Simulation of fluid slip at 3D hydrophobic microchannel wall(2)

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

182L.Zhuetal./JournalofComputationalPhysics202(2005)181–195

drainagemeasurementsinasolutionofnonadsorbingpolymer.Watanabeetal.[6,7]found uidslipatthewallofahydrophobicduct/pipewithrelativelylargescalegeometry(15·15mm).RuckensteinandRajora

[8]studiedthe uidslipinaglasscapillarywithliquid-repellentsurfaces.Alargeslipwasinferredatthewallfrompressuredropversus owmeasurements.BarratandBocquet[9]predictedcomputationallysig-ni cantslipinnanoporousmedia.Thiswascon rmedexperimentallybyChuraevetal.[10].ZhuandGra-nick[11]studiedexperimentallytheslipinanoscillatingsurfaceforceequipment.Pitetal.[12]investigated uidslipbetweenspinningparalleldisks.ThompsonandTroian[13]simulatedNewtonianliquidsundershear,viamoleculardynamics.Theirresultsuggestedthatthereisanonlinearrelationshipbetweenthemagnitudeofslipandthelocalshearrateatasolidsurface.Foracomprehensivereviewof uidslippageoverhydrophobicsurfaces,see[14]andthereferencestherein.Thehydrophobicityphenomenaarenotwellunderstood.Forreaderswhoareinterestedinhydrophobicity,werefertothefollowingpapersandrefer-encestherein:[15–21].

Recently,TrethewayandMeinhart[1]measuredthevelocitypro lesofdeionizedwater owingthrougha3Dmicrochannelwithacross-sectionof30·300lm.Theyfoundthatwhenthemicrochannelsurfaceishydrophilic(thewallattractswatermolecules),theconventionalassumptionofano-slipbound-aryconditionisvalid.However,whenthemicrochannelsurfaceishydrophobic(thewallrepelswatermol-ecules),asigni cantslip(approximately10%ofthefree-streamvelocity)nearthewallwasmeasured.Thevelocityerrorintheexperimentalmeasurementiswithin2%,andthesliplengtherroriswithin±0.45lm.

Inthispaper,wedescribethenumericalsimulationofthe uidsliponhydrophobicmicrochannelwallsusingthelatticeBoltzmannmethod.Inthe rstpartofourwork,wereportcomputersimulationswiththesinglephase(component)latticeBoltzmannmethod(LBM)for owin3Dmicrochannels,focusingonmodelingoftheslipboundarycondition.Inthesecondpart,weaddressthemechanismof uidslipwiththemultiphase(multicomponent)latticeBoltzmannmethod(theS-Cmodel).Wewanttopointoutthat,inbothcases,weaddressmodelingofthe uidslipgeneratedbyhydrophobicityinwater ow,notthe uidslipgeneratedbyKne ectsforgas ow.

2.Numericalmethods–latticeBoltzmannmethods

ThelatticeBoltzmannmethodisanalternativetotraditionalnumericalmethodsforsolvingincompress-ibleNavier–Stokesequations.Insteadofsolvingforthemacroscopicquantitiesvelocityandpressure(orstreamfunctionandvorticity)directly,LBMdealswiththesingleparticlevelocitydistributionfunctionsf(x,n,t)(xrepresentsthespatialcoordinates,ntheparticlevelocitycomponents,andtisthetimevariable)basedonasimpli edBoltzmannequation.ForapplicationofthelatticeBoltzmannmethodintheareaofmicroscale ows,see[27,40,41].

Inthe rstpartofourwork1wefocusonmodelingtheslipboundaryconditionusinga19-discretevelocitylatticeBoltzmannmodel(D3Q19)[28,29].InthelatticeBoltzmannmethod,thebounce-backschemeisusuallyusedtomodeltheno-slipboundarycondition.(Wenotethatthebounce-backschemecanitselfalsogenerateslip.Ananalysisoftheslipgeneratedbybounce-backforsimple owscanbefoundin[37].Wefoundthat,ona neenoughgrid,theamountofslipcausedbythebounce-backschemealoneisnegligiblecomparedtotheamountobservedinexperiment.Knudsennumberrelatedslipusingthebounce-backschemeformicroscale owcanbefoundin[40,41].)Ithasalsobeensuggestedintheliteraturethatspecularre ectionmaybeusedtomodelaslipboundarycondition.However,thespecularre ectionschemeusedinourworkresultedin100%slipofthe uidonthewalls.Instead,wehaveemployedacom-

Preliminaryresultshavebeenpresentedatthe2002ASMEInternationalMechanicalEngineeringCongress&Exposition,NewOrleans,Louisiana,November,2002.See[25].1