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| Preface | v | |
| 1 | Review of Mathematical Principles and Applications in Food Processing | 1 |
| 1.1 | Graphing and Fitting Equations to Experimental Data | 1 |
| 1.1.1 | Variables and Functions | 1 |
| 1.1.2 | Graphs | 2 |
| 1.1.3 | Equations | 2 |
| 1.1.4 | Linear Equations | 3 |
| 1.1.5 | Nonlinear Equations | 4 |
| 1.2 | Linearization of Nonlinear Equations | 5 |
| 1.3 | Nonlinear Curve Fitting | 6 |
| 1.4 | Logarithmic and Semi-Logarithmic Graphs | 8 |
| 1.5 | Intercept of Log-Log Graphs | 14 |
| 1.6 | Roots of Equations | 16 |
| 1.6.1 | Polynomials | 16 |
| 1.6.1.1 | Quadratic Equation | 16 |
| 1.6.1.2 | Factoring | 16 |
| 1.6.1.3 | Iteration Technique | 17 |
| 1.7 | Programming Using Visual BASIC for Applications in Microsoft Excel | 18 |
| 1.8 | Use of Spreadsheets to Solve Engineering Problems | 20 |
| 1.9 | Simultaneous Equations | 23 |
| 1.9.1 | Substitution | 23 |
| 1.9.2 | Elimination | 23 |
| 1.9.3 | Determinants | 25 |
| 1.10 | Solutions to a System of Linear Equations Using the "Solver" Macro in Excel | 27 |
| 1.11 | Power Functions and Exponential Functions | 29 |
| 1.12 | Logarithmic Functions | 31 |
| 1.13 | Differential Calculus | 32 |
| 1.13.1 | Definition of a Derivative | 32 |
| 1.13.2 | Differentiation Formulas | 33 |
| 1.13.3 | Maximum and Minimum Values of Functions | 35 |
| 1.14 | Integral Calculus | 38 |
| 1.14.1 | Integration Formulas | 38 |
| I.14.2 Integration Techniques | 39 | |
| 1.14.2.1 | Constants | 39 |
| 1.14.2.2 | Integration by Parts | 39 |
| 1.14.2.3 | Partial Fractions | 39 |
| 1.14.2.4 | Substitution | 39 |
| 1.15 | Graphical Integration | 41 |
| 1.15.1 | Rectangular Rule | 41 |
| 1.15.2 | Trapezoidal Rule | 42 |
| 1.15.3 | Simpson's Rule | 42 |
| 1.16 | Differential Equations | 43 |
| 1.17 | Finite Difference Approximation of Differential Equations | 44 |
| Problems | 46 | |
| Suggested Reading | 50 | |
| 2 | Units and Dimensions | 51 |
| 2.1 | Definition of Terms | 51 |
| 2.2 | Systems of Measurement | 52 |
| 2.3 | The SI System | 52 |
| 2.3.1 | Units in SI and Their Symbols | 52 |
| 2.3.2 | Prefixes Recommended for Use in SI | 53 |
| 2.4 | Conversion of Units | 54 |
| 2.4.1 | Precision, Rounding-Off Rule, Significant Digits | 54 |
| 2.5 | The Dimensional Equation | 55 |
| 2.6 | Conversion of Units Using the Dimensional Equation | 55 |
| 2.7 | The Dimensional Constant (Gc) | 57 |
| 2.8 | Determination of Appropriate SI Units | 57 |
| 2.9 | Dimensional Consistency of Equations | 58 |
| 2.10 | Conversion of Dimensional Equations | 59 |
| Problems | 61 | |
| Suggested Reading | 63 | |
| 3 | Material Balances | 65 |
| 3.1 | Basic Principles | 65 |
| 3.1.1 | Law of Conservation of Mass | 65 |
| 3.1.2 | Process Flow Diagrams | 65 |
| 3.1.3 | System Boundaries | 67 |
| 3.1.4 | Total Mass Balance | 67 |
| 3.1.5 | Component Mass Balance | 69 |
| 3.1.6 | Basis and "Tie Material" | 71 |
| 3.2 Material Balance Problems Involved in Dilution, Concentration, | ||
| and Dehydration | 72 | |
| 3.2.1 | Steady State | 72 |
| 3.2.2 | Volume Changes on Mixing | 73 |
| 3.2.3 | Continuous Versus Batch | 74 |
| 3.2.4 | Recycle | 75 |
| 3.2.5 | Unsteady State | 77 |
| 3.3 | Blending of Food Ingredients | 80 |
| 3.3.1 | Total Mass and Component Balances | 80 |
| 3.3.2 | Use of Specified Constraints in Equations | 85 |
| 3.4 | Multistage Processes | 89 |
| Problems | 98 | |
| Suggested Reading | 103 | |
| 4 | Gases and Vapors | 105 |
| 4.1 | Equations of State for Ideal and Real Gases | 105 |
| 4.1.1 | The Kinetic Theory of Gases | 105 |
| 4.1.2 | Absolute Temperature and Pressure | 106 |
| 4.1.3 | Quantity of Gases | 107 |
| 4.1.4 | The Ideal Gas Equation | 108 |
| 4.1.4.1 | P-V-T Relationships for Ideal Gases | 108 |
| 4.1.5 | van der Waal's Equation of State | 110 |
| 4.1.6 | Critical Conditions for Gases | 112 |
| 4.1.7 | Gas Mixtures | 112 |
| 4.2 | Thermodynamics | 114 |
| 4.2.1 | Thermodynamic Variables | 115 |
| 4.2.2 | The Relationship Between Cp and Cv for Gases | 116 |
| 4.2.3 | P-V-T Relationships for Ideal Gases in Thermodynamic Processes | 117 |
| 4.2.4 Changes in Thermodynamic Properties, Work, and Heat Associated | ||
| with Thermodynamic Processes | 117 | |
| 4.2.5 Work and Enthalpy Change on Adiabatic Expansion or Compression | ||
| of an Ideal Gas | 118 | |
| 4.2.6 Work and Enthalpy Change on Isothermal Expansion or Compression | ||
| of an Ideal Gas | 118 | |
| 4.3 | Vapor-Liquid Equilibrium | 119 |
| 4.3.1 | The Clausius-Clapeyron Equation | 120 |
| 4.3.2 | Liquid Condensation from Gas Mixtures | 120 |
| Problems | 123 | |
