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- 1. DK1481_title 3/4/05 2:05 PM Page 1 Engineering Properties of Foods Third Edition M. A. Rao Syed S. H. Rizvi Ashim K. Datta Boca Raton London New York Singapore A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc.
- 2. Published in 2005 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2005 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8247-5328-3 (Hardcover) International Standard Book Number-13: 978-0-8247-5328-3 (Hardcover) Library of Congress Card Number 2004056967 This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Engineering properties of foods / edited by M.A. Rao, Syed S.H. Rizvi, Ashim K. Datta.-- 3rd ed. p. cm. -- (Food science and technology; 142) ISBN 0-8247-5328-3 (alk. paper) 1. Food--Analysis. 2. Food industry and trade. I. Rao, M. A., 1937- II. Rizvi, S. S. H., 1948- III. Datta, Ashim K. IV. Food science and technology (Marcel Dekker, Inc.); 142. TP372.5.E54 2005 664--dc22 2004056967 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Taylor & Francis Group is the Academic Division of T&F Informa plc.
- 3. iii Preface We are pleased to present the third edition of Engineering Properties of Foods. The third edition is comprehensive, with seven new chapters: Mass–Volume– Area-Related Properties of Foods, Properties Relevant to Infrared Heating of Foods, Electrical Conductivity of Foods, Ultrasound Properties, Kinetic Data for Biochemical and Microbiological Processes during Thermal Processing, Gas Exchange Properties of Fruits and Vegetables, and Surface Properties. Two of the previous chapters, Thermal Properties and Dielectric Properties, have been completely rewritten. Thus, 9 out of 16 chapters are new. We have systemat- ically searched and included physical, chemical, and biological properties that are of practical importance and for which signiﬁcant data exist. We have added Professor Ashim Datta as a co-editor to help with this rather large undertaking. In looking for experts on topics, we have also made an effort to expand the international participation of authors. We have added authors/co-authors from four additional countries. We have made a special effort to follow a consistent format for the chapters so that readers can follow it easily. Thus, chapters include an introduction, property deﬁnition, measure- ment procedure, modeling, representative data compilation, and applications. We have concentrated on clear physical understanding of the properties and their variations, supplemented by representative and sufﬁcient data, staying away from extensive data collection, for which electronic formats are likely to be more suitable. By providing a succinct presentation of each prop- erty in a consistent format, we hope to make it useful to the student as well as the professional. As computer-aided engineering (modeling) is becoming more commonplace, the primary use of food properties data is expected to be in computer modeling of food processes. Data correlations with compositions and temperature are particularly useful in this context since they will allow easy inclusion of variable properties in computer models. We have included such correlations as much as possible.
- 4. iv Rao, Rizvi, and Datta Our sincere thanks to all the authors and reviewers whose participation and comments certainly enhanced the chapters.We thank the editors at Marcel Dekker for their patience and help. M.A. Rao, Syed S.H. Rizvi, and Ashim K. Datta
- 5. v The Editors M.A. Rao is a professor of food engineering at Cornell University, Ithaca, New York. He focuses his research on the measurement and interpretation of rheological properties of foods. Many original papers, reviews, and book chap- ters were contributed by Rao and co-workers, including the book: Rheology of Fluid and Semisolid Foods: Principles and Applications,Aspen Publishers Inc., 1999 (Kluwer Academic/Plenum Publishers, Inc). Professor Rao serves as the scientiﬁc editor of the food engineering and physical properties section of the Journal of Food Science. He was elected a fellow of the Institute of Food Technologists in 1997 and the Association of Food Scientists and Technologists (India) in 2000. He received the Scott Blair Award for Excellence in Rheology from the American Association of Cereal Chemists in 2000 and the Distin- guished Food Engineer award from IAFIS/FPEI-ASAE in 2003. Syed S.H. Rizvi, Ph.D., is professor of food process engineering and inter- national professor of food science at Cornell University, Ithaca, New York. His teaching and research focus on engineering aspects of food processing and manufacturing operations. He has authored or co-authored over 100 research articles, co-edited ﬁve books, and holds seven patents. He previously taught at Clemson University and The Ohio State University and worked at Nestle and Glaxo. A fellow of the Institute of Food Technologists, Professor Rizvi has received many awards in recognition of his teaching and research efforts including the Chancellor Medal for Excellence in Teaching, State University of New York; International Dairy Foods Association Research Award in Food Processing; and Marcel Loncin Research Prize, Institute of Food Technologists. He received his B.S. and M.S. degrees from Panjab University, M.Eng. (chem- ical engineering) from the University of Toronto, and Ph.D. from The Ohio State University.
- 6. vi Rao, Rizvi, and Datta Ashim K. Datta, Ph.D., is a professor of biological engineering at Cornell University, Ithaca, New York. He has a Ph.D. degree (1985) in agricultural engineering from the University of Florida, Gainesville. Dr. Datta has served as a visiting professor at the University of Minnesota and the Katholieke Universiteit Leuven, Belgium. His research interests are in the fundamental studies of heat and mass transport relevant to food processing. His current research focuses on combined microwave and conventional heating and on modeling of microbiological and chemical safety during food processing. Dr. Datta is a member of the American Society of Agricultural Engineers, American Institute of Chemical Engineers, and Institute of Food Technologists. He has authored and co-authored two books: Handbook of Microwave Tech- nology for Food Applications and Biological and Bioenvironmental Heat and Mass Transfer, and he serves on the editorial boards of several journals.
- 7. vii Contributors Marialuci Almeida Cornell University Ithaca, New York Ashim K. Datta Cornell University Ithaca, New York F.J. Francis University of Massachusetts Amherst, Massachusetts Marc E. Hendrickx Katholieke Universiteit Leuven Leuven, Belgium Indrawati Katholieke Universiteit Leuven Leuven, Belgium Jeroen Lammertyn Katholieke Universiteit Leuven Heverlee, Belgium Zacharias B. Maroulis National Technical University of Athens Athens, Greece T. Matsuura University of Ottawa Ottawa, Ontario, Canada Michael J. McCarthy University of California Davis, California Kathryn L. McCarthy University of California Davis, California Joseph McGuire Oregon State University Corvallis, Oregon Paul Nesvadba Rubislaw Consulting Limited Aberdeen, U.K. Bart M. Nicolaï Katholieke Universiteit Leuven Heverlee, Belgium Ximena Quintero Frito-Lay Plano, Texas
- 8. viii Rao, Rizvi, and Datta G.S.V. Raghavan McGill University Ste-Anne de Bellevue, Quebec, Canada M. Shaﬁur Rahman Sultan Qaboos University Muscat, Sultanate of Oman D. Rana University of Ottawa Ottawa, Ontario, Canada M.A. Rao Cornell University Geneva, New York V.N. Mohan Rao Frito-Lay Plano, Texas Syed S.H. Rizvi Cornell University Ithaca, New York George D. Saravacos National Technical University Athens, Greece and Rutgers University New Brunswick, New Jersey Arnab Sarkar University of California Davis, California Sudhir K. Sastry The Ohio State University Columbus, Ohio Wendy Schotsmans Katholieke Universiteit Leuven Heverlee, Belgium R. Paul Singh University of California Davis, California Chantal Smout Katholieke Universiteit Leuven Leuven, Belgium S. Sourirajan Ottawa, Ontario, Canada G. Sumnu Middle East Technical University Ankara, Turkey Ann M. Van Loey Katholieke Universiteit Leuven Leuven, Belgium Bert E. Verlinden Katholieke Universiteit Leuven Heverlee, Belgium Lu Wang University of California Davis, California
- 9. ix Table of Contents Chapter 1 Mass-Volume-Area–Related Properties of Foods.......................1 M. Shaﬁur Rahman I. Introduction .................................................................................................1 II. Fundamental Considerations .....................................................................2 A. Volume ....................................................................................................2 1. Boundary Volume .............................................................................2 2. Pore Volume ......................................................................................2 B. Density....................................................................................................2 1. True Density.....................................................................................2 2. Material Density...............................................................................3 3. Particle Density ................................................................................3 4. Apparent Density .............................................................................4 5. Bulk Density.....................................................................................4 C. Porosity...................................................................................................4 1. Open Pore Porosity...........................................................................4 2. Closed Pore Porosity.........................................................................4 3. Apparent Porosity.............................................................................5 4. Bulk Porosity ....................................................................................5 5. Bulk-Particle Porosity ......................................................................5 6. Total Porosity....................................................................................5 D. Surface Area...........................................................................................5 E. Pore Size Distribution ...........................................................................6 III. Measurement Techniques...........................................................................6 A. Density Measurement ...........................................................................6 1. Apparent Density .............................................................................6 2. Material Density.............................................................................11 3. Particle Density ..............................................................................14 4. Bulk Density...................................................................................14
