Table Of ContentSoft 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
