Simulation of fluid slip at 3D hydrophobic microchannel walls by the lattice Boltzmann meth(9)

Fluid slip along hydrophobic microchannel walls has been observed experimentally by Tretheway and Meinhart [Phys. Fluids, 14 (3) (2002) L9]. In this paper, we show how fluid slip can be modeled by the lattice Boltzmann method and investigate a proposed mec

190L.Zhuetal./JournalofComputationalPhysics202(2005)181–195

Position on bottom channel wall (microns)25020015010050

011.21.4

Slip length (microns)Position on side channel wall (microns)Slip length (y-direction)300Slip length (z-direction)30252015105(c)(a)011.21.4(b)Slip length (microns)

Fig.5.(a)and(b)depicthowthe uidsliplengthvariesalongtheperimeterofthechannelatstreamwisepositionofx=300lm.(a)Variationofsliplengthasafunctionofyalongthetoporbottomwall.(b)Variationofsliplengthasafunctionofzalongthesidechannelwalls.(c)Measurementsampleplaneandthelocationsofsliplengthplottedin(a)and(b).

(separatedby30lm).However,themagnitudesaresimilar,rangingbetween1.1and1.4lm.Fig.5(c)showsthemeasurementsampleplaneandthelocationsofsliplengthplottedinFigs.5(a)and(b).

3.2.Multi-componentlatticeBoltzmannsimulation

Inthesecondpartofourwork,weinvestigatedapossiblegeneratingmechanismforapparent uidslip

[2],viathemulti-componentlatticeBoltzmannmethod(theS-Cmodel).Weperformedthesimulationona0.1·1·2lm3microchannel.Thegridspacingis5nm.Thenon-dimensionalhydrophobicwallforceusedinthesimulationis0.2,correspondingtoaphysicalforceof4·10À3dyn/cm3withadecaylengthof6.5

Fluid slip along hydrophobic microchannel walls has been observed experimentally by Tretheway and Meinhart [Phys. Fluids, 14 (3) (2002) L9]. In this paper, we show how fluid slip can be modeled by the lattice Boltzmann method and investigate a proposed mec

L.Zhuetal./JournalofComputationalPhysics202(2005)181–195191

nm,aswasspeci edinSection2.Theappropriatemagnitudeofthisforceisnotwellde ned.However,Vinogradova[21]modeledattractivehydrophobicinteractionsasadecayingexponentialwithamagnitudeof1dynandadecaylengthofbetween5and15nm.Forthecurrentsimulation,theforcefunctionwaschosensothatthesimulationresultswouldbeconsistentwithexperimentalobservations.Whilethedecaylength,k=6.5nm,isconsistentwiththevaluesofVinogradova[21],themagnitudeofthehydrophobicforce,4·10À3dyn,issigni cantlylower.Thedi erencemayarisefrompossiblenon-uniformitiesinthehydrophobicOTScoatingsinthemicrochannels.Thisrepulsivehydrophobicforcecausesthedensityofthesynthetic uidusedtosimulatewaterinthemulti-componentlatticeBoltzmannsimulationtobegreaterthan1.Werescaledthedensityto1forthe uidusedtomodelwaterbythemaximumdensityinthesim-ulationresult(about1.07).

Weperformedsimulationsonaseriesofgraduallyre nedgrids.Thenumberofnodesinthezdirectionwas10,15,20,25,30.Wefoundthatthe uidslippercentagewasconvergentasthegridwasre ned.

Fig.6showsthe uiddensitiesasafunctionofdistanceawayfromthesidewallatthecross-sectionx=1lmandz=50nm.Thex-axisisthedensityandthey-axisisthedistancefromthesidewall.Fig.6(a)showsthedensityofthe uidusedtosimulatewaterinthemodelalongtheydirection(inthemiddleofthezdirection)onacross-sectioninthemiddleofthechannel(xdirection).Fig.6(b)showsthedensityofthe uidusedtosimulatewatervapor/air.Wecanseethatthedensityofwaterisdecreasedandthatofwatervapor/airisincreasedclosetothewalls.Fig.7givesadetailedpictureofthedensitychangeclosetothewall.Sakuraietal.[20]havealsoobservedadrasticdecreaseofthewatermoleculenumberdensityatamonolayer–waterinterfacefromthesimulationresultsofwaterbetweenhydrophobicsurfaces,viamoleculardynamics.Ourresultsareconsistentwiththeirs.

