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

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

JournalofComputationalPhysics202(2005)

181–195

/locate/jcp

Simulationof uidslipat3Dhydrophobicmicrochannel

wallsbythelatticeBoltzmannmethodq

LuodingZhu

a

ba,*,DerekTrethewayb,LindaPetzolda,b,CarlMeinhartbDepartmentofComputerScience,UniversityofCaliforniaSantaBarbara,SantaBarbara,CA93106,USADepartmentofMechanicalandEnvironmentalEngineering,UniversityofCaliforniaSantaBarbara,SantaBarbara,CA93106,USA

Received15September2003;receivedinrevisedform15April2004;accepted5July2004

Availableonline14August2004

Abstract

FluidslipalonghydrophobicmicrochannelwallshasbeenobservedexperimentallybyTrethewayandMeinhart

[Phys.Fluids,14(3)(2002)L9].Inthispaper,weshowhow uidslipcanbemodeledbythelatticeBoltzmannmethodandinvestigateaproposedmechanismfortheapparent uidslip[Phys.Fluids(2003)].Byapplyinganexponentiallydecayinghydrophobicrepulsiveforceof4·10À3dyn/cm3withadecaylengthof6.5nm,ane ective uidslipof9%ofthemainstreamvelocityisobtained.Theresultisconsistentwithexperimentall-PIVdataandwiththeproposedmechanism.

Ó2004ElsevierInc.Allrightsreserved.

Keywords:Fluidslip;Slipboundarycondition;Hydrophobicity;Micro uidic;LatticeBoltzmannmethod

1.Introduction

Inclassical uidmechanics,theassumptionofno-slipatasolidboundaryisusedastheboundarycon-ditionforviscous owsatrigidwalls.However,for owsatmicro-andnanoscales,thisassumptionmaynolongerbeaccurate.Manyresearchershaveinvestigatedthe uidslipphenomenon[3–12,14,21].Choietal.

[3]investigatedexperimentallytheslipe ectsofwater owinhydrophilic/hydrophobicmicrochannelsandfoundthesliplengthtovaryapproximatelylinearlywiththe owshearrate.Lummaetal.[4]measuredthe owpro lenearawallbydouble-focus uorescencecross-correlation;theiranalysisyieldsalargeapparent uidslipatthewall.Hornetal.[5]observedthehydrodynamicslippage,whichwasdeducedfromthin lmq

*ThisworkwassupportedbyNSF/ITRACI-0086061.Correspondingauthor.

E-mailaddress:zhuld@cs.ucsb.edu(L.

Zhu).

0021-9991/$-seefrontmatterÓ2004ElsevierInc.Allrightsreserved.doi:10.1016/j.jcp.2004.07.004