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1、PHYSICALREVIEWE88,053003(2013)Radialviscousfingering:Wettingfilmeffectsonpattern-formingmechanismsPedroH.A.AnjosandJoseA.Miranda´*DepartamentodeF´ısica,UniversidadeFederaldePernambuco,Recife,Pernambuco50670-901,Brazil(Received27August2013;published6November2013)Weconsi
2、dertheinterfacialmotionbetweentwoimmiscibleviscousfluidsintheconfinedgeometryofaradialHele-Shawcell.Inthisframework,weinvestigatetheinfluenceofathinwettingfilmtrailingbehindthedisplacedfluidonthelinearandweaklynonlineardynamicsofthesystem.Morespecifically,weexaminehowthein
3、terfaceinstabilityandthepatternformationmechanismsoffingertipsplittingandfingercompetitionareaffectedbythepresenceofsuchafilminthelowcapillarynumberlimit.Ourtheoreticalanalysisiscarriedoutbyemployingamode-couplingtheory,whichallowsanalyticassesstowetting-inducedchangesi
4、npatternmorphologyattheonsetofnonlinearities.DOI:10.1103/PhysRevE.88.053003PACSnumber(s):47.15.gp,47.54.−r,47.20.Ma,68.08.BcI.INTRODUCTIONleavingafilmoffinitethicknessbehind.Inparticular,ParkandHomsy[12]haveshownthat,inthelimitoflowcapillaryTheviscousfingering(Saffman-T
5、aylor)problem[1]hasnumberCa(relativemeasureofviscousandinterfacialtensionbeenextensivelystudiedduringthepastfiftyyearsorso[2].forces),theinclusionoftheeffectsduetothethinwettingfilmItcomesaboutinthenarrowpassagebetweentwoclose2/3leadstoanorderCacorrectiontothepressured
6、ifferenceparallelplatesofaHele-Shawcell,whenalowviscosityboundarycondition.fluiddisplacesamoreviscousone.Undersuchcircumstances,Infact,comparisonbetweentheory[12,16,17]andexperi-aninstabilitydevelopsatthefluid-fluidinterfaceleadingtoments[13,14]inrectangularHele-Shawcel
7、lsrevealedthatthethegrowthoffingerlikeshapes.InthechannelgeometryofadditionofthethinwettingfilmcorrectionintotheYoung-arectangularHele-Shawcell[1,35]long,smoothsteadyLaplaceconditionisindeednecessarytoprovideamorestatefingersareformed.Ontheotherhand,inradialHele-satisfa
8、ctoryagreementbetweentheoreticalandexperimentalShawcells[68],wherethelessviscousfluidisinjectedresults.Thesefindingsreinforcedthetheo
