mozzarella cheese (1 week old to 4 weeks old) at 20°C and 0.005 to 20 Hz. Furthermore, Figure 5.18 shows that at 60°C the trend is reversed, and now the cheese has a more viscous character at longer time scales (lower frequencies) at all storage treatments. Another interesting behavior is reported in the literature for casein gels, which are more liquid-like at 20°C and lower frequencies (0.001 to 1 Hz) but more solid-like at 40°C (Roefs, 1986). Besides a host of compositional factors (moisture content, amount and kind of proteins, pH, salt content, etc.), perhaps another factor that may lead to such seemingly opposite results is the range of frequency involved. For theoretical analysis of loss tangent–frequency relationship, Campanella and Peleg (1997) used discrete relaxation times to calculate the frequencies where the

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loss tangent peaks are observed. They examined a variety of commodities, including a fresh cheese called tybo Argentino (Bertola et al., 1992). They calculated two loss tangent peaks for this cheese at 4.3 × 10–3 and 1.0 × 10–1 Hz using the limited relaxation constants. Below and above the peak locations, the loss tangent–frequency relationship is, of course, opposite (i.e., increasing and decreasing). Moreover, for a given material the peak can appear at a higher or lower frequency depending on the material characteristics, which, of course, change with the conditions. It is suggested that the frequency at which a peak appears can be used to evaluate the degree of solidity of materials: the lower it is the more solid is the material on the corresponding time scale. As mentioned before, refrigerated storage of Mozzarella cheese is preferably practiced in pizza establishments. Although Mozzarella is classified as an unripened variety and can be consumed immediately after production, it is well known that significant and desirable changes occur during a brief refrigerated storage. Fresh Mozzarella cheese melts poorly to a tough and overly elastic consistency, and therefore is unacceptable for use on pizza (Kindstedt, 1991). It usually takes one to three weeks of storage for desired functional properties to develop, primarily as a result of significant proteolysis (Kindstedt et al., 1989; Farkye et al., 1991; Kiely et al., 1993). Ak and Gunasekaran (1996) determined the dynamic rheological properties of commercial LMPS Mozzarella cheese during one month of refrigerated storage. Their results confirm the expected decrease of G′ and G″ with aging due to limited breakdown of protein matrix. One of the significant features of this publication is that Ak and Gunasekaran compared the measured G′ values with those calculated from stress relaxation data using an approximation equation known as the Alfrey’s rule (Tobolsky, 1960; Ferry, 1980). This relatively simple and useful procedure generated results in Figure 5.19. Hence, the comparison between measured and calculated G′ values of Mozzarella cheese provides a way of checking the validity of measurements. The resulting satisfactory agreement (Figure 5.19) is taken to indicate that true material properties are measured (Zoon et al., 1990). Interested readers will find many publications on other approximation equations and conversion techniques of varying complexity and precision (Ferry, 1980; Baumgaertel and Winter, 1989; Zoon et al., 1990; Elster et al., 1991; Emri and Tschoegl, 1993; Tschoegl and Emri, 1993). Some of these techniques are integrated into the analysis software of advanced rheometers. After three weeks of storage at refrigeration temperature, dynamic viscoelastic parameters of Mozzarella cheese made at three cooking temperatures (38, 41, and 44°C) are determined using SAOS measurements (Yun et al., 1994). Dynamic parameters, G′ and G″, are not affected by different cooking temperatures. It is well known that within the linear viscoelastic region G′ of Mozzarella cheese is greater than G″. In the nonlinear region, specifically at strain amplitudes of 10% and higher, the viscous contributions became dominant (G″ > G′), most likely due to structural damage by large deformations (Yun et al., 1994). This type of shift in behavior is not observed for Cheddar (60 week old) and Cheshire (20 week old and 60 week old) cheeses although the same strain range (0 to 20%) is examined (Tunick et al., 1990). Applying different cooking temperatures does not result in different proteolytic activity of the residual coagulant, and therefore the percentages of intact αs-caseins and β-casein remaining in the cheeses after two weeks of storage at 4°C are similar. © 2003 by CRC Press LLC

100 Data Fitting

G(t) (kPa)

80 60 40 20 0

−3

−2

−1

0 log time (s) (a)

1

2

3

1000

100 G′ (kPa)

Measured Calculated 10

1 0.01

0.1

1

10

100

1000

Frequency (rad/s) (b)

FIGURE 5.19 Calculation of dynamic storage modulus from linear stress relaxation data using the Alfrey’s rule. (a) Shear stress relaxation of LMPS Mozzarella cheese at 20°C. The slope of the regression line = –2.303 H*. (b) Measured and calculated shear relaxation modulus of LMPS Mozzarella cheese at 20°C. (After Ak and Gunasekaran, 1996. With permission.)

