高等化工传递过程原理（研究生）全册配套完整课件3

高等化工传递过程原理（研究生）全册配套完整课件3BasicConceptsFluxDrivingForce

ConstitutiveEquation

TransportPropertyFluxBulkMovementConvectivetransportConvectiveFluxSmallscalemoleculardisplacementMolecular(orDiffusive)transportMolecular(orDiffusive)FluxFlux=ConvectiveFlux+MolecularFluxFlux=(“concentration”)×(“transportvelocity”)TransportofChemicalSpeciesmassfractionmolefractionBulkvelocityorreferencevelocityofamixtureSpeciesvelocityrelativetothemixture:diffusivevelocitySpeciesFluxReferencevelocityMolarunitsMassunits0Ni

niv

Ji

jivM

JiM

jiMFluxrelationshipsTransformationsbetweenSpeciesFluxes

GradientEnergyfluxFluxofspeciesiTemperatureConcentrationofspecieiConcentrationofspeciesjElectricalpotentialPressureOtherexternalforcesConduction(Fourier)Diffusion-thermoeffect(Dufour)Thermaldiffusion(Soret)BinaryDiffusion(Fick)Multicomponentdiffusion(Maxwell-Stefan)Ionmigration(M-S)Pressurediffusion(M-S)M-SMolecularFlux=f(TransportProperties,Drivingforces)Drivingforces=GradientsDominantgradient:PrimarytransportpropertyOthergradients:SecondarytransportpropertiesConstitutiveEquationsforMolecularTransport

LinearFlux-GradientLaws

(ClassicConstitutiveEquations):

MolecularFlux=-TransportProperty×Gradient

HeatTransport--Fourier’sLawofConduction

MomentumTransport--Newton’sLawofViscosity

MassTransport—Fick’sLawofDiffusionFick’slawforbinarymixturesofAandBDiffusionofChemicalSpeciesMagnitudesofTransportCoefficientsBinaryDiffusivity(Fick’s)HeatConductionForisotropicmaterialsForanisotropicmaterialsMagnitudesofTransportCoefficientsThermalconductivityStressandMomentumFluxMagnitudesofTransportCoefficientsViscosityTransportcoefficients(Diffusivities)

Classicconstitutiveequations:MolecularFlux=-“Diffusivity”דConcentrationGradient”PrandtlnumberSchmidtnumberLewisnumberConvectionrelativetoDiffusionorconductionPecletnumberPeAmeasureofconvectivetransportrelativetomolecular-basedtransportMechanismofMolecularTransport

