Table Of ContentFundamentals of
Food Process Engineering
Third Edition
FOOD SCIENCE TEXT SERIES
The Food Science Text Series provides faculty with the leading teaching tools. The Editorial Board
has outlined the most appropriate and complete content for each food science course in a typical
food science program, and has identified textbooks of the highest quality, written by leading food
science educators.
Series Editor
Dennis R. Heldman, Ph.D.,Heldman Associates, San Marcos, California
Editorial Board
David A. Golden, Ph.D., Professor of Food Microbiology, Department of Food Science and Technology,
University of Tennessee
Richard W. Hartel,Professor of Food Engineering, Department of Food Science, University of Wisconsin
Hildegarde Heymann,Professor of Food Sensory Science, Department of Food Science and Technology,
University of California—Davis
Joseph H. Hotchkiss,Professor, Institute of Food Science and Institute for Comparative and Environmental
Toxicology, and Chair, Food Science Department, Cornell University
Michael G. Johnson, Ph.D.,Professor of Food Safety and Microbiology, Department of Food Science,
University of Arkansas
Joseph Montecalvo, Jr.,Professor, Department of Food Science and Nutrition, California Polytechnic and
State University—San Luis Obispo
S. Suzanne Nielsen,Professor and Chair, Department of Food Science, Purdue University
M. Shafiur Rahman, Ph.D.,Associate Professor and Head, Department of Food Science and Nutrition, Sultan
Qaboos University, Oman
Juan L. Silva,Professor, Department of Food Science, Nutrition and Health Promotion,
Mississippi State University
Titles
Elementary Food Science, Fourth Edition,Ernest R. Vieira (1996)
Essentials of Food Sanitation,Norman G. Marriott (1997)
Essentials of Food Science, Second Edition,Vickie A. Vaclavik and Elizabeth W. Christian (2003)
Food Analysis, Third Edition,S. Suzanne Nielsen (2003)
Food Analysis Laboratory Manual,S. Suzanne Nielsen (2003)
Food Science, Fifth Edition,Norman N. Potter and Joseph H. Hotchkiss (1995)
Fundamentals of Food Process Engineering, Third Edition,Romeo T. Toledo (2007)
Introduction to Food Processing,P.G. Smith (2003)
Modern Food Microbiology, Seventh Edition,James M. Jay, Martin J. Loessner, and David A. Golden (2005)
Physical Properties of Food, Serpil Sahin and Servet Gülüm Sumnu (2006)
Principles of Food Chemistry, Third Edition,John M. de Man (1999)
Principles of Food Processing,Dennis R. Heldman and Richard W. Hartel (1997)
Principles of Food Sanitation, Fifth Edition,Norman G. Marriott and Robert B. Gravani (2006)
Sensory Evaluation of Food: Principles and Practices,Harry T. Lawless and Hildegarde Heymann (1998)
Fundamentals of
Food Process Engineering
Third Edition
Romeo T. Toledo
University of Georgia
Athens, Georgia
Romeo T. Toledo
Department of Food Science
and Technology
University of Georgia
Athens, GA 30602
USA
[email protected]
Library of Congress Control Number: 2005935292
ISBN-10: 0-387-29019-2 e-ISBN-10: 0-387-29241-1
ISBN-13: 978-0-387-29019-5 e-ISBN-13: 978-0-387-29241-0
Printed on acid-free paper.
First and second editions ©1999, 1991 by Aspen Publishers, Inc. All rights reserved.
©2007 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher
(Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection
with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation,
computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such,
is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
9 8 7 6 5 4 3 2 1
springer.com
Preface
Since the publication of the first edition in 1981 and the second edition in 2001, this textbook has
beenwidelyadoptedforFoodEngineeringcoursesworldwide.Theauthorexpresseshisgratitudeto
colleagues who have adopted this textbook and to those who have made constructive criticisms on
thematerial.Thisneweditionnotonlyincorporateschangessuggestedbycolleagues,butadditional
material has been added to include facilitated problem solving using a computer, and new food
processing and food product technologies. New sections have been added in most of the chapters
reflectingthecurrentstateofthetechnology.Theexpandedcoveragemayresultinnotenoughtime
availableinaschooltermtocoverallareas;therefore,instructorsareadvisedtocarefullyperusethe
bookandselectthemostappropriatesectionstocoverinaschoolterm.Theadvantageoftheexpanded
coverageistheeliminationoftheneedforasupplementarytextbook.
