Handbook of Food and Bioprocess Modeling Techniques (Food Science and Technology)

Half Title......Page 1
Series Title......Page 2
Title......Page 3
Copyright Page......Page 4
Dedication......Page 5
Preface......Page 7
The Editors......Page 9
Contributors......Page 11
Contents......Page 13
CHAPTER 1: Mathematical Modeling Techniques in Food and Bioprocesses: An Overview......Page 15
Table of Contents......Page 0
1.1 MATHEMATICAL MODELING......Page 16
1.2 CLASSIFICATION OF MATHEMATICAL MODELING TECHNIQUES......Page 17
1.4.1 Physics-Based Models (Chapter 2 through Chapter 8)......Page 18
1.4.1.2 Lattice Boltzmann Models (Chapter 2)......Page 19
1.4.1.5 Stochastic Models (Chapter 8)......Page 20
1.4.2.2 Multivariate Analysis (Chapter 10)......Page 21
1.4.3 Some Generic Modeling Techniques (Chapter 16 through Chapter 18)......Page 23
1.5 CHARACTERISTICS OF FOOD AND BIOPROCESSES......Page 24
REFERENCES......Page 25
2.1 INTRODUCTION......Page 27
2.2.1 Discretising Kinetic Theory......Page 28
2.2.2 1-D Diffusion......Page 30
2.2.3 Equivalence with Finite-Volume Schemes......Page 33
2.2.4 Fluid Flow......Page 35
2.2.5 Boundary Conditions......Page 36
2.2.6 What Makes Lattice Boltzmann Special?......Page 38
2.3.1 Lattice Boltzmann Scheme for Emulsions......Page 39
2.3.2 Lattice Boltzmann Scheme for Suspensions......Page 41
2.4.1 Emulsification in Microchannel T-Junctions......Page 45
2.4.2 Shear-Induced Diffusion in Microfiltration Processes......Page 46
REFERENCES......Page 49
CHAPTER 3: Fluid Flow and Its Modeling Using Computational Fluid Dynamics......Page 53
3.1 INTRODUCTION TO FLUID FLOW MODELING......Page 54
3.2 DYNAMICS OF FLUIDS......Page 55
3.3.1 Conservation of Mass......Page 56
3.3.3 Conservation of Energy......Page 58
3.4.1 Density......Page 59
3.4.2 Viscosity......Page 60
3.5.1 Flow Regime......Page 62
3.5.2.1 Free-Surface Flows......Page 63
3.5.2.2 Discrete Particle Model......Page 64
3.5.2.3 Multiphase Models......Page 65
3.7 FLOW MODELING......Page 66
3.8 DISCRETIZATION......Page 69
3.8.1 Meshing......Page 70
3.8.1.1 Modeling: Steps Involved in Setting Up a CFD Problem......Page 71
3.8.2.3 Refer to the Code’s Validation......Page 77
3.8.2.6 Assumptions......Page 78
3.9.1.1 Problem Description......Page 79
3.9.1.2 Governing Equations......Page 81
3.9.1.4 Geometry and Mesh Creation......Page 82
3.9.1.6 Validation......Page 83
3.9.1.7 Summary......Page 84
3.9.2.1 Problem Description......Page 85
3.9.2.5 Results and Discussion......Page 87
3.9.3 Case Study 3: Modeling Flows in Extrusion Dies......Page 88
3.9.3.1 Problem Description and Assumptions......Page 89
3.9.3.5 Results and Discussion......Page 90
3.9.3.6 Summary......Page 93
REFERENCES......Page 94
CHAPTER 4: Heat Transfer......Page 97
4.2 DEVELOPMENT OF PHYSICS-BASED MODELS IN HEAT TRANSFER......Page 99
4.3 PROBLEM FORMULATION IN HEAT TRANSFER: CONDUCTION AND CONVECTION......Page 100
4.3.2 Transient......Page 101
4.3.7 Uncertainty or Stochastic Variations......Page 102
4.5 THERMAL PROPERTIES......Page 103
4.6.2 Heat Source Term for Electromagnetic Heating: Microwaves......Page 104
4.6.2.1 Electromagnetic Interaction with a Food Material and Dielectric Properties......Page 105
4.6.2.2 Modeling of Microwave Heating: Solutions for Idealized Plane Wave......Page 106
4.6.2.3.1 Governing Equations......Page 108
4.6.2.3.3 Numerical Solution and Experimental Verification......Page 109
4.6.2.4 Factors Affecting Heat Generation: Food Volume......Page 110
