Food Engineering Series

Series EditorGustavo V. Barbosa-Cánovas, Washington State University, USA

Advisory BoardJosé Miguel Aguilera, Catholic University, ChileXiao Dong Chen, Monash University, AustraliaJ. Peter Clark, Clark Consulting, USARichard W. Hartel, University of Wisconsin, USAAlbert Ibarz, University of Lleida, SpainJozef Kokini, Purdue University, USAMichèle Marcotte, Agriculture & Agri-Food Canada, CanadaMichael McCarthy, University of California, USAKeshavan Niranjan, University of Reading, United KingdomMicha Peleg, University of Massachusetts, USAShafiur Rahman, Sultan Qaboos University, OmanM. Anandha Rao, Cornell University, USAYrjö Roos, University College Cork, IrelandWalter L. Spiess, University of Karlsruhe, GermanyJorge Welti-Chanes, Monterrey Institute of Technology, Mexico

For further volumes:http://www.springer.com/series/5996

M. Anandha Rao

Rheology of Fluid, Semisolid, and Solid Foods

Principles and ApplicationsThird Edition

1 3

ISSN 1571-0297ISBN 978-1-4614-9229-0 ISBN 978-1-4614-9230-6 (eBook)DOI 10.1007/978-1-4614-9230-6Springer New York Heidelberg Dordrecht London

Library of Congress Control Number: 2013951523

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M. Anandha RaoDepartment of Food Science Cornell UniversityGeneva, NY, USA

v

Preface to the Third Edition

Following the very good acceptance of the second edition of Rheology of Fluid and Semisolid Foods: Principles and Applications, it is an honor and a pleasure to present the third edition.

Again, the book is divided into eight chapters: Chap. 1—Introduction: Food Rheolo-gy and Structure, Chap. 2—Flow and Functional Models for Rheological Properties of Fluid Foods, Chap. 3—Measurement of Flow and Viscoelastic Properties, Chap. 4—Rheology of Food Gum and Starch Dispersions, Chap. 5—Rheological Behavior of Processed Fluid and Semisolid Foods, Chap. 6—Rheological Behavior of Food Gels, Chap. 7—Role of Rheological Behavior in Sensory Assessment of Foods and Swallo-wing, and Chap. 8—Application of Rheology to Fluid Food Handling and Processing.

Several changes have been incorporated in this third edition and these revisions should help readers better appreciate the important role that rheological properties play in food science, as well as to utilize them to characterize foods. The new topics covered in the second edition have been listed in the preface of that edition. In the third edition, the contents of the second edition have been left intact. Additional topics covered in the 3rd edition include: In Chap. 1, a section on microstructure in general and on na-nometer-scale milk protein fibrils together with their quantitative characterization in terms of persistence and contour lengths. In Chap. 2, a section on the phase diagram of a colloidal glass of hard spheres and its relationship to milk protein dispersions were added. Additions in Chap. 3 include, sections on Microrheology, including detailed descriptions of single particle and multiparticle micro rheological measurements, and Diffusive Wave Spectroscopy. In Chap. 4, a short section on starch spherulites was added. Because the Bostwick consistometer is used extensively for quality control of pureed foods, e.g., baby foods, in Chap. 5, a section on correlation of Bostwick con-sistometer data in terms of property-based dimensionless groups was added. Chapter 6 contains a new section on the effect of calcium on the morphology and functionality of whey protein nanometer-scale fibrils. In Chap. 7, it was pointed out that the roles of tribology and rheology are considered for the sensory perception of foods.

vi Preface to the Third Edition

Department of Food ScienceCornell UniversityGeneva, NY, USAMay 18, 2013

My association with the Riddet Institute, Massey University, NZ, helped shape the changes I made in this third edition. I thank Prof. Harjinder Singh for inviting me to work at the Riddet Institute, 2007–2011. My special thanks to Dr. Simon Loveday for valuable collaboration. Again, the mistakes in this book are mine and I hope that many of them can be corrected in a future edition.

