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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-?uidhydrodynamicequationsforcomplex?uids,whereonekindisasimpleNewtonian?uid,whiletheotheriseitherliquid-crystallineorpolymeric/elastomeric,thusbeingapplicabletolyotropicliquidcrystals,polymersolutions,andswollenelastomer
3、s.Theprocedurecaneasilybegeneralizedtoothercomplex?uidsolutions.Specialemphasisislaidonsuchnonlinearitiesthatoriginatefromthe2-?uiddescription,likethetransportpartofthetotaltimederivatives.Itisshownthatthepropervelocities,withwhichthehydrodynamicquantitiesareconvected,cannotbechosenatwill,s
4、incetherearesubtlerelationsamongthem.Withinallowedcombinationstheconvectivevelocitiesaregenerallymaterialdependent.Theso-calledstressdivisionproblem,i.e.howthenematicorelasticstressesaredistributedbetweenthetwo?uids,isshowntodependpartiallyonthechoiceoftheconvectedvelocities,butisotherwisea
5、lsomaterialdependent.Asetofreasonablysimpli?edequationsisgivenaswellasalinearizedversionofane?ectiveconcentrationdynamicsthatmaybeusedforcomparisonwithexperiments.arXiv:cond-mat/0404134v1[cond-mat.soft]6Apr200411IntroductionThethermodynamicandhydrodynamicpropertiesofmulti-componentcomplex?u
6、idsaredeterminedbythemicroscopicdegreesoffreedomoftheirconstituentsandthecouplingbetweenthesedegreesoffreedom.Suchsystemscanexhibitratherrichphasebehavioranddynamics,especiallywhenoneormorecomponentsisastructuredormacromolecular?uid[1].Dueinparttothecouplingofinternaldegreesoffreedom,theses
7、ystemscanalsoexhibitnovel?ow-inducedstructuralevolutionphenomena,includingshear-inducedphasetransformationsand?owalignmentofconstituentsonmicroscopictomesoscopiclengthscales.Suchstructuralevolutioninturnleadstononlinearrheologicalbehavior,suchasstressove