| Suggested Reading | 124 | |
| 5 | Energy Balances | 125 |
| 5.1 | General Principles......................................................... • | 125 |
| 5.2 | Energy Terms | 126 |
| 5.2.1 | Heat | 126 |
| 5.2.2 | Heat Content, Enthalpy | 126 |
| 5.2.3 | Specific Heat of Solids and Liquids | 126 |
| 5.3 | Enthalpy Changes in Foods During Freezing | 131 |
| 5.3.1 Correlation Equations Based on Freezing Points of Food Products | ||
| Unmodified from the Natural State | 131 | |
| 5.3.2 Enthalpy Changes During the Freezing of Foods Calculated | ||
| from Molality of Liquid Water Fraction of the Food | 133 | |
| 5.3.3 | Freezing Point Depression by Solutes | 134 |
| 5.3.4 | Amount of Liquid Water and Ice at Temperatures Below Freezing | 134 |
| 5.3.5 Sensible Heat of Water and Ice at Temperatures Below the | ||
| Freezing Point | 134 | |
| 5.3.6 | Total Enthalpy Change | 135 |
| 5.3.7 | Specific Heats of Gases and Vapors | 136 |
| 5.4 Properties of Saturated and Superheated Steam................... | ||
| 5.4.1 The Steam Tables....................................... | ||
| 5.4.1.1 The Saturated Steam Table........................ | ||
| 5.4.1.2 The Superheated Steam Tables.................... | ||
| 5.4.1.3 Double Interpolation from Superheated Steam Tables. | ||
| 5.4.2 Properties of Steam Having Less Than 100% Quality........ | ||
| 5.5 Heat Balances............................................... | ||
| Problems....................................................... | ||
| Suggested Reading............................................... | ||
| Flow of Fluids.................................................. | ||
| 6.1 The Concept of Viscosity...................................... | ||
| 6.2 Rheology................................................... | ||
| 6.2.1 Viscometry............................................ | ||
| 6.2.1.1 Viscometers Based on Fluid Flow Through a Cylinder | ||
| 6.2.1.2 Derivation of the Poiseuille Equation............... | ||
| 6.2.1.3 Velocity Profile and Shear Rate for a Power Law Fluid | ||
| 6.2.1.4 | Glass Capillary Viscometers | 160 |
| 6.2.1.5 | Forced Flow Tube or Capillary Viscometry | 161 |
| 6.2.1.6 | Evaluation of Wall Effects in Tube Viscometry | 166 |
| 6.2.1.7 | Glass Capillary Viscometer Used as a Forced Flow Viscometer | 167 |
| 6.2.2 | Effect of Temperature on Rheological Properties | 170 |
| 6.2.3 | Back Extrusion | 172 |
| 6.2.4 Determination of Rheological Properties of Fluids Using | ||
| Rotational Viscometers | 178 | |
| 6.2.4.1 | Wide Gap Rotational Viscometer | 180 |
| 6.2.4.2 | Wide Gap Viscometer with Cylindrical Spindles | 182 |
| 6.3 | Continuous Viscosity Monitoring and Control | 186 |
| 6.3.1 | Capillary Viscometer | 186 |
| 6.3.2 | Rotational Viscometer | 186 |
| 6.3.3 | Viscosity Sensitive Rotameter | 186 |
| 6.4 | Flow of Falling Films | 187 |
| 6.4.1 | Films of Constant Thickness............................................................j | 87 |
| 6.4.2 | Time-Dependent Film Thickness | 189 |
| 6.4.3 | Processes Dependent on Fluid Film Thicknesses | 192 |
| 6.5 | Transportation of Fluids | 193 |
| 6.5.1 Momentum Balance........................................................................................................j93 | ||
| 6.5.2 | The Continuity Principle | 195 |
| 6.6 | Fluid Flow Regimes | I95 |
| 6.6.1 | The Reynolds Number | 196 |
| 6.6.2 | Pipes and Tubes | 198 |
| 6.6.3 | Frictional Resistance to Flow of Newtonian Fluids | 198 |
| 6.6.4 | Frictional Resistance to Flow of Non-Newtonian Fluids | 202 |
| 6.6.5 | Frictional Resistance Offered by Pipe Fittings to Fluid Flow | 204 |
| 6.7 | Mechanical Energy Balance: The Bernoulli Equation | 205 |
| 6.8 | Pumps | 210 |
| 6.8.1 | Types of Pumps and Their Characteristics | 210 |
| 6.8.2 | Factors to Be Considered in Pump Selection | 211 |
| 6.8.3 | Performance Curves of Pumps | 212 |
| Problems | 214 | |
| Suggested Reading | 221 | |
| 7 | Heat Transfer | 223 |
| 7.1 | Mechanisms of Heat Transfer | 223 |
| 7.1.1 | Heat Transfer by Conduction | 223 |
| 7.1.2 | Fourier's First Law of Heat Transfer | 223 |
| 7.1.3 | Estimation of Thermal Conductivity of Food Products | 224 |
| 7.1.4 | Fourier's Second Law of Heat Transfer | 226 |
| 7.1.5 | Temperature Profile for Unidirectional Heat Transfer Through a Slab | 228 |
| 7.1.6 | Conduction Heat Transfer Through Walls of a Cylinder | 230 |
| 7.1.7 The Temperature Profile in the Walls of a Cylinder in Steady-State | ||
| Heat Transfer | 230 | |
| 7.1.8 | Heat Transfer by Convection | 232 |
| 7.1.8.1 | Natural Convection | 232 |
| 7.1.8.2 | Forced Convection | 233 |
| 7.1.9 | Heat Transfer by Radiation | 233 |