4.6.2.6.2 Exponentially Decaying Heat Generation from the Surface......Page 111
4.6.4 Heat Source Term for Electromagnetic Heating: Ohmic......Page 112
4.6.4.2 Modeling of Ohmic Heating......Page 113
4.6.7 Heat Source Term for Ultrasonic Heating......Page 114
4.7.1 Thermal Resistance Formulation: Steady State......Page 115
4.7.3 Lumped Parameter Analysis......Page 117
4.7.4 Analytical Solution to the Heat Equation: Application to Canning......Page 118
4.7.4.1 Example: Canning of Solid Foods......Page 119
4.7.4.1.1 Analytical Solution: Ball’s Formula......Page 120
4.7.6 Optimization of Conductive Heating......Page 121
4.8.1 Formulations of Convective Heat Transfer......Page 122
4.8.2 Modeling Using a Heat Transfer Coefficient......Page 123
4.8.3 Modeling by Solving the Governing Equations of Fluid Flow Together with Heat Transfer......Page 125
4.8.4 Modeling Conjugate Problems by Considering Both the Fluid and Solid......Page 129
4.9.1.2 Using Measured Enthalpy Data......Page 133
4.9.2 Simple Model for Pure Materials: Pseudo Steady-State Formulation......Page 134
4.9.4 Presence of Microwaves and Radio-Frequency Heating......Page 135
4.9.5 Presence of High Pressure......Page 136
4.9.6 Presence of Ohmic Heating......Page 137
4.10 PROBLEM FORMULATION IN HEAT TRANSFER: RADIATION......Page 138
4.10.1 Radiative Modeling in Simple Situations......Page 139
4.10.3 Numerical Solution for More Complex Geometries and for Spectrally Dependent Properties: Using the Radiative Transport Equation......Page 140
4.10.4 Numerical Solution for More Complex Geometries and Spectrally Dependent Properties: Using Monte Carlo......Page 141
4.11 HEAT TRANSFER COUPLED WITH OTHER PHYSICS......Page 143
4.11.2 Heat Transfer Coupled with Microwaves......Page 144
4.11.2.1 Need for Coupled Solutions......Page 146
4.11.3 Heat Transfer Coupled with Biochemical Reactions: Modeling of Safety and Quality......Page 147
4.11.4 Heat Transfer Coupled with Mechanics: Thermomechanics......Page 149
4.12 CONCLUDING REMARKS......Page 151
REFERENCES......Page 152
CHAPTER 5: Mass Transfer: Membrane Processes......Page 157
5.1.2 Membrane Processes......Page 158
5.1.3 Microfiltration and Ultrafiltration......Page 159
5.1.4 Nanofiltration and Reverse Osmosis......Page 160
5.1.6 Mode of Operation and Module Design......Page 161
5.1.8 Fouling......Page 162
5.2.1 Classification of Models......Page 163
5.2.2 Concentration Polarization Models......Page 164
5.2.2.1 Food and Bioprocess Examples......Page 167
5.2.2.2 Worked Example......Page 168
5.2.3 Membrane Fouling Models......Page 169
5.2.3.1 Food and Bioprocess Examples......Page 171
5.2.3.2 Worked Example......Page 172
5.2.4 Force Balance Models......Page 173
5.2.5 Membrane Models......Page 174
5.2.5.1 Food and Bioprocess Examples......Page 175
5.3.1 Introduction......Page 176
5.3.3 Model Development......Page 177
5.3.4 Hydrodynamics of Gas-Sparged UF......Page 180
5.3.5 Effect of Operating Conditions on Permeate Flux......Page 181
5.4 CONCLUDING REMARKS......Page 182
NOMENCLATURE......Page 185
REFERENCES......Page 187
CHAPTER 6: Simultaneous Heat and Mass Transfer......Page 191
6.1 INTRODUCTION......Page 192
6.2.1 Background......Page 193
6.2.2.1 Basic Formula......Page 196
6.2.2.2 One-Dimensional Water Removal from a Temperature-Controlled Column: A Hypothetical Experimentation to Evaluate the Mechanisms Described in Section 6.2.2.1......Page 200