The experimental data from various reports on dynamic rheological properties of Mozzarella cheese are compared in Table 5.9. It is fair to conclude that the results from several studies show good agreement.

MOZZARELLA: TIME–TEMPERATURE SUPERPOSITION EXAMPLE Here we illustrate a bit tedious but quite simple approach and carry out the TTS (or time–frequency superposition) procedure with the help of a spreadsheet program. Data are taken from Subramanian and Gunasekaran (1997b). The original values of storage modulus for low-fat, part-skim Mozzarella are plotted in Figure 5.20 and also given for 30, 40 and 50°C in Table 5.10, along with columns of some manipulations. The last column (log shifted frequency) is plotted against the log G′ values,

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TABLE 5.9 Magnitudes of Linear Viscoelastic Properties for Low-Moisture, ω = 10 rad/s) Part-Skim Mozzarella Cheese during Refrigerated Storage (ω Dynamic Property G′ (kPa) G″ (kPa) tan δ (-) Test conditions

Nolan et al. (1989b)

Diefes et al. (1993)

Yun et al. (1994)

Ak and Gunasekaran (1996)

33.6 16 0.48 20°C 0.5% strain —

95.5 34.1 0.36 20°C 0.5% 2 weeks

58–64 19–21 0.33–0.35 22°C 1% 3 weeks

105.7 35.6 0.34 20°C 0.5% 3 weeks

Storage modulus (kPa)

1000

10°C 20°C 30°C 40°C 50°C 60°C 70°C

100

10

1 0.1

1

10

100

1000

Frequency (rad/s)

FIGURE 5.20 Frequency dispersion of storage modulus (G′) of 1-week-old low-fat, partskim Mozzarella cheese at indicated temperatures and 0.05% strain amplitude. (After Subramanian and Gunasekaran, 1997b. With permission.)

as shown in Figure 5.21. The reference temperature for shifting is chosen to be 40°C. The superposition shown in the figure is obtained by the logarithmic shift factors of 0.35, 0, and –1 for 30, 40, and 50°C, respectively. Three points shall be noted: (a) shift factor is zero at the reference temperature; (b) size of shifting is different for the same temperature difference, that is, the shift factor is temperature dependent; and (c) at a temperature lower than the reference temperature the shift factor is greater than 1 (i.e., log aT is positive) and smaller than 1 at a temperature higher than the reference. The entire master curve is shown in Figure 5.22. One may of course obtain better and faster superposition by using more rigorous shifting schemes, such as those described in Gordon and Shaw (1994).

FETA CHEESE Feta cheese is the most famous member of the pickled cheese category, where ripening takes place in brine. Feta is a white, soft cheese with a salty and slightly

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TABLE 5.10 Data for Time–Temperature Superposition Example Temperature (°C)

Frequency (rad/s)

30

G’ (Pa)

log frequency

log G’

Shifted Frequency log freq + log aT

0.63

62250

–0.202

4.794

0.148

3.14

84650

0.497

4.928

0.847

6.28

96100

0.798

4.983

1.148

31.42

129000

1.497

5.111

1.847

62.83

147000

1.798

5.167

2.148

125.66

168000

2.099

5.225

2.449

0.63

54000

–0.202

4.732

–0.202

3.14

74400

0.497

4.872

0.497

40

6.28

84150

0.798

4.925

0.798

31.42

113000

1.497

5.053

1.497

62.83

128000

1.798

5.107

1.798

125.66

149000

2.099

5.173

2.099

0.63

29250

–0.202

4.466

–1.202

3.14

43250

0.497

4.636

–0.503

6.28

51500

0.798

4.712

–0.202

31.42

75500

1.497

4.878

0.497

62.83

87900

1.798

4.944

0.798

125.66

104000

2.099

5.017

1.099

50

Source: After Subramanian and Gunasekaran, 1997b.

