Transport Phenomena of Foods and Biological Materials

252 Pages·2017·214.05 MB·English

by  Gekas, Vassilis

TRANSPORT
PHENOMENA
OF
FOODS
AND BIOLOGICAL
MATERIALS
Food Engineering
R. Paul Singh, Series Co-Editor
University of California, Davis
Dennis R. Heldman, Series Co-Editor
Weinberg Consulting Group, Inc.
Washington, D.C.
Published Titles
Advances in Food Engineering, R. Paul Singh and M. A.
Wirakartakusumah
Transport Phenomena ofFo ods and Biological Materials, Vassilis
Gekas
Forthcoming Titles
Food Engineering: Principles and Applications, B. 0. Balaban
Project Management in Food Industry, Trevor Newman and R.
Paul Singh
TRANSPORT
PHENOMENA
OF
FOODS
AND BIOL<X;ICAL
MATERIALS
Vassilis Gekas, Ph.D.
Department of Food Engineering
Lund University
Lund, Sweden
CRC Press
Boca Raton Ann Arbor London Tokyo
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Catalog record is available from the Library of Congress.
This book represents information obtained from authentic and highly regarded
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Direct all inquiries to CRC Press, Inc., 2000 Corporate Blvd., N. W., Boca Raton,
Florida, 33431.
© 1992 by CRC Press, Inc.
International Standard Book Number 0-8493-7901-6
TABLE OF CONTENTS
Chapter 1
Introduction .............................................................................. 1
I. Definitions ........................................................................... 1
A. Food and Bioengineering ............................................ 1
B. Unit Operations and Physical Models ......................... 2
1. Unit Operations ................................................... 2
2. Physical Models .................................................. 2
11. Aim and Scope .................................................................... 3
References ................................................................................... 4
Chapter 2
General Models of Transport Phenomena ............................. 5
I. Rigorous Mathematical Models .......................................... 5
A. TheGDE ..................................................................... 5
1. In One Dimension ............................................... 5
2. Extension in Three Dimensions and Other
Geometries .......................................................... 8
3. Including Convection and Source Terms ............ 9
4. Physical Meaning of the Time Derivatives ....... 11
5. Methods of Solution of the ODE ...................... 12
a. Analytical Solutions .................................. 13
b. Numerical Solutions .................................. 16
B. The Particular Transport Cases - Analogies ........... 18
1. Mass and Heat Transfer. .................................... 18
2. Momentum Transfer .......................................... 21
C. The Steady-State Case ............................................... 21
1. The General Resistance Model ......................... 21
2. Resistances in Series and in Parallel ................. 23
D. Interfacial Transport and Transfer Coefficients ........ 25
1. Heat Transfer ..................................................... 26
2. Mass Transfer .................................................... 28
3. Momentum Transfer .......................................... 29
4. Solution of the ODE with Interfacial
Limitations ........................................................ 29
11. Semie mpirical Models ....................................................... 30
A. Dimensionless Numbers ............................................ 32
V
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1. Momentum Transfer .......................................... 32
2. Ratios of Diffusivities ....................................... 34
3. The Peclet Number ............................................ 34
4. The Grashof Number ......................................... 35
5. The Graetz Number ........................................... 35
6. The Stanton Number ......................................... 35
7. The Psychrometric Ratio ................................... 36
B. Correlations ............................................................... 36
1. Forced Convection ............................................ 36
a. Turbulent Flow .......................................... 36
b. Laminar Flow ............................................ 38
c. Correction for Physical Property
Variations .................................................. 38
2. Free or Natural Convection ............................... 39
3. Use of Correlations ........................................... 39
a. Example 1 .................................................. 40
b. Example 2 .................................................. 41
Ill. Phenomenological Models ............................................... .41
A. Irreversible Thermodynamics .................................. .42
1. Example 1: Biological Membranes ................... 44
2. Example 2: Membrane Technology ................. .45
B. The Chemical Potential as Driving Force ................ .47
C. The Electrochemical Potential as Universal
Driving Force ............................................................ 50
1. Example A ......................................................... 50
2. Example B ......................................................... 50
3. Example C ......................................................... 52
IV. The Stefan-Maxwell Approach ......................................... 53
V. Empirical Models .............................................................. 54
List of Symbols ......................................................................... 59
References ................................................................................. 61
Chapter 3
Characterization and Properties of Food and
Other Biological Materials .................................................... 63
I. Classification and Rheological Behavior .......................... 63
A. Foods ......................................................................... 63
vi
B. Microbial Cells .......................................................... 68
11. Cases of Transport Phenomena ......................................... 69
A. Foods ......................................................................... 69
B. Other Biological Materials ........................................ 70
1. Mass Transfer .................................................... 70
2. Heat Transfer ..................................................... 71