LimitationonLengthandTimeScales

LinearFlux-GradientLaws(ClassicConstitutiveEquations)forMolecularTransport:Flux=-(Transportproperty)×(Gradient)TheoreticalunderstandingoftransportphenomenainmolecularbasisThemoleculartransportofenergy,speciesandmomentumarebasedultimatelyontherandommotionsofmolecules.Models:todescriberandommotionsofmolecules,andrelatethemolecularmotionstotransportfluxesLatticeModelAccordingtoelementarykinetictheoryforlowdensitygases:ApplicationofLatticeModeltoGasesTheKineticTheoryofGasesReference:Sears,F.W.,AnIntroductiontoThermodynamics,TheKineticTheoryofGases,andStatisticalMechanics,2nded.,Addison-Wesley,Reading,MA.1953Hirschfelder,J.O.,Curtiss,C.F.,andBird,R.B.,TheMolecularTheoryofGasesandLiquids,J.Wiley&Sons,NewYork,1954Chapman–EnskogTheoryLennard-Jones(6-12)potential:GasesLiquidsSolidsChapman,S.andCowling,T.G.,TheMathematicalTheoryofNon-UniformGases,3rded.,UniversityPress,Cambridge,1970Chapman–EnskogTheoryandGasViscosityChapman–EnskogTheoryandGasThermalConductivityandDiffusivityStokes-EinsteinModelDiffusioninLiquidsHiss,T.G.andCussler,E.L.,“DiffusioninHighViscosityLiquid”,AIChEJ.,19,698(1973)Eyring’sratetheoryFreeVolumeGlasstone,S.,Laidler,K.J.,andEyring,H.,TheoryofRateProcesses,McGraw-Hill,NewYork(1941)Eyring,H.,“Viscosity,Plasticity,andDiffusionasExamplesofAbsoluteReactionRates”,J.Chem.Phys.,4,283(1936)DiffusioninLiquidsTransportpropertiesdatasource1.J.Millat,J.H.Dymond,C.A.NietodeCastro,“TransportPropertiesofFluids:TheirCorrelation,PredictionandEstimation”,NewYork,IUPAC,CambridgeUniversityPress,19962.CarlL.Yaws,“HandbookofTransportPropertiesData:Viscosity,ThermalConductivity,andDiffusionCoefficientsofLiquidsandGases”,Houston,Tex,GulfPub.Co.,19953.R.C.Reid,J.M.Prausnitz,B.E.Poling,“ThePropertiesofGasesandLiquids”4thed.,McGraw-Hill,NewYork,1987LatticeModelforDiffusivitiesinSolidsSubstitutionaldiffusionInterstitionaldiffusionInterstitionaldiffusionSubstitutionaldiffusionElementaryjump-ratetheoryLimitationonLengthScaleEstimatesofminimumsystemdimensionsforcontinuumtransportmodelsusingbulkpropertiesBasedonanidealgasatP=1atmandT=293K,withM=30g/molBasedondensity=1000kg/m3,andM=30g/molLimitationonLengthScaleLimitationonTimeScaleConservationEquationsforHeatandMassTransferTransportModel:EquationsgoverningthetransportphenomenaThreemajorparts:

ConstitutiveequationsConservationequationsforinteriorpointsConservationequationsforboundarypointsGeneralFormsofConservationEquationsControlvolumeforformulatingadesiredbalanceequationAunitvectorndefinedateverypointonthesurfaceisnormaltothesurfaceanddirectedoutward.ConservationEquationsforFiniteVolumesAfixedcontrolvolume:,V=constant,S=constantAmovingcontrolvolume:,V=V(t),S=S(t)TheLeibnizformulafordifferentiatingavolumeintegralControlvolumeenclosingpartofaninterfaceForthepossibilityofasourcetermataninternalinterface,iftherateofformationperunitareaofinterfaceisdonatedasBs(r,t)

ConservationEquationsforPointsinsideaPhase

ThedifferentialformofthegeneralconservationequationThesurfaceintegralisconvertedtoavolumeintegralbytheapplicationofthedivergencetheorem.DifferentialOperationsinRectangularCoordinatesGradientforadifferentiablescalarfunctionDivergenceforadifferentiablevectorfunctionLaplacianforadifferentiablescalarfunctionDifferentialOperationsinCylindricalCoordinatesGradientforadifferentiablescalarfunctionDivergenceforadifferentiablevectorfunctionLaplacianforadifferentiablescalarfunctionDifferentialOperationsinSphericalCoordinatesGradientforadifferentiablescalarfunctionDivergenceforadifferentiablevectorfunctionLaplacianforadifferentiablescalarfunctionPointConservationEquationsforInterfacesTheboundaryconditions

ControlvolumeenclosingpartofaninterfacebetweenphaseAandphaseB.TheSurfaceSAandSBareeachaconstantdistancelfromtheinterface.ConvectiveandDiffusiveFluxesThegeneralconservationequationataninteriorpointisrewrittenas:ThebalanceataninterfaceisSummaryforGeneralConservationEquationsGeneralconservationequationsforinteriorpointsandinterfacesinteriorpointspointsatinterfacesWiththemassaveragevelocityFluxContinuityandSymmetryConditionswithinaGivenPhaseF

isacontinuousfunctionofpositionatallinteriorpoint.

symmetryplaneaxisymmetricorsphericallysymmetricTotalmassconservationatinteriorpointsContinuityEquation:applicationofthegeneralconservationequationstototalmassContinuityEquationtionRectangular:Cylindrical:Spherical:

TotalmassconservationatinterfaceAlternativeConservationEquationsMaterialderivative(orsubstantialderivative):

iftheamountofanyquantityperunitmassisdenotedas

ConservationofHeatForsolidsorpurefluidsConservationofHeatRectangular:Cylindrical:Spherical:

HeatTransferatInterfaces1.InterfacialEnergyBalancefortheusualsituation

HeatTransferatInterfaces2.ThermalEquilibriumataninterfaceUsuallyassumption:Certainsituations:3.SymmetryConditionssymmetryplaneaxisymmetricorsphericallysymmetricConservationofChemicalSpeciesConstantandWithFick’sLawforConservationofChemicalSpeciesRectangular:Cylindrical:Spherical:

MassTransferatInterfacesInterfacialSpeciesBalanceSpeciesEquilibriumatInterfaceSymmetryConditionssymmetryplaneaxisymmetricorsphericallysymmetricAnalysisonMassTransfer(I)

SteadyandTransientProblemsTransportofChemicalSpeciesFluxesofChemicalSpeciesReferencevelocityMolarunitsMassunits0Ni

niv

Ji

jivM

JiM

jiMFluxrelationshipsDiffusionofChemicalSpeciesFick’slawforbinarymixturesofAandBOne-DimensionalSteadyProblemsExample1:DirectionalSolidificationofaDiluteBinaryAlloyExample2:Diffusioninabinarygaswithaheterogeneousreaction

Example3:DiffusioninadiluteliquidsolutionwithareversiblehomogeneousreactionExample4:TransientdiffusioninasolidfromasurfacefixedconcentrationDopingofsemiconductorsI.C.C=0,y≥0,t=0B.C.C=Cs,y=0C=0,y→∞

TransientProblemsSimilaritymethod(combinationofvariables)TheErrorFunctionDopingofsemiconductorsA2mmthicksiliconwaferistobedopedwithantimony(Sb)inordertocreateap-typeregion.ThiscanbedonebypassingaSbCl3/H2gasmixtureoverthesurfaceofthewaferat1200oC,whichfixesthesurfaceSbconcentrationat1023atoms/m3.Supposethatthedonordensity(whichisjustanothertermfortheSbconcentration)ishopedtobegreaterthanorequalto3×1022/m3,overadepthof1μmbelowthesurface.Determinehowlongthewafershouldbeexposedtothisatmosphereinordertoachievethis.Example5:TransientdiffusioninaSymmetricSlab>0AnalysisonMassTransfer(II)

TransportofChemicalSpeciesCharacteristictimefordiffusion

CharacteristictimeforheatconductionInfiniteorsemi-infinitedimensionapproximationPseudo-steadyApproximationPseudo-steadyProblemsExample6:Pseudo-steady

DiffusioninaMembranePseudo-steadyapproximationExample7:Pseudo-steadyEvaporationofaColumnofLiquidAnalyticalExpressionsofMassTransferCoefficientsfromModelsConcentrationprofileinliquidFilmModelforInterfacialMassTransfer

ConcentrationprofileattimetinasurfaceelementUnsteadyModelsforInterfacialMassTransferSurfaceagedistributionfunctionforpenetrationmodelPenetrationModelforInterfacialMassTransferDistributionfunctionofageofsurfaceelementsforrandomsurfacerenewalmodelSurfaceRenewalModelforInterfacialMassTransferMasstransferinalaminarflowInthiscase,apuresolventflowinglaminarlyinacylindricaltubesuddenlyentersasectionwherethetube’swallsaredissolving.Theproblemistocalculateshowthemasstransfercoefficientvarieswiththefluid’sflowandthesolute’sdiffusion.Inotherwords,itfindsthemasstransferasafunctionofquantitieslikeReynoldsandSchmidtnumbers.Forforcedflowsinshorttubes(smallξ),solutetransferoccursmainlynearthewall.ThethinnessoftheregionofinterestmakesthecurvatureterminLapalciannegligible.Thefluidfarawaythetube’swall(nearthetube’saxis)ispuresolvent.Levequeapproximation:theneglectofsurfacecurvatureandlinearizationofthevelocityprofilegammafunctionFromexperiments,theSherwoodnumberintheearlypartoftheentranceregion:MassTransferCoupledwithChemicalReactionTransportofChemicalSpeciesHeterogeneousReactionHomogeneousReactionEffectofTransportPhenomenaonReactionOctaveLevenspiel,Ind.Eng.Chem.Res.1999,38,4140-4143EffectsofReactiononMassTransferTwodistincteffectsofchemicalreactionsonmasstransfer:TomaintainahighconcentrationdifferenceToenhancetherateatgivenlevelofconcentrationdifference