| 7.1.9.1 | Types of Surfaces | 233 |
| 7.1.9.2 | Effect of Distance Between Objects on Heat Transfer | 236 |
| 7.1.9.3 | Radiant Energy Exchange | 236 |
| 7.1.10 | Microwave and Dielectric Heating | 240 |
| 7.1.10.1 | Energy Absoiption by Foods in a Microwave Field | 240 |
| 7.1.10.2 | Relative Heating Rates of Food Components | 242 |
| 7.2 | Temperature Measuring Devices | 243 |
| 7.2.1 | Liquid-in-Glass Thermometers | 244 |
| 7.2.2 | Fluid-Filled Thermometers | 245 |
| 7.2.3 | Bimetallic Strip Thermometers | 245 |
| 7.2.4 | Resistance Temperature Devices (RTDs) | 245 |
| 7.2.5 | Thermocouples | 245 |
| 7.2.6 | Radiation Pyrometers | 247 |
| 7.2.7 | Accurate Temperature Measurements | 247 |
| 7.3 | Steady-State Heat Transfer | 248 |
| 7.3.1 | The Concept of Resistance to Fleat Transfer | 248 |
| 7.3.2 Combined Convection and Conduction: The Overall Heat | ||
| Transfer Coefficient | 249 | |
| 7.4 | Heat Exchange Equipment | 251 |
| 7.4.1 | Heat Transfer in Heat Exchangers | 253 |
| 7.4.2 | The Logarithmic Mean Temperature Difference | 254 |
| 7.5 | Local Heat Transfer Coefficients | 257 |
| 7.5.1 | Dimensionless Quantities | 257 |
| 7.5.2 | Equations for Calculating Heat Transfer Coefficients | 258 |
| 7.5.2.1 Simplified Equations for Natural Convection to | ||
| Air or Water | 258 | |
| 7.5.2.2 | Fluids in Laminar and Turbulent Flow Inside Tubes | 259 |
| 7.5.2.3 | Heat Transfer to Non-Newtonian Fluids in Laminar Flow | 259 |
| 7.5.2.4 Adapting Equations for Heat Transfer Coefficients | ||
| to Non-Newtonian Fluids | 260 | |
| 7.6 | Unsteady-State Heat Transfer | 267 |
| 7.6.1 | Heating of Solids Having Infinite Thermal Conductivity | 267 |
| 7.6.2 | Solids with Finite Thermal Conductivity | 268 |
| 7.6.3 | The Semi-Infinite Slab with Constant Surface Temperature | 269 |
| 7.6.4 | The Infinite Slab | 271 |
| 7.6.5 | Temperature Distribution for a Brick-Shaped Solid | 271 |
| 7.6.6 | Use of Heissler and Gurney-Lurie Charts | 272 |
| 7.7 Calculating Surface Heat Transfer Coefficients from Experimental | ||
| Heating Curves | 275 | |
| 7.8 | Freezing Rates | 276 |
| Problems | 279 | |
| Suggested Readings | 282 | |
| 8 | Kinetics of Chemical Reactions in Foods | 285 |
| 8.1 | Theory of Reaction Rates | 285 |
| 8.2 | Types of Reactions | 286 |
| 8.2.1 | Unimolecular Reactions | 286 |
| 8.2.2 | Bimolecular Reactions | 287 |
| 8.2.3 | Reversible Reactions | 287 |
| 8.3 | Enzyme Reactions | 289 |
| 8.4 | Reaction Order | 291 |
| 8.4.1 | Zero-Order Reactions | 291 |
| 8.4.2 | First-Order Reactions | 291 |
| 8.4.3 | Second-Order Reactions | 292 |
| 8.4.4 | nth-Order Reactions | 292 |
| 8.5 | Reactions Where Product Concentration Is Rate Limiting | 292 |
| 8.6 | The Reaction Rate Constant | 293 |
| 8.7 | Temperature Dependence of Reaction Rates | 294 |
| 8.7.1 | The Arrhenius Equation | 294 |
| 8.7.2 | The Q,0 Value | 295 |
| 8.7.3 | The z Value | 295 |
| 8.8 | Determination of Reaction Kinetic Parameters | 296 |
| 8.9 | Use of Chemical Reaction Kinetic Data for Thermal Process Optimization | 297 |
| Problems | 298 | |
| Suggested Reading | 299 | |
| 9 | Thermal Process Calculations | 301 |
| 9.1 Processes and Systems for Stabilization of Foods for Shelf-Stable Storage: | ||
| Systems Requirements | 301 | |
| 9.1.1 In-Can Processing..........................................................................................................30 j | ||
| 9.1.1.1 | Stationary Retorts | 301 |
| 9.1.1.2 | Hydrostatic Cooker | 302 |
| 9.1.1.3 | Continuous Agitating Retorts | 303 |
| 9.1.1.4 | Crateless Retorts | 304 |
| 9.1.2 | Processing Products Packaged in Flexible Plastic Containers | 306 |
| 9.1.3 | Processing in Glass Containers | 308 |
| 9.1.4 | Flame Sterilization Systems | 308 |
| 9.1.5 | Continuous Flow Sterilization: Aseptic or Cold Fill | 308 |
| 9.1.6 | Steam-Air Mixtures for Thermal Processing | 309 |
| 9.2 | Microbiological Inactivation Rates at Constant Temperature | 310 |
| 9.2.1 | Rate of Microbial Inactivation | 310 |
| 9.2.2 | Shape of Microbial Inactivation Curves | 310 |
| 9.2.3 | Sterilizing Value or Lethality of a Process | 314 |
| 9.2.4 | Acceptable Sterilizing Value for Processes | 314 |
| 9.2.5 | Selection of Inoculation Levels in Inoculated Packs | 316 |
| 9.2.6 | Determination of D Values Using the Partial Sterilization Technique | 317 |
| 9.2.7 | The Heat Resistance of Spoilage Microorganisms | 318 |
| 9.2.8 | F0 Values Used in Commercial Sterilization of Canned Foods | 319 |
| 9.2.9 | Surface Sterilization | 319 |
| 9.3 | Effect of Temperature on Thermal Inactivation of Microorganisms | 321 |