acid taste. It is traditionally made from sheep’s milk or a mixture of sheep and goat’s milk (Anifantakis, 1991). However, significant amounts of Feta cheese are now produced from cow’s milk (Scott, 1986; Tamime et al., 1991). Many types of pickled cheeses have traditionally been made and consumed for centuries in the Balkans and the Mediterranean region (Abd El-Salam et al., 1993). Today, Feta cheese is no longer a regional variety but marketed and consumed all over the world (Tamime et al., 1991). One of the main steps in cheesemaking is the concentration of the major constituents by means of whey removal. Ultrafiltration (UF) process offers an alternative way of concentrating milk before the formation and handling of the curd. It is successfully applied in Feta cheesemaking (Tamime and Kirkegaard, 1991). There are several publications on sensory, textural, and rheological properties of Feta cheese (Samal et al., 1993; Pappas et al., 1996; Lalos et al., 1996; Katsiari et al., 1997; Wium et al., 1997; Wium and Qvist, 1997; Sipahioglu et al., 1999), and only a few of them included dynamic properties (Wium and Qvist, 1997; Wium and

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5.4

log G′ (Pa)

5.2 5

30°C 40°C

4.8

50°C

4.6 4.4 −1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

log (ω a T)

FIGURE 5.21 Partial time–temperature superposition for G′ of 1-week-old low-fat, part-skim Mozzarella cheese with Tref = 40°C. (After Subramanian and Gunasekaran, 1997b. With permission.) 6

Log G′ (Pa)

5.5 5 4.5 4 3.5 3

−3

−1

1 Log (ω a T) (rad/s)

3

5

FIGURE 5.22 Master curve for G′ of 1-week-old low-fat, part-skim Mozzarella cheese with Tref = 40°C. (After Subramanian and Gunasekaran, 1997b. With permission.)

Qvist, 1998). Wium and Qvist (1997) determined rheological properties of three types of UF-Feta cheese using uniaxial compression and dynamic testing. Before we present some results from this study, it is useful to highlight two important issues noted by Wium and Qvist. The first one is related to the effect of loading normal force (i.e., compression) on the dynamic properties. They stated “a variation of 5% in the size of the gap between the parallel plates, and thereby of the compression of the sample, may change the moduli by a factor of two (or more).” When experimental conditions of dynamic rheological investigations are carefully examined, it is possible to see cases where the gap setting is smaller than thickness of the sample (see Table 5.2), implying that the specimen is actually compressed before the oscillatory shear tests.

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In a recent study, Pearce and Bellmer (2002) showed that higher loading normal force (20 vs. 5 N) results in greater initial G′ values for commercial Cheddar and Mozzarella cheese, among other food products. For instance, the mean initial G′ values of Mozzarella cheese loaded to 5 and 20 N were 52 and 62 kPa (i.e., 1.2 times). That ratio for Cheddar cheese is 1.06. Similar but smaller effect of normal force on the average G″ values is observed (Pearce and Bellmer, 2002). We shall note that whenever normal forces are applied to prevent slippage the cheese samples are allowed for stress relaxation to occur before starting the oscillatory measurements (Nolan et al., 1989a; Diefes et al., 1993; Ma et al., 1996; Mounsey and O’Riordan, 1999; Messens et al., 2000). However, Pearce and Bellmer (2002) stated that the effects of loading normal force on some semisolid materials are not eliminated or minimized by simply allowing the sample to rest prior to testing. All these, on one hand, may explain partially the variation in property values reported by separate laboratories for the same cheese, but on the other hand, and perhaps more importantly, point out the urgent need for standardized test protocols in terms of sample dimension, preparation, contact surface conditions, and so on, as remarked also by Wium and Qvist (1997) and Pearce and Bellmer (2002). The second important point emphasized by Wium and Qvist (1997) is that when the same gap setting is used with all samples, the exact weight/size of the individual specimen would affect the result. This is probably one of the factors contributing largely to the variations in dynamic property data from different investigations. To eliminate this source of variation, Wium and Qvist (1997) determined the weight of individual specimens and used only those with weights within 1% of the mean. Returning to the results of Wium and Qvist (1997), we note that the complex modulus of the three types of UF Feta cheese ranged from 40 to 173 kPa, and the loss tangent (tan δ) varied between 0.17–0.25 (Figure 5.23), indicating more elastic than viscous character. These two viscoelastic parameters are useful to differentiate texture among UF Feta cheeses. Drake et al. (1999) also employed SAOS tests on 13 commercial and experimental cheeses to inspect if dynamic data can be used to differentiate firmness of these cheeses. They found out that, in general, the frequency Tin Feta Red Brick Feta Blue Brick Feta

tan δ (-)

0.25

0.2

0.15 0.01

0.1

1

10

Frequency (Hz)

FIGURE 5.23 Variation of loss tangent with the frequency of oscillation for three kinds of UF Feta cheeses. (After Wium and Qvist, 1997. With permission.)