M. Anandha Rao, PhD

vii

Contents

1 Introduction: Food Rheology and Structure ........................................... 1Stress and Strain Tensors .............................................................................. 3Viscometric Properties ................................................................................. 4Shear Stress–Shear Rate Relationships ........................................................ 5Units in Rheological Measurement .............................................................. 5Types of Fluid Flow Behavior ...................................................................... 6

Newtonian Behavior ............................................................................. 7Shear-Thinning Behavior ..................................................................... 8Yield Stress ........................................................................................... 8Shear-Thickening Behavior .................................................................. 8Time-Dependent Behavior ................................................................... 8

Apparent Viscosity ....................................................................................... 9Intrinsic Viscosity ......................................................................................... 9Stress–Strain Behavior of Solid Foods ........................................................ 13Linear Viscoelasticity ................................................................................... 14

Linear Viscoelasticity in Differential Form .......................................... 16Length Scale of Food Molecules and Foods ................................................ 17Phase Transitions in Foods ........................................................................... 19Glass Transition in Foods ............................................................................. 19Appendix 1-A ............................................................................................... 21

Momentum and Heat Transport Equations for Incompressible Fluids ... 21References .................................................................................................... 24Suggested Reading ....................................................................................... 26

2 Flow and Functional Models for Rheological Properties of Fluid Foods ............................................................................................. 27Time-Independent Flow Behavior ............................................................... 28

Newtonian Model ................................................................................. 28Power Law Model ................................................................................ 29Herschel–Bulkley Model ...................................................................... 30Casson Model ....................................................................................... 31Quemada Model ................................................................................... 32

Contentsviii

Apparent Viscosity—Shear Rate Relationships of Shear-Thinning Foods ................................................................................ 33

Cross and Carreau Models .................................................................. 34Models for Time-Dependent Flow Behavior ............................................. 35

Weltman Model .................................................................................. 35Tiu–Boger Model ............................................................................... 36

Role of Solids Fraction in Rheology of Dispersions .................................. 37Colloidal Glass ................................................................................... 41Rheology of Protein Dispersions ........................................................ 43Modulus of Gels of Fractal Floes ....................................................... 44

Effect of Soluble and Insoluble Solids Concentration on Apparent Viscosity of Foods ...................................................................................... 46Peclet Number of Dispersions .................................................................... 48Emulsions ................................................................................................... 50Effect of Temperature on Viscosity ............................................................ 52

Combined Effect of Concentration and Temperature ......................... 55Mixing Rules for two Component Blends ................................................. 55Treatment of Rheological Data Using Models ........................................... 57References .................................................................................................. 57

3 Measurement of Flow and Viscoelastic Properties ............................... 63Rotational Viscometers .............................................................................. 65

Concentric Cylinder Viscometer ........................................................ 65Parallel Disk Geometry ...................................................................... 75Mixer Viscometer ............................................................................... 76

Yield Stress of Foods Using a Vane ........................................................... 80Structural Characteristics of Dispersions ........................................... 82

Torsion Gelometer for Solid Foods ............................................................ 83Pressure-Driven Flow Viscometers ............................................................ 84

Capillary/Tube Viscometer ................................................................. 84Sample Calculation, Test No. 5 .......................................................... 87Glass Capillary Viscometer ................................................................ 88Slit (Channel) Rheometer ................................................................... 90Miscellaneous Viscometers ................................................................ 92

Viscosity Measurement at High Temperatures ........................................... 93In-Plant Measurement of Flow Behavior of Fluid Foods .......................... 96

Tomographic Techniques .................................................................... 97Vibrational Viscometers ..................................................................... 99

Extensional Flow Viscometry .................................................................... 99Uniaxial Extension ............................................................................. 100Biaxial Extension ................................................................................ 104Planar Extension ................................................................................. 106Cogswell’s Treatment of Extensional Flow ........................................ 107

