models.cfd.phase_separation.pdf

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1、SolvedwithCOMSOLMultiphysics4.3bPhaseSeparationIntroductionPhaseseparationoccurswhenabinarysystemisquenchedfromastable,homogeneousone-phasestateintothetwo-phaseregionofitsphasediagram.Thespontaneousseparationoftwoimmisciblefluidsissometimesreferredtoasspinodaldecomposition.Ea

2、chphasetendstoseparateintopurecomponents.ThismodeldemonstrateshowtousethePhaseFieldinterfacetomodeltheprocessofphaseseparation,seeRef.1formoreinformation.ModelDefinitionThissimplebenchmarkmodeltakestwoinitiallymixed,immisciblephasesandobservestheirseparationintopurecomponents

3、.Thecomponentsarerepresentedbyaphasefieldfunction,φ,andareconsideredpurewhenφ=±1.Theinitialmixtureiscreatedbyputtingφequaltoarandomnumberwithzeromeanandastandarddeviationof0.05.Theinitialrandomperturbationinitiatestheseparationintopurephases.Theseparationofthetwoimmisciblepha

4、sesisdescribedbytheCahn-Hilliardequation:∂φγλ=∇⋅------∇ψ(1)∂t2εwhereφisthedimensionlessphasefieldvariable,sothatthevolumefractionsofthecomponentsofthefluidare()1+φ2and()1–φ2.Thevariableγisthemobility3(m·s/kg),thequantityλisthemixingenergydensity(N),andεisacapillarywidththatsc

5、aleswiththethicknessoftheinterface(m).Thelattertwoparametersarerelatedtothesurfacetensioncoefficientthroughtheequation22λσ=--------------(2)3εTheequationgoverningψis22ψ∇=–⋅ε∇φ+()φ–1φ(3)©2013COMSOL1

6、PHASESEPARATIONSolvedwithCOMSOLMultiphysics4.3bBOUNDARYCONDITIONSAcontactangle

7、isimposedontheboundaries.Mathematically,theboundaryconditionis22n⋅εε∇φ=tan()πθ2–∇φ–()n⋅∇φn(4)wandγλn⋅------∇ψ=0(5)2εInCOMSOLMultiphysics,theonlyinputrequiredisacontactangle,θw.Thetotalmassinthesystemiscomputedbyintegratingthephasefieldvariableoverthedomain:φ=φdV(6)intThisint

8、egratedquantityshouldremainconstantduringtheseparationofthetwophases.ResultsandDiscussionFigure1showstheevolutionofthephasefieldvariable.Initially,thetwophasesarecompletelymixedexceptforarandomperturbationaroundφ=0.Byt=1sthephaseshavestartedtoseparate.Att=2s,purephaseshavesta

9、rtedtoform,andtwosecondslateronlypurephasesexist.Aftert=4s,thepureph