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sweep tests are useful to distinguish the cheese types. However, within a cheese type, especially for commercial cheeses, the differences in G′ and G″ of full-fat and low-fat kinds are not significant (e.g., Velveeta and Velveeta Lite).

IMITATION CHEESE Imitation cheeses may offer some significant advantages, such as lower price, flexibility to better manipulate functional properties suitable for some applications, and longer shelf life. The main disadvantages are inferior flavor quality compared to the natural cheese and an image of being unnatural (Anon, 1989). Many types of imitation cheese are produced and sold in the U.S., with the major portion of production being Mozzarella, to be used as an ingredient (Graf, 1981; Bachmann, 2001). In line with increasing use of ingredient cheese, several investigations on the textural and functional characteristics of imitation cheeses have been reported (e.g., Yang and Taranto, 1982; Kiely et al., 1991; Mulvihill and McCarthy, 1994). Dynamic rheological properties of imitation Mozzarella cheese have lately been studied by many researchers (Nolan et al., 1989b; Mounsey and O’Riordan, 1999; Mounsey and O’Riordan, 2001). Nolan et al. (1989b) reported that both elastic and viscous components of the shear modulus increase with 1% addition of calcium caseinate, but a 2% addition causes a large and unexpected decrease in storage modulus and an increase in loss modulus. Mounsey and O’Riordan (1999) assessed the usefulness of dynamic quantities from SAOS tests as indicators of meltability for imitation cheese manufactured with various levels of pregelatinized maize starch. The loss tangent values measured at 22°C decreased from 0.4 to 0.28 when the starch content increased from 0 to 9%, signifying that the addition of starch resulted in more solid behavior. The increasing starch content also causes considerable reduction in meltability as determined by the modified version of tube method (see Chapter 8). It is further noted that the effect of starch on dynamic viscoelastic properties is more pronounced at higher temperatures (Figure 5.24). 1.6 control with no starch with 9% starch

Loss tangent (-)

1.2

0.8

0.4

0 20

30

40

50

60

70

80

90

100

Temperature (°C)

FIGURE 5.24 Temperature dependency of the loss tangent for imitation cheeses containing 0 and 9% pregelatinized starch. (After Mounsey and O’Riordan, 1999.)

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In another study, Mounsey and O’Riordan (2001) examined the rheology, meltability, and microstructure of imitation cheese as affected by the addition of native starches from different sources (maize, waxy-maize, potato, wheat, rice). The use of native starches to partially replace (15%) casein in the control cheese resulted in marked differences in microstructure of imitation cheese, such as smaller fat globules, better emulsification of fat, and greater disruption of protein matrix. These modifications in the structure decreased meltability of the cheese regardless of the type of starch added. On the other hand, the effect of starch addition on dynamic properties of the cheese varied greatly depending on the origin of starch and the temperature range. Among the different starches examined, the rice starch appears to have potential to partially replace the casein, as it has the least effect on the properties of imitation cheese.

QUARG CHEESE Quarg or Quark is an acid-coagulated (pH 4.6), soft, fresh cheese with high moisture content (often 80% or more) (Scott, 1986). It is normally prepared from pasteurized skim milk, but half-fat and full-fat Quarg-based products with a range of vegetables and fruits may also be prepared. Other uses of Quarg cheese include blending into a sauce or dressing, adding to bakery products, and consuming as is at breakfast. Small amounts of rennet are sometimes used in the production of Quarg to obtain firmer coagula and minimize casein losses during whey separation (Kroger, 1979; Kelly and O’Donnell, 1998). Kelly and O’Donnell (1998) studied the rheological characteristics of experimental Quarg cheese by SAOS. The storage modulus as a function of strain amplitude is shown in Figure 5.25. The data in this figure indicate that the plasmin hydrolyzed pasteurized milk Quarg cheese has lower G′ values than that treated with potassium

Storage modulus (kPa)

100 PC PK PP 10

1 0.1

1

10

Strain amplitude (%)

FIGURE 5.25 Strain-sweep test for different experimental quargs. PC: quarg prepared from pasteurized milk; PK: quarg prepared from pasteurized milk containing potassium iodate; PP: quarg prepared from pasteurized milk digested premanufacture with plasmin. (After Kelly and O’Donnell, 1998.)