ThemasstransferrateenhancementbyhomogeneousreactionTherateenhancementfactorI:KeypointsaboutrateenhancementfactorIRatiooftheratesatthesameconcentrationdifference

orkA0

,dependedontherealfluidmechanics;theanalyticalexpressionisunavailablefromfirstprinciplesorkA,morecomplex,nohopetogettheanalyticalexpressionfromfirstprinciplesTheratioIturnsouttobealmostindependentofthefluidmechanicsinvolved;canbedevelopedonthebasisofverycrudemodelsofthefluidmechanicsinvolvedI

is,ingeneral,acomplicatedfunctionofthecompositionofthephasesinvolved;simplifiedequationsemergefromtheconsiderationofthelimitingconditionsReactiontimetrMasstransfertimetmDimensionlessratioΦ

Φ=tm/tr

Ameasureoftherelativerateofreactiontomasstransfer

I=f(Φ)acomplexfunctionSlowreactionregime:Φ<<1I=1Fastreactionregime:Φ>>1Instantaneousreactionregime(uplimit):PhysicalinterpretationonrateenhancementeffectCase:onlyonereactionmaytakesplaceinonephasewiththechemicalkinetic:

Usingfilmtheoryforthedilutesolution,onedimensionalandsteadycase

SteeperconcentrationgradientattheinterfaceEnhancementfactorlargerthanunityTheconditionwheretheenhancementeffectisnegligible:Averagecurvature<<Averagegradient/filmthickness

SlowReactionΦ<0.2Thespeciesconcentrationrelationships

FastReactionAmajorsimplification:Φ>>1InstantaneousReactionWithfilmmodelandFick’slaw102~103PhysicalinterpretationofmasstransferwithinstantaneousirreversiblereactionTheSlow-FastTransitionThetransitionregionaroundΦ=1Withfilmtheory

ForafirstorderirreversiblereactionfilmtheorysurfacerenewaltheoryTheFast-InstantaneousTransition

ReferencesandFurtherReadingsAstarita,G.,Savage,D.W.andBisio,A.GasTreatingwithChemicalSolvents,NewYork,Wiley,1983Cussler,E.L.Diffusion,3rded.,CambridgeUniversityPress,NewYork,2007MulticomponentmasstransferdrivenbyseveraldrivingforcesReviewonFick’sLawMolarfluxwithrespecttomolaraveragevelocityMolarfluxwithrespecttomassaveragevelocityFailuresofFick’sLawCaseI:MulticomponentsystemsFick’slawisinvalid.ConventionalApproachesformoleculartransport(Fick’sLaw):Transferfluxofeachcomponentisproportionalitsownconcentrationgradient.Validonlyforcertainspecialcases:IdealbinarysystemVerydilutesystem

Forn-componentsystemsMolarfluxwithrespecttomassaveragevelocityMatrixRepresentationTHEGENERALIZEDFICK’SLAWMolarfluxwithrespecttomolaraveragevelocityMolarfluxwithrespecttovolumeaveragevelocityMassfluxwithrespecttomassaveragevelocityAlternativeFormsoftheGeneralizedFick’sLawTransformationsbetweenFick’sDiffusivitiesOntheDijM,Dij,DijVorDijωetc...ConclusionontheFick’sLawformultcomponentsystems:OtherExamplesofFailureofFick’sLaw