- 10. x Rao, Rizvi, and Datta B. Measurement Techniques of Porosity.................................................14 1. Direct Method.................................................................................14 2. Optical Microscopic Method ..........................................................14 3. Density Method ..............................................................................14 C. Surface Area.........................................................................................15 1. Boundary Surface Area..................................................................15 2. Pore Surface Area...........................................................................15 3. Cross-Sectional Area ......................................................................16 IV. Speciﬁc Data..............................................................................................16 A. Predictions of Density .........................................................................16 1. Gases and Vapors ...........................................................................17 2. Liquid Foods ...................................................................................18 3. Density of Solid Foods....................................................................19 B. Predictions of Porosity.........................................................................22 C. Prediction of Surface Area ..................................................................25 1. Euclidian Geometry........................................................................25 2. Non-Euclidian or Irregular Geometry ..........................................26 3. Theoretical Prediction....................................................................26 4. Size Distribution.............................................................................30 V. Summary....................................................................................................33 Acknowledgments ..............................................................................................33 List of Symbols ..................................................................................................33 Greek Symbols ...................................................................................................34 Subscripts...........................................................................................................34 Superscripts........................................................................................................35 References...........................................................................................................35 Chapter 2 Rheological Properties of Fluid Foods......................................41 M. A. Rao I. Introduction ...............................................................................................41 II. Rheological Classiﬁcation of Fluid Foods................................................42 A. Rheological Models for Viscous Foods................................................47 1. Models for Time-Independent Behavior .......................................47 2. Rheological Models for Thixotropic Foods ....................................51 3. Effect of Temperature on Viscosity ...............................................52 4. Combined Effect of Temperature and Shear Rate.......................54 5. Effect of Concentration on Viscosity.............................................54 B. Rheological Models for Viscoelastic Fluid Foods...............................56 1. Normal Stress Data on Fluid Foods .............................................56 2. Creep Compliance Studies on Foods.............................................57 III. Structure of Fluid Foods via Solution Viscosity and Physicochemical Approach........................................................................59 A. Solution Viscosity.................................................................................60 B. Physicochemical Approach ..................................................................61 IV. Measurement of Flow Properties of Fluid Foods....................................61 A. Fundamental Methods ........................................................................61 1. Capillary Flow ................................................................................61 2. Couette Flow Viscometers .............................................................63 3. Plate-and-Cone Viscometers ..........................................................65
- 11. Table of Contents xi 4. Parallel Plate Geometry.................................................................66 5. Slit (Channel) Rheometers ............................................................67 6. Extensional Flows ..........................................................................68 B. Empirical Methods...............................................................................71 1. Adams Consistometer ....................................................................71 2. Bostwick Consistometer.................................................................71 3. Efﬂux Tube Viscometer..................................................................72 C. Imitative Methods................................................................................72 1. Mixers for Determining Flow Properties .....................................73 2. In-Plant Measurement of Rheological Behavior of Fluid Foods ......77 V. Flow of Fluid Foods in Tubes...................................................................81 A. Isothermal Flow of Fluids in Tubes ...................................................82 1. Velocity Proﬁles and Volumetric Flow Rate Relationships.........82 2. Friction Losses for Power Law Foods in Pipes ............................83 3. Pressure Drop Across Valves and Fittings...................................87 4. Friction Losses for Herschel–Bulkley Fluids...............................87 5. Calculation of Kinetic Energy for Non-Newtonian Fluids..........88 VI. Conclusion..................................................................................................89 List of Symbols ..................................................................................................89 Greek Symbols ...................................................................................................90 Subscripts...........................................................................................................91 Superscript .........................................................................................................91 References...........................................................................................................91 Chapter 3 Rheological Properties of Solid Foods.....................................101 V. N. Mohan Rao and Ximena Quintero I. Introduction .............................................................................................101 II. Quasistatic Tests for Solid Foods...........................................................102 A. Introduction........................................................................................102 B. Some Simple Tests.............................................................................104 C. Rheological Modeling.........................................................................108 D. Creep...................................................................................................109 E. Relaxation...........................................................................................111 III. Dynamic Testing of Solid Foods.............................................................113 A. Introduction........................................................................................113 B. Theoretical Considerations ...............................................................114 1. Resonance .....................................................................................114 2. Direct Stress–Strain Tests...........................................................117 C. Application of Resonance ..................................................................120 D. Application of Direct Stress–Strain Tests........................................123 IV. Failure and Glass Transition in Solid Foods ........................................126 A. Failure in Solid Foods........................................................................126 B. Glass Transition of Solid Foods........................................................128 1. Factors that Affect Glass Transition...........................................129 2. Measurement of Glass Transition...............................................129 3. Importance of Glass Transition in Solid Foods..........................131 V. Empirical and Imitative Tests ...............................................................132 A. Introduction........................................................................................132 B. Texture Proﬁle Analysis....................................................................133
- 12. xii Rao, Rizvi, and Datta C. Texture (Shear) Press........................................................................135 D. Warner–Bratzler Shear .....................................................................136 E. FMC Pea Tenderometer ....................................................................136 F. Penetrometer......................................................................................137 G. Other Empirical Methods .................................................................137 VI. Conclusions..............................................................................................138 References.........................................................................................................139 Chapter 4 Thermal Properties of Unfrozen Foods ..................................149 Paul Nesvadba I. Introduction .............................................................................................149 A. The Importance of Thermal Properties for the Quality and Safety of Foods ...........................................................................149 B. Modeling and Optimization of Processes.........................................150 II. Sources of Data on Thermal Properties ................................................151 A. Measurement .....................................................................................151 B. Literature ...........................................................................................151 C. Computerized and On-Line Databases ............................................151 D. Software for Predicting Thermal Properties of Foods ....................152 III. Density.....................................................................................................152 A. Deﬁnition of Powder Bulk Density...................................................154 IV. Speciﬁc Heat Capacity............................................................................154 A. Latent Heat of Melting .....................................................................156 B. Speciﬁc and Latent Heat of Fats......................................................156 V. Thermal Conductivity.............................................................................157 A. Predictive Equations .........................................................................157 B. Inﬂuence of Structure of Food on Thermal Conductivity...............160 VI. Measurement Methods for Thermal Conductivity .................................16 A. The Basis of Operation of the Needle Probe...................................161 B. Reference Materials...........................................................................165 VII. Other Properties Relevant to Thermal Processing of Foods................165 A. Compressibility and Thermal Expansion ........................................165 B. Glass Transitions...............................................................................166 C. Sorption and Hydration Properties..................................................167 VIII. Conclusions..............................................................................................167 Symbols, Names, and Dimensions..................................................................167 References.........................................................................................................168 Chapter 5 Thermal Properties of Frozen Foods ......................................175 R. Paul Singh and Arnab Sarkar I. Introduction .............................................................................................175 II. Experimental Approaches to Measuring the Thermal Properties of Frozen Foods .......................................................................................176 A. Initial Freezing Point and Unfrozen Water.....................................176 B. Density................................................................................................177 C. Thermal Conductivity........................................................................177 D. Enthalpy.............................................................................................177