Measurement of Viscoelastic Behavior of Fluid Foods ............................. 109Oscillatory Shear Flow ....................................................................... 109Types of Dynamic Rheological Tests ................................................. 112

Contents ix

Axial Motion between Coaxial Cylinders (Segel-Pochettino Geometry) ........................................................................................... 115Vibrating Sphere Rheometer .............................................................. 117Mechanical Models of Dynamic Rheological Data ............................ 117Time-Temperature Superposition ....................................................... 118Time-Temperature Superposition of Locust Bean (LB) Gum and Pectin Dispersions ....................................................................... 119Critical Stress and Strain .................................................................... 119Creep-Compliance Behavior .............................................................. 121Transient Viscoelastic Flow ................................................................ 124Stress-Relaxation ................................................................................ 126Static Measurement of Modulus ......................................................... 129Relationship among Rheological Parameters ..................................... 130Deborah Number ................................................................................ 134Microrheology .................................................................................... 134Single-Particle Microrheology ........................................................... 135Diffusive Wave Spectroscopy (DWS) ................................................ 137Multiparticle Video Microscopy ......................................................... 138Microstructure from Microrheology ................................................... 139Commercial Rheometers .................................................................... 140Some Precautions with Foods ............................................................ 140

Appendix 3–A ............................................................................................ 142Analysis of Flow in a Concentric Cylinder Geometry ....................... 142

Appendix 3–B ............................................................................................ 146Analysis of Steady Laminar Fully Developed Flow in a Pipe ........... 146

Appendix 3–C ............................................................................................ 151Analysis of Flow in a Cone-Plate Geometry ...................................... 151

References .................................................................................................. 153

4 Rheology of Food Gum and Starch Dispersions ................................... 161Rheology of Food Gum Dispersions .......................................................... 161

Rheological Models for Apparent Viscosity–Shear Rate Data ........... 161Rheological Properties of Binary Mixtures of Equal Concentration ..................................................................................... 167Effect of Biopolymer Concentration on Zero-Shear Viscosity........... 168Concentration Dependence of the Zero-Shear Viscosity of Gum Mixtures ..................................................................................... 171Concentration Dependence of the Zero-Shear Viscosity of Amylopectin Solutions ....................................................................... 172Viscoelastic Behavior of Food Gum Dispersions ............................... 173Cox–Merz Rule for Biopolymer Dispersions ..................................... 174Constitutive Equations Based on Molecular Structure ....................... 177

Rheology of Heated Starch Dispersions .................................................... 182Starch Granules and Composition ...................................................... 182Starch Gelatinization .......................................................................... 183Gelatinization Temperature and Extent of Gelatinization .................. 185

Contentsx

Viscous and Viscoelastic Properties During Heating of Starch Dispersions ................................................................................................. 186

Model of Dolan et al. .......................................................................... 186Model for η*-Temperature Data (Yang and Rao 1998) ...................... 187Rheological Properties of Gelatinized Starch Dispersions ................. 192Rheology of Starch Dispersions with Intact Granules ....................... 192Role of Particles in Shear-Thickening Nonfood Dispersions ............. 194Size Distribution of Intact Starch Granules ........................................ 196Antithixotropic Behavior of Cross-Linked Starch Dispersions .......... 196Starch Granule Mass Fraction and Viscosity ...................................... 198Mass Fraction versus Relative Viscosity ............................................ 201Effect of Starch Concentration ........................................................... 203Yield Stress and Structural Characteristics of Dispersions ................ 203Effect of Temperature on Flow Behavior ........................................... 204

Dynamic Rheological Behavior of Starch Dispersions .............................. 205Effect of Particle Characteristics on Modulus .................................... 205

Role of Continuous and Dispersed Phases on Viscoelastic Properties of Starch Dispersions ................................................................ 206

Cross-Linked Waxy Maize Starch Dispersions .................................. 2074 % Tapioca Starch Dispersions .......................................................... 208

Effect of Sugar on Rheology of Starch Dispersion .................................... 210Rheological Behavior of Starch–Protein Dispersions ................................ 211

