general nonlinear 2-fluid hydrodynamics of complex fluids and soft matter

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1、GeneralNonlinear2-FluidHydrodynamicsofComplexFluidsandSoftMatterH.Pleiner†,J.L.Harden‡†Max-Planck-InstituteforPolymerResearch,55021Mainz,Germany‡ChemicalEngineering,JohnsHopkinsUniversity,Baltimore,MD21218,USAappearedinNonlinearProblemsofContinuumMechanics,SpecialissueofNoticesofUniversitie

2、s.SouthofRussia.Naturalsciences,p.46-61(2003)AbstractWediscussgeneral2-fluidhydrodynamicequationsforcomplexfluids,whereonekindisasimpleNewtonianfluid,whiletheotheriseitherliquid-crystallineorpolymeric/elastomeric,thusbeingapplicabletolyotropicliquidcrystals,polymersolutions,andswollenelastomer

3、s.Theprocedurecaneasilybegeneralizedtoothercomplexfluidsolutions.Specialemphasisislaidonsuchnonlinearitiesthatoriginatefromthe2-fluiddescription,likethetransportpartofthetotaltimederivatives.Itisshownthatthepropervelocities,withwhichthehydrodynamicquantitiesareconvected,cannotbechosenatwill,s

4、incetherearesubtlerelationsamongthem.Withinallowedcombinationstheconvectivevelocitiesaregenerallymaterialdependent.Theso-calledstressdivisionproblem,i.e.howthenematicorelasticstressesaredistributedbetweenthetwofluids,isshowntodependpartiallyonthechoiceoftheconvectedvelocities,butisotherwisea

5、lsomaterialdependent.Asetofreasonablysimplifiedequationsisgivenaswellasalinearizedversionofaneffectiveconcentrationdynamicsthatmaybeusedforcomparisonwithexperiments.arXiv:cond-mat/0404134v1[cond-mat.soft]6Apr200411IntroductionThethermodynamicandhydrodynamicpropertiesofmulti-componentcomplexflu

6、idsaredeterminedbythemicroscopicdegreesoffreedomoftheirconstituentsandthecouplingbetweenthesedegreesoffreedom.Suchsystemscanexhibitratherrichphasebehavioranddynamics,especiallywhenoneormorecomponentsisastructuredormacromolecularfluid[1].Dueinparttothecouplingofinternaldegreesoffreedom,theses

7、ystemscanalsoexhibitnovelflow-inducedstructuralevolutionphenomena,includingshear-inducedphasetransformationsandflowalignmentofconstituentsonmicroscopictomesoscopiclengthscales.Suchstructuralevolutioninturnleadstononlinearrheologicalbehavior,suchasstressove