Fick’slawisonlyvalidforconcentrationdrivingforceDrivingForcesforDiffusionCompositiondrivingforce(chemicalpotentialgradientatconstantTandP)ElectricalpotentialgradientPressuregradientTemperaturegradientOtherexternalfieldgradientsFick’slawisnotvalidforconfinedspaces(suchasmicro-/nano-poroussystems).OnFick’sLawKeypoints:.5.Maxwell-StefanTheoryThespeciesvelocityisdeterminedbyseveralfactors:ThemovementofthemixtureaswholeThedrivingforcesofthespeciesforrelativemovementFrictionofthespecieswithitssurroundingsInthemotionofamolecularspecies,itstotaldrivingforceandtotalfrictionarebalancedeachotherDrivingForcesPotentialGradient

Potentialgradient:Itcanbeignored!TotalDrivingForceCompositiondrivingforcePressuredrivingforceElectricaldrivingforceTemperaturedrivingforceothersAboutdrivingforcesAspeciesisdrivenbyitsownpotentialgradientThegravitypotentialgradientisratherunimportantThegradientofthechemicalpotentialismuchmoreimportantExternalfieldgradientsareotherimportantdrivingforcesFrictionResistanceFrictionofjoniinonemoleofthemixture(xi,i=1,2,…,n):Totalfrictiononi:(Maxwell-Stefandiffusivity)Constitutiveequation(Maxwell-Stefan)Balance:Drivingforce+Friction=0(totaldrivingforceoni)=-(totalfrictiononi)GeneralizedMaxwell-StefanEquation

MatrixFormulationoftheMaxwell-StefanEquations

Forbinarysystems:Fordilutesystems:ForonetracecomponentsystemsForsystemswithidenticaldiffusivitiesBOOTSTRAPPROBLEMTheGeneralizedBootstrapEquationFluxeswithrespecttoafixedpointTheGeneralizedBootstrapEquationEquimolarCounterdiffusionStefanDiffusionFluxRatiosSpecifiedExamplesofthebootstrapproblemSummaryonM-SEquationsTheconstitutiveequationofaspeciescontainsdrivingforcesonthespeciesandfrictiontermswithallotherspecies.ThefrictiontermscontainsanewtypediffusivityThenumberofindependentconstitutiveequationsisonelessthanthenumberofcomponents.Toobtainvelocitiesorfluxeswithrespecttoaphaseinterfaceorafixedcoordinatesystem,thebulkvelocityofthemixtureoranextra‘bootstrap’relationisneeded.GeneralizedMaxwell-StefanEquation

MulticomponentmasstransferdrivenbyseveraldrivingforceswithapplicableCaseI:MoleFractionGradientwithoutFluxThesystemisatsteady.Thegasisideal,isothermalandisobaric.Bootstrapequations:Maxwell-Stefanequations:MolarfractionandfluxofspeciesC:MolarfractionandfluxofspeciesA:InthecaseofDiscreteMaxwell-StefanEquation

FortheonedimensionprobleminathinfilmSteady,nohomogeneousreactionandonedimensionproblemsinarectangularcoordinatesystemCaseII:GasdiffusionwithHeterogeneousReactionToestimatetheoverallrateofthereactionofethanolBootstrapequations:Maxwell-Stefanequations:ThesolutionofthedifferentialequationsyieldsDiscreteMaxwell-Stefanequations:ThesolutionofthediscreteequationsyieldsM-SapproachforelectrolytesKeypoints:Species:ionsandsolventmoleculesElectroneutralityrelationBootstrapequationElectricdrivingforce(important)Fordilutesolutionofstagnantwater

FordilutesolutionofstagnantwaterFortheonedimensionprobleminsideathinfilm:steadyandnohomogeneousreactioninarectangularcoordinatesystematroomtemperatureCaseIII:ElectroneutralityZeroelectriccurrentM-SequationsCaseIV:PolarizationinelectrolysisM-Sequations:bootstraps:Limitingcurrentwhen:atroomtemperature专题报告Maxwell-Stefan方法在传质过程模型化中的应用近期国际刊物文献(不能是review)

.选择自己感兴趣的主题，限于Maxwell-Stefan方法。精读：详细推导其中的关系式，从其所引用的原始文献中找出所省略掉的内容。12月9日交原文和报告(电子版给助教）