Gluten/Starch ...................................................................................... 212Soy Protein/Corn Starch ..................................................................... 213Cowpea Protein/Cowpea Starch ......................................................... 216Whey Protein Isolate/Cross-Linked Waxy Maize Starch Dispersions .............................................................................. 218

Rheology of Starch–Gum Dispersions ....................................................... 220References .................................................................................................. 223

5 Rheological Behavior of Processed Fluid and Semisolid Foods ........... 231Fruit Juices and Purees: Role of Soluble and Insoluble Solids .................. 231

Role of PF Insoluble Solids ................................................................ 233Size Distribution of Fruit Juice Solids ................................................ 235Serum Viscosity of PF Dispersions .................................................... 237Rheological Properties of Frozen Concentrated Orange Juice (FCOJ) ................................................................................................ 237Viscoelastic Properties of Tomato Concentrates ................................ 244Rheological Properties of Tomato Pastes ........................................... 246Role of Composition of Tomato Pastes .............................................. 248Model for Apparent Viscosity of PF Dispersions ............................... 249Yield Stress of Structured Food Products ........................................... 250

Correlation of Bostwick Consistometer Data in Terms of Property-Based Dimensionless Groups ...................................................... 251

Contents xi

Rheological Properties of Chocolate .......................................................... 254Rheology of Milk and Milk Concentrates .................................................. 255Rheology of Mayonnaise, Salad Dressing, and Margarine ........................ 255

Stress Overshoot Data of Mayonnaise ............................................... 256Creep-Compliance Behavior of Mayonnaise ..................................... 258

Rheology of Salad Dressings ..................................................................... 259Processed Foods as Soft Materials ............................................................. 261Structural Analyses of Food Dispersions ................................................... 262

Role of Suspended Particles in Soy Milk ........................................... 262Structural Components of Yield Stress ...................................................... 263

Texture Map Based on Vane Yield Stress ........................................... 265High Pressure Processing of Milk and Milk Proteins ........................ 265Kinetics of Thermal and Pressure-induced Changes .......................... 266Mechanisms of Heat-induced and Pressure-induced Changes ........... 267Structural Changes in Milk Proteins ................................................... 268Effect of Pressure Release Rates ........................................................ 268Ultrahigh Pressure Homogenization of Milk ..................................... 269Structural Changes due to UHPH Treatment ...................................... 269Myofibrillar Proteins .......................................................................... 271Soy Proteins ........................................................................................ 272Egg Proteins ........................................................................................ 274

Appendix 5–A ............................................................................................ 274Literature Values of Rheological Properties of Foods ........................ 274

References .................................................................................................. 323

6 Rheological Behavior of Food Gels......................................................... 331Rheological Tests to Evaluate Properties of Gel Systems .......................... 332Mechanisms of Gelation ............................................................................ 332Classification of Gels ................................................................................. 333Theoretical Treatment of Gels .................................................................... 338

Rubber Elasticity ................................................................................ 338Cascade Theory .................................................................................. 341Percolation Theory ............................................................................. 342Fractal Model ...................................................................................... 344

Gel Point and Sol-Gel Transition by Rheological Measurements ............. 345Rheological Definition of “Gel Point” ............................................... 345Extrapolation of G′ Value ................................................................... 348Critical Viscoelastic Behavior at the Gelation Threshold................... 349Influence of Concentration and Temperature on Gel Time ................ 350Evaluation of Structure Development during Biopolymer Gelation .......................................................................... 352Effect of Temperature on the Rate of Structure Formation and Kinetic Data ................................................................................. 354Structure Development Rate ............................................................... 355

Contentsxii

Kinetics of Gelation ............................................................................ 357Evaluation of Structure Loss during Melting/Softening of Biopolymer Gels ................................................................................. 359

Mixed Polymer Gels .................................................................................. 365Polysaccharide-Polysaccharide Mixtures ........................................... 366Protein-Polysaccharide Mixtures ........................................................ 368Biopolymer Mixtures under Flow Fields ........................................... 373Phase Diagrams and Modeling ........................................................... 374Low-Fat Spreads ................................................................................. 376

