unexpected secondary flows in reverse nonequilibrium shear flow simulations antonia statt资料.pdf

该【unexpected secondary flows in reverse nonequilibrium shear flow simulations antonia statt资料 】是由【宝钗文档】上传分享，文档一共【14】页，该文档可以免费在线阅读，需要了解更多关于【unexpected secondary flows in reverse nonequilibrium shear flow simulations antonia statt资料 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。:..PHYSICALREVIEWFLUIDS4,043905(2019)Unexpectedsecondary?owsinreversenonequilibriumshear?owsimulationsAntoniaStatt,*,?,PrincetonUniversity,Princeton,NewJersey08544,USA(Received9November2018;published25April2019)Wesimulatedtwoparticle-based?uidmodels,namelymultiparticlecollisiondynamicsanddissipativeparticledynamics,undershearusingreversenonequilibriumsimulations(RNES).Incubicperiodicsimulationboxes,theexpectedshear?owpro?leforaNewto-nian?uiddeveloped,consistentwiththe?,unexpectedsecondary?owsalongthesheargradientformedwhenthesimulationboxwaselongatedinthe??owpro?lewasobtainedwhenthesimulationboxwaslongerintheshear-gradientdimensionthanthe?owdimension,whilethesecondary?owswerealwayspresentwhenthe?owdimensionwasatleast25%largerthantheshear-?owssatisfytheboundaryconditionsimposedbytheRNESandgiveatotal?ow?eldwithalowerrateofviscousdissipationthanthecorrespondingunidirectional??owinsimulationboxesthatareelongatedinthe?owdimension,anplex?:.(RNES)developedbyMüller-Plathe[1,2]isawell-putingtransportcoef?cientsofparticle-based?[1]andwaslaterextendedtotheshearviscosity[2].RNEShasbeenusedtocalculatethethermalconductivityofsimpleliquids[1,3],salts[4],carbonnanotubes[5,6],andsilicon[7];tostudytheLudwig-Soreteffect[3,8];andtomeasuretheshearviscositiesofsimple?uids[9],polymersolutionsandmelts[10?12],ionicliquids[13],alcohols[14],andwater[15].plexsystemsundershear,includingcolloidalsuspensionsofnanoparticles[16?20],surfactantsolutions[21],andasphalt[22].Morerecently,putetransportpropertiesbutalsotoinvestigatedynamicphenomenaliketheshear-inducedreorientationofdiblock-copolymerlamellae[23]andtheaggregationofpatchyparticlesin?ow[24].TheunderlyingideaofRNESistoimposean?effect?onasysteminanunphysicalwayandmeasurethe?cause.?Inmanynonequilibriumsimulationtechniques,agradient(cause)isimposedanda?ux(effect)ismeasured[25],,inRNES,stresscanbegeneratedbyanunphysicaltransferofmomentumbetweenparticles[2],drivingthesystemoutofequilibriumandresultinginaphysicalmomentum??owpro??uxandmeasuredgradient,*******@?Presentaddress:McKettaDepartmentofChemicalEngineering,UniversityofTexasatAustin,Austin,Texas78712,USA;******@-990X/2019/4(4)/043905(14)043905-1?2019AmericanPhysicalSociety:..STATT,HOWARD,]]a]a]a]a[0[[a/τ[zzxv-20-20--40-40-2002040-40-60-40-200204060-(a)x[a](b)x[a]?owinducedbyRNESin(a)acubicbox(80a×80a×80a)and(b)anorthorhombicbox(125a×80a×80a).ponentofthevelocity,=1aatz=±?cient(.,shearviscosity)canbeextractedwithinthelinear-[1,26].Itisquicklyparedtoequilibriummethods,suchastheGreen-Kuborelations[27],todeterminetransportcoef?-,whicheliminatesarti?cialwalleffectsthatcouldcausemeasured?uidpropertiestodifferfromthebulkinsmall,wall-boundedsimulationboxes[28].Additionally,RNEScanbemadetoconservemomentumandenergyandactsasitsownthermostat[26],avoidingthechallengesofapplyinganexternalthermostatoutofequilibrium[29].Becauseofitsstraightforwardimplementationand?exibility,RNESiswidelyusedandisimplementedinmanysimulationpackages,includingLAMMPS[30],HOOMD-BLUE[31],OPENMD[32],andESPRESSO[33].Despitethesemanypositiveattributes,wehaveuncoveredapreviouslyunappreciatedlimitationofRNESforsimulatingshear??,weobtainednotonlystandardshear?ow[(a)],butplicated?owpatterns[(b)],ponentsalongthesheargradient,?,wesystematicallyinterrogatethe?ow?eld,stress,andviscousdissipationinRNESasfunctionsofthesimulationboxgeometryandtheshearratetodeterminewhyandwhenRNESdoesnotgeneratetheexpectedshear??owsemergeduetotheperiodicboundaryconditionsandarenotspeci?ctothe?uidmodelortheRNESalgorithm,suggestingahydrodynamicinstabilityinherenttothe???rstsummarizedetailsoftheRNESalgorithmforsimulatingshear??nedtobeofsizeLx×Ly×Lz,withxbeingthedirectionof?owandzbeingthedirectionofthesheargradient().