| 9.4 | Inactivation of Microorganisms and Enzymes in Continuously Flowing Fluids | 323 |
| 9.4.1 | Time and Temperature Used in the Pasteurization of Fluid Foods | 323 |
| 9.4.2 | Microbial Inactivation in Continuously Flowing Fluids | 326 |
| 9.4.3 | Nutrient Degradation..............................................- | 329 |
| 9.4.4 | High-Pressure Pasteurization | 332 |
| 9.4.4.1 | High-Pressure Systems | 332 |
| 9.4.4.2 | High-Pressure Pasteurization | 334 |
| 9.4.4.3 | High-Pressure Sterilization | 335 |
| 9.4.5 | Sterilization of Fluids Containing Discreet Particulates | 336 |
| 9.5 | Sterilizing Value of Processes Expressed as F0 | 336 |
| 9.6 | Thermal Process Calculations for Canned Foods | 337 |
| 9.6.1 | The General Method | 337 |
| 9.6.2 Heat Transfer Equations and Time-Temperature Curves | ||
| for Canned Foods | 340 | |
| 9.6.3 | Plotting Heat Penetration Data | 343 |
| 9.6.3.1 | Determination of fh and j | 343 |
| 9.6.3.2 | Determination of fc and jc | 344 |
| 9.6.4 | Formula Methods for Thermal Process Evaluation | 349 |
| 9.6.4.1 | Stumbo's Procedure | 350 |
| 9.6.4.2 | Hayakawa's Procedure | 350 |
| 9.6.5 | Evaluation of Probability of Spoilage from a Given Process | 363 |
| 9.6.5.1 | Constant Temperature Processes | 363 |
| 9.6.5.2 | Process Temperature Change | 364 |
| 9.7 | Broken Heating Curves | 365 |
| 9.8 | Quality Factor Degradation | 371 |
| Problems | 374 | |
| Suggested Reading | 377 | |
| 10 | Refrigeration.............................................................. • • • | 379 |
| 10.1 | Mechanical Refrigeration System | 379 |
| 10.1.1 | Principle of Operation: The Heat Pump | 379 |
| 10.1.2 | Refrigerants | 380 |
| 10.1.3 | The Refrigeration Cycle | 382 |
| 10.1.4 | The Refrigeration Cycle as a Series of Thermodynamic Processes | 383 |
| 10.1.5 The Refrigeration Cycle on the Pressure/Enthalpy Diagram | ||
| for a Given Refrigerant | 383 | |
| 10.1.5.1 | Example Problems on the Use of Refrigerant Charts | 386 |
| 10.1.6 | The Condenser and Evaporator | 392 |
| 10.1.6.1 Problems with Heat Exchange in Systems Using | ||
| Zeotropic Refrigerants | 393 | |
| 10.1.7 | The Compressor | 395 |
| 10.2 | Refrigeration Load | 397 |
| 10.2.1 | Heat Incursion Through Enclosures | 397 |
| 10.2.2 | Heat Incursion Through Cracks and Crevices | 397 |
| 10.2.3 | Heat Incursion Through Open Doors | 398 |
| 10.2.4 | Heat Generation | 399 |
| 10.2.5 | The Unsteady-State Refrigeration Load | 401 |
| 10.3 | Commodity Storage Requirements | 402 |
| 10.4 | Controlled Atmosphere Storage | 402 |
| 10.4.1 | Respiration | 402 |
| 10.4.2 | CA Gas Composition | 404 |
| 10.5 | Modified Atmosphere Packaging | 409 |
| Problems | 410 | |
| Suggested Reading | 411 | |
| 11 | Evaporation | 413 |
| 11.1 | Single-Effect Evaporators | 413 |
| 11.1.1 | The Vapor Chamber | 414 |
| 11.1.2 | The Condenser | 415 |
| 11.1.3 | Removal of Noncondensible Gases | 417 |
| 11.1.4 | The Heat Exchanger | 419 |
| 11.2 | Improving the Economy of Evaporators | 422 |
| 11.2.1 | Vapor Recompression | 423 |
| 11.2.2 | Multiple-Effect Evaporators | 423 |
| 11.3 | Entrainment | 427 |
| 11.4 | Essence Recovery | 428 |
| Problems | 428 | |
| Suggested Reading | 429 | |
| 12 | Dehydration | 431 |
| 12.1 | Water Activity | 431 |
| 12.1.1 | Thermodynamic Basis for Water Activity | 431 |
| 12.1.2 | Osmotic Pressure | 433 |
| 12.1.3 | Water Activity at High Moisture Contents | 433 |
| 12.1.3.1 | Gibbs-Duhem Equation | 435 |
| 12.1.3.2 | Other Equations for Calculating Water Activity | 438 |
| 12.1.4 | Water Activity at Low Moisture Contents | 439 |
| 12.1.4.1 | The GAB (Guggenheim-Anderson-de Boer) Equation | 440 |
| 12.1.4.2 | Other Equations for Sorption Isotherms of Foods | 442 |
| 12.2 | Mass Transfer | 443 |
| 12.2.1 | Mass Diffusion | 443 |
| 12.2.2 | Mass Transfer from Surfaces to Flowing Air | 446 |
| 12.3 | Psychrometry | 449 |
| 12.3.1 | Carrying Capacity of Gases for Vapors | 449 |
| 12.3.2 | The Psychrometric Chart | 450 |
| 12.3.3 Use of Psychrometric Chart to Follow Changes in the Properties | ||
| of Air-Water Mixtures Through a Process | 452 | |
| 12.4 | Simultaneous Heat and Mass Transfer in Dehydration | 453 |
| 12.5 | The Stages of Drying | 455 |
| 12.6 | Prediction of Drying Times from Drying Rate Data | 456 |
| 12.6.1 Materials with One Falling Rate Stage Where the Rate | ||
| of Drying Curve Goes Through the Origin | 456 | |
| 12.6.2 | Materials with More Than One Falling Rate Stage | 458 |
| 12.6.3 | The Constant Drying Rate | 458 |
| 12.7 | Spray Drying | 461 |
| 12.7.1 | Drying Times in Spray Drying | 462 |
| 12.8 | Freeze Drying | 465 |