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iodate prior to pasteurization and acidification. Similar trends, but with lower magnitudes, are observed for heat-treated Quarg cheeses.

PROCESSED CHEESE Processed cheese is manufactured by heating and blending comminuted natural cheeses of different types and maturity into a homogeneous mass in the presence of an emulsifying agent and other ingredients (Price and Bush, 1974; Caric and Kalab, 1987; Zehren and Nusbaum, 1992). The use of other dairy and nondairy ingredients in the manufacture of processed cheese make it possible to obtain a variety of textures and functional properties (Rayan et al., 1980; Savello et al., 1989; Kalab et al., 1991). Taneya et al. (1979) reported on viscoelastic properties of hard and soft processed cheeses. Their results show that for hard processed cheese, unlike for Cheddar and Gouda cheeses, only a feeble peak appears at about 60°C (Figure 5.26). The significant modification of protein matrix, fat globule clumping, and redistribution of fat during processed cheesemaking (Rayan et al., 1980) are probably responsible for the observed differences in dynamic properties of natural and processed cheeses. As mentioned before, Nolan et al. (1989a) studied dynamic properties of Cheddar and pasteurized process American cheeses as a function of frequency and temperature. Significant temperature and frequency effects on the complex viscosity of process cheese are observed (Table 5.11). For instance, the complex viscosity at 60°C for 1 rad/s is 100 times that for 100 rad/s. It is interesting to note that the elastic character of pasteurized process cheese is dominant even at 60°C, where tan δ values are below 0.5 (Figure 5.27). This finding is significant, as it shows that the criterion used as meltability index for natural cheeses (e.g., temperature at which tan δ = 1.0) may not be applicable to pasteurized processed cheese. Meltability of process cheese containing 14-week-old Cheddar and different emulsifying salts (disodium phosphate or trisodium citrate) has been measured by dynamic stress rheometry (Sutheerawattananonda and Bastian, 1998) in the Soft Hard

tan δ (−)

1

0.5

0 −5

10

25

40

55

70

Temperature (°C)

FIGURE 5.26 Temperature dispersion of loss tangent for two types of process cheese. (After Taneya et al., 1979. With permission.)

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TABLE 5.11 Equation of Complex Viscosity at Different Frequencies for Pasteurized Process Cheese Frequency (rad/s)

Complex Viscosity (kPa.s) Equation

Evisc (cal/g mol)

1 10 100

η* = 1.50 × 10–6 exp(Evisc/RT) η* = 1.09 × 10–6 exp(Evisc/RT) η* = 8.65 × 10–7 exp(Evisc/RT)

11804 10192 9138

Note: These equations are valid between 26 and 60°C. Source: After Nolan et al., 1989a.

0.5

26°C 35°C 45°C 60°C

tan d (-)

0.4

0.3

0.2

0.1 10

100 Frequency (rad/s)

FIGURE 5.27 Dependence of loss tangent of pasteurized processed cheese on frequency at different temperatures. (After Nolan et al., 1989a.)

temperature range from 25 to 90°C at a rate of 10°C/min. These researchers cautiously show that there was no more variation in dynamic moduli measured at two gap settings (2 and 4 mm) if the cheese samples are bonded to the plates with ethyl-2cyanoacrylate and the exposed cheese surfaces are coated with silicone oil (Figure 5.28). It is further demonstrated that at room temperature both the serrated plates and the cyanoacrylate bonding produce repeatable results, but at higher temperature the former technique gives better repeatability. The lowest temperature at which the loss tangent became equal to one (i.e., G′ = G″) is called the transition temperature and is used as a parameter for quantitative comparison (Sutheerawattananonda and Bastian, 1998). The process cheese made with trisodium citrate, TSC, has a lower transition temperature (56.5°C) than that formulated with disodium phosphate, DSP, (64.6°C). It is also remarked that the texture of process cheese containing DSP as an emulsifying salt is more elastic than process cheese containing TSC. Considering the ease of flow, the dynamic viscosity graphs of process cheese with TSC and DSP as a function of temperature are shown in Figure 5.29. It is clear that process cheese with TSC has a better overall meltability

© 2003 by CRC Press LLC

1000 G' - 2 mm G' - 4 mm

Moduli (kPa)

