Fluid dynamics of floating particles

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1、J.FluidMech.(2005),vol.530,pp.31–80.
c2005CambridgeUniversityPress31doi:10.1017/S0022112005003575PrintedintheUnitedKingdomFluiddynamicsoffloatingparticlesByP.SINGH12ANDD.D.JOSEPH1DepartmentofMechanicalEngineering,NewJerseyInstituteofTechnology,Newark,NJ07102,USAsinghp@njit.edu2DepartmentofAer

2、ospaceEngineeringandMechanics,UniversityofMinnesota,Minneapolis,MN55455,USAjoseph@aem.umn.edu(Received14March2003andinrevisedform5November2004)Wehavedevelopedanumericalpackagetosimulateparticlemotionsinfluidinterfaces.Theparticlesaremovedinadirectsimulationrespectingthefundamentalequationsofm

3、otionoffluidsandsolidparticleswithouttheuseofmodels.Thefluid–particlemotionisresolvedbythemethodofdistributedLagrangemultipliersandtheinterfaceismovedbythemethodoflevelsets.Thepresentworkfillsagapsincetherearenoothertheoreticalmethodsavailabletodescribethenonlinearfluiddynamicsofcapillaryattract

4、ion.Twodifferentcasesofconstrainedmotionsoffloatingparticlesarestudiedhere.Inthefirstcase,westudymotionsoffloatingspheresundertheconstraintthatthecontactangleisfixedbytheYoung–Duprelaw;thecontactlinemustmovewhenthe´contactangleisfixed.Inthesecondcase,westudymotionsofdisks(shortcylinders)withflatend

5、sinwhichthecontactlineispinnedatthesharpedgeofthedisk;thecontactanglemustchangewhenthedisksmoveandthisanglecanchangewithinthelimitsspecifiedbytheGibbsextensiontotheYoung–Duprelaw.Thefactthat´sharpedgedparticlesclingtointerfacesindependentofparticlewettabilityisnotfullyappreciatedandneedsstudy

6、.Thenumericalschemepresentedhereisatpresenttheonlyonewhichcanmovefloatingparticlesindirectsimulation.Wesimulatetheevolutionofsingleheavier-than-liquidspheresanddiskstotheirequilibriumdepthandtheevolutiontoclustersoftwoandfoursspheresandtwodisksunderlateralforces,collectivelycalledcapillaryatt

7、raction.NewexperimentsbyWang,Bai&Josephontheequilibriumdepthoffloatingdiskspinnedattheedgearepresentedandcomparedwithanalysisandsimulations.1.IntroductionIntheworkwhichfollows,wewillbeconsideringthemotionsofparticleswhichfloatintheinterfacebetweentwo