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

with The Advancement Of Computers, The Use Of Modeling To Reduce Time And Expense, And Improve Process Optimization, Predictive Capability, Process Automation, And Control Possibilities, Is Now An Integral Part Of Food Science And Engineering. New Technology And Ease Of Use Expands The Range Of Techniques That Scientists And Researchers Have At Their Disposal Making It Increasingly Important For The User To Be Aware Of And Have A Good Working Knowledge Of The Alternatives. unique In Its Scope, The Handbook Of Food And Bioprocess Modeling Techniques Provides A Comprehensive Overview Of The Modeling Options Available To Today’s Researcher. The Book Covers A Wide Range Of Topics Including Transport Processes, Reaction Kinetics, Probabilistic Modeling, Data Mining, Neural Network And Genetic Algorithms. Both Mesoscale And Macroscale Modeling Are Covered. Each Chapter Is Complete With A Clear, Succinct Description Of A Specific Modeling Technique, Followed By Detailed Examples Of The Utilization, Application, Benefits, And Limitations Of The Technique Described. By Having Both Physics-based And Observation-based Models Explained In One Place, The Researcher Can Find Not Only The Most Appropriate Tool Or Combination Of Tools For The Application, But Also Those That Best Suit The Technical Expertise Of The Personnel Involved. The Book Emphasizes Problem Formulation And Explains The Choice And Structure Of The Modeling Technique From An Application Point Of View, Making It Exceedingly Practical And Easy-to-use. The International Panel Of Authors And Contributors Ensures The Quality Of The Individual Chapters And The Usefulness Of The Information Across Wide-ranging Food Products And Processes. an Indispensable Resource For The Full Range Of Contemporary Modeling Techniques, The handbook Of Food And Bioprocess Modeling Techniques Provides Food And Bioprocess Researchers In Industry And Academia With An Invaluable Comprehensive Working Reference. 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 Mathematical modeling techniques in food and bioprocessing: an overview / Ashim K. Datta and Shyam S. Sablani Lattice Boltzmann simulation of microstructures / R.G.M. van der Sman Fluid flow and its modeling using computational fluid dynamics / Ashwini Kumar and Ilhan Dilber Heat transfer / Ashim K. Datta Mass transfer: membrane processes / David hughes, Taha Taha, and Zhanfeng Cui Simultaneous heat and mass transfer / Xiao Dong Chen Reaction kinetics / Maria C. Giannakourou and Petros S. Taoukis Probabilistic modeling / Bart M. Nicolaï, Nico Scheerlinck, and Maarten L.A.T.M. Hertog Experimental design and response-surface methodology / Shuryo Nakai, Eunice C.Y. Li-Chan, and Jinglie Dou Multivariate analysis / Ioannis S. Arvanitoyannis Data mining / Geoffrey Holmes Artificial neural network modeling / Shyam S. Sablani Genetic algorithm / T. Morimoto Fractal analysis / Mohammad Shafiur Rahman Fuzzy modeling / Haitham M.S. Lababidi and Christopher G.J. Baker Monte carlo simulation / Kevin Cronin and James P. Gleeson Dimensional analysis / Law Chung Lim, Shyam S. Sablani, and Arun S. Mujumdar Linear programming / Eli Feinerman and Sam Saguy The publication of the Handbook of Food and Bioprocess Modeling Techniques brings together for the first time in one volume all the conventional and emerging modeling techniques currently available. Calling on the most recognized specialists in the industry, the editors have succeeded in creating an indispensable reference. Rather than promote one modeling system, this volume looks at the pros, cons, and proper applications of every significant, contemporary modeling system. With numerous examples in food industry applications, this volume is a valuable resource for professionals and students