Simulation of fluid slip at 3D hydrophobic microchannel wall(3)

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)181–195183

binationofbounce-backandre ectiontosimulatetheslipboundarycondition.Thus,theslipboundaryconditionismodeledbyassigningaprobabilityofqforbounce-backand1Àqforspecularre ectionwhenaparticlevelocitydistributionfunctionfj(x,t)hitsawall(100%bounce-backifnjisperpendiculartoawall).Byvaryingthevalueofq,di erentslipboundaryconditionsmaybemodeled.Anobviousshortcomingofthisapproachisitslackofpredictabilityoftheamountofslip.AsimilarschemehasbeenusedbySucci[55]tostudyslipmotionat uidsolidinterfaceswithheterogeneouscatalysis.Suchanideawasmentionedin

[34,35],andcanbedatedbackto1867whenMaxwellstudiedthemicroscopicmodelingofthesolidbound-ary[42].Itwasonceusedin[43]totreattheno-slipboundaryconditioninthelatticegasmethod,andhasalsobeenmentionedinthecontextofdirectsimulationMonteCarlo(DSMC)[44].(InDSMC,specularre ectioniscombinedwiththefulldi usioncondition.)Thecombinationofbounce-backandspecularre ectionisdi culttoimplementinacomplexgeometry.Amethodforaddressingthatissuehasbeenpro-posedin[45].

Inthesecondpartofourwork,wemakeuseofthemulticomponentlatticeBoltzmannmethod[49–52]toinvestigateapossiblemechanism[2]forgeneratingtheapparent uidsliponahydrophobicwall.Thegen-eralideaofthemechanismisasfollows.Thewaterusedinthelaboratoryexperimentwasnotdegasedandcontainsasmallamountofabsorbedgas.Thehydrophobicwallmayrepelthewatermoleculeswithinaregionveryclosetothewallbutisneutraltowatervaporandairmolecules.Asaresult,thewaterdensitynearthewallmaydecline,creatingadepletedlayerveryclosetothewall.Thus,athinlayerofwater–air/watervapormixturewithsigni cantlydi erentwaterandair/watervapordensities(comparedtothewell-mixedair–waterunderstandardconditions)mayformintheregionveryneartothewall.Becausetheva-pordensityismuchsmallerthanthatofwater,theaveragedensityofthethinlayerdeclinescomparedtotheaveragemixturedensityelsewhere.Sincethepressuredropbetweentheinletandoutletthatdrivesthe owcanbetreatedasapproximatelyconstantoncross-sectionsoftheinletandoutlet,thethinlayermaymovefasterthantheusuallymixedwater–air(e.g.,inthecaseofahydrophilicwall),whichmayresultinapparentsliponthehydrophobicwall.

Wetestedtheabovepropositionbysimulatingthewater–air/watervaportwo-phasesystemwiththemulticomponentlatticeBoltzmannmethodfor owina3Dhydrophobicmicrochannel.Thehydrophobicwallsweremodeledbyapplyingforcesinaregionveryclosetothewalls.Theseforcesarerepulsivetothewatermolecules,andareneutraltotheair/watervapormoleculedistributionfunctions.Theseforcesexpo-nentiallydecayawayfromthewall.Theinitialwater–airmixtureisassumedtobeuniform.Theinitialden-sityoftheairinthewateriscalculatedunderstandardconditions(at20°Cand1atm).ThemulticomponentlatticeBoltzmannmodelweuseistheS-Cmodel,see[49–52],exceptthatweintroducedtheadditionalhydrophobicwallforcesintotheformulation.Thewallforcetermwasinsertedintotheright-handsideoftheequationswhichareusedtoupdatethevelocitiesforcomputingthenewequilibriumveloc-itydistributions.

Numerousresearchershaveexaminedhydrophobicsurfacesandtherelatedforces.Whilethee ectsofhydrophobicforceshavebeenobserved,theformandmagnitudeofthehydrophobicforceisnotwellunderstood.Asa rstapproximation,wemodeledthehydrophobicforceasasimpleexponentialdecaywithamagnitudeandadecaylength.AsimilarforcefunctionwasexploredbyVinogradova[21].Wesetthemagnitudeanddecaylengthtobeconsistentwithexperimentalobservations.Thedecaylengthisconsistentwiththeexperimentallengthscalesatreducedviscositylayer(5nm)[23,16]ornanobubbles(10–30nm)[22],aswellasthevalueassumedbyVinogradova(decaylength5–10nm)[21].ThemagnitudeisthreeorderssmallerthanthatassumedbyVinogradova[21].

2.1.SinglecomponentlatticeBoltzmannmethod

TheLBMsusedinourworkareinthe rstpartthesinglephaseisothermalLBGKmodel[28,29],andinthesecondpartthemultiphaseS-Cmodel[49,50].