- 13. Table of Contents xiii E. Speciﬁc Heat ......................................................................................178 F. Thermal Diffusivity ...........................................................................178 III. General Observations on the Reliability of Experimental Data.........181 IV. Modeling of the Thermal Properties of Frozen Foods..........................184 A. Prediction of Unfrozen Water During Freezing of Foods ...............184 1. Density ..........................................................................................189 2. Thermal Conductivity ..................................................................190 3. Enthalpy........................................................................................194 4. Apparent Speciﬁc Heat ................................................................197 B. Limitations of Predictive Models......................................................199 List of Symbols ................................................................................................200 Greek Symbols .................................................................................................200 Subscripts.........................................................................................................201 References.........................................................................................................201 Chapter 6 Properties Relevant to Infrared Heating of Foods ................209 Ashim K. Datta and Marialuci Almeida I. Introduction .............................................................................................209 II. Fundamentals of Infrared Interactions with Materials.......................210 A. Electromagnetic Spectrum and Near-, Mid- and Far-Infrared Electromagnetic Waves......................................................................210 B. Interaction between Infrared Radiation and Food Materials ........210 C. Sources of Infrared Radiation in Heating Applications ....................212 D. Emission and Emissivity...................................................................212 E. Reﬂection, Absorption, and Transmission........................................214 F. Absorptivity and Emissivity .............................................................218 G. Attenuation or Extinction .................................................................219 III. Use of the Radiative Properties in Modeling of Heat Transfer ..........220 IV. Measurement of Radiative Properties of Foods....................................221 V. Radiative Property Data for Food Systems ..........................................224 A. Radiative Property Data for Water, Ice, and Water Vapor .............224 B. Properties of Other Pure Food Components....................................225 C. Spectral Variation of Radiative Property Data: Potato Tissue as an Example ...................................................................................225 D. Moisture Dependence of Radiative Property Data .........................227 E. Temperature Dependence of Radiative Property Data ....................228 F. Dependence of Radiative Property Data on Food Structure..........230 G. How Processing Can Change Food Radiative Properties...............232 H. Summary: Use of Radiative Property Data in Modeling ...............234 Acknowledgments ............................................................................................235 References.........................................................................................................235 Chapter 7 Thermodynamic Properties of Foods in Dehydration ...........239 S. S. H. Rizvi I. Introduction .............................................................................................239 II. Thermodynamics of Food–Water Systems.............................................240 A. Chemical Potential and Phase Equilibria .......................................242 B. Fugacity and Activity ........................................................................244
- 14. xiv Rao, Rizvi, and Datta C. Water Activity in Foods.....................................................................246 D. Measurement of Water Activity........................................................252 1. Measurements Based on Colligative Properties........................252 2. Measurements Based on Psychrometry .....................................255 3. Measurements Based on Isopiestic Transfer .............................256 4. Measurements Based on Suction (Matric) Potential.................256 E. Adjustment of Water Activity ...........................................................256 F. Moisture Sorption Isotherms............................................................261 1. Theoretical Description of MSIs..................................................261 2. Effect of Temperature ..................................................................268 III. Sorption Energetics.................................................................................272 A. Differential Quantities ......................................................................273 B. Integral Quantities............................................................................276 D. Hysteresis and Irreversibility...........................................................281 E. Kinetic Aspects...................................................................................287 IV. Dehydration Principles and Processes ..................................................288 A. Drying Behavior.................................................................................290 B. Constant-Rate Period ........................................................................293 C. Falling-Rate Period............................................................................295 D. Equilibrium Moisture Content .........................................................301 E. Energy Requirements........................................................................304 V. Conclusion................................................................................................307 List of Symbols ................................................................................................308 Greek Symbols .................................................................................................309 Subscripts.........................................................................................................310 Superscripts......................................................................................................310 References.........................................................................................................310 Chapter 8 Mass Transfer Properties of Foods.........................................327 George D. Saravacos I. Introduction .............................................................................................327 II. Phase Equilibria......................................................................................329 A. Vapor–Liquid Equilibria....................................................................329 B. Gas–Liquid Equilibria.......................................................................333 C. Liquid–Liquid and Liquid–Solid Equilibria ....................................335 D. Gas–Solid and Vapor–Solid Equilibria.............................................336 Water Activity ....................................................................................336 III. Diffusion...................................................................................................338 A. Diffusion in Gases .............................................................................339 B. Diffusion in Liquids...........................................................................340 C. Diffusion in Solids .............................................................................341 1. Introduction ..................................................................................341 2. Diffusion in Polymers...................................................................343 3. Molecular Simulations .................................................................344 D. Estimation of Diffusivity in Solids...................................................345 1. Sorption Kinetics..........................................................................345 2. Permeation Measurements..........................................................346 3. Distribution of Penetrant.............................................................347 4. Drying Rate...................................................................................349
- 15. Table of Contents xv IV. Interphase Mass Transfer ......................................................................349 A. Mass Transfer Coefﬁcients ................................................................349 B. Penetration Theory ............................................................................351 C. Analogies of Heat and Mass Transfer..............................................352 D. Effect of Surfactants..........................................................................353 V. Mass Transfer in Foods ..........................................................................354 A. Moisture Transport............................................................................354 1. Moisture Diffusion........................................................................354 2. Diffusion in Porous Foods............................................................356 3. Interphase Moisture Transfer .....................................................360 B. Diffusion of Solutes ...........................................................................360 C. Diffusion of Aroma Compounds........................................................362 VI. Other Mass Transfer Processes .............................................................364 A. Extraction...........................................................................................364 B. Distillation and Gas Absorption.......................................................366 C. Crystallization....................................................................................368 D. Food Packaging ..................................................................................370 Acknowledgments ............................................................................................372 List of Symbols ................................................................................................372 Greek Symbols .................................................................................................373 References.........................................................................................................373 Chapter 9 Physicochemical and Engineering Properties of Food in Membrane Separation Processes .......................................381 D. Rana, T. Matsuura, and S. Sourirajan I. Introduction .............................................................................................381 II. Transport Theories..................................................................................382 A. Case 1: Preferential Sorption of Water at the Membrane– Solution Interface ..............................................................................382 1. Basic Transport Equations ..........................................................382 2. Relationship between (DAM/Kδ)NaCl and DAM/Kδ for Other Solutes...........................................................................................384 3. RO Process Design .......................................................................387 B. Case II: Surface Force–Pore Flow Model; Generation of Interfacial Surface Force Parameters and Their Application ........389 1. Analysis Fundamentals ...............................................................389 2. Quantities Ra, Rb, and d .............................................................390 3. Deﬁnitions of Dimensionless Quantities ....................................390 4. Basic Transport Equations ..........................................................391 5. Liquid Chromatography for the Determination of Interfacial Interaction Force Parameters......................................................396 6. Data on Interfacial Surface Force Parameters ..........................397 7. Data on Pore Size and Pore Size Distribution...........................398 III. Problems in Membrane Separation and Concentration of Liquid Foods ........................................................................................................403 A. Application of Water Preferential Sorption Model..........................406 1. Separation of Undissociated Organic Solutes Such as Sugars Present in High Concentration ...................................................413 2. Separations of Undissociated Polar Organic Solutes Present in Low Concentrations.................................................................413
