Table Of ContentAdvances in Mathematical Fluid Mechanics
Dieter Bothe
Arnold Reusken
Editors
Transport
Processes
at Fluidic
Interfaces
Advances in Mathematical Fluid Mechanics
Serieseditors
GiovanniP.Galdi,Pittsburgh,USA
JohnG.Heywood,Vancouver,Canada
RolfRannacher,Heidelberg,Germany
AdvancesinMathematicalFluidMechanicsisa forumforthe publicationofhigh
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Dieter Bothe • Arnold Reusken
Editors
Transport Processes
at Fluidic Interfaces
Editors
DieterBothe ArnoldReusken
FachbereichMathematik InstitutfuRrGeometrieundPraktische
TechnischeUniversitaRtDarmstadt Mathematik
Darmstadt,Germany RWTHAachenUniversity
Aachen,Germany
ISSN2297-0320 ISSN2297-0339 (electronic)
AdvancesinMathematicalFluidMechanics
ISBN978-3-319-56601-6 ISBN978-3-319-56602-3 (eBook)
DOI10.1007/978-3-319-56602-3
LibraryofCongressControlNumber:2017942773
MathematicsSubjectClassification(2010):35JXX,76D05,76T99,65M08,65M60,65N08,65N30
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Preface
In multiphase processes, interfaces play a prominent role as the surface at which
the bulk phases are in contact. If the bulk phases are fluids, i.e., gas or liquid,
theseinterfacesareoftenfreetomoveanddeform;hencegeometricpropertiessuch
as the shape and curvature, but also physical quantities such as surface tension,
areoffundamentalimportance.Inmanycases,suchfluidinterfacesexhibitfurther
physicochemicalpropertiesstemmingfrompartialmassbeingaccumulatedatthe
interface, like inherent surface viscosities. Typically, such adsorbed species are
surface-activeagents,so-calledsurfactants,andtheinterplaybetweensorptionand
transport processes then leads to inhomogeneoussurface tension, causing surface
stresses.Thesefewfactsalreadyshowthattheinterfacebetweenfluidsoftencomes
as a phase in itself, and, for this reason, we call this a “fluidic interface” rather
than a fluid interface.The behaviorof a multiphase flow system is determinedby
the complexinterplaybetween the bulk phases and the interface, mediated by the
transportofmass,momentumandenergyattheinterfaceaswellasthetransferof
thesequantitiesacrossit.Thisincludesthedynamicsoftheinterfacesthemselves,
heat and mass transportbetween the fluids, adsorptioneffects at the interface and
transportofspeciesontheinterface,variableinterfaceproperties,andphasechange.
In general, these processes are strongly coupled and properties of the interface
playa dominantrole. Therefore,a rigorousunderstandingof the behaviorofsuch
complex flow problems must be based on physically sound mathematical models
accounting especially for local processes at the interface. The realization of this
requiresinterdisciplinaryresearchwithexpertisefromAppliedAnalysis,Numerical
Mathematics,InterfacePhysics,andChemistryaswellasrelevantresearchareasin
theEngineeringSciences.
Against this background, the German Research Foundation (Deutsche
Forschungsgemeinschaft, DFG) has funded a targeted research program in the
form of a national priority program (SPP) on “Transport Processes at Fluidic
Interfaces,”runningfrom2010to2016,tofurtherdevelopandexpandsuchmodels,
to analyze their mathematical properties, and to develop and advance numerical
methods for the rigorous simulation of these mathematical models. Important
goals of this SPP 1506 have been: (1) to derive and expandmathematical models
v
vi Preface
that describe relevant physico-chemicalinterface phenomena, (2) to improve and
deepen the understanding of mechanisms and phenomena occurring at fluidic
interfaces by means of rigorous mathematical analysis of the underlying systems
ofpartialdifferentialequations,(3)to developandanalyzenumericalmethodsfor
thesimulationofmultiphaseflowproblemswhichresolvethelocalprocessesatthe
interface, and (4) to validate these models and the numerical simulation methods
by means of specifically designed experiments. This book is the closing report
of this priority program SPP 1506 “Transport Processes at Fluidic Interfaces.” It
summarizes the major findings obtained in 22 research projects with 32 principal
investigators from 20 German universities and research centers, covering a
wide range of research topics from mathematical analysis of relevant classes of
partial differential equations, to development, analysis, and application of tailor-
made numerical methods, to specifically designed high-resolution measurement
techniques,to detailedstudiesof particularinterfacialprocesses.Thesetopicsand
the researchers that participated in the priority programare from several different
disciplines, fostering the strongly interdisciplinary nature of the work done in the
SPP1506.
The authors and the editors of this book would like to thank the Deutsche
ForschungsgemeinschaftforfundingtheSPP1506“TransportProcessesatFluidic
Interfaces.”OurspecialthanksgotoDr.FrankKiefer(DFG)forhiscontinuedsup-
port.Wearealsoverygratefultotheinternationalreferees,whoevaluatednewand
renewalproposalsduringthedurationofthepriorityprogram.WethankProf.Akio
Tomiyama(KobeUniversity)foractingasaresearchfellowwithinthisprogram,by
supportingtheguidingmeasureonTaylorbubblesandTaylorflowwithinnumerous
discussionsandbyprovidingvaluabledata.Finally,wethanktheeditorsofthisbook
series,especiallyPaoloGaldi(UniversityofPittsburgh)forthepossibilitytoinclude
this closing report in the series on “Advances in Mathematical Fluid Mechanics,”
andSpringerVerlag,Heidelberg,fortheconstructiveandpleasantcollaborationin
preparingthisvolume.