用离散型Maxwell-Stefan方程预测盐酸溶液中加入痕量氯化钠时钠离子的扩散方向（参见讲义中的图7.5和图7.7；膜厚度用10微米）。Problem4onpage181Maxwell-StefanDiffusivityRelationshipBetweenFickandMaxwell-StefanDiffusionCoefficientsOnlywithcompositiondrivingforceForbinary(1-2)systems:M-SdiffusivitiesingasesUsingbinarygasdiffusivitiesinmulticomponentcalculationsM-SdiffusivitiesinliquidsForbinarysystems:Thermodynamicfactorforthesystemethanol-waterat40°Cobtainedfromdifferentactivitycoefficientmodels.ParametersfromGmehlingandOnken(1977ffVol.I/lap.133).Fordilutebinaryliquidmixtures:Wilke-ChangEquation=diffusioncoefficientofspeciesi(thesolute)ininfinitelylowconcentrationinspeciesj(thesolvent)[cm2/s]Mj

=molarmassofthesolvent[g/mol]T=temperature[K]=viscosityofthesolvent[mPas=cP]Vi=molarvolumeofsolute1atitsnormalboilingpoint[cm3/mol]associationfactorforthesolventCaldwellandBabb(1956)recommendedbyDannerandDaubert(1983)Vignes(1966)recommendedbyReid(1987)LefflerandCullinan(1970)ConcentratedbinaryliquidmixturesMaxwell-StefanDiffusionCoefficientforMulticomponentLiquidMixturesMaxwell-Stefandiffusioncoefficientsfortheternarysystem2-propanol(l)-water(2)-glycerol(3)andthebinaries2-propanol-glycerolandwater-glycerolGeneralizedVignesEquationThreediffusivitiesinthemixturetoluene(1)-chlorobenzene(2)-bromobenzene(3)at30°C.Thetrianglesarethebest-fitlogarithmicinterpolationsKooijmanandTaylor(1991)Maxwell-StefandiffusioncoefficientpredictedbygeneralizedVignesEquationforanonidealliquidmixtureWesselinghandKrishna(1990)NaClaqueoussolutionsat25oC,atvarioussaltconcentrations.Numberingis1=Na+;2=Cl-;3=H2OLaity,R.W.,DiffusionofIonsinanElectricField,J.Phys.Chem.,67,671-676(1963)M-SdiffusivitiesinElectrolytesolutionsDiffusivitiesinsodiumchloridesolutionsIon-WaterdiffusivitiesinaqueoussolutionsCation-aniondiffusivitiesItisnotveryaccuratewithdeviationsupto30%.Evenso,itcanbeusefulbecauseion-ionfrictionisoftenasmallpartofthetotalfrictionduetolowionicconcentrations,soweneednotevaluateitaccuratelyDiffusivitiesofionsoflikechargeOneofthefewcasesinwhichMaxwell-Stefandiffusivitiesarenegative.Thefrictionofanionwithitssurroundingstendstobereducedbyaddingionsoflikecharge.Theneteffectmaynotbeareduction,becauseionsofunlikechargemustalsobeaddedtoretainelectroneutrality.Maxwell-StefanapproachvsFickequationsForaternarymixturewithonlyconcentrationgradientsM-S:Fick:CaseI:anidealternarygasmixtureFickdiffusioncoefficientsplottedasafunctionofcompositionforthethreepossiblechoicesof"component3."ThethreeMaxwell-StefandiffusioncoefficientsinthesystemH2-N2-CC12F2.NotethattheMaxwell-Stefancoefficientsareindependentofcomposition.TheMaxwell-StefandiffusioncoefficientspredictedusingageneralizedVignesequationforanonidealliquidmixtureCaseII:anonidealternaryliquidmixtureTheFickdiffusioncoefficientsasafunctionofcompositionandcomponentnumberingforanonidealliquidmixtureMSFickSimplebehaviorofcoefficients+-Independenceofreferenceframe+-Easilyextendedtootherdrivingforces+-Numberofcoefficientsn(n-1)/2(n-1)2Coeff’sindependentofdrivingforces+-Coefficientsindependentofsequence+-Integrationwiththermodynamics+-Lookslike'chemicalengineering'-+AdvantagesanddisadvantagesofthetwodescriptionsEffectiveDiffusivityMethodsforMulticomponentDiffusionDefinitions:Acceptabletheoretically?RelationshipBetweenEffectiveandMaxwell-StefanDiffusionCoefficients:ForthecasesofRelationshipBetweenEffectiveandFickDiffusionCoefficients:AllbinarydiffusioncoefficientsequalIndilutemixtureswhereonecomponentisinalargeexcessWhenspeciesidiffusesthroughn-1stagnantgasesLimitingCases:WilkeEquationOtherEquationsforEffectiveDiffusivity12MassTransferinPoresDoyouremember?Threemainresistanceswithintwophases