6.2.2.3 Microstructural Interpretation of Drying Profiles That Support the Model Analysis in Section 6.2.2.1......Page 202
6.2.3.1 Biot Number Analysis......Page 208
6.2.3.2 Lewis-Number Analysis......Page 211
6.2.4 Drying of Shrinkable Materials......Page 213
6.3.1.1 Mass-Transfer Model......Page 214
6.3.1.2 Heat-Transfer Model......Page 222
6.3.1.3 Momentum Transfer Model......Page 224
6.3.1.4 Prediction of Physical Properties of the Products......Page 226
6.3.2 Baking Bread......Page 228
6.3.2.1 Inside the Bread......Page 229
6.4 CONCLUDING REMARKS......Page 231
NOMENCLATURE......Page 232
ACKNOWLEDGMENTS......Page 235
REFERENCES......Page 237
CHAPTER 7: Reaction Kinetics......Page 247
7.1 INTRODUCTION......Page 248
7.2.3 Chemical Changes......Page 249
7.2.4 Microbiological Changes......Page 251
7.3.1.1 Simple Kinetics......Page 252
7.3.1.2 Complex Kinetics......Page 253
7.3.2 Reaction Order......Page 254
7.3.2.1 Common Types of Reactions......Page 255
7.3.3.1 Differential Methods......Page 256
7.3.3.3 Method of Half Lives......Page 257
7.3.4.1 The Arrhenius Equation......Page 258
7.3.4.3 The z-Value......Page 259
7.3.4.5 Effects of Other Environmental Factors......Page 260
7.4.1.1 First Step......Page 262
7.4.1.2 Second Step......Page 263
7.4.1.3 Third Step......Page 264
7.4.2 Modeling the Effect of Temperature and Relative Humidity Storage Conditions (Nonenzymatic Browning of a Cheese Powder)......Page 267
7.5 FUTURE TRENDS......Page 270
REFERENCES......Page 271
CHAPTER 8: Probabilistic Modeling......Page 277
8.2.1 Random Variables......Page 278
8.2.3 Random Fields and Random Waves......Page 280
8.4.1 Principle......Page 281
8.4.2 Application to Lumped Capacitance Heat Transfer......Page 282
8.5.1 Principle......Page 284
8.5.3 Application to Heat Conduction......Page 287
8.5.3.2 Perturbation Analysis......Page 288
8.6.1 Principle......Page 291
8.6.2 Application to Lumped Capacitance Heat Transfer......Page 292
8.6.3 Application to Heat Conduction......Page 294
8.7 CLOSING REMARKS/FUTURE TRENDS......Page 297
GLOSSARY......Page 298
NOMENCLATURE......Page 299
REFERENCES......Page 300
CHAPTER 9: Experimental Design and Response-Surface Methodology......Page 303
9.2.1 Factor Screening......Page 304
9.3.1.1 Effects of Main Factors......Page 305
9.3.2 Fractional Factorial Designs......Page 306
9.3.2.1 Two-Level Design Example......Page 307
9.3.2.2 Three-Level Design Example......Page 310
9.3.2.3 How to Select Designs......Page 316
9.4.1 Introduction......Page 318
9.4.2 Central Composite Designs......Page 319
9.4.3 Mixture Designs......Page 320
9.4.4 Sequential Simplex Optimization......Page 322
9.4.5 Random-Centroid Optimization......Page 324
9.4.6.3 Shape Design and Market Survey......Page 326
9.4.6.4 Site-Directed Mutagenesis......Page 327
GLOSSARY......Page 329
REFERENCES......Page 330
CHAPTER 10: Multivariate Analysis......Page 333
10.1 INTRODUCTION AND ELEMENTARY CONCEPTS......Page 334
10.2 PRINCIPAL COMPONENT ANALYSIS......Page 336
10.3 FACTOR ANALYSIS......Page 337
10.4 DISCRIMINANT ANALYSIS......Page 339
10.5 CANONICAL CORRELATION ANALYSIS......Page 340
10.6 CLUSTER ANALYSIS......Page 341
10.6.2 Hierarchical Divisive Methods......Page 342
10.6.3 Nonhierarchical Clustering Methods......Page 343
10.7.1 Meat and Meat Products......Page 344
10.7.1.1 Beef......Page 347
10.7.1.2 Pork......Page 348
10.7.1.3 Poultry......Page 349
10.7.2.2 Multivariate Analysis and Technological Developments in Cheese Manufacturing......Page 350
