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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 | |