- 16. xvi Rao, Rizvi, and Datta 3. Separation of Partially Dissociated Organic Solutes Present in Low Concentration...................................................................416 4. Problem of Separations of Low Concentrations of Undissociated Organic Solutes in Concentrated Sugar Solutions ............................................................................418 5. Separation of Solutions of Partially Dissociated Acids Present in Concentrated Sugar Solutions..................................419 B. Application of Transport Equations to Real Fruit Juice Concentration.....................................................................................421 C. Application of Transport Equations for the Concentration of Green Tea Juice .................................................................................426 D. Some Illustrative Examples of the Surface Force–Pore Flow Model ..................................................................................................431 1. Parametric Studies on Solute Separation and Product Rate ...431 2. Another Parametric Study on Solute Concentration Proﬁle and Solution Velocity Proﬁle .......................................................434 E. Some Data on the Ultraﬁltration of Proteins .................................437 1. Ultraﬁltration of Bovine Serum Albumin (BSA) and a-Casein ........................................................................................437 2. Effects of Fouling on Membrane Performance and Pore Size and Pore Size Distribution ..........................................................440 3. Fractionation of the Protein–Sugar System and the Protein–Protein System in the Aqueous Solutions .....................443 F. Application of Pervaporation in the Recovery and Concentration of Food Flavors...................................................................................445 IV. Recent Literature on Membrane Applications......................................447 A. Dairy Product Industry.....................................................................447 1. Reverse Osmosis...........................................................................447 2. Nanoﬁltration ...............................................................................448 3. Ultraﬁltration ...............................................................................448 4. Microﬁltration...............................................................................448 B. Beverage Industry .............................................................................449 1. Reverse Osmosis...........................................................................449 2. Ultraﬁltration ...............................................................................450 3. Microﬁltration...............................................................................450 C. Edible Oil Industry............................................................................450 1. Reverse Osmosis...........................................................................451 2. Ultraﬁltration ...............................................................................451 3. Microﬁltration...............................................................................451 V. Conclusion................................................................................................452 List of Symbols ................................................................................................453 Greek Symbols .................................................................................................454 References.........................................................................................................455 Chapter 10 Electrical Conductivity of Foods .............................................461 Sudhir K. Sastry I. Introduction .............................................................................................461 II. Basic Deﬁnitions .....................................................................................462 III. Liquid Foods ............................................................................................462
- 17. Table of Contents xvii A. Theory of Electrolytic Conductivity..................................................462 1. Strong Electrolytes.......................................................................464 2. Weak Electrolytes.........................................................................464 B. Relations between Electrical Conductivity and Other Transport Properties ...........................................................................................465 C. Effect of Temperature........................................................................466 D. Effect of Electric Field Strength.......................................................467 E. Effect of Ingredients..........................................................................468 1. Electrolytic Solutes.......................................................................468 2. Inert Suspended Solids................................................................468 3. Hydrocolloids ................................................................................469 4. Phase Transitions of Suspended Solids......................................471 5. Effect of Nonelectrolytic Solutes .................................................474 IV. Solid Foods...............................................................................................474 A. Effect of Microstructure ....................................................................474 B. Effects of Temperature and Electric Field Strength.......................475 1. Gels and Noncellular Solids ........................................................475 2. Solids with Undisrupted Cellular Structure..............................476 3. Modeling of Cell Membrane Breakdown....................................479 4. Reversibility and Repair of Pores ...............................................479 5. Extension to Eukaryotic Cells.....................................................480 C. Effect of Frequency............................................................................482 1. Relation to Dielectric Constant...................................................484 D. Ingredient Effects ..............................................................................487 V. Solid–Liquid Mixtures ............................................................................488 A. Models for Effective Electrical Conductivity ...................................488 1. Maxwell Model..............................................................................488 2. Meredith and Tobias (1960) Model .............................................489 3. Series Model .................................................................................489 4. Parallel Model...............................................................................489 5. Kopelman Model...........................................................................489 6. Probability Model .........................................................................490 7. Comparison of Models..................................................................490 B. Effects of Solids in Tube Flow ..........................................................490 VI. Methods of Measurement of Electrical Conductivity...........................492 List of Symbols ................................................................................................496 Greek Letters and Other Symbols .................................................................496 Subscripts/Superscripts Not Explained Elsewhere.......................................497 References.........................................................................................................497 Chapter 11 Dielectric Properties of Foods .................................................501 Ashim K. Datta, G. Sumnu, and G.S.V. Raghavan I. Introduction .............................................................................................501 II. Basic Principles.......................................................................................502 A. Radiofrequency vs. Microwave Heating ...........................................509 III. Measurement Principles.........................................................................509 A. Waveguide and Coaxial Transmission Line Methods......................510 B. Short-Circuited Line Technique........................................................510
- 18. xviii Rao, Rizvi, and Datta C. Open-Ended Probe Technique...........................................................511 D. Time Domain Reﬂectometry (TDR) Method....................................512 E. Free-Space Transmission Technique ................................................512 F. Microstrip Transmission Line...........................................................513 G. Six-Port Reﬂectometer Using an Open-Ended Coaxial Probe .......513 H. Colloid Dielectric Probe (Hewlett Packard).....................................514 I. Test Cell with Boonton RX-Meter ....................................................514 J. Cavity Perturbation Technique.........................................................514 1. Solid Sample Preparation............................................................517 2. Liquid Sample Preparation .........................................................517 3. Semisolid Samples........................................................................517 K. Summary of Dielectric Property Measurement Techniques...........517 IV. Frequency and Temperature Dependence.............................................518 A. Frequency Dependence......................................................................518 A. Frequency Dependence in Food Materials.......................................521 B. Temperature Dependence in Water, Salt Solutions, and Foods .....522 1. Dielectric Properties below Freezing and above Boiling Temperatures................................................................................526 2. Temperature Dependence of Loss Factor and Runaway Heating..........................................................................................530 V. Composition Dependence........................................................................531 A. Moisture Dependence ........................................................................531 B. Dielectric Properties of Carbohydrates............................................533 1. Starch ............................................................................................534 2. Sugar .............................................................................................536 3. Gums .............................................................................................536 C. Dielectric Properties of Proteins.......................................................538 D. Dielectric Properties of Fat...............................................................541 E. Dielectric Properties of Meats ..........................................................542 F. Dielectric Properties of Fish and Seafood .......................................543 G. Dielectric Properties of Fruits and Vegetables................................545 H. Dielectric Properties of Dairy Products ...........................................547 VI. Dielectric Properties of Insect Pests......................................................550 VII. Dielectric Properties of Packaging Materials .......................................551 VIII. Effects of Processing and Storage on Dielectric Properties of Foods...551 A. Baking.................................................................................................551 B. Drying.................................................................................................554 C. Cooking...............................................................................................554 D. Mixing.................................................................................................554 E. Storage................................................................................................554 IX. Assessment of Food Quality by Using Dielectric Properties...............555 X. Further Sources of Data.........................................................................557 Acknowledgment..............................................................................................557 References.........................................................................................................557 Chapter 12 Ultrasound Properties .............................................................567 Michael J. McCarthy, Lu Wang, and Kathryn L. McCarthy I. Introduction .............................................................................................567 II. Fundamentals of Acoustics.....................................................................569
