Flowing Matter PDF
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Soft and Biological Matter Federico Toschi Marcello Sega Editors Flowing Matter Soft and Biological Matter SeriesEditors DavidAndelman,SchoolofPhysicsandAstronomy,TelAvivUniversity, TelAviv,Israel WenbingHu,SchoolofChemistryandChemicalEngineering,Departmentof PolymerScienceandEngineering,NanjingUniversity,Nanjing,China ShigeyukiKomura,DepartmentofChemistry,GraduateSchoolofScienceand Engineering,TokyoMetropolitanUniversity,Tokyo,Japan RolandNetz,DepartmentofPhysics,FreeUniversityofBerlin,Berlin,Germany RobertoPiazza,DepartmentofChemistry,MaterialsScience,andChemical Engineering“G.Natta”,PolytechnicUniversityofMilan,Milan,Italy PeterSchall,VanderWaals-ZeemanInstitute,UniversityofAmsterdam, Amsterdam,TheNetherlands GerardWong,DepartmentofBioengineering,CaliforniaNanoSystemsInstitute, UCLA,LosAngeles,CA,USA “SoftandBiologicalMatter”isaseriesofauthoritativebookscoveringestablished andemergentareasintherealmofsoftmatterscience,includingbiologicalsystems spanningallrelevantlengthscalesfromthemoleculartothemesoscale.Itaimsto serve a broad interdisciplinary community of students and researchers in physics, chemistry,biophysicsandmaterialsscience. Pure research monographs in the series, as well as those of more pedagogi- cal nature, will emphasize topics in fundamental physics, synthesis and design, characterization and new prospective applications of soft and biological matter systems. The series will encompass experimental, theoretical and computational approaches. Topics in the scope of this series include but are not limited to: poly- mers, biopolymers, polyelectrolytes, liquids, glasses, water, solutions, emulsions, foams,gels,ionicliquids,liquidcrystals,colloids,granularmatter,complexfluids, microfluidics,nanofluidics,membranesandinterfaces,activematter,cellmechanics andbiophysics. Bothauthoredandeditedvolumeswillbeconsidered. Moreinformationaboutthisseriesathttp://www.springer.com/series/10783 Federico Toschi (cid:129) Marcello Sega Editors Flowing Matter Funded by the Horizon 2020 Framework Programme of the European Union Editors FedericoToschi MarcelloSega DepartmentofAppliedPhysics ForschungszentrumJu¨lich UniversityofTechnologyEindhoven HelmholtzInstituteErlangen-Nu¨rnberg Eindhoven,TheNetherlands forRenewableEnergy Nuremberg,Germany Funded by the Horizon 2020 Framework Programme of the European Union Thisarticle/publicationisbasedupontheworkfromCOSTActionMP1305,supportedby COST(EuropeanCooperationinScienceandTechnology). COST(EuropeanCooperationinScienceandTechnology;www.cost.eu)isafundingagency forresearchandinnovation networks.OurActions helpconnect researchinitiatives across Europeandenablescientiststogrowtheirideasbysharingthemwiththeirpeers.Thisboosts theirresearch,careerandinnovation. ISSN2213-1736 ISSN2213-1744 (electronic) SoftandBiologicalMatter ISBN978-3-030-23369-3 ISBN978-3-030-23370-9 (eBook) https://doi.org/10.1007/978-3-030-23370-9 ©TheEditor(s)(ifapplicable)andTheAuthor(s)2019.Thisbookisanopenaccesspublication. Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicateifchangesweremade. The images or other third party material in this book are included in the book’s Creative Commons licence,unlessindicatedotherwiseinacreditlinetothematerial.Ifmaterialisnotincludedinthebook’s CreativeCommonslicenceandyourintendeduseisnotpermittedbystatutoryregulationorexceedsthe permitteduse,youwillneedtoobtainpermissiondirectlyfromthecopyrightholder. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG. Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface FlowingMatteristhetermthatprobablybestdescribesthemacroscopicbehaviour emerging from the coordinated dynamics of microscopic entities. Flowing Matter, therefore, goes well beyond the realm of classical fluid mechanics, traditionally dealingwiththedynamicsofmoleculesinliquids,toincludethedynamicsoffluids with a complex internal structure as well as the emergent dynamics of interacting activeagents. FlowingMatterresearchliesattheborderbetweenphysics,mathematics,chem- istry, engineering, biology, and earth sciences, to cite a few. Flowing Matter also involves an extensive range of different experimental, numerical, and theoretical