SteadyStateModelingofElectroultrafiltrationatConst

FullTerms&Conditionsofaccessandusecanbefoundat=lsst20Downloadby:[ZhejiangUniversityofTechnology]Date:06April2016,At:01:06SeparationScienceandTechnologyISSN:0149-6395(Print)1520-5754(Online)Journalhomepage::JohnM.Radovich,BahmanBehnam&ClaudyMullon(1985)Steady-StateModelingofElectroultrafiltrationatConstantConcentration,SeparationScienceandTechnology,20:4,315-329,DOI:10.1080/01496398508060682Tolinktothisarticle::05Dec2006.SubmityourarticletothisjournalArticleviews:15ViewrelatedarticlesCitingarticles:18ViewcitingarticlesSEPARATIONSCIENCEANDTECHNOLOGY,20(4),pp.315-329,1985Steady-StateModelingofElectroultrafiltrationatConstantConcentrationJOHNM.RADOVICHandBAHMANBEHNAMSCHOOLOFCHEMICALENGINEERINGANDMATERIALSSCIENCEUNIVERSITYOFOKLAHOMANORMAN.OKLAHOMA73019CLAUDYMULLONBIOLOGICALTRANSPORTLABORATORYCHEMICALENGINEERINGDEPARTMENTWASHINGTONUNIVERSITYST.LOUIS,MISSOURI63130AbstractAsimplemathematicalmodelwasdevelopedtopredictthesteady-stateelectroultrafdtration(acombinationofultrafdtrationandelectrophoresis)fluxforprocessingbovineserumalbumin(BSA)solutionsatconstantconcentration.Theassumptionthatthewallconcentrationisanexponentialfunctionoftheelectricfieldstrengthgavealineardependenceoffluxonelectricfieldstrength.Thisdependencewasexperimentallyconfirmedforelectroultrafdtrationof1-4wt%BSAsolutionsatpH7.4,usingAmiconXM-50membraneswithatransmembranepressuredropof5psig.Themathematicalmodelusesthevaluesofthesolutionandsolventfluxesfornormalultrafdtrationplustheelectrophoreticmobilityofthesolutetopredicttheelectroultrafltrationflux.Thedifferencebetweenthemodelpredictionsandthemeasuredperformancewas7.5%.INTRODUCTIONThefluxandselectivityoftheultrafitrationprocesshavebeenimprovedbycombiningitwithanelectrophoreticforcewhichactsontheretainedsolutestocontrolconcentrationpolarizationwhenprocessingproteinsolutions(1-4)andcolloidalsuspensions(5,6).Duringultrafiltration,theCopyright@1985byMarcelDekker,Inc.3150149-6395/85/2004-0315$3.50/0Downloadedby[ZhejiangUniversityofTechnology]at01:0606April2016316RADOVICH,BEHNAM.ANDMULLONsteady-statesolutionfluxoccurswhentheconvectivetransportofretainedsolutetowardthemembrane(duetothebulktransportofsolventthroughthemembrane)isbalancedbythebacktransportofretainedsolutefromthemembrane(duetotheconcentrationgradient),accordingtothesimplefilmtheoryofconcentrationpolarization(7).Whenanelectrophoreticforceactsagainstthetransmembranepressureforceforconvectivetransport,thesteady-statefluxresultsfromabalanceofconvective,forwardtransport,anddiffusivepluselectrophoreticbacktransport.Theone-dimensional,steady-state,solutebalanceinthefluidboundarylayeraboveamembranewhichcompletelyretainsthesoluteiswhereJisthesolventflux,Cisthesoluteconcentration,Disthesolutediffusivity,uisthesolute’selectrophoreticmobility,andEistheelectricfieldstrength.The“solvent”referstothesolutionoftruesolventandcompletelypermeablesolutes.AssumingthatuandDareconstantandthatelectroosmosisinthemembraneisnegligible,integrationacrosstheboundarylayergivesJ=kIn(C,/C,)+uE(2)whereC,andC,arethesoluteconcentrationsatthemembranesurfaceandinthebulksolution,respectively,andkisanaveragemasstransfercoefficient.Previousexperimentalresults(I-.?,5,6)indicatedthatJwasalinearfunctionofE,buttheslopewasnotequaltou.AssumingthattheslopeofJvsEwasuwouldmeanthatC,mustnotdependonE.Atsteady-state,C,ismaintainedatavalue“highenoughtoprovideaconcentrationboundarylayerwithasignificantphysicalbarriertowatertransport”(7)tocounterbalancetheconvectiontransportwhichisalsobalancedbytheelectrophoretictransport.IfEchanges,thenC,mustchange.AsEincreases,C,decreasesbecausethechargedsoluteistransportedawayfromthemembranebytheelectricfield(seealsoFig.2ofRef.11).AmathematicalmodeltopredictthevariationofJ(andC,)withEisderivedinthispaperandusedtoanalyzeexperimentalresultsforthesteady-stateelectroultrafitrationofbovineserumalbumin(BSA)solutions.MATHEMATICALMODELC,,,isassumedtobeanexponentialfunctionofEsince,experimentally,JappearstobealinearfunctionofE.ItisalsoassumedthattheoperatingDownloadedby[ZhejiangUniversityofTechnology]at01:0606April2016STEADY-STATEMODELINGOFELECTROULTRAFILTRATION317conditionsaresuchthatC,isnotequaltoC,,theconstant,solutegellayerconcentration,orthatapplyingEimmediatelydecreasesC,suchthatitisalwayslessthanC,.Therefore,C,=Cmoe-BE(3)whereBisaconstant.Theboundaryconditionsare:atE=0,C,=C,,,;atE=E,,C,=cb.ThefirstboundaryconditionstatesthattheconcentrationatthemembraneforE=0istheconcentration,CmO,forultrafilteringwithouttheelectricfieldforthesamefluiddynamicconditions.Thesecondboundaryconditionindicatesthatatsomecriticalelectricfieldstrength,E,,theconcentrationgradientintheboundarylayer,hasbeeneliminated.Thus,andwhereE*isadimensionless,electricfieldstrength(=E/EJandJufisthesolutionfluxforultrafiltrat