| 12.8.1 | Drying Times for Symmetrical Drying | 466 |
| 12.9 | Vacuum Belt Dryer | 469 |
| Problems | 470 | |
| Suggested Reading | 473 | |
| 13 | Physical Separation Processes | 475 |
| 13.1 | Filtration | 475 |
| 13.1.1 | Filtrate Flow Through Filter Cake | 476 |
| 13.1.2 | Constant Pressure Filtration | 478 |
| 13.1.3 Filtration Rate Model Equations for Prolonged Filtration When | ||
| Filter Cakes Exhibit Time-Dependent Specific Resistance | 482 | |
| 13.1.4 | Exponential Dependence of Rate on Filtrate Volume | 482 |
| 13.1.5 Model Equation Based on Time-Dependent Specific Cake | ||
| Resistance | 484 | |
| 13.1.6 | Optimization of Filtration Cycles | 485 |
| 13.1.7 | Pressure-Driven Membrane Separation Processes | 487 |
| 13.1.8 | Membrane System Configurations | 489 |
| 13.1.9 Transmembrane Flux in Pressure-Driven Membrane Separation | ||
| Processes (Polarization Concentration and Fouling) | 491 | |
| 13.1.10 | Solute Rejection | 494 |
| 13.1.11 | Sterilizing Filtrations | 495 |
| 13.1.12 | Ultrafiltration | 497 |
| 13.1.13 | Reverse Osmosis | 498 |
| 13.1.14 | Temperature Dependence of Membrane Permeation Rates | 502 |
| 13.1.15 | Other Membrane Separation Processes | 502 |
| 13.2 | Sieving | 502 |
| 13.2.1 | Standard Sieve Sizes | 503 |
| 13.3 | Gravity Separations | 504 |
| 13.3.1 | Force Balance on Particles Suspended in a Fluid | 504 |
| 13.3.1.1 | B uoy ant Force | 505 |
| 13.3.1.2 | Drag Force | 506 |
| 13.3.2 | Terminal Velocity | 507 |
| 13.3.3 | The Drag Coefficient | 507 |
| Problems | 510 | |
| Suggested Reading | 511 | |
| 14 | Extraction | 513 |
| 14.1 | Types of Extraction Processes | 513 |
| 14.1.1 | Single-Stage Batch Processing | 514 |
| 14.1.2 | Multistage Cross-Flow Extraction | 514 |
| 14.1.3 | Multistage Countercurrent Extraction | 514 |
| 14.1.4 | Continuous Countercurrent Extractors | 515 |
| 14.2 | General Principles | 516 |
| 14.2.1 | Diffusion | 516 |
| 14.2.2 | Solubility | 517 |
| 14.2.3 | Equilibrium | 517 |
| 14.3 | Solid-Liquid Extraction: Leaching | 518 |
| 14.3.1 | The Extraction Battery: Number of Extraction Stages | 518 |
| 14.3.2 Determination of the Number of Extraction Stages Using | ||
| the Ponchon-Savarit Diagram | 519 | |
| 14.3.3 The Lever Rule in Plotting Position of a Mixture of Two Streams in | ||
| an X-Y Diagram | 520 | |
| 14.3.4 Mathematical and Graphical Representation of the Point J in the | ||
| Ponchon-Savarit Diagram | 521 | |
| 14.3.5 | Mathematical and Graphical Representation of the Point P | 521 |
| 14.3.6 Equation of the Operating Line and Representation on | ||
| the X-Y Diagram | 522 | |
| 14.3.7 Construction of the Ponchon-Savarit Diagram for the Determination | ||
| of the Number of Ideal Extraction Stages | 523 | |
| 14.4 | Supercritical Fluid Extraction | 528 |
| 14.4.1 | Extraction Principles | 529 |
| 14.4.2 | Critical Points of Supercritical Fluids Used in Foods | 530 |
| 14.4.3 | Critical Point of Mixtures | 530 |
| 14.4.4 | Properties of Supercritical Fluids Relative to Gases | 530 |
| 14.4.5 | Supercritical Fluid Extraction Parameters | 530 |
| Problems..........................................................................................................53 j | ||
| Suggested Reading | 532 | |
| A.l Conversion Factors Expressed as a Ratio | 533 | |
| A.2 Properties of Superheated Steam | 537 | |
| A.3 Saturated Steam Tables: English Units | 539 | |
| A.4 Saturated Steam Tables: Metric Units | 541 | |
| A.5 Flow Properties of Food Fluids | 543 | |
| A.6 Psychrometric Chart: English Units | 545 | |
| A.7 Psychrometric Chart: Metric Units | 547 | |
| A.8 Average Composition of Foods (From USDA Handbook 8) | 549 | |
| A.9 Thermal Conductivity of Construction and Insulating Materials | 553 | |
| A.10 Thermal Conductivity of Foods | 555 | |
| A/11 Spreadsheet Program for Calculating Thermophysical Properties of Foods | ||
| from Their Composition | 557 | |
| A.12 Correlation Equations for Heat Transfer Coefficients | 559 | |
| A.13 Visual BASIC Program for Evaluating Temperature Response of a | ||
| Brick-Shaped Solid | 563 | |
| A.14 Visual BASIC Program for Evaluating Local Heat Transfer Coefficient from | ||
| Temperature Response of a Brick-Shaped Solid | 567 | |
| A.15 Thermal Conductivity of Water as a Function of Temperature | 569 | |
| A. 16 Density of Water as a Function of Temperature | 571 | |
| A. 17 Viscosity of Water as a Function of Temperature | 573 | |
| Index | 575 | |
Absolute pressure 106
Absolute temperature 106
Accuracy definition 51
Adiabatic processes, gases 117, 118
Air classification 508-509
Arrhenius equation 294
Ascorbic acid ha if-life 12