approaches. The three main research areas in Flowing Matter are complex fluids, activematter,andcomplexflows: – Complex fluids research aims at understanding the interplay between macro- scopic rheological properties and changes in the internal fluid structure. Exam- ples of complex fluids include dense fluid-fluid or solid-fluid suspensions, nematicliquids,softglasses,andyieldstressfluids. – Activemattercoversthestudyofthebehaviourofpopulationsofactiveagents, thedevelopmentofmathematicalmodels,andthequantificationofthestatistical andfluid-dynamicpropertiesofthesesystems.Activematterisanexampleofan intrinsicallyoutofequilibriumsystem. – ComplexflowsemergeeveninsimpleNewtonianfluidssuchaswaterandspana widerangeofchaotic,i.e.,unpredictable,behaviours.Fullydevelopedturbulence isstillconsideredtobeoneoftheoutstandingproblemsinclassicalphysics. Many relevant scientific and technological problems today lie across two or even three of these major research areas. It is clear, therefore, that a multidisciplinary approach is needed in order to develop a unified picture in the field. The Flowing MatterMP1305COSTActionwasestablishedin2014,aimingatbringingtogether thescientificcommunitiesworkingontheseareasandathelpingtoadvancetowards aunifiedapproachandunderstandingofFlowingMatter. v vi Preface During the 4years of its activity, Flowing Matter managed to foster scientific exchange between researchers active in its different areas, filling what was a gap in the communication network and facilitating the exchange of methods and best practices. This book is the last activity organised by the MP1305 COST Action and represents just a small part of its heritage, beyond the many scientific meetings, discussions,andpublicationsthatwerefosteredbytheCOSTAction. This book is meant for young scientists as well as for any researcher aiming at broadening his/her view on Flowing Matter. This book reflects, in a very concise way, the original spirit of the COST Action and covers, from its main topics, differentmethodologies,experiments,theory,numericalmethods,andapplications. Nuremberg,Germany MarcelloSega Eindhoven,TheNetherlands FedericoToschi February2019 Contents 1 NumericalApproachestoComplexFluids................................ 1 MarcoE.Rosti,FrancescoPicanoandLucaBrandt 2 BasicConceptsofStokesFlows ............................................ 35 ChristopherI.TrombleyandMariaL.Ekiel-Jez˙ewska 3 MesoscopicApproachtoNematicFluids.................................. 51 ŽigaKos,JureAplinc,UrbanMur,andMihaRavnik 4 AmphiphilicJanusParticlesatInterfaces ................................ 95 AndreiHonciuc 5 UpscalingFlowandTransportProcesses ................................. 137 MatteoIcardi,GianlucaBoccardoandMarcoDentz 6 RecentDevelopmentsinParticleTrackingDiagnostics forTurbulenceResearch .................................................... 177 NathanaëlMachicoane,PeterD.Huck,AliciaClark,AlbertoAliseda, RomainVolkandMickaëlBourgoin 7 NumericalSimulationsofActiveBrownianParticles.................... 211 AgneseCallegariandGiovanniVolpe 8 ActiveFluidsWithintheUnifiedColouredNoiseApproximation...... 239 UmbertoMariniBettoloMarconi,ClaudioMaggi, andAlessandroSarracino 9 Quadrature-BasedLatticeBoltzmannModelsforRarefied GasFlow ...................................................................... 271 VictorE.AmbrusandVictorSofonea , Index............................................................................... 301 vii Chapter 1 Numerical Approaches to Complex Fluids MarcoE.Rosti,FrancescoPicano,andLucaBrandt 1.1 IntroductiontoComplexFluidsandRheology Wearesurroundedbyavarietyoffluidsinoureverydaylife.Besideswaterandair, itiscommontodealwithfluidswithpeculiarbehaviourssuchasgel,mayonnaise, ketchup and toothpaste, while water, oil and other so-called simple (Newtonian) fluids“regularly”flowwhenweapplyaforce,theresponseisdifferentforcomplex fluids. In some cases, we need to apply a stress larger than a certain threshold for the material to start flowing, for example, to extract toothpaste from the tube; the same paste would behave as a solid on the toothbrush when exposed only to the gravitationalforce.Inothercasesthehistoryofpastdeformationshasaroleinthe present behaviour. Rheology studies and classifies