Fig.8showsthenormalizedstreamwisevelocitypro leandalocalblowupalongtheydirectionatcross-sectionx=1lmforz=50nm.Thex-axisisthenormalizedvelocity,andthey-axisisthepositionfromthesidewall(unit:micron).Thesolidline(in(a)and(b))isthevelocitypro lewhennowallforcesarepresent.

Fluid slip along hydrophobic microchannel walls has been observed experimentally by Tretheway and Meinhart [Phys. Fluids, 14 (3) (2002) L9]. In this paper, we show how fluid slip can be modeled by the lattice Boltzmann method and investigate a proposed mec

192L.Zhuetal./JournalofComputationalPhysics202(2005)181–195

Thedottedline(inpart(a)),orthedashedline(inpart(b))isthecasewherewallforcesareintroduced.Incontrasttotheformercase,thelatterresultsinapparentslipatthewalls.(SeeFig.8(b)forthelocalblowupnearthesidewall.)WecanseefromFigs.6–8thatintheregionveryclosetothewalls,thewaterdensitydecreasesandthewatervapor/airdensityrises.Thisenablesthe uidsliponthewalls(approximately9%offreestreamvelocity)comparedtothesolidlinesinFig.8,whichillustratethecasewherenohydrophobicwallforceswereapplied.

Fluid slip along hydrophobic microchannel walls has been observed experimentally by Tretheway and Meinhart [Phys. Fluids, 14 (3) (2002) L9]. In this paper, we show how fluid slip can be modeled by the lattice Boltzmann method and investigate a proposed mec

L.Zhuetal./JournalofComputationalPhysics202(2005)181–195193

4.Summaryanddiscussion

WiththesinglephaselatticeBoltzmannmethod(D3Q19model),wesimulatedthe owofwaterina3Dmicrochannelwithhydrophilic/hydrophobicwalls.Theclassicbounce-backschemewasusedtomodelthehydrophilicwalls,whileacombinationofbounce-backandspecularre ectionwasappliedtomodelthepartialslipboundaryconditionatthehydrophobicwalls.Goodquantitativeagreementwasobservedbe-tweenthesimulationsandpreviousexperimentalresults.Inthecaseofhydrophilicwalls,thesimulationresultagreesalmostexactlywiththeanalyticsolution.Inthecaseofhydrophobicwalls,a10%slipwasattainedbyassigningtheprobabilityofbounce-backto0.03andtheprobabilityofre ectionto0.97.ThevalueofqisconsistentwithSucciÕswork[55].Thisseemstoindicatethatpartial uidslipgeneratedbyhydrophobicitymaybemodeledbyacombinationofbounce-backandspecularre ection.However,itremainstobefurtherveri edwhetherthecombinationschemecanaccuratelycapturetheslipmotioncausedbyhydrophobicity.See[55]fordetails.

WiththemultiphaselatticeBoltzmannmethod(theS-Cmodel),weinvestigatedapossiblemechanismfor uidslip.Duetocomputationallimitations,thecorrespondingphysicalsizeofthesimulationdomainwas0.1·1·2lm,whereastheexperimentalresultswereobtainedinamicrochannelwithacross-sectionof30·300lm.Thehydrophobicwallsweremodeledbyapplyinganexponentiallydecayingforceof4·10À3dynwithadecaylength6.5nmfromthewall,whichisconsistentwiththeworkofVinogradona

[21].Thisforcerepelsthewatermolecules,buthasnoe ectontheair/watervapormolecules.Theforceproducesaslipofapproximately9%ofthemainstreamvelocity,whichcorrespondstotheexperimentall-PIVresults.Itindicatesthatthepresenceofadepletedwaterlayer(lowdensityregion)nearthehydro-phobicsurfacemayproducetheapparent uidslipobservedexperimentally.

Acknowledgment

WethankthefollowingpeoplefortheirusefulconversationsanddiscussionsofthelatticeBoltzmannmethod:ShulinHou,ShiyiChen,HudongChen,NicosMartys,XiaoboNie,andLishiLuo.

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