电场作用下超滤膜的浓差极化比模型

　收稿日期:2002-06-13＊基金项目:(2000056117);(20006005)　作者简介:(1968-),,,.文章编号:1000-565X(2003)03-0036-04电场作用下超滤膜的浓差极化比模型＊陈　山　蔡妙颜　郭祀远　李　琳　肖凯军　陈　健(,510640)摘　要:针对电场作用下的超滤膜浓差极化现象,根据传递过程中的质量守恒定律并结合膜的吸附-扩散分离理论,推导出了电超滤过程中的浓差极化比理论模型,并对该模型的影响因素如溶质的电泳速度和吸附-扩散作用等进行了分析.关键词:电场;超滤;传质;浓差极化;模型中图分类号:TQ021.4　　　　文献标识码:A　　.,,,.,.,.,()[1],,.,,,;,,,,[2].,,,,,[3].,,,,[4],.,(),.1　浓差极化比模型的推导　　,3:ΔpFp;cmcb,Fc(Fp);Fe.FeFp,.1　Fig.1　Schematicdiagramofmasstransferneartheultrafiltrationmembrane(自然科学版)313JournalofSouthChinaUniversityofTechnologyVol.31　No.320033(NaturalScienceEdition)March　2003　　,,1,.1-2-3-4,,Jc=Jcp+UEc-Ddcdy(1):J;c;cp;D;UE,UE=μEE,μE,E.,,R=1-cpcb(2),cb,cp=(1-R)cb(3)(3)(1),Ddcdy=-Jc+UEc+J(1-R)cb(4),c=(1-R)Jcb+G(UE-J)expy(UE-J)DUE-J(5),G.:y=0,c=cs(cs);y=δ(δ),c=cb,(UE-J)cb-(1-R)Jcb(UE-J)cs-(1-R)Jcb=expδ(UE-J)D(6):K=Dδ;cscb,,.,R≈1,(5)cscb=expδ(J-UE)D=expJ-UEK(7),JE[5]:J=KmE+J0(8):Km=d2032μ·η·ε,;J0=-d2032μ·ε·dpddz,,dpddzz(),d0,μ,η,ε.(8)(7),cscb=expKmE+J0-UEK=exp(Km-μE)·E+J0K(9),(J-UE),.,.,.,.2.2　Fig.2　Schematicdiagramoftheultrafiltrationprocessconsideringwithmembraneadsorption　　,,Langmuir[6]:Γw=Γ∞wNw(1-c)1+Nw(1-c)+Nsc(10)Γs=Γ∞sNsc1+Nw(1-c)+Nsc(11),ΓwΓs,Γ∞wΓ∞s,NwNs、.(10)(11)():cm=ΓsΓs+Γw=Nc1-(1-N)c(12),N=NsΓ∞sNwΓ∞w.cmcp,cp=Nc1-(1-N)c(13)(13),cpc,　3　:37　　　(13)(4),Ddcdy=-Jc+UEc+J·Nc1-(1-N)c(14),-lncJN+UE-J-MUE(JN+UE-J)(UEN-UE+J-JN)+MUEN(JN+UE-J)(UEN-UE+J-JN)+MJ(JN+UE-J)(UEN-UE+J-JN)-MJN(JN+UE-J)(UEN-UE+J-JN)+MUEN-UE+J-JN-MNUEN-UE+J-JN+yD=G′(15),M=ln[JN+UE-J+(1-N)(J-UE)c].(15),:(1),J,UEK;(2),c,M.,-lncJN+UE-J+yD=G0(16),G0.:y=0,c=cs;y=δ,c=cb,cscb=expδD(J-JN-UE)(17)(8)(17),cscb=exp(1-N)KmE-μEE+J0K(18)(18)(9),,N,.2　讨　论2.1　传质系数K的确定(7)、(9)(17)、(18),cs,(cb、cpKm),cs,K.,K.K=Sh·Dde,Sh,de,de=2HWH+W,HW.,ShK.()(),[7]::Sh=0.073Re0.74Sc0.34deL0.32(19):Sh=0.147Re0.74Sc0.34deL0.32X0.19(20)(19)(20),Re,Sc,L,X=de·Jυ,υ.(19)(20)(7)(17),.(1):cscb=exp13.7×(J-UE)·deD·Re0.74·Sc0.34Lde0.32(21):cscb=exp13.7×(J-UE)·deDRe0.74Sc0.34Lde0.32(22)(2):cscb=exp13.7×(J-JN-UE)·deD·Re0.74·Sc0.34Lde0.32(23):cscb=exp13.7×(J-JN-UE)·deD0.81Re0.74·Sc0.34Lde0.32(24)2.2　膜吸附平衡常数N的影响(),N1,J-JN-UE0,cscb1,;(),N1,δD(J-38　　　(自然科学版)31　JN-UE)0,cscb1,,,.,:、、、1[8].,,.,.3　结　论　　,、.:(1);(2)、-;(3);(4),.参考文献:[1]　SaltonstallCW.Dialysisandultrafiltration:Estimat-ingquantitativeseparations[J].AmericanBiotech-nologyLaboratory,1992,10(1):10-18.[2]　JagannadhSN,MuralidharaHS.Electrokineticsme_thodstocontrolmembranefouling[J].IndEngResDes,1996,35(9):1133.[3]　HuotariHannaM,HuismanIngmarH,TragardhGun.Electricallyenhancedcross_flowmembranefiltrationofoilywastewaterusingthemembraneasacathode[J].JournalofMembraneScience,1999,156(1):49-60.[4]　BowenWR.Electrochemicalaspectsofmicrofiltra-tionandultrafiltration[A].HowellJA,SanchezV,FieldRW,eds.MembranesinBioprocessing[M].Cambridge:ChapmandHall,1993.265-292.[5]　,,.[J].,1999,19(2):33-36.[6]　DatwaniSammyS,StebeKathleenJ.Monolayerpene-trationbyachargedamphiphile:Equilibriumanddy-namics[J].ColloidsandSurfacesA:PhysicochemicalandEngineeringAspects,2001,192(1):109-129.[7]　.[J].,1986,6(2):16-22.[8]　.[J].,1984,4(2,3):66-69.ConcentrationPolarizationRatioModelofUltrafiltrationinElectricFieldChenShan　CaiMiao_yan　GuoSi_yuan　LiLin　XiaoKai_jun　ChenJian(ResearchInstituteofLightIndustry&ChemicalEng.,SouthChinaUniv.ofTech.,Guangzhou510640,China)Abstract:Accordingtothephenomenonofconcentrationpolarizationinelectro_ultrafiltrationprocess,themodelofconcentrationpolarizationratiowasestablishedbasedontheprincipleofmassconservationmechanismandthetheoryofadsorption_diffusion.Theinfluencefactorsofconcentrationpolarizationratiosuchassoluteelectrophoresisrateandadsorption_diffusionwereanalyzed.Keywords:electricfield;ultrafiltration;masstransfer;concentrationpolarization;model　3　:39