the response of different fluids and materialstoanapplied force,andtothisend,howthemacroscopic behaviour islinkedtothemicroscopicstructureofthefluid.Hence,whilesimplefluidsmade byidenticalmoleculesshowalinearresponsetotheappliedforces,complexfluids withamicrostructure,suchassuspensions,mayshowaverycomplexresponseto theappliedforces. Inthischapter,weintroducenumericalapproachesforcomplexfluidsfocusing onthewaytheadditionalstressduetothepresenceofamicrostructureismodelled and how rigid and deformable intrusions can be simulated. We will assume the reader has a solver for the momentum and mass conservation equations, typically using a finite-difference or finite-volume representation. An alternative approach, also very popular, are Lattice–Boltzmann methods; these will not be considered here,thusthereaderisreferredtoRefs.[1,2]. M.E.Rosti·L.Brandt((cid:2)) LinnéFLOWCentreandSeRC,KTHMechanics,Stockholm,Sweden e-mail:[email protected] F.Picano DepartmentofIndustrialEngineering,UniversityofPadova,Padua,Italy ©TheEditor(s)(ifapplicable)andTheAuthor(s)2019 1 F.Toschi,M.Sega(eds.),FlowingMatter,SoftandBiologicalMatter, https://doi.org/10.1007/978-3-030-23370-9_1 2 M.E.Rostietal. NewtonianandNon-NewtonianRheology The macroscopic rheological behaviour of a viscous fluid is well characterised in a Couette flow, i.e. the flow between two parallel walls of area A and at distance b: the upper wall moving at constant (low) velocity U and the lower at rest. To 0 keeptheupperwallmovingatconstantvelocityweneedtoapplyaforceF which is proportional to the wall area: F ∝ A. Therefore it is more general to consider the stress τ = F/A instead of the force F itself. In a Newtonian fluid the shear stressisproportionaltothevelocityoftheupperwallandtotheinverseofthewall distanceb,i.e.τ ∝U /b.ThislinearresponsedefinesNewtonianfluids,suchasair, 0 water,oilandmanyothers.Notethat,inasimpleCouetteflowtheratioU /bequals 0 thewall-normalderivative of thevelocity profileand theshear(deformation) rate: du/dy = γ˙ = U /b.Thus,foraNewtonianfluidwecanexpressthelawrelating 0 theappliedforcewiththeresponse,i.e.theshearstressτ withtheshearrateγ˙,as τ =μγ˙, (1.1) wheretheproportionalitycoefficientμiscalleddynamicviscositywithdimension PasintheSI.ManyNewtonianfluidsexist,eachwithadifferentvalueofviscosity, and therefore flowing at different velocity when subject to the same stress. The viscositycoefficientofaNewtonianfluiddoesnotdependontheshearrate,butmay varywiththetemperature.Indeed,theviscosityusuallyincreaseswithtemperature ingases,whileitdecreasesinliquids.Thisbehaviourisrelatedtotheeffectofthe temperatureonthemolecularstructureofthefluid,butthisisoutsidethescopeof presentchapterandthereaderisrefereedtospecialisedtextbooks. Fluids that exhibit a non-linear behaviour between the shear stress τ and the shearrateγ˙ arecallednon-Newtonianandfluidswhoseresponsedoesnotdepend explicitly on time but only on the present shear rate are denoted generalised Newtonian fluids. In particular, when the shear stress increases more than linearly with the shear rate, the fluid is called dilatant or shear-thickening, whereas in the case of opposite behaviour, i.e. when the shear stress increases less than linearly withtheshearrate,thefluidiscalledpseudoplasticorshear-thinning.Examplesof typicalprofilesoftheshearstressτ asafunctionoftheshearrateγ˙ forNewtonian, shear-thickeningandshear-thinningfluidsareshownintheleftpanelofFig.1.1.The ratiooftheappliedstressandtheresultingdeformationrateistheso-calledapparent effectiveviscosityμ = τ/γ˙:itincreaseswithγ˙ forshear-thickeningfluids,while e itreducesforshear-thinningones,whichmeansthatthefluidityofshear-thickening fluidsreducesincreasingtheshearrate,whiletheoppositeistrueforshear-thinning fluids. Examples of shear-thinning fluids are ketchup, mayonnaise and toothpaste, while corn-starch water mixtures and dense non-colloidal suspensions usually exhibitashear-thickeningbehaviour.Notethat,sometimes,thesamefluidscanhave plasticorelasticresponsesdependingontheflowconfiguration. Complex fluids may behave as solids, with a finite deformation, when the appliedstressisbelowacertainthresholdτ ,whileforstressesaboveit,theystart 0
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