Back extrusion, fluids 172-178
Base unit definition 51
Bernoulli equation 205-207
BET equation, sorption, water activity 439-440
Black body radiation 233
Blending of ingredients, material balance formulation 80-85
Brick-shaped solid 271-272
Broken heating curve, thermal process 365-371
Bromley's equation, water activity 438
Buoyant force 504-506
Cartesian coordinate system 2
Clausius-Clapeyron equation 120
Combined conduction and convection 249
Component mass balance, equation formulation 69-70
Compressor, refrigeration, power requirement 395-397
Concentration changes material balance 72-73
Conduction heat transfer 223-232
Conservation of mass, law 65
Consistency index 154
Constant rate air drying, heat and mass transfer 458-461
Constant rate drying 455
Constraints in material balance problems 85-88
Continuity principle 195-196
Continuous versus batch process 74-75
Controlled atmosphere storage 403-409
Convection heat transfer 232-233
Conversion factors, table 533-535
Conversion of units using dimensional equation 55-58
Correlation coefficient 3
Critical conditions, gases 112
Crystallization process flow diagram 66
Crystallization, material balance 93
Crystallizer, mass balance equation formulation 70
Curve fitting 1
Curve fitting linear 5
Curve fitting, non-linear 5
D value, microbial inactivation 310
Derivative, definition 32
Derived unit definition 51
Determinants in Microsoft Excel 26, 27
Dialysis 502
Dielectric heating 240-244
Differential equations 43-44
Differential equations by finite difference 44-45
Differentiation formulas 33
Diffusion, in extraction 516-517
Dimensional consistency of equations 58-61
Dimensional constant gc 57
Dimensional equation 55
Dimensional equations, conversion 59-61
Dimensionless quantities 257-258
Drag coefficient 507-508
Drag force 506-507
Drying stages 455-456
Drying times prediction from drying data 456-456
Ejector, steam jet, evaporator vacuum 417-419
Energy Balance Equation 125, 126
Energy exchange thermal radiation 236-242
Enthalpy 126
Enthalpy change, freezing 131-136, 135-136
Entrainment, evaporators 427-428
Entropy 115
Enzyme reactions 289-291
Equilibrium in extraction 517
Equilibrium, thermodynamic 115
Evaporator economy 422
Evaporator vacuum, maintenance 417-419
Evaporator, boiling point, fluids 415
Evaporator, condenser 415-417
Evaporator, falling film 421
Evaporator, heat exchanger 419-422
Evaporator, multiple effect 423-427
Evaporators single effect, components 413-^22
Exponential functions 29
Extraction stages, determination 518-519
Extraction, continuous, conveyor 516
Extraction, continuous, rotating basket 515
Extraction, counlercurrent, 514
Extraction, material balance 90-93
Extraction, single stage, batch 514
Extrinsic thermodynamic property 114
Falling films, constant thickness 187-189
Falling films, time dependent thickness 189-192
Falling fluid film, processes 192-193
Falling rate drying 456
Filter cake resistance, determination 477-482
Filter cake resistance, time dependent 482-485
Filter medium resistance 477-482
Filter, plate and frame 477
Filter, rotary vacuum 477
Filter, vertical leaf 477
Filtrate flow, filer cake 476-478
Filtration cycle, optimization 485-487
Filtration test cell 479
Filtration, constant pressure 478-482
Filtration, depth 475
Filtration, filter aid 476
Filtration, surface 475
Finned heat transfer surfaces 192-193
Flame sterilization system 308
Flexible pouch thermal processing 306-308
Flow behavior index 154
Flow resistance Newtonian fluids 198-202
Flow resistance non-Newtonian fluids 202-204
Flow resistance, pipe fittings 204-205
Fo value of thermal process, general method 336-339
Fo values, commercial sterilization 319
Fourier's first law 223
Fourier's second law 220-228
Freeze drying 465-469
Freezing load, entering product 401-402
Freezing point depression 133-134
Freezing rates 276-279
Frozen food, liquid water 134-135
GAB equation, water sorption isotherm 440-442
Gage pressure 106
Gas mixtures 112-114
Gas mixtures, condensation 120-122
Gases, density determination by ideal gas equation 109
Gases, kinetic theory 105, 106
Gases, quantity 107, 108
Gases, Van der Waals constants 111
Generation time of microorganisms 11
Gibbs-Duhem equation, water activity 436-438
Glass containers, thermal processing 308
Graetz number 258
Graph logarithmic 8
Graph semi-logarithmic 8
Graphical integration by rectangular rule 41
Graphical integration by Simpson's rule 42
Graphical integration by trapezoidal rule 42
Graphing 1
Grashof number 257
Gray body radiation 233
Gurney-Lurie charts 273
Hayakawa's procedure, tables 350-360
Heat and mass transfer, dehydration 453-455