Darmstadt,Germany DieterBothe
Aachen,Germany ArnoldReusken
February2017
Contents
PartI NumericalMethodsforSharpInterfaceModels
1 ALE-FEM for Two-Phase and Free Surface Flows
withSurfactants ............................................................ 5
Sashikumaar Ganesan, Andreas Hahn, Kristin Simon,
andLutzTobiska
2 HighOrderUnfittedFiniteElementMethodsforInterface
ProblemsandPDEsonSurfaces.......................................... 33
ChristophLehrenfeldandArnoldReusken
3 An Extended Discontinuous Galerkin Framework
forMultiphaseFlows....................................................... 65
ThomasUtz,ChristinaKallendorf,FlorianKummer,BjörnMüller,
andMartinOberlack
4 BuildingBlocksforaStrictlyConservativeGeneralizedFinite
VolumeProjectionMethodforZeroMachNumberTwo-Phase
Flows......................................................................... 93
MatthiasWaidmann,StephanGerber,MichaelOevermann,and
RupertKlein
5 TimeDiscretizationforCapillaryFlow:BeyondBackwardEuler.... 121
StephanWellerandEberhardBänsch
6 UpwindSchemesforScalarAdvection-DominatedProblems
intheDiscreteExteriorCalculus ......................................... 145
MichaelGriebel,ChristianRieger,andAlexanderSchier
7 DiscreteExteriorCalculus(DEC)fortheSurfaceNavier-Stokes
Equation..................................................................... 177
IngoNitschke,SebastianReuther,andAxelVoigt
vii
viii Contents
PartII AnalysisandSimulationofDiffusiveInterfaceModels
8 DiffuseInterfaceModelsforIncompressibleTwo-PhaseFlows
withDifferentDensities.................................................... 203
HelmutAbels,HaraldGarcke,GüntherGrün,andStefanMetzger
9 Sharp Interface Limits for Diffuse Interface Models
forTwo-PhaseFlowsofViscousIncompressibleFluids................ 231
HelmutAbels,YuNingLiu,andAndreasSchöttl
10 Two-PhaseFlowwithSurfactants:DiffuseInterfaceModels
andTheirAnalysis ......................................................... 255
HelmutAbels,HaraldGarcke,KeiFongLam,andJosefWeber
11 Phase FieldModelsforTwo-PhaseFlow withSurfactants
andBiomembranes......................................................... 271
SebastianAland
12 Micro-Macro-ModelsforTwo-PhaseFlowofDilutePolymeric
Solutions:MacroscopicLimit,Analysis,andNumerics................ 291
GüntherGrünandStefanMetzger
13 Fully Adaptive and Integrated Numerical Methods
fortheSimulationandControlofVariableDensityMultiphase
FlowsGovernedbyDiffuseInterfaceModels ........................... 305
Michael Hintermüller, Michael Hinze, Christian Kahle,
andTobiasKeil
14 Dynamical Stability of Diffuse Phase Boundaries
inCompressibleFluids..................................................... 355
HeinrichFreistühlerandMatthiasKotschote
PartIII ExperimentalandNumericalInvestigationofInterfacial
Phenomena
15 ExperimentalandComputationalAnalysisofFluidInterfaces
InfluencedbySolubleSurfactant......................................... 395
Chiara Pesci, Holger Marschall, Talmira Kairaliyeva,
VamseekrishnaUlaganathan,ReinhardMiller,andDieterBothe
16 Complex Patternsand Elementary Structures of Solutal
MarangoniConvection:ExperimentalandNumericalStudies ....... 445
Kerstin Eckert, Thomas Köllner, Karin Schwarzenberger,
andThomasBoeck
17 TransportatInterfacesinLipidMembranesandEnantiomer
Separation................................................................... 489
Oleg Boyarkin, Stefan Burger, Thomas Franke, Thomas
Fraunholz,RonaldH.W.Hoppe,SimonKirschler,KevinLindner,
MalteA.Peter,FlorianStrobl,andAchimWixforth
Contents ix
18 StructureFormationinThinLiquid-LiquidFilms..................... 531
SebastianJachalski,DirkPeschka,StefanBommer,RalfSeemann,
andBarbaraWagner
PartIV TaylorBubbles:Experiments,SimulationandValidation
19 Taylor Bubbles in Small Channels: A Proper Guiding
Measure for Validation of Numerical Methods
forInterfaceResolvingSimulations...................................... 577
MartinWörner
20 X-Ray Microtomographyof Taylor Bubbles with Mass
TransferandSurfactantsinCapillaryTwo-PhaseFlow............... 589
StephanBoden,MohammadrezaHaghnegahdar,andUweHampel
21 ExperimentalInvestigationand Modelling of LocalMass
TransferRatesinPureandContaminatedTaylorFlows .............. 609
Sven Kastens, Christoph Meyer, Marko Hoffmann,
andMichaelSchlüter
22 ComparativeSimulationsofTaylorFlowwithSurfactants
BasedonSharp-andDiffuse-InterfaceMethods ....................... 639
Sebastian Aland, Andreas Hahn, Christian Kahle,
andRobertNürnberg
23 DirectNumericalSimulationsofTaylorBubblesinaSquare
Mini-Channel: Detailed Shape