Thesuccessofthistextbookhasbeenattributedtotheexpansivecoverageofsubjectareasspecified
intheInstituteofFoodTechnologistsmodelcurriculumforfoodsciencemajorsintheUnitedStatesof
Americaandtheuseofexamplesutilizingconditionsencounteredinactualfoodprocessingoperations.
Thisthemecontinuesinthethirdedition.Inadditiontotheemphasisonproblemsolving,technological
principlesthatformthebasisforaprocessarepresentedsothattheprocesscanbebetterunderstood
and selection of processing parameters to maximize product quality and safety can be made more
effective. The third edition incorporates most of what was in the second edition with most of the
material updated to include the use of computers in problem solving. Use of the spreadsheet and
macros such as the determinant for solving simultaneous linear equations, the solver function, and
programminginVisualBASICareusedthroughoutthebook.Themanualproblem-solvingapproach
hasnotbeenabandonedinfavorofthecomputerapproach.Thus,userscanstillapplytheconcepts
to better understand a process rather than just mechanically entering inputs into a pre-programmed
algorithm.
Entirelynewsectionsincludeenthalpychangecalculationsinfreezingbasedonthefreezingpoint
depression,evaporativecooling,interpretationofpumpperformancecurves,determinationofshape
factorsinheatexchangebyradiation,unsteady-stateheattransfer,kineticdataforthermaldegrada-
tionoffoodsduringthermalprocessing,pasteurizationparametersforshelf-stablehigh-acidfoodsand
long-liferefrigeratedlow-acidfoods,high-pressureprocessingoffluidandpackagedfoods,concen-
tration of juices, environmentally friendly refrigerants, modified atmosphere packaging of produce,
sorptionequationsforwateractivityofsolidfoods,theosmoticpressureandwateractivityrelation-
ships, vacuum dehydration, new membranes commercially available for food processing and waste
treatment,andsupercriticalfluidextraction.
v
vi Preface
This edition contains much new hard-to-find data needed to conduct food process engineering
calculationsandwillbeveryusefulasasourcebookofdataandcalculationtechniquesforpracticing
foodengineers.
Athens,Georgia RomeoT.Toledo
Contents
Preface............................................................................ v
1 ReviewofMathematicalPrinciplesandApplicationsinFoodProcessing............ 1
1.1 GraphingandFittingEquationstoExperimentalData........................... 1
1.1.1 VariablesandFunctions.............................................. 1
1.1.2 Graphs............................................................. 2
1.1.3 Equations.......................................................... 2
1.1.4 LinearEquations.................................................... 3
1.1.5 NonlinearEquations................................................. 4
1.2 LinearizationofNonlinearEquations......................................... 5
1.3 NonlinearCurveFitting..................................................... 6
1.4 LogarithmicandSemi-LogarithmicGraphs.................................... 8
1.5 InterceptofLog-LogGraphs................................................ 14
1.6 RootsofEquations......................................................... 16
1.6.1 Polynomials........................................................ 16
1.6.1.1 QuadraticEquation........................................... 16
1.6.1.2 Factoring.................................................... 16
1.6.1.3 IterationTechnique........................................... 17
1.7 ProgrammingUsingVisualBASICforApplicationsinMicrosoftExcel........... 18
1.8 UseofSpreadsheetstoSolveEngineeringProblems............................ 20
1.9 SimultaneousEquations .................................................... 23
1.9.1 Substitution ........................................................ 23
1.9.2 Elimination......................................................... 23
1.9.3 Determinants....................................................... 25
1.10 SolutionstoaSystemofLinearEquationsUsingthe“Solver”MacroinExcel...... 27
1.11 PowerFunctionsandExponentialFunctions................................... 29
1.12 LogarithmicFunctions...................................................... 31
1.13 DifferentialCalculus....................................................... 32
1.13.1 DefinitionofaDerivative............................................. 32
1.13.2 DifferentiationFormulas ............................................. 33
1.13.3 MaximumandMinimumValuesofFunctions........................... 35
1.14 IntegralCalculus........................................................... 38
1.14.1 IntegrationFormulas................................................. 38
vii
viii Contents
1.14.2 IntegrationTechniques............................................... 39
1.14.2.1 Constants.................................................. 39
1.14.2.2 IntegrationbyParts.......................................... 39
1.14.2.3 PartialFractions............................................. 39
1.14.2.4 Substitution................................................ 39
1.15 GraphicalIntegration....................................................... 41