Ill. Transport Properties .......................................................... 72
A. Thermal Properties .................................................... 72
1. Literature Data ................................................... 75
2. Models ............................................................... 76
a. Effect of Temperature ............................... 77
b. Effect of Composition ............................... 78
3. Measurement of Thermal Properties ................. 80
B. Mass Transfer Properties ........................................... 80
1. Sorption Isotherms ............................................ 81
2. Mass Diffusivity or Diffusion Coefficient ........ 85
a. Ordinary and Binary Diffusion ................. 85
b. Secondary Diffusion Mechanisms ............ 89
c. Diffusion in a Multicomponent System .... 90
d. Measurement of the Diffusion
Coefficient ................................................. 92
e. Models for the Diffusion Coefficient ........ 94
f. Literature Data on the Diffusion
Coefficient ................................................. 95
IV. Cell Structure and Multiphase Transport Mechanisms ..... 97
A. Description ................................................................ 97
B. Pathways of Transport ............................................. 100
List of Symbols ....................................................................... 105
References ............................................................................... 107
Chapter4
Transport Phenomena of Liquid Products ........................ 111
I. Heat and Mass Transfer in Non-Newtonian Pipe Flow .. 111
A. Laminar Flow .......................................................... 111
B. Turbulent Flow ........................................................ 116
1. Rigorous Models ............................................. 116
a. Momentum .............................................. 117
Vll
b. Mass and Heat Transfer ........................... 117
2. Semie mpirical Models ..................................... 120
11. Transport Phenomena in Agitated Systems .................... 121
A. General Concepts .................................................... 121
B. Dimensionless Numbers .......................................... 123
List of Symbols ....................................................................... 130
References ............................................................................... 132
Chapter 5
Transport Phenomena in Solid Foods ................................ 133
I. Simultaneous Heat and Mass Transfer ............................ 133
A. Simultaneous Transfer to the Product ..................... 133
B. Simultaneous Transfer within the Product .............. 136
1. TheCrust ......................................................... 136
2. Evaporation Zone ............................................ 138
II. Short-Cut Models ............................................................ 139
A. Regular-Regime Model ........................................... 139
1. Constant-Rate Period ....................................... 139
2. Penetration Period ........................................... 141
3. Regular-Regime Period ................................... 141
4. Drying Curves ................................................. 141
B. The Shrinking-Core Model ..................................... 143
Ill. The Problem of Shrinkage .............................................. 145
A. The Approach of Crank ........................................... 145
B. Development of a Modified Crank Model .............. 146
1. Volume Change Following the Direction of
Diffusion ......................................................... 147
2. Isotropic, Three-Dimensional Volume
Change ............................................................ 147
3. Arbitrary Volume Change ............................... 148
C. Other Approaches .................................................... 148
IV. Use of the Chemical Potential as the Driving Force ....... 149
A. Early Attempts ........................................................ 149
B. The Bahia-Blanca Approach ................................... 151
1. Multicomponent-Multiphase Transport With
Reaction ........................................................... 151
viii
2. Averaging Volume Method ............................. 152
3. The Mass Transfer Equation for a
Two-Component System ................................. 152
4. Prediction of Phase Mass Conductivities ........ 155
5. Application in One-Dimensional Drying ........ 157
V. Irreversible Thermodynamics and Simultaneous
Transport ......................................................................... 157
List of Symbols ....................................................................... 163
References ............................................................................... 166
Chapter 6
Transport Phenomena and the Source Term .................... 167
I. The Mass Transfer Source Term: Transport
and Reaction .................................................................... 167
A. In Foods ................................................................... 169
1. Zero-Order Reactions ...................................... 169
2. First- Order Reactions ...................................... 169
3. Simultaneous Reactions .................................. 170
4. Other Models ................................................... 170
a. Empirical Model ...................................... 170
b. The Casolari Model ................................. 172
B. Enzymatic Reaction (Immobilized Systems) .......... 172
11. The Heat Transfer Source Term ...................................... 176
A. Viscous Heat ........................................................... 177
B. Latent Heat .............................................................. 180
C. Radiation Source ..................................................... 181
1. Electrical Properties of Foods ......................... 181
2. Electrical Source Term .................................... 181
List of Symbols ....................................................................... 185
References ............................................................................... 187
Chapter 7
Transport Phenomena Models in Some Unit Operations
and Processing Equipment .................................................. 189
I. Processing Equipment for Liquids .................................. 189
A. Heat Exchangers ...................................................... 189
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