- 19. Table of Contents xix A. Speed of Sound, Density, and Elastic Moduli..................................569 B. Amplitude and Attenuation ..............................................................571 1. Scattering......................................................................................572 2. Absorption.....................................................................................572 C. Impedance, Reﬂection, and Refraction.............................................573 D. Doppler Shift Frequency and Velocity .............................................574 III. Ultrasonic Measurement Techniques ....................................................575 A. Ultrasonic Methods............................................................................576 1. Pulsed-Echo...................................................................................576 2. Pitch-and-Catch............................................................................578 3. Interferometry ..............................................................................578 4. Spectral Analysis..........................................................................579 5. Ultrasonic Imaging.......................................................................579 B. Transducer Selection .........................................................................580 C. Interpretation of Ultrasonic Measurements....................................582 IV. Compilation of Acoustic Properties........................................................582 A. Composition........................................................................................582 1. Solutions and Beverages..............................................................582 2. Concentrated Solutions................................................................587 3. Oils ................................................................................................588 4. Emulsions......................................................................................589 5. Muscle Foods.................................................................................593 B. Phase Transitions ..............................................................................594 1. Freezing.........................................................................................594 2. Crystallization of Fats..................................................................594 3. Gelation.........................................................................................596 C. Texture................................................................................................597 1. Firmness of Fruits/Vegetables.....................................................597 2. Cheese ...........................................................................................597 3. Starch Products ............................................................................598 D. Viscosity..............................................................................................599 1. Viscosity and Attenuation............................................................599 2. Viscosity and UDV .......................................................................600 V. Conclusion................................................................................................603 List of Symbols ................................................................................................604 Greek Symbols .................................................................................................604 Subscripts.........................................................................................................605 Superscripts......................................................................................................605 References.........................................................................................................605 Chapter 13 Kinetic Data for Biochemical and Microbiological Processes during Thermal Processing .....................................................611 Ann M. Van Loey, Chantal Smout, Indrawati, and Marc E. Hendrickx I. Introduction .............................................................................................611 II. Fundamental Considerations .................................................................614 A. Primary Kinetic Models ....................................................................615 1. Zero-Order Model .........................................................................616 2. First-Order Model ........................................................................617
- 20. xx Rao, Rizvi, and Datta 3. Biphasic Model .............................................................................618 4. Fractional Conversion Model.......................................................618 B. Secondary Kinetic Models.................................................................619 1. Inﬂuence of Temperature on the Reaction Rate Constant .......619 2. Selection of a Temperature Coefﬁcient Model ...........................620 III. Measurement Techniques.......................................................................621 IV. Speciﬁc Data on Properties ....................................................................623 A. Microbial Inactivation .......................................................................623 B. Enzyme Inactivation..........................................................................625 C. Texture Degradation..........................................................................626 D. Color Degradation..............................................................................627 E. Flavor Degradation............................................................................629 F. Nutrient Degradation........................................................................630 References.........................................................................................................633 Chapter 14 Gas Exchange Properties of Fruit and Vegetables................645 Bart M. Nicolaï, Jeroen Lammertyn, Wendy Schotsmans, and Bert E. Verlinden I. Introduction .............................................................................................645 II. Fundamental Considerations .................................................................646 A. Respiration and Fermentation..........................................................646 1. Respiration Rate...........................................................................648 2. Respiration and Fermentation Models .......................................649 3. Gas Transport Properties ............................................................653 B. Measurement Techniques..................................................................655 1. Oxygen Consumption and Carbon Dioxide Production Rate....655 2. Measurement of O2 and CO2 Concentration ..............................656 3. Measurement of Heat of Respiration..........................................659 4. Skin Resistance and Gas Diffusion Properties..........................660 C. Gas Exchange Data for Selected Fruits and Vegetables ................663 III. Applications .............................................................................................663 Acknowledgments ............................................................................................671 List of Symbols ................................................................................................671 References.........................................................................................................672 Chapter 15 Surface Properties....................................................................679 Joseph McGuire I. Introduction .............................................................................................679 II. Fundamental Considerations .................................................................680 A. Deﬁnitions ..........................................................................................680 B. The Gibbs Adsorption Equation .......................................................682 C. The Contact Angle .............................................................................684 1. Critical Surface Tension...............................................................686 2. Polar and Dispersive Contributions to Surface Energy............686 3. An Equation of State Relationship between Interfacial Energies ........................................................................................690 D. Effects of Adsorbed Layer Composition and Structure on Interfacial Energy..............................................................................690
- 21. Table of Contents xxi III. Measurement Techniques.......................................................................693 A. Evaluation of the Contact Angle ......................................................693 B. Evaluation of Liquid Surface Tension..............................................694 C. Evaluation of γL d and γS d ...................................................................696 IV. Surface Property Data............................................................................697 V. Summary..................................................................................................699 References.........................................................................................................699 Chapter 16 Colorimetric Properties of Foods ............................................703 F. J. Francis I. Introduction .............................................................................................703 II. Physiological Basis of Color ...................................................................704 III. Measurement of Color ............................................................................705 A. Spectrophotometry.............................................................................705 B. Tristimulus Colorimetry....................................................................711 C. Specialized Colorimeters ...................................................................712 IV. Presentation of Samples.........................................................................714 V. Research and Quality Control Approaches ...........................................717 VI. Color Tolerances ......................................................................................720 VII. Development of Instruments..................................................................723 VIII. Conclusion................................................................................................726 References.........................................................................................................727 Index .................................................................................................................733