1.15.1 RectangularRule.................................................... 41
1.15.2 TrapezoidalRule.................................................... 42
1.15.3 Simpson’sRule..................................................... 42
1.16 DifferentialEquations...................................................... 43
1.17 FiniteDifferenceApproximationofDifferentialEquations....................... 44
Problems...................................................................... 46
SuggestedReading.............................................................. 50
2 UnitsandDimensions.......................................................... 51
2.1 DefinitionofTerms ........................................................ 51
2.2 SystemsofMeasurement.................................................... 52
2.3 TheSISystem............................................................. 52
2.3.1 UnitsinSIandTheirSymbols ........................................ 52
2.3.2 PrefixesRecommendedforUseinSI................................... 53
2.4 ConversionofUnits........................................................ 54
2.4.1 Precision,Rounding-OffRule,SignificantDigits......................... 54
2.5 TheDimensionalEquation.................................................. 55
2.6 ConversionofUnitsUsingtheDimensionalEquation........................... 55
2.7 TheDimensionalConstant(G ).............................................. 57
c
2.8 DeterminationofAppropriateSIUnits........................................ 57
2.9 DimensionalConsistencyofEquations........................................ 58
2.10 ConversionofDimensionalEquations ........................................ 59
Problems...................................................................... 61
SuggestedReading.............................................................. 63
3 MaterialBalances.............................................................. 65
3.1 BasicPrinciples ........................................................... 65
3.1.1 LawofConservationofMass......................................... 65
3.1.2 ProcessFlowDiagrams .............................................. 65
3.1.3 SystemBoundaries.................................................. 67
3.1.4 TotalMassBalance.................................................. 67
3.1.5 ComponentMassBalance............................................ 69
3.1.6 Basisand“TieMaterial” ............................................. 71
3.2 MaterialBalanceProblemsInvolvedinDilution,Concentration,
andDehydration........................................................... 72
3.2.1 SteadyState........................................................ 72
3.2.2 VolumeChangesonMixing........................................... 73
3.2.3 ContinuousVersusBatch............................................. 74
3.2.4 Recycle............................................................ 75
3.2.5 UnsteadyState...................................................... 77
3.3 BlendingofFoodIngredients................................................ 80
3.3.1 TotalMassandComponentBalances................................... 80
Contents ix
3.3.2 UseofSpecifiedConstraintsinEquations............................... 85
3.4 MultistageProcesses........................................................ 89
Problems...................................................................... 98
SuggestedReading.............................................................. 103
4 GasesandVapors.............................................................. 105
4.1 EquationsofStateforIdealandRealGases..................................... 105
4.1.1 TheKineticTheoryofGases............................................ 105
4.1.2 AbsoluteTemperatureandPressure...................................... 106
4.1.3 QuantityofGases ..................................................... 107
4.1.4 TheIdealGasEquation................................................. 108
4.1.4.1 P-V-TRelationshipsforIdealGases............................... 108
4.1.5 vanderWaal’sEquationofState......................................... 110
4.1.6 CriticalConditionsforGases............................................ 112
4.1.7 GasMixtures ......................................................... 112
4.2 Thermodynamics ........................................................... 114
4.2.1 ThermodynamicVariables.............................................. 115
4.2.2 TheRelationshipBetweenC andC forGases............................ 116
p v
4.2.3 P-V-TRelationshipsforIdealGasesinThermodynamicProcesses............ 117
4.2.4 ChangesinThermodynamicProperties,Work,andHeatAssociated
withThermodynamicProcesses ......................................... 117
4.2.5 WorkandEnthalpyChangeonAdiabaticExpansionorCompression
ofanIdealGas........................................................ 118
4.2.6 WorkandEnthalpyChangeonIsothermalExpansionorCompression
ofanIdealGas........................................................ 118
4.3 Vapor-LiquidEquilibrium.................................................... 119
4.3.1 TheClausius-ClapeyronEquation........................................ 120
