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JournalofColloidandInterfaceScience258(2003)266–275flowwithstepchangeinzetapotentialL.-M.Fu,J.-Y.Lin,andR.-J.Yang∗DepartmentofEngineeringScience,NationalChengKungUniversity,Tainan,70101TaiwanReceived11April2002;accepted16October2002AbstractThetermelectroosmoticflowreferstothebulkflowofanaqueoussolutioninducedbytheapplicationoftheelectricfieldtothezetapotential.ThecharacteristicsofEOFinamicrochanneldependuponthenatureofthezetapotential,i.e.,whetheritisuniformornonuniform.Inthisstudy,thefullNavier–StokesequationandtheNernst–PlanckequationareusedtomodelthechangeinEOFcharacteristicsthatoccurwhenastepchangeinzetapotentialisapplied.Itisfoundthatthethicknessoftheelectricaldoublelayergraduallyincreasesdownstreamfromthelocationatwhichthezetapotentialisincreased.Theresultsindicatethatastepchangeinzetapotentialcausesasignificantvariationinthevelocityprofileandinthepressuredistribution.2003ElsevierScience(USA).Allrightsreserved.Keywords:Electroosmoticflow;Zetapotential;Electricaldoublelayer1.IntroductionEOFdescribesfluidmotionthatisinducedbyanappliedelectricfield,andthatisthereforedifferentfromthetradi-tionalpressure-drivenflow.Inthelattercase,whentheve-locityfieldisinasteadystate,thevelocityprofileassumesaparabolicshapeinthefullydevelopedregion.Inanelectric-drivenflow,anexternallyelectricfieldactsonthenetfluidchargeofafluidinthevicinityofthewallandproducesabodyforcethatthendrivesfluidmotion.SincetheReynoldsnumberofthefluidmotionislow,eventhefluidthatisfarremovedfromthewallisalsopromptedintomotionduetotheeffectsofviscosity.Whenthevelocityfieldisinasteadystate,itisobservedthattheshapeofthevelocityprofileinthefullydevelopedregionisflat,i.e.,itisquitedifferentfromtheparabolicshapewitnessedintraditionalpressure-drivenflow.SincehydrationcausesthewallofthesilicamicrochanneltobenegativelychargedatmostpHconditions,anaccumu-lationofpositiveions(counterions)occursintheaqueoussolutionadjacenttothewall.Thiscounterion-richregionisreferredtoastheelectricaldoublelayer(EDL).Thepoten-tialbetweenthewallandthisbufferisknownasthezetapo-tential,ζ.Whenanelectricfieldisappliedtangentiallytothe*Correspondingauthor.E-mailaddress:rjyang@mail.ncku.edu.tw(R.-J.Yang).EDL,itsdiffuselayeroftheEDLisdrawntowardthenega-tiveelectrodeandthisresultsinEOFinthesamedirection.ThemagnitudeoftheEOFcanbeapproximatelyexpressedasafunctionofitsvelocity,i.e.,VEOF=(εζ/µ)E,whereεisthedielectricconstantofthefluid,ζthezetapotential,µtheviscosity,andEtheappliedelectricfieldintensity[1].Fromtheexpressionabove,itcanbeseenthatthemagnitudeofEOFisdirectlyrelatedtothezetapotential,whichinturnisafunctionoftheionicvalence,theionicconcentrationoftheelectrolytesolution,andthesurfacepropertiesofthemicrochannelwall.Forasystemwithasimpleelectrolytesolutionandahomogeneouschannelwall,thezetapotentialisconsideredtobeuniform.EOFplaysaveryimportantpartinmanyseparationprocesses,e.g.,intheseparationofbiologicalparticles,includingDNAandprotein.However,adhesionofsomeoftheseparticlestothechannelwall,orpollutioncausedbythechip-producingprocess,maycausethezetapotentialalongthemicrochannelwalltobecomenonuniform.Therefore,theoriginalEOFcharacteristicswillbesomewhatchanged.Researchershaveidentifiedsomedifferencesinthemi-crochannelflowsubjecttononuniformzetapotential.An-dersonandIdol[2]havedevelopedaninfinite-seriessolu-tionforthecaseofflowinacylindricalmicrochannelwithazetapotentialvaryingasacosineorsinefunctionintheflowdirection.Herretal.[3]experimentallyinvestigatedtheEOFflowfieldandthesampledispersionrateinopencapil-lariesforastepchangeinthezetapotential(i.e.,ζ1=0and0021-9797/03/$–seefrontmatter2003ElsevierScience(USA).Allrightsreserved.doi:10.1016/S0021-9797(02)00078-4L.-M.Fuetal./JournalofColloidandInterfaceScience258(2003)266–275267ζ20).Intheirwork,theypresentedasimplemodelthatdescribedthefluidvelocityandthedispersionrate.Strooketal.[4]studiedtwodifferenttypesofsurface-chargechangeinrectangularchannels.Thefirsttypeconcernedthesurface-chargevariationalongadirectionperpendiculartotheap-pliedelectricalfield,i.e.,aconditionthatgeneratesamul-tidirectionalEOF.Thesecondtypeisrelatedtothesurface-chargevariationalongadirectionparalleltotheelectricalfield,whichgeneratesare-circulatingflow.Potoˆceketal.[5]alsoinvestigatedtheinfluenceofadiscretestepchangeinthezetapotentialonthevelocityprofileoftheEOF.Longetal.[6]consideredasimilartypeofzetapotentialvariationinplanerandcylindricalcapillariesanddevelopedapprox-imatesolutionsbyconsideringtheheterogeneityintermsofsmallperturbationstothevelocity.RenandLi[7]usedthecontinuityequationtoexplainthephysicalphenomenonofmicrochannelflowwithnonuniformzetapotential.NotethatRefs.[2–5]assumedathinelectricaldoublelayerandRefs.[6,7]focuseduponflowinthefullydevelopedre-gion.OnelimitationofallofthesestudiesistheassumptionthatthenetchargedensityfieldconformstoanequilibriumBoltzmanndistribution.Itisknownthattheflowfieldaf-fectsthenetchargedensity,whichmaythennotconformtotheBoltzmanndistribution.Therefore,itappearsinappropri-atetoadoptthisdistributionasacompletedescri