SchematicdiagramofadsorbentorcatalystparticledepictingthethreemaindiffusionresistancesMacropore>50nmMesopore2~50nmMicropore<2nm

Poresizedistributionofzeolite-X,molecularsievecarbonandactivatedcarbonThemechanismsofmasstransferinaporeThreeContributionstoMassFluxFluxofthespecieswithinaporousmedium

Contributionsofbulk,KnudsonandsurfacediffusionfortransferofH2Sacrossacatalyticmembrane(350nmpores)carryingtheClausreaction:2H2S+SO2=3/8S8+2H2O

H2SfluxacrosmembranceThedustygasmodelThemostconvenientapproachtomodelingcombinedbulkandKnudsendiffusionAssumptions:ThedustconcentrationC'n+1isspatiallyuniformThedustismotionless,sothatN'n+1=0ThemolarmassofthedustparticlesEffectiveMaxwell-StefanDiffusivitiesGeneralizationtonon-idealfluidmixtureEffectiveKnudsenDiffusivitiesMatrixFormForidealgasesForidealmixtureswithoutexternalforcesForidealgaseousmixturesViscousflowMembraneProcessesPressuregradientinporousmediumgaseousmixtures

三元气体混合物He(1)－Ne(2)－Ar(3)扩散通过一个惰性多孔膜。膜内的孔可以看作是平行圆柱孔，膜的空隙率为70％。试确定在100nm、200nm和300nm三种孔径条件下，三个组分的稳态传质通量和方向。已知条件如下：上游压力P0＝210×103Pa，下游压力Pδ＝190×103Pa，温度T=300K，气体粘度μ＝22×10-6Pa·s，膜厚度δ=9.6×10-3m，膜两侧的组成为：x10=0.4x1δ=0.4x20=0.4x2δ=0.3x30=0.2x3δ=0.3

组分在压力为100×103Pa和温度为300K的主体相气体中的二元Fick扩散系数为D12=1.068×10-4

㎡/sD13=0.724×10-4

㎡/sD23=0.316×10-4

㎡/s

ProblemSurfaceDiffusionThemechanismsofmasstransferinaporeThreeContributionstoTotalMassFluxFluxofthespecieswithinaporousmediumSinglefilediffusion(SFD)mechanism:Forthecaseinwhichthemoleculesaretoolargetopassoneanother,themechanismofcountersorptioncannotprevailbecausethereisaroomforonlyonetypeofmolecularspeciesatanygiventime.Completemechanism:Forthecaseinwhichthemoleculesaresmallenoughtopassoneanotherwithinalargeroom,thepossibilityofcountersorptioncannotberuledout.Maxwell-StefanequationforsurfacediffusionMaxwell-Stefanequationsforsinglefilediffusion(SFD)CompleteMaxwell-StefanequationsforsurfacediffusionMaxwell-StefansurfacediffusivityIfthejumpfrequencyremainsconstant,independentofsurfacecoverageIfthejumpfrequencydecreaseswithsurfacecoverageMicroporediffusionisanactivatedprocessMaxwell-Stefanmicroporediffusivityofn-butaneinsilicalite-1Countersorptioncoefficient:

theinteractionofadsorbatei–adsorbatejThesurfacechemicalpotentialgradientsForgaseousmixtureForliquidmixtureatnottoohighpressurefordilutesolutionThesurfacediffusionfluxesCompleteMaxwell-StefanequationSFDMaxwell-StefanequationTheMatrixform:ThedefinitionofamatrixofFicksurfacedif