4.3.2 LiquidCondensationfromGasMixtures.................................. 120
Problems...................................................................... 123
SuggestedReading.............................................................. 124
5 EnergyBalances............................................................... 125
5.1 GeneralPrinciples .......................................................... 125
5.2 EnergyTerms .............................................................. 126
5.2.1 Heat................................................................. 126
5.2.2 HeatContent,Enthalpy................................................. 126
5.2.3 SpecificHeatofSolidsandLiquids...................................... 126
5.3 EnthalpyChangesinFoodsDuringFreezing.................................... 131
5.3.1 CorrelationEquationsBasedonFreezingPointsofFoodProducts
UnmodifiedfromtheNaturalState....................................... 131
5.3.2 EnthalpyChangesDuringtheFreezingofFoodsCalculated
fromMolalityofLiquidWaterFractionoftheFood........................ 133
5.3.3 FreezingPointDepressionbySolutes .................................... 134
5.3.4 AmountofLiquidWaterandIceatTemperaturesBelowFreezing............ 134
5.3.5 SensibleHeatofWaterandIceatTemperaturesBelowthe
FreezingPoint ........................................................ 134
5.3.6 TotalEnthalpyChange................................................. 135
5.3.7 SpecificHeatsofGasesandVapors...................................... 136
x Contents
5.4 PropertiesofSaturatedandSuperheatedSteam.................................. 138
5.4.1 TheSteamTables...................................................... 139
5.4.1.1 TheSaturatedSteamTable....................................... 139
5.4.1.2 TheSuperheatedSteamTables................................... 141
5.4.1.3 DoubleInterpolationfromSuperheatedSteamTables................ 142
5.4.2 PropertiesofSteamHavingLessThan100%Quality....................... 143
5.5 HeatBalances.............................................................. 143
Problems...................................................................... 149
SuggestedReading.............................................................. 152
6 FlowofFluids................................................................. 153
6.1 TheConceptofViscosity .................................................... 153
6.2 Rheology.................................................................. 155
6.2.1 Viscometry........................................................... 155
6.2.1.1 ViscometersBasedonFluidFlowThroughaCylinder............... 156
6.2.1.2 DerivationofthePoiseuilleEquation.............................. 156
6.2.1.3 VelocityProfileandShearRateforaPowerLawFluid............... 158
6.2.1.4 GlassCapillaryViscometers ..................................... 160
6.2.1.5 ForcedFlowTubeorCapillaryViscometry......................... 161
6.2.1.6 EvaluationofWallEffectsinTubeViscometry ..................... 166
6.2.1.7 GlassCapillaryViscometerUsedasaForcedFlowViscometer ....... 167
6.2.2 EffectofTemperatureonRheologicalProperties........................... 170
6.2.3 BackExtrusion........................................................ 172
6.2.4 DeterminationofRheologicalPropertiesofFluidsUsing
RotationalViscometers................................................. 178
6.2.4.1 WideGapRotationalViscometer................................. 180
6.2.4.2 WideGapViscometerwithCylindricalSpindles.................... 182
6.3 ContinuousViscosityMonitoringandControl................................... 186
6.3.1 CapillaryViscometer................................................... 186
6.3.2 RotationalViscometer.................................................. 186
6.3.3 ViscositySensitiveRotameter........................................... 186
6.4 FlowofFallingFilms........................................................ 187
6.4.1 FilmsofConstantThickness............................................ 187
6.4.2 Time-DependentFilmThickness......................................... 189
6.4.3 ProcessesDependentonFluidFilmThicknesses........................... 192
6.5 TransportationofFluids...................................................... 193
6.5.1 MomentumBalance ................................................... 193
6.5.2 TheContinuityPrinciple................................................ 195
6.6 FluidFlowRegimes......................................................... 196
6.6.1 TheReynoldsNumber ................................................. 196
6.6.2 PipesandTubes....................................................... 198
6.6.3 FrictionalResistancetoFlowofNewtonianFluids......................... 198
6.6.4 FrictionalResistancetoFlowofNon-NewtonianFluids..................... 202
6.6.5 FrictionalResistanceOfferedbyPipeFittingstoFluidFlow................. 204
6.7 MechanicalEnergyBalance:TheBernoulliEquation ............................ 205
6.8 Pumps..................................................................... 210
6.8.1 TypesofPumpsandTheirCharacteristics................................. 210