G" - 2 mm G" - 4 mm 100

10 0.01

0.1

1

10

Applied stress (kPa)

FIGURE 5.28 Storage and loss moduli of process Cheddar cheese measured at 2 and 4 mm gap settings. (After Sutheerawattananonda and Bastian, 1998. With permission.) 10 DSP TSC

ln η * (Pa.s)

8

6

4

2 20

40

60

80

100

Temperature (ºC)

FIGURE 5.29 Variation of dynamic viscosity with temperature for process cheeses containing two emulsifying salts. DSP: disodium phosphate; TSC: trisodium citrate. (After Sutheerawattananonda and Bastian, 1998. With permission.)

than that with DSP, as both the transition temperature and dynamic viscosity values are lower for the former type. Similarly, Savello et al. (1989), using the empirical method of Olson and Price (1958), report that rennet casein process cheese models prepared with DSP have poor meltability, whereas those prepared with TSC melt well. However, it is further shown that the acid casein cheese emulsified with DSP has good meltability. At this point a comparison of complex viscosity results from the two reports mentioned above may be given. There is considerable difference in complex viscosities from the two studies (Figure 5.30): for instance, at 35°C the process cheese (PC) of Nolan et al. (1989a) has complex viscosity nearly six and three times bigger than the process cheeses (PC–TSC and PC–DSP) of Sutheerawattananonda and Bastian © 2003 by CRC Press LLC

Complex viscosity (Pa.s)

100000

10000

PC PC-DSP PC-TSC

1000

100 20

30

40 50 Temperature (ºC)

60

70

FIGURE 5.30 Comparison of complex viscosity of pasteurized processed cheese from two studies. (After Nolan et al., 1989a; and Sutheerawattananonda and Bastian, 1998, for PC-DSP and PC-TDC data.)

(1998), respectively. The moisture content of process cheeses in the latter study vary between 38.59 and 39.75%, and pH vary between 5.52 and 5.73. No composition information is given in the former study, but the moisture content can be expected to be similar based on USDA specifications for processed American cheese. More than the moisture, it is probably the difference in pH that causes such large variations in numerical values of dynamic properties of processed cheese, as also evidenced in the next paragraph. Lee and Klostermeyer (2001) have recently reported on the effect of pH on dynamic oscillatory properties of reduced-fat model processed cheese spreads made from sodium caseinate. The fat content is largely replaced by water, and the resulting processed cheese spreads have a composition of fat, protein, and moisture as 12, 12, and 73%, respectively. The pH adjustment between 5.0 and 6.0 is made using sodium polyphosphate salts. The authors report that the visual evaluation of properties of the processed cheese spreads indicate a change from a brittle, soft solid to a sticky liquid with the pH increasing from 5.0 to 6.0. At high pH the dynamic rheological response of the cheese spread resembles that of a dilute polymeric solution, where the G″ is greater than G′, the moduli increase rapidly with frequency, and the complex viscosity is practically independent of frequency. At low pH the dynamic behavior of the cheese spread resembles that of a weak gel where the G′ is greater than G″, the moduli weakly dependent on frequency, and the complex viscosity decrease rapidly with frequency (Ross-Murphy and Shatwell, 1993). The remarkable changes in rheological behavior of processed cheese within one pH unit are probably related to protein–protein and protein–water interactions (Lee and Klostermeyer, 2001). The increase in pH results in a decrease in protein–protein interactions and an increase in hydration of proteins, all of which lead to an increased liquid-like behavior (Figure 5.31). In this figure, it can be noticed that for the same pH the reduced-fat model spread (20°C) has a considerably higher tan δ value than process Cheddar cheese (23°C). It is also of interest to remark that at 92°C the tan δ values of process Cheddar cheeses are 1.5 (pH 5.64) and 2.8 (pH 5.62), depending upon the emulsifying salt (Sutheerawattananonda and Bastian,

© 2003 by CRC Press LLC

Loss tangent (-)

4 reduced-fat

3

regular 2

1

0 5

5.2

5.4

5.6

5.8

6

pH

FIGURE 5.31 Effect of pH on loss tangent of reduced-fat caseinate processed cheese (after Lee and Klostermeyer, 2001) and processed Cheddar cheese (after Sutheerawattananonda and Bastian, 1998).

1998), whereas that of reduced-fat cheese spread at 20°C and pH 6.0 is about 4.0 (Figure 5.31). These results asser