10.7.2.4 Yogurt......Page 351
10.8.1.2 Experimental......Page 352
10.8.1.5 Discussion......Page 353
10.9 FUTURE TRENDS......Page 354
GLOSSARY......Page 357
REFERENCES......Page 360
CHAPTER 11: Data Mining......Page 367
11.1 INTRODUCTION......Page 368
11.2 DATA PRE-PROCESSING......Page 369
11.3.1 Classification......Page 372
11.3.3 Association Rules......Page 374
11.3.6 Online Learning......Page 375
11.5 APPLICATIONS......Page 376
11.5.2 Case Study 2: Horticulture......Page 378
11.5.2.2 Results......Page 379
GLOSSARY......Page 380
REFERENCES......Page 381
FURTHER READING......Page 383
CHAPTER 12: Artificial Neural Network Modeling......Page 385
12.1 INTRODUCTION......Page 386
12.2.1 Biological Neural Networks......Page 387
12.2.2.1 Model of an Artificial Neuron......Page 388
12.3 NETWORK ARCHITECTURE......Page 390
12.3.2 Multilayer Feedforward Networks......Page 391
12.4.2 Training of ANN Networks......Page 392
12.5 APPLICATIONS......Page 393
12.5.1.3 Solution Procedure......Page 395
12.5.2.1 Background......Page 399
12.5.2.3 Solution Procedure......Page 400
12.5.3.2 Problem Definition......Page 403
12.5.3.3 Solution Procedure......Page 404
GLOSSARY......Page 408
NOMENCLATURE......Page 409
APPENDIX B......Page 410
REFERENCES......Page 411
CHAPTER 13: Genetic Algorithms......Page 415
13.2 FUNDAMENTAL INTRODUCTION TO GENETIC ALGORITHMS......Page 416
13.2.1 Definition of Individual......Page 418
13.2.3 Definition of Fitness......Page 419
13.2.4.1 Crossover......Page 420
13.2.4.3 Selection and Reproduction......Page 421
13.2.5 Searching Procedure of an Optimal Value (Artificial Evolution Process)......Page 423
13.2.7 Improvement of Evolution Performance......Page 425
13.3.1 Optimization Problem......Page 426
13.3.4 Flow Chart of the Genetic Algorithm......Page 427
13.3.5 Searching Process of an Optimal Value (Artificial Evolution Process)......Page 429
13.4.1 Dynamic Optimization Problem......Page 430
13.4.2 Plant Materials and Measuring Systems......Page 431
13.4.6 Searching Process of an Optimal Value......Page 432
13.4.7 An Intelligent Control System for Dynamic Optimization......Page 433
13.4.8 Dynamic Responses of the Rate of Water Loss......Page 434
13.4.9 Identification of the Rate of Water Loss to Temperature Using the Neural Network......Page 435
13.4.10 Searching Process of an Optimal Value......Page 436
13.4.11 Optimal Control Performances in a Real System......Page 438
13.5 CONCLUSIONS......Page 439
International Conferences on Genetic Algorithms......Page 440
REFERENCES......Page 441
14.1 INTRODUCTION......Page 445
14.3.1 What Is Fractal Dimension?......Page 446
14.3.2.1 Changing the Coarse-Graining Level......Page 447
14.3.2.2 Using a Fractal Relation......Page 451
14.3.2.5 Using Power Spectrum......Page 455
14.4 CONCLUSIONS......Page 456
GLOSSARY......Page 457
REFERENCES......Page 458
CHAPTER 15: Fuzzy Modeling......Page 461
15.1 INTRODUCTION......Page 462
15.2.1 Image Analysis and Quality Control......Page 464
15.2.2 Fuzzy Models in Fuzzy Control Applications......Page 467
15.3 FUZZY SET THEORY......Page 469
15.3.1 Fuzzy Logic......Page 470
15.3.2 Fuzzy Set Operations......Page 471
15.4 FUZZY MODELING......Page 473
15.4.1 Linguistic Variables......Page 474
15.4.2 Membership Functions......Page 475
15.4.3 Fuzzy Rule Base......Page 476
15.4.3.1 Aggregation of Fuzzy Rules......Page 477
15.4.4 Fuzzy Inference......Page 478
15.4.4.1 Mamdani-Type Fuzzy Inference......Page 479