- 22. 1 1 Mass-Volume-Area–Related Properties of Foods M. SHAFIUR RAHMAN Sultan Qaboos University, Muscat, Sultanate of Oman I. INTRODUCTION Mass-volume-area–related properties are one of ﬁve groups (acoustic, mass-volume-area–related, morphological, rheological, and surface) of mechanical properties (Rahman and McCarthy, 1999). These properties are needed in process design, for estimating other properties, and for product characterization or quality determination. The geometric char- acteristics of size, shape, volume, surface area, density, and porosity are important in many food materials handling and processing opera- tions. Fruits and vegetables are usually graded depending on size, shape, and density. Impurities in food materials are separated by density differences between impurities and foods. Knowledge of the bulk den- sity of food materials is necessary to estimate ﬂoor space during storage and transportation (Mohsenin, 1986; Rahman, 1995). When mixing, transportation, storing and packaging particulate matter, it is impor- tant to know the properties of bulk material (Lewis, 1987). Surface areas of fruits and vegetables are important in investigations related to spray coverage, removal of residues, respiration rate, light reﬂec- tance, and color evaluation, as well as in heat transfer studies in heating and cooling processes (Mohsenin, 1986). In many physical and
- 23. 2 Rahman chemical processes, the rate of reaction is proportional to the surface area; thus, it is often desirable to maximize the surface area. Density and porosity have a direct effect on the other physical properties. Volume change and porosity are important parameters in estimating the diffusion coefﬁcient of shrinking systems. Porosity and tortuosity are used to calculate effective diffusivity during mass transfer pro- cesses. Mechanical properties of agricultural materials also vary with porosity. This chapter provides terminology, measurement techniques, and prediction models of selected mass-volume-area–related properties. II. FUNDAMENTAL CONSIDERATIONS A. Volume 1. Boundary Volume Boundary volume is the volume of a material considering the geometric boundary. A material’s volume can be measured by buoyancy force; liquid, gas, or solid displacement; or gas adsorption; it can also be estimated from the material’s geometric dimensions. Estimation equa- tions of the boundary volume of shapes of regular geometry are given in Table 1.1. 2. Pore Volume Pore volume is the volume of the voids or air inside a material. B. Density Density is one of the most important mechanical properties and so is widely used in process calculations. It is deﬁned as mass per unit volume: (1.1) The SI unit of density is kg/m3. In many cases foods contain multicomponent phases, such as solid, liquid, and gaseous or air. In this case, a simple deﬁnition such as that given above cannot be sufﬁ- cient to relate the mass and volume. In this case, different terminology should be deﬁned. Rahman (1995) clearly explained different forms of density used in process calculations and characterizing food products. The deﬁnitions are given as follows. 1. True Density True density (ρT) is the density of a pure substance or a composite material calculated from its components’ densities considering conser- vation of mass and volume. Density Mass Volume m V = =
- 24. Mass-Volume-Area–Related Properties of Foods 3 2. Material Density Material density (ρm) is the density measured when a material has been thoroughly broken into pieces small enough to guarantee that no closed pores remain. 3. Particle Density Particle density (ρp) is the density of a particle, which includes the volume of all closed pores but not the externally connected pores. In TABLE 1.1 Volume and Surface Area of Some Common Shapesa a Where a and b, respectively, are major and minor semiaxes of the ellipse of rotation, e is the eccentricity given by e = , r1 and r2, respectively, are the radii of base and top, and L is the altitude. Sphere Cylinder V r and A r V r L and A = = = = 4 3 4 2 3 2 2 π π π πrr rL V a and A a V abc and A ab 2 3 2 2 6 2 + = = = = π Cube Brick ( ++ + = = +( ) bc ca V ab and A b ) Prolate spheroid 4 3 2 2 2 π π 22 4 3 2 1 2 π π π ab e Sin e V a b A − = =( ) Oblate spheroid and aa b e e e V L 2 2 1 1 3 + + − = ⎛ ⎝⎜ ⎞ ⎠⎟ π π ln Frustam right cone rr r r r A r r L r r1 2 1 2 2 2 1 2 2 1 2 2 + + = + + −( ) ( )and π ( ) 1 b a⁄( ) 2 –[ ]
- 25. 4 Rahman this case, the particle is not modiﬁed structurally, as in the case of material density. 4. Apparent Density Apparent density (ρa) is the density of a substance including all pores remaining in the material. 5. Bulk Density Bulk density (ρB) is the density of a material when packed or stacked in bulk. The bulk density of packed materials depends on the geometry, size, and surface properties of individual particles (Lewis, 1987). C. Porosity Porosity indicates the volume fraction of void space or air in a material and is deﬁned as: (1.2) Different forms of porosity are used in food process calculations and food products characterization (Rahman, 1995). These are deﬁned below: 1. Open Pore Porosity Open pore porosity is the volume fraction of pores connected to the exterior boundary of a material and is given by (εop): (1.3) There may be two types of open pores: one type is connected to the exterior boundary only, and another type is connected to the other open pores as well as to the exterior geometric boundary. The level of open and closed pores depends on what component (helium, nitrogen, toluene, or mercury) is used in the measurement. 2. Closed Pore Porosity Closed pore porosity (εcp) is the volume fraction of pores closed inside the material and not connected to the exterior boundary of the material. It can be deﬁned as: Porosity Air or Void Volume Total Volume = Open pore porosity Volume of open pore Total volum = ee of material op a p ε ρ ρ = −1
- 26. Mass-Volume-Area–Related Properties of Foods 5 (1.4) 3. Apparent Porosity Apparent porosity is the volume fraction of total air or void space in the material boundary and is deﬁned as (εa = εop + εcp): (1.5) 4. Bulk Porosity Bulk porosity (εB) is the volume fraction of voids outside the boundary of individual materials when packed or stacked as bulk: (1.6) 5. Bulk-Particle Porosity Bulk-particle porosity is the volume fraction of the voids outside the individual particle and open pore to the bulk volume when packed or stacked as bulk. (1.7) 6. Total Porosity Total porosity is the total volume fraction of air or void space (i.e., inside and outside of the materials) when material is packed or stacked as bulk. (1.8) D. Surface Area Two types of surface area are used in process calculations: outer bound- ary surface of a particle or object, and pore surface area for a porous Closed Pore Porosity Volume of closed pores Total = vvolume of material cp p m ε ρ ρ = −1 Apparent Porosity Volumeof all pores Totalvolum = eeof material a a m ε ρ ρ = −1 BulkPorosity Volumeof voidsoutsidematerials = 'bboundary Totalbulkvolumeof stackedmaterials εBB b a = −1 ρ ρ ε ε εBP B op= + ε ε ε ε ε εT a B op cp B= + = + +
- 27. 6 Rahman material.An object can be characterized using Euclidian or non-Euclidian geometries. Euclidian geometric shapes always have characteristic dimensions and have an important common peculiarity of smoothness of surface; examples include spheres, cubes, and ellipsoids. E. Pore Size Distribution In addition to size and shape, particle or pore size population needs to be determined. Pore size distribution is most commonly used to char- acterize populations. Similar techniques are also used for particle size distribution. III. MEASUREMENT TECHNIQUES A. Density Measurement 1. Apparent Density a. Geometric Dimension Method The apparent density of a shape of regular geometry can be determined from the volume calculated from the characteristic dimensions and mass. This method is not suitable for soft and irregularly shaped mate- rials, where it is not easy to measure the characteristic dimensions (Rahman, 1995). Little information exists in the literature about the density measurement of frozen foods. Keppeler and Boose (1970) used a thick-walled cylindrical metal container to measure the density of frozen sugar solution. The density determination method consists of ﬁnding the mass of a frozen sample with a known volume. The unfrozen sample is placed in the cylindrical container and then frozen at the desired temperature. The excess frozen sample can be removed with a sharp knife. Then the cylinder and frozen sample should be weighed immediately. From the mass of the sample and the volume of the cylinder, density can be calculated. Rahman and Driscoll (1994) wrapped the metal container with electrical tape to reduce the heat gain during weighing. This method is only suitable for liquid and soft materials, where no void exists in the packing. b. Buoyant Force Method In this procedure, buoyant force can be determined from sample weight in air and liquid. The apparent density can be calculated from the equation: (1.9) where m and G are the mass (in kilograms) of the sample in air and liquid (i.e., water), respectively, and ρw is the density of the liquid. The ρ ρa w m G = ×
- 28. Mass-Volume-Area–Related Properties of Foods 7 methods of weighing the samples are shown in Figure 1.1 for a top- loading balance and an analytical balance. Two errors may often occur with this method, and hence precautions should be taken during mea- surement. The ﬁrst may be due to mass transfer from the sample to liquid, i.e., the exchange of solid, liquid, or gas from the sample to liquid. This can be avoided by enclosing the sample in cellophane or polythene or coating with a thin layer of polyurethane varnish or wax. The sample could be tied with a thin string and dipped in wax a couple of times and solidiﬁed before measurement. Samples can also be covered with silicon grease in order to make them impervious to water (Loch-Bonazzi et al., 1992). Lozano et al. (1980) measured plastic ﬁlm-coated samples of fresh and dried fruits and vegetables and samples without coating and found that no signiﬁcant moisture was taken up when the uncoated samples were used. The above authors noted that this was due to the very brief time required for measurement. However, coating is the best possible option for accuracy, and care must be taken to prepare the coating. The second error may be due to partial ﬂoating of the sample. In this case, a liquid with a lower density than that of the sample can be used. Mohsenin (1986) described a simple technique with a top-loading balance that applies to large objects such as fruits and vegetables (Fig- ure 1.2). The sample is ﬁrst weighed on the scale in air and then forced into water by means of a sinker rod. Second readings are then taken with the sample submerged. The density can then be calculated as: (1.10) where G1 refers to the sinker plus the sample and G2 refers to the sinker only in water or liquid. Again, if the solid is lighter than the liquid, Figure 1.1 Top-loading balance for measurement of buoyant force for a sam- ple lighter than liquid. Source: Mohsenin, N.N. 1986. ρ ρ ρ a s w w m G G = − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 1 2/ /
- 29. 8 Rahman another solid can be attached, heavier than the liquid, to the object as a sinker. In the case of coated sample with a sinker, the following equation can be used: (1.11) where G1 refers to the sinker plus the wax-coated sample, G2 the sinker only, and G3 the wax only. G3 can be calculated as: (1.12) The mass of wax can be calculated from the difference between the masses of coated and uncoated samples. The density of wax is usually around 912 kg/m3; however, it could vary based on the source. Thus, the density of wax should be measured separately. Mohsenin (1986) also suggested that a solution of 3 cm3 wetting agent in 500 cm3 distilled water can reduce errors due to surface tension and submer- gence in water. Ramaswamy and Tung (1981) used a buoyant force determination technique to measure the apparent density of frozen apple. They used water at 2 to 3˚C, and the apple was frozen at –20 to –35˚C with a sinker. There is a real need to develop accurate and easy measurement techniques for frozen samples at subzero temperature. c. Volume Displacement Method i. Liquid Displacement Method. The volume of a sample can be measured by direct measurement of volume of liquid displaced. The Figure 1.2 Analytical balance for measurement of buoyant force. Container Brass sinker rod or thread Specimen Stand Scale ρ ρ ρ a s w w m G G G = − − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 1 2 3/ / G mwax wax 3 = ρ