STARCH GELS ......................................................................................... 377Effect of calcium on the morphology and functionality of whey protein nanofibrils ..................................................................... 380

References .................................................................................................. 381

7 Role of Rheological Behavior in Sensory Assessment of Foods and Swallowing ......................................................................... 391Stimuli for Evaluation of Viscosity ............................................................ 392

Stimuli Associated with Tilting Container and Stirring ..................... 393Stimuli Associated with Oral Evaluation of Viscosity ....................... 395Comparison of Oral and Nonoral Assessment Techniques ................ 396

Sensory Assessment of Viscosity of Gum Dispersions .............................. 397Perceived Thickness of Gum Dispersions .......................................... 398

Spreadability: Using Force and Under Normal Gravity ............................ 399Application of Fluid Mechanics ................................................................. 400

Fluid Mechanics of Spreadability ....................................................... 401Creaminess, Smoothness, and Slipperiness ........................................ 401

Role of Size, Shape, and Hardness of Particles ......................................... 402Role of Rheology in Perception of Flavor and Taste ................................. 403

Role of Hydrocolloid Concentration .................................................. 404Engineering Approach ........................................................................ 405

Role of Rheology in Swallowing ............................................................... 405A Model of the Swallowing Process .................................................. 406Flow Rate and Cumulative Volume for a Newtonian Fluid ............... 407Effect of Fluid Rheology on the Swallowing Process ........................ 408Effect of Rheology on Time to Swallow 1.0 mL ................................ 410

References .................................................................................................. 412

8 Application of Rheology to Fluid Food Handling and Processing ....... 415Velocity Profiles in Tubes .......................................................................... 415Energy Requirements for Pumping ............................................................ 418

Mechanical Energy Balance Equation ................................................ 418Pump Selection and Pipe Sizing ................................................................ 421

Pump Discharge Pressure ................................................................... 422Power Requirements for Pumping ...................................................... 422

Contents xiii

Power Consumption in Agitation ............................................................... 423Role of Flow Behavior in Agitation ................................................... 424Estimation of the Constant ks of an Agitator ...................................... 426

Residence Time Distribution in Aseptic Processing Systems .................... 426Interpretation of RTD Data ................................................................. 427Sizing Holding Tube Length .............................................................. 428Experimental RTD Data ..................................................................... 429Helical Flow ....................................................................................... 429

Heat Transfer to Fluid Foods...................................................................... 430Thermorheological Models ................................................................ 430Thermorheogy of Starch Dispersions ................................................. 431Model of Dolan et al. (1989) .............................................................. 431

Continuous Flow Sterilization.................................................................... 435Heat Transfer to Shear-Thinning Fluids ............................................. 435Physical Model of Non-Isothermal Laminar Flow Tube Sterilizer .... 436Continuous Sterilization of a Fluid Food Containing Starch ............. 437Analysis of the Heating Section ......................................................... 439Analysis of Cooling Section ............................................................... 440Length of Heating Section .................................................................. 440Influence of Rheological Behavior on the Heating Length ................ 442

Role of Rheology in Thermal Processing of Canned Foods ...................... 442Heat Penetration Parameters ............................................................... 442Numerical Solution of Transport Equations ....................................... 444Estimated Heat Penetration Parameters and Broken Heating Phenomena ......................................................................................... 445

Heat Transfer to a Starch Dispersion in an Intermittently Rotated Can ..... 446Intermittent Rotation Profile ............................................................... 448Thermorheological Behavior of the Model Food ............................... 449

Empirical Correlations for Heat Transfer to Fluids Flowing in Tubes ....... 450Newtonian Fluid ................................................................................. 452Power Law Fluid ................................................................................ 452

Empirical Correlations for Heat Transfer to Canned Fluids ...................... 452References .................................................................................................. 454

Index ................................................................................................................ 457