Meat balance calculations 143-149
Heat exchange calculations 255-256
Heat exchanger, double pipe 251
Heat exchanger, multiple pass 253
Heat exchanger, plate 253
Heat exchanger, shell and tube 252
Heat exchanger, swept surface 252
Heat generation, produce 399-400
Heat incursion, refrigerated rooms 397-398
Heat penetration curves, parameters 340-349
Heat pump, refrigeration system 379-380
Heat resistance, microorganisms, acid and pasteurized foods 319
Heat resistance, microorganisms, low acid food 318
Heat transfer coefficient, forced convection 259-260
Heat transfer coefficient, local 257-267
Heat transfer coefficient, natural convection 259
Heat transfer coefficient, overall 249-251
Heat transfer resistance 248
Heat transfer to non-Newtonian fluids 260-266
Heissler charts 274-276
Herschel-Bulkley fluids 155
High pressure systems 332-333
Hydrostatic cooker 302-303
Ideal gas equation 108
Ideal gases, PVT relationships 108, 109
Inactivation curves, shape, equations 310-314
Infinite slab 271
Inoculated packs, inoculation levels 316-317
Integral, definition 38
Integration by partial fractions 39
Integration by parts 39
Integration by substitution 39
Integration formulas 38-39
Intercept from regression analysis 3
Intercept of full log and semi-logarithmic graph 15
Intrinsic thermodynamic property 114
Irradiation, thermal 233
Isothermal processes, gases 117-119
Juice blending material balance 68-69
Kinetic constants, chemical reactions, food 291
Kinetic parameters, reactions, determination
296-297
Kirchoff's law 233-234
Lambert's law 236
Laminar flow 196-197
Lang-Steinberg equation, water activity 438-439
Law of conservation of mass 65
Least cost formulations 85-88
Lethality, thermal process 314
Linearization 2, 5
Logarithmic functions 31
Logarithmic graph 8
Log-mean temperature difference 254-255
Mass diffusion, drying 443-446
Mass transfer, air drying 446-449
Mass transfer, membranes 494-495
Maximum and minimum values by differential
calculus 35-37
Maximum fluid velocity 158, 159
Meats blend, material balance equation formulation 71
Mechanical energy balance, fluid flow 205-207
Membrane permeation rate, temperature effect 502
Membrane separations 487-489
Membrane systems 489-491
Microbial growth curve 10
Microbial inactivation rates, constant temperature 310-314
Microbial inactivation rates, temperature effect 321-323
Microbial inactivation, flowing fluids 323-329
Microbial inactivation, high pressure 335
Microwave heating 240-244
Modified atmosphere packaging 409-410
Momentum balance 193-195
Net positive suction head 213
Newtonian fluid 153-154
Newton-Raphson iteration process 16
Non-linear equations by regression 4
Non-Newtonian fluid 153-154
Norrish's equation, water activity 435-436
Nusselt number 257
Nutrient degradation, heated flowing fluids 329-332
Partial sterilization technique, D value 317-318
Pasteurization, flowing fluids, time-temperature 323-326
Pasteurization, high pressure 323-336
Peclet number 258
Pipe dimensions, table 198
Plotting linear equations 3
Poiseuille equation 155-157
Polarization concentration, membrane 491-495
Ponchon-Savarit, extraction 519-528
Power functions 29
Prandtl number 257
Precision definition 51
Preserves, jams and jellies 89-90
Pressure, gage, absolute, and vacuum 106
Pressure-enthalpy diagram, refrigeration cycle 383-384
Probability of spoilage, thermal process 363-364
Process flow diagrams, drawing 65-66
Programming in Microsoft Excel 20
Protein Efficiency Ratio (PER) by regression 3
Pseudoplastic fluid 155
Psychrometric chart 450-453
Psychrometry, equations 449-453
Pump selection 211—212
Pump, types 210
Pumps, perfonnance curves 212-214
Q10 value, reaction rates 295
Quality factor degradation 371-373
Radiant energy view factors 236-242
Radiation heat transfer 233-243
Radiation pyrometers 247
Radiation, thermal, energy exchange 236-242
Radiation, thermal, spectrum 233
Rayleigh number 258
Reaction order, first order 291-292
Reaction order, nth order 292
Reaction order, second order 292
Reaction order, zero order 291
Reaction rate constant 293-294
Reaction rate constant, temperature dependence 294
Reaction rate, product limiting 292-293
Reaction rates, theory 285
Reactions, bimolecular 287
Reactions, enzyme 289-291
Reactions, food, kinetic constants 291
Reactions, reversible 287-289
Reactions, unimolecular 286
Recycle, material balance 76
Reflectivity, radiation 233
Refrigerant charts, enthalpy-pressure diagram
386-389
Refrigerants 380-382
Refrigerants currently used 381
Refrigerants, global warming potential 380-381
Refrigeration condenser, heat exchange 192-393
Refrigeration cycle 382-383