- 30. Mass-Volume-Area–Related Properties of Foods 9 difference between the initial volume of the liquid in a measuring cylinder and the volume of the liquid plus immersed material (coated) is the volume of the material. Coating is necessary so that liquid does not penetrate in the pores. A nonwetting ﬂuid such as mercury is better to use for displacement since in this case samples do not need coating. The use of a speciﬁc gravity bottle and toluene has been practiced for many years (Bailey, 1912). A small-neck speciﬁc gravity bottle is not suitable for large objects; thus, a special design is required. The volume of a speciﬁc gravity bottle can be measured using distilled water. Toluene has many advantages when used as reference liquid (Mohsenin, 1986): 1. Little tendency to soak on the sample 2. Smooth ﬂow over the surface due to surface tension 3. Low solvent action on constituents, especially fats and oils 4. Fairly high boiling point 5. Stable speciﬁc gravity and viscosity when exposed to the atmo- sphere 6. Low speciﬁc gravity Toluene is carcinogenic; thus, adequate precautions need to be taken in using it. The experiment should be performed inside a fume chamber (Rahman et al., 2002). Rahman and Driscoll (1994) reported the use of a method for irregular and small frozen food particles such as grain or cereals. The procedures were as follows: eight cylindrical glass bottles of diameter 2 cm with small necks ﬁlled three-fourths full (20 g) with sample and the rest of the way with toluene were frozen at –40˚C. After freezing, the bottles were immediately placed inside glass wool insulation col- umns of inner and outer diameter of 2 and 7 cm, respectively. The temperature was then recorded from one bottle by a thermocouple placed inside the center of the bottle. At different temperatures, the bottles were taken out, one at a time, from the glass wool insulation, and toluene was added to completely ﬁll the bottle. The bottle was closed immediately, and the weight was determined. From the mass and volume of the sample, which was estimated by subtracting the volume of toluene from the volume of the bottle, the density was cal- culated. The volume of toluene was estimated from the mass and density at the respective temperatures. Rahman and Driscoll (1994) used this method to measure the density of frozen seafood at different temperatures and found reproducibility within 1%. Commercial mercury porosimeters are available to measure the volume of porous and nonporous solids. The principle of mercury intru- sion porosimetry is based on the fact that mercury ordinarily behaves as a nonwetting liquid (i.e., the contact angle of mercury is larger than 90˚). Because it is nonwetting, mercury will not ﬂow into the openings of porous solid bodies unless it is forced to do so by a pressure gradient
- 31. 10 Rahman (Clayton and Huang, 1984). The mercury injection method of measuring effective porosity is based on the fact that, due to the surface tension and nonwetting properties of mercury, a porous sample can be immersed in mercury without entry of mercury into the sample at atmospheric pressure. Thus, the apparent volume of the sample can be determined by displacement of mercury from a sample chamber of known volume. ii. Gas Pycnometer Method. Different commercial gas pycnometers for volume measurement are available. The gases air, nitrogen, and helium can be used. Mohsenin (1986) described a method to measure volume using high-pressure air (Figure 1.3). The test material is placed in tank 2 and air is supplied to tank 1 when valve 2 is closed. When suitable manometer displacement is achieved, valve 1 is closed and equilibrium pressure P1 is read. Now valve 3 is closed and valve 2 is opened, and pressure P3 is read. Under this condition with valves 1 and 3 closed, the volume of sample in tank 2 is measured as Vs. Then the volume of the sample in tank 2 is estimated based on ideal gas law as: (1.13) where V1 is the empty volume of tanks 1 or 2. Commercial automatic helium gas pycnometers are available to measure volumes of samples. Figure 1.4 shows the operating principle of the Horiba helium pycnometer VM-100. If a sample of volume Vs is placed in a sample cell with volume Vsc, pressure P1 is applied to the sample cell, and the valve is then opened and gas passed through an expansion cell with volume Vec, the pressure will decrease to P2 due to the expansion of the gas. The volume Vs of the sample may be obtained Figure 1.3 Air comparison pycnometer. Source: Mohsenin, N.N. 1986. V V V P P P s = + × −⎛ ⎝⎜ ⎞ ⎠⎟1 1 3 1 3 Valve 1 Valve 2 Valve 3 To manometer Air out Air in Tank 1 Tank 2
- 32. Mass-Volume-Area–Related Properties of Foods 11 from the known volumes Vsc and Vec and the ratio of pressures P1 and P2 using the following formula (Horiba Bulletin: HRE-8815A): (1.14) The above equation is derived based on the ideal gas law. In order to measure the apparent density, the sample needs to be coated with wax before placing inside the pressure chamber. iii. Solid Displacement Method. The apparent volume of an irregular solid can be measured by a solid displacement or glass bead displace- ment method. Glass beads have an advantage over sand due to their uniform size and shape, thus producing reproducible results. 2. Material Density a. Pycnometer Method Material density can be measured when a material is ground enough to guarantee that no closed pores remain. Both liquid and gas displace- ment methods (pycnometer) can be used to measure the volume of ground material. When liquid is used, care must be taken to use suf- ﬁcient liquid to cover the solid’s surface or pores. This difﬁculty can be overcome by: 1. Gradually exhausting the air from the bottle by a vacuum pump to promote the escape of the air trapped under the surface 2. When air bubbles escape after several cycles of vacuuming and releasing the vacuum, ﬁlling the bottle with toluene and allow- ing the temperature to reach 20˚C b. Mercury Porosimetry Pore volumes can be measured by gas adsorption techniques or mercury porosimetry. In addition, pore characteristics and size distribution can Figure 1.4 Operating principle of Horiba helium pycnometer VM-100. Source: Horiba Bulletin: HRE-8815A. Vs Vx P1 Vex Vs Vx P2 Vex V V P P Vx xc ec= + − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 1 1 1 2( )/
- 33. 12 Rahman also be determined by these methods. Both techniques are very well deﬁned and generally accepted methods for characterization of pores. Modern mercury porosimeters can achieve pressures in excess of 414 MPa, which translates into a pore size of 0.003 nm. The upper end of this technique can measure pores up to 360 nm. Gas adsorption, on the other hand, can measure pores as small as 4 Å and up to 5000 Å (Particulars, 1998). In comparison to gas adsorption, mercury porosim- etery takes less time, with a typical analysis taking less than an hour. Gas adsorption can take from a couple of hours to 60 hours to complete (Particulars, 1998). Both techniques involve constructing an isotherm, either of pres- sure versus intrusion volume in the case of mercury porosimetry or volume adsorbed versus relative pressure in the case of gas adsorption. Total pores or pore size distribution can be derived from these iso- therms. As pressure is applied, the pressure at which the mercury intrudes into the pores is measured. The smaller the pore, the higher is the pressure required to force the mercury into the pores. The pres- sure is increased and the amount of mercury that intrudes is monitored at a series of pressure points that represent corresponding pore sizes. If decreasing pressures are included in the analysis, then a series of volumes and pore sizes can be obtained as the mercury extrudes out of the pores. Very often, a difference exists between the intrusion and extrusion curves because the pores may form bottlenecks or restric- tions. In this case, some of the mercury may be left in the sample. This evidence can provide valuable data regarding the shape of pores in sample (Particulars, 1998). Mercury porosimetry uses the Washburn equation, which is based on the capillary law governing the penetration of a liquid into small pores (Figure 1.5): (1.15) Mercury porosimetry is suitable for measurement of smaller open pores since it uses high pressure. In the case of mercury porosimetry for material density, the sample need not be ground since high pressure forces mercury to penetrate into the pores. However, it does not guar- antee that mercury has intruded into all pores even at very high pressure (Rahman et al., 2002). When high pressure is used, the com- pressibility of solids should be considered for accuracy. If the sample chamber is closed and the hydrostatic pressure of mercury in the cham- ber is increased to a very great value, the mercury will enter the pores, compressing the trapped air in the pores to negligible volume. The volume of mercury injected is therefore equal to the pore volume. An advantage of mercury porosimetry is that both apparent vol- ume and pore volume are directly determined without coating the D Cos P v = 4 τ θ
- 34. Mass-Volume-Area–Related Properties of Foods 13 sample. This method may not be very precise if the volume occupied by compressed air is not determined. The sample can not be used for further tests, even after extensive cleaning procedures, due to contam- ination with mercury. c. Gas Adsorption Method In the gas adsorption method, the sample is cooled, usually to cryogenic temperatures, and then is exposed to the inert adsorptive gas, typically nitrogen, at a series of precisely controlled pressures. As the pressure increases, a number of the gas molecules are adsorbed onto the surface of the sample. This volume of adsorbed gas is measured using sensitive pressure transducers. As the pressure increases, more and more gas is adsorbed. First the very small micropores, less than 20 Å, are ﬁlled, followed by the free surface and ﬁnally the rest of the pores. Each pressure corresponds to a pore size, and from the volume of gas adsorbed, the volume of these pores can be obtained. By collecting data as the pressure reduces, then a desorption isotherm can be derived as well and observed for any hysteresis and hence again information on pore shape. Obviously, using this technique the BET surface area can also be derived (Particulars, 1998). Figure 1.5 The relation of intrusion pressure to the pore diameter. Source: Rahman, M.S. 2000. Pressure (P) Diameter (D) P Dn = 4g cos q
- 35. 14 Rahman 3. Particle Density Particle density can be measured by the volume displacement method used in apparent density measurement without coating the particle or object. Care should be taken to avoid any structural changes during the measurement. Large particles cannot be placed in a side narrow- neck speciﬁc gravity bottle or pycnometer; thus, a special design is required for foods containing such particles. 4. Bulk Density Bulk density can be determined by stacking or placing a known mass of particles into a container of known volume, such as a measuring cylinder. Material can be ﬁlled into a speciﬁc geometric container of known volume, and the excess amount on the top of the cylinder can be removed by sliding a string or ruler along the top edge of the cylinder. Gentle tapping of the cylinder vertically down to a table may also be done. This method considers all pores inside as well as outside the individual particles. After the excess has been removed, the mass of the sample can be measured and the bulk density can be estimated as: (1.16) B. Measurement Techniques of Porosity 1. Direct Method In this method, the bulk volume of a piece of porous material is measured ﬁrst, and then the volume is measured after compacting the material to destroy all its voids. Porosity can be determined from the difference of the two measured volumes. This method can be applied if the mate- rial is very soft and no repulsive or attractive force is present between the surfaces of solid particles. 2. Optical Microscopic Method In this method the porosity can be determined from the microscopic view of a random section of the porous medium. This method is reliable if the sectional (two-dimensional) porosity is same as the three-dimen- sional porosity. Image analysis is necessary to estimate the surface area of pores. 3. Density Method Porosity can also be estimated from the densities of the materials from Equation (1.3) to Equation (1.6). Alternatively, pore volume can be measured directly by liquid or gas displacement methods, described earlier in the discussion of density measurements. ρB B m V =