[2],twoexchangeslabsofwidthwareconstructedatz=±Lz/tduringthesimulation,?owdirection,p?,isselectedfromtheupperslab,whiletheparticlewiththemostpositivex+x?+momentum,px,,043905-2:..UNEXPECTEDSECONDARYFLOWSINREVERSE?×Ly×Lz,wherexisthe??Lz/4(bottom,blue)and+Lz/4(top,red).urinthetopandbottomslabs,drivingashear-inducedphysicalmomentum?uxback(green).Theexpectedvelocity?eldgivenbyEq.(4),vx(z),px=p+?p?.Theexchangeofmomentumgeneratesaxxphysicalmomentum?uxwithacorrespondingshearstress,τzx,atsteadystate[2]:pxτzx=.(1)2LxLytHere,pxdenotestheaverageamountofmomentumexchangedduringtheintervalt,,?ow?,pressible?owofaNewtonian?uid,thestandardcontinuityequationandmomentumbalancesgoverningthe?oware[34]?·v=0,(2)ρv·?v=??p+?·τ,(3)whereρisthedensity,pisthepressure,andτ=μ[?v+(?v)T](z=±Lz/4)andauniformpressure,whichimpliesthatthereisno?-stateshear?ow?eld,vx(z),?????γ˙(?Lz/2?z),z<?Lz/4vx(z)=γ˙z,|z|<Lz/4,(4)????γ˙(Lz/2?z),z>Lz/4where˙γ=τzx/?ow?,thestandardCouette?ow(|z|<Lz/4)isextendedoutsidetheexchangeregions,resultinginanoveralltriangularpro?,thewidthoftheexchangeregionswshouldbeassmallaspossibletominimallydisturbthisexpected?ow?eld[23],whilestillkeepingtheregionslargeenoughtocontainasuf?-3:..STATT,HOWARD,ANDPANAGIOTOPOULOSheshearviscosityμfromthemeasured?ow?eldwithinthelinear-responseregime,?vxμγ,˙|z|<Lz/4τzx=μ=.(5)?z?μγ,˙|z|>Lz/4Theshearrate˙γcanbevariedbytuningthemomentumexchangeratetochangeτzx,andμisusuallyextractedfromaseriesofmeasurementsatdifferent˙,infrequentmomentumswapsmaynotleadtoasteady?owpro?le[35,36].Analogousproblemshavebeenreportedforthedeterminationofthermalcoef?cientsusingRNES[7].AssuggestedinRef.[36],thisissuecanbepartiallyalleviatedwithaweaker,morefrequentexchangeofmomentum,.,bychoosingpairswithmomentaclosetoatargetvalueinsteadofthemaximum[35].Thismodi?cationallowsthe?owratetobetunedmoreprecisely[35,37],andalsoleadstoaweakersystem-sizedependenceandbetterconvergenceofthemeasuredviscosity[37].Forhighshearrates,thevelocitiesintheexchangeregionsdeviatefromtheexpectedBoltzmanndistributions[35].Thevelocitydistributioninthelowerslabdevelopsashouldertowardlowervalues,whereasthedistributionintheupperslabdevelopsashouldertowardhighervaluesbecausetheimposedmomentumtransferexceedsthesystem?,putationalmethods[35].essibleshearratesdependonthe?,,Müller-Plate[1]originallyusedaboxthatwasthreetimeslongerinthegradientdirectionthaninthe?owdirection(Lz=3Lx).NikoubashmanandHowardchoseLz=Lxtosimulatepolymersolutionsinshear[11],[23].Generally,andasisstandardinmolecularsimulations[38],thesimulationboxmustbelargeenoughinalldimensionstoavoidunphysicalself-interactionsthroughperiodicboundaries,?ow[39],thesimulationboxcansimilarlybeexpandedalongthe?owdimensiontomatchtheexpecteddeformation(Lx>Lz).,,elongatingtheboxinthe??owfortwo?uids,onemodeledusingmultiparticlecollisiondynamics(MPCD)[40,41]andtheotherusingdissipativeparticledynamics(DPD)[42?44].BothMPCDandDPDareparticle-basedmesoscalemodelsthatfaithfullyresolvehydrodynamicinteractionsandincorporatetheeffectsofthermal?uctuations[45].Thesemodelswerechosenforputationalef?ciency,puta-tionallydemandingLennard-Jones?uidmodelusingRNESwithconventionalmoleculardynamicssimulations[2].Inthisarticle,wewilldescribethemodelparametersandourresultsusing aastheunitoflength,εastheunitofenergy,,τ=ma2/?[40,41].±a/2duringbinningtoensureGalileaninvariance[46,47].Intheensuingcollisionstep,theparticlevelocitiesrelativetothecell-averagevelocitywererotatedbya?xedangleαaroundanaxisrandomlychosenfromtheunit043905-4:..UNEXPECTEDSECONDARYFLOWSINREVERSE?,alsocalledstochasticrotationdynamics,?uidarecontrolledbytheparticlenumberdensity,therotationan-gle,thetemperature,andthetimebetweencollisions[40,41,48].Wechosethedensityasρ=5a?3andtherotationangleasα=130?,-Boltzmannrescalingthermostat[49,50]toeachcelltomaintainaconstanttemperatureT=?uid,wherekBisBoltzmann?,wecon?[51],givingμ=?uid[42,52],adissipativeforce,?uctuation-.[44].Weemployedstandardparameters:amaximumconservativeforceof25ε/a,adragcoef?,acutoffofrc=1a,[44].Theparticlenumberdensi