Refrigeration evaporator, heat exchange 192-193
Refrigeration load calculations 397-402
Refrigeration load, cooling of entering product 401-402
Refrigeration, coefficient of performance 385
Refrigeration, cooling capacity 384
Regression, linear 2
Regression, polynomial 2
Rejection, solute, membranes 494-495
Resistance temperature devices 245
Respiration of produce 402
Retort, spray, full water immersion 307
Retort, steam-air medium 306
Retorts, continuous, agitating 303-304
Retorts, crateless 304-305
Retorts, stationary 301-302
Reverse osmosis 498-502
Reynolds number 196
Rheology 155
Roots of polynomial equations by factoring 16
Roots of polynomial equations by iteration 16
Roots of polynomial equations by Newton-Raphson 16
Roots of quadratic equations 16
Rotational viscometer, narrow gap 178-180
Rotational viscometer, wide gap 182-187
Rounding-off rule 54
Semi-infinite slab 269-271
Semi-logarithmic graph 8
Shear rate 153
Shear rate at wall 158, 159
Shear stress 153
SI base and derived units 53
SI system of units 52
SI units prefixes 53, 54
Sieves, standard sieve sizes 503
Sieving, particle size analysis 503
Significant digits 54
Simpson's rule, integration 42
Simultaneous equations solution by determinants 25
Simultaneous equations solution by elimination 23
Simultaneous equations solution by substitution 23
Slope from regression analysis 3
Slope of a function from the derivative 33
Slope of full log and semi-logarithmic graph 15
Slope-Intercept form of line 3
Solubility of solute in extraction 517
Solver Macro in Microsoft Excel 27
Sorption isotherms, equation, low moisture foods 442-443
Specific heat at constant pressure, gases 116
Specific heat at constant volme, gases 116
Specific heat, solids and liquid 127-131
Specific heats, gases and vapors 136-138
Sperry equation, filtrate flow 478
Spray drying 461-465
Spreadsheets 20
Steady state material balance 72
Steam quality 138, 139
Steam, saturated, properties 139-141
Steam, superheated, properties 141-143
Stephan-Boltzman's law 234
Sterilization, continuous flow 308-309
Sterilization, fluids with particulates 336
Sterilization, high pressure 335-336
Sterilization, surfaces, packaging materials 319-321
Sterilizing filtration 495-497
Sterilizing value, thermal process 314
Sterilizing value, thermal process, acceptable value 314-316
Storage conditions, fresh produce 403
Stumbo's procedure, tables 350-352
Supercritical conditions, in extraction 530
Supercritical fluid extraction 528-531
Supercritical fluid extraction system 529
System boundaries, setting-up 67
Temperature effects, rheological properties
170-172
Temperature measurements 247
Temperature profile, steady state conduction
228-231
Termnal velocity 507
Thermal conductivity from composition 224-225
Thermal process calculations, formula method 349-364
Thermal process effects on quality 371-373
Thermal process optimization, reaction rate data 297-298
Thermal process, broken heating curve 365-371
Thermal processing, steam-air mixtures 309-310
Thermal stabilization of foods, process and systems
301-310
Thermocouples 245-246
Thermodynamic processes, refrigeration cycle
383-386
Thermodynamic properties 114
Thermodynamics, first and second laws 115
Thermometers, bimetallic strip 245
Thermometers, liquid in glass 244-245
Total mass balance, equation formulation 67
Transmissivity, radiation 233
Turbulent flow 196-197
Ultrafiltration, material balance 96-98
Units of terms in equations 57-58
Units, systems of measurement 52
Unsteady state heat transfer 267-276
Unsteady state heating, infinite thermal conductivity 267-268
Unsteady state material balance 73-80
Vacuum 106
Vacuum belt drying 469-470
Van der Waals equation of state 110-112
Vapor pressure, liquids 119-120
Vapor recompression, evaporator 423
Velocity profile Newtonian fluid 157
Velocity profile non-Newtonian fluid 158-159
Viscometer, forced flow 161, 167-170
Viscometer, glass capillary 160-161
Viscometer, tube 161-166
Viscometry, tube 155
Viscosity, apparent 154-155
Viscosity, definition 153
Visual BASIC Microsoft Excel 18
Visual Basic programming 18
Volume changes on mixing 73-74
Wall effects tube viscometer 166-167
Water activity from osmotic pressure 433
Water activity, definition 431
Water activity, electrolyte solutions 438
Water activity, food deterioration 432
Water activity, high moisture 433-438
Water activity, low moisture foods 439-443
Water activity, rnulticomponent solutions 436-438
Water activity, sugar solutions 435-436
Water activity, thermodynamic basis 431-432
Wein's displacement law 234-235
Z value, reaction rates 295-296
Z values, quality degradation, foods 298