15.4.5 Fuzzification and Defuzzification......Page 481
15.4.5.1 Center-of-Area Method......Page 483
15.4.5.4 Mean-Max Membership......Page 484
15.4.5.5 Center of Sums......Page 485
15.5.1 Mamdani-Type System......Page 486
15.5.2 Sugeno-Type System......Page 489
15.5.3 Implementing the Fuzzy Model in MATLAB&sup®;......Page 490
15.6 DEVELOPING AND TUNING MEMBERSHIP FUNCTIONS......Page 493
15.6.1.1 Artificial Neural Networks......Page 494
15.6.1.2 Integrating Neural Networks and Fuzzy Systems......Page 495
15.6.1.3 Adaptive Network Fuzzy Inference Systems......Page 496
15.6.1.4 Developing ANFIS in MATLAB: Bread Extrusion Problem......Page 498
15.6.2 Genetic Algorithms......Page 501
15.6.2.1 Genetic Tuning of Membership Functions......Page 502
15.6.2.2 Genetic Learning of the Rule-Base......Page 503
REFERENCES......Page 504
CHAPTER 16: Monte Carlo Simulation......Page 509
16.1.2 Uncertainty in Food and Bioprocess Engineering......Page 510
16.1.3 Monte Carlo Simulation as a Probabilistic Modeling Tool......Page 511
16.1.5 Chapter Outline......Page 512
16.2 DIRECT MONTE CARLO SIMULATION......Page 513
16.2.2.1 Analysis of Experimental Data......Page 515
16.2.2.2 Selection of Probability Distribution Functions......Page 517
16.2.4 Sampling of Input Random Variables......Page 521
16.2.5 Generation of Output......Page 522
16.2.6 Analysis of Output......Page 523
16.3.1.2 Example of Correlated Parameters......Page 524
16.3.2.1 Mathematical Basis......Page 526
16.3.2.2 Example of Parameters with Noise......Page 527
16.3.3 Variance Reduction......Page 529
16.3.3.1 Mathematical Basis......Page 530
16.3.3.2 Sampling Strategies......Page 531
16.4.1 Introduction......Page 532
16.4.2 Thermal Processing of Hazelnuts......Page 533
16.4.3 Batch Thermal Processing of Packed Food in a Retort......Page 535
GLOSSARY......Page 536
NOMENCLATURE......Page 537
REFERENCES......Page 538
17.1 INTRODUCTION......Page 541
17.3.1 Buckingham’s P Theorem......Page 542
17.3.2 Dimensional Analysis of Governing Differential Equations......Page 545
17.3.3 Dimensional Analysis on Transport Equations......Page 546
17.3.3.1 Mass-Transfer Equation......Page 547
17.3.3.2 Energy Equation......Page 548
17.3.3.3 Momentum-Transfer Equation......Page 549
17.4 LIST OF DIMENSIONLESS NUMBERS......Page 550
17.6 APPLICATIONS OF DIMENSIONAL ANALYSIS......Page 559
17.6.1 Convective Heat-Transfer Coefficients in Cans......Page 560
17.6.2 Fastest Particle Flow in an Aseptic Processing System......Page 562
17.7 SCALE-UP......Page 563
NOTATION......Page 565
REFERENCES......Page 567
CHAPTER 18: Linear Programming......Page 571
18.1 INTRODUCTION......Page 572
18.2.2 General Formulation of a LP Problem......Page 573
18.2.3 Example 1: The Problem of a Hypothetical Juice Manufacturer: Underlying Assumptions of LP......Page 574
18.2.5 Binding and Nonbinding Constraints, Shadow Prices......Page 576
18.2.6 Opportunity and Reduced Costs of the Activities......Page 577
18.3.1 Well-Behaved Problem......Page 578
18.3.2 Example 2: Food-Blending Problem......Page 582
18.3.3.1 Unbounded Solution......Page 584
18.4 TYPICAL APPLICATION......Page 585
18.4.2 Example 3: Reconstituted Juice-Blend Formulation......Page 586
18.4.3 Example 4: Restaurant Management......Page 589
18.5.2 Product Development......Page 593
18.6 CONCLUDING REMARKS......Page 594
18.A.2 Optimizing a Diet for Children......Page 595
GLOSSARY......Page 598
REFERENCES......Page 599