- 36. Mass-Volume-Area–Related Properties of Foods 15 C. Surface Area 1. Boundary Surface Area Boundary surface area is mainly estimated from geometric dimensions or measured by image analysis or contour analysis. Leaf and stalk surface area are measured by contact-printing the surface on a light- sensitive paper and then estimating the area with a planimeter, or by tracing the area on graph paper and counting the squares or determin- ing the mass of the paper. In this method, the mass-area relationship of the paper should be developed ﬁrst. Another method is the use of an air-ﬂow planimeter, which measures the area as a function of the surface obstructing the ﬂow of air (Mohsenin, 1986). The surface area of fruits and vegetables can be estimated from the peeled or skin area. In this method, fruit is peeled in narrow strips and the planimeter sum of the areas of tracings of the strips is taken as the surface area. Similarly, strips of narrow masking tape can be used to cover the surface; from the length and width of the tape, the surface area can be estimated. A transient heat transfer study can also be used to estimate the surface area (Mohsenin, 1986). The simplest method of obtaining the surface area of a symmetrical convex body such as an egg is the projection method using a shadow- graph or photographic enlarger. Using the proﬁle of the egg, equally spaced parallel and perpendicular lines can be drawn from the axis of symmetry to the intersection with the proﬁle. Then using manual computation, by integration, the surface area can be obtained by sum- ming up the surfaces of revolution for all of the divided segments (Mohsenin, 1986). 2. Pore Surface Area Pore surface area can be deﬁned as the surface of the pores in a porous medium exposed to ﬂuid ﬂow either per unit volume or per unit mass of the solid particles. a. Methods Based on Adsorption The quantity of an inert vapor that can be adsorbed on the pore surface is dependent on the area of the surface. The quantity of a gas or vapor adsorbed is proportional to a surface area that inclines the tiny molecular interstices of the porous material, whereas the surface area pertinent to ﬂuid ﬂow does not include this portion of surface area. b. Methods Based on Fluid Flow Mohsenin (1986) noted that the Carman–Kozeny equation can be employed to measure the speciﬁc surface of the nonuniform pore space. Kozeny showed that permeability can be written for steady state and stream line ﬂow (Re < 2.0) through porous media:
- 37. 16 Rahman (1.17) (1.18) where f is a dimensionless constant, εop is the open pore porosity, A is the speciﬁc surface area (m2/m3), and u is the approach or velocity of the ﬂuid in the empty column (m/sec). Carman modiﬁed the above equation considering f = 1/5, the result is known as the Carman–Kozeny equation given by: (1.19) The value of f depends on the particle shape, porosity, and particle size range and lies between 3.5 and 5.5 with a common value of 5 (Holland, 1973). The values of A can be calculated from the above equation by knowing the porosity and permeability. The permeability can be calcu- lated from the well-known Darcy’s equation: (1.20) An inert ﬂuid needs to be used. This method is more commonly used for rocks and is not suitable for fragile solids, such as foods. Also, the surface of dead-end pores cannot be included in the ﬂuid ﬂow method. c. Mercury Intrusion Mercury intrusion measures the characteristics of pores. Surface area is determined from the intruded volume using geometric dimensions of a preassumed geometric shape of the pores. 3. Cross-Sectional Area Cross-sectional area is the area of a surface after longitudinal or trans- verse section of a material. It is necessary when ﬂuid is ﬂowing over an object. The methods of boundary surface area can also be used. IV. SPECIFIC DATA A. Predictions of Density In most engineering design, solids and liquids are assumed to be incom- pressible, i.e., density moderately changes with temperature and pres- sure.Actually, the density of solids and liquids changes with temperature k f A op = ε3 2 Re ( ) = − ρ µ ε a op u A1 k A op op = − ε ε 3 2 2 5 1( ) Q k A P L = ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ( )∆ µ
- 38. Mass-Volume-Area–Related Properties of Foods 17 and pressure. Gases and vapors are compressible and thus are affected by temperature and pressure. 1. Gases and Vapors The ideal gas equation is commonly used to estimate the density of gases and vapors. The ideal gas equation is based on unhindered move- ment of gas molecules within a conﬁned space, thus at constant temperature when molecular energy is constant, the product of pres- sure and volume is constant. At low pressure, most gases obey the ideal gas equation, which can be written as: (1.21) One kg mole ideal gas occupies 22.4 m3 at 273 K and 1 atm. As pressure is increased, the molecules are drawn closer together, and attractive and repulsive forces between the molecules affect molecular motion. At low pressure when molecules are far apart, only an attrac- tive force exists. At high pressures, the pressure–volume–temperature relationship deviates from ideality (Toledo, 1993). Gases that deviate from ideal behavior are considered real gases. One of the most com- monly used equations of state for real gases is Van der Waal’s equation. For n moles of gas, Van der Waal’s equation of state is: (1.22) Values of a and b for different gases are given in Table 1.2 (Toledo, 1993). TABLE 1.2 Values of Van der Waal’s Constants for Different Gases Gas a (Pa [m3/kg mole]2) b (m3/kg mole) Air 1.348 × 105 0.0366 Ammonia 4.246 × 105 0.0373 Carbon dioxide 3.648 × 105 0.0428 Hydrogen 0.248 × 105 0.0266 Methane 2.279 × 105 0.0428 Nitrogen 1.365 × 105 0.0386 Oxygen 1.378 × 105 0.0319 Water vapor 5.553 × 105 0.0306 Source: Toledo, R.T. 1993. Fundamentals of Food Process Engineering. 2nd ed. Chapman & Hall, New York. PV nRT= P n a V V nb nRT+ × − = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ( ) 2 2
- 39. 18 Rahman 2. Liquid Foods a. Milk and Dairy Products The density of whole and skim milk as a function of temperature can be calculated from the equations developed by Short (1955): (1.23) (1.24) Phipps (1969) reported an equation for the estimation of the den- sity of cream as a function of temperature and fat content with an accuracy of ±0.45%: (1.25) where Xf is the mass fraction of fat. Roy et al. (1971) reported equations for estimating the density of fat from buffalo’s and cow’s milk: (1.26) (1.27) b. Fruit Juices and Purees The apparent density of a sucrose solution can be estimated as a function of sucrose concentration (Xw: 0 to 1.0) at 20˚C (Chen, 1989): (1.28) where Co = 997.2, C1 = 3.858, C2 = 1.279 × 10–2, C3 = 6.192 × 10–5, C4 = –1.777 × 10–7, and C5 = –4.1997 × 10–10, respectively. For fruit juices, the density versus the refractive index of sugar solution can be esti- mated as (Riedel, 1949): (1.29) where ϑ is the refractive index. For the density of tomato juice, Choi and Okos (1983) developed a predictive equation based on the water (Xw) and solids (Xs) fractions: Whole milk: ρa t t= − + −1035 0 0 358 0 0049 0 000102 . . . . tt3 Skim milk: ρa t t t= − + −1036 6 0 146 0 0023 0 000152 . . . . 33 ρa t t t X= − − − − ⎛ ⎝⎜ ⎞ ⎠⎟1038 2 0 17 0 003 133 7 475 52 . . . . . ff Buffalomilk: ρa t= −923 84 0 44. . Cow's milk: ρa t= −923 51 0 43. . ρa j w j j C X= = ∑100 0 5 ( ) ρ ϑ ϑ a = − + × × 2 2 1 2 62 4 0 206 16 0185 . . .
- 40. Mass-Volume-Area–Related Properties of Foods 19 (1.30) ρw = 9.9989 × 102 – 6.0334 × 10–2 t – 3.6710 × 10–3 t2 (1.31) (1.32) Bayindirli (1992) proposed a correlation to estimate the apparent density of apple juice as a function of concentration (B: 14 to 39˚Brix) and temperature (20 to 80˚C) as: (1.33) Ramos and Ibarz (1998) correlated the apparent density of peach (Equation 1.34) and orange (Equation 1.35) juices as a function of concentration (B: 10 to 60˚Brix) and temperature (0 to 80˚C) as: (1.34) (1.35) Ibarz and Miguelsanz (1989) correlated the apparent density of depectinized and clariﬁed pear juice as (B: 10 to 71˚Brix and t: 5 to 70˚C): (1.36) Telis-Romero et al. (1998) correlated the apparent density of Brazilian orange juice as affected by temperature (0.5 to 62˚C) and water content (Xw: 0.34 to 0.73) as: (1.37) 3. Density of Solid Foods The density of food materials depends on temperature and composition. Choi and Okos (1985) presented correlations for the densities of the major food components at a temperature range of –40 to 150˚C (Table 1.3). Density of food materials varies nonlinearly with moisture content. Lozano et al. (1983) developed a general form of correlation to predict the density of fruits and vegetables during air drying. They found a wide variation in values and shapes of the curves when plotting apparent density against Mw /Mw o of carrot, potato, sweet potato, and whole and sliced garlic. They found that the following form of the equation can predict the density of all fruits and vegetables considered. (1.38) The parameters of the models are provided by Lozano et al. (1983) for different food materials. ρ ρ ρa w w s sX X= + ρs t t= × + × − ×− − 1 4693 10 5 4667 10 6 9643 103 1 3 2 . . . ρa B t= + ⎡⎣ ⎤⎦ −830 350 0 01 0 564exp( . ) . ρa t B B= − + +1006 6 0 5155 4 1951 0 0135 2 . . . . ρa t B B= − + +1025 4 6 0 3289 3 2819 0 0178 2 . . . . . ρa B t= + −988 8 5 13 0 546. . . ρa wX t= − −1428 5 454 9 0 231. . . ρ = + + −g hy q ry[exp( )]
- 41. 20 Rahman a. Fruits and Vegetables The particle density of granular and gelatinized corn starches was measured in the range 0 < Mw < 1.0 and correlated as (Maroulis and Saravacos, 1990): (1.39) Lozano et al. (1979) correlated the apparent density of apple above freezing as: (1.40) Singh and Lund (1984) noted that the above correlation is not valid up to zero moisture content and they correlated the apparent density of apple up to zero moisture content above frozen as: (1.41) Again Lozano et al. (1980) correlated the apparent and particle density of apple during air drying by an exponential form of equation for whole range of moisture content above frozen as: (1.42) (1.43) Lozano et al. (1980) noted that the apparent density changed in an almost linear fashion between full turgor and Mw = 1.5. Beyond that as moisture content decreased, the change in apparent density became steeper and showed that the apparent volume change became slower. The material density increased as moisture content decreased from full TABLE 1.3 Density of Major Food Components at the Temperaturea Range of –40 to 150˚C Material Equation Air ρT = 1.2847 × 101 – 3.2358 × 10–3t Protein ρT = 1.3300 × 103 – 0.5184t Carbohydrate ρT = 1.5991 × 103 – 0.31046t Fat ρT = 9.2559 × 102 – 0.41757t Fiber ρT =1.3115 × 103 – 0.36589t Ash ρT = 2.4238 × 103 – 0.28063t Water ρT = 9.9718 × 102 + 3.1439 × 10–3t – 3.7574 × 10–3t2 Ice ρT = 9.1689 × 102 – 0.1307t a t in degrees C. Source: Choi, Y. and Okos, M.R. 1985. In Food Engineering and Process Applications, Vol. 1, Transport Phenomena. Le Maguer, M. and Jelen, P., Eds. Elsevier Applied Science, London. ρp w w w wM M M M= + − + −1442 837 3646 448 18502 3 4 ρa wM= +636 102[ln ] ρa wM= − −852 462 0 66[exp( . )] ρa wM= + +684 68 1 0 0054. [ln( . )] ρp w wM M= − − −1540 0 051 1150 2 40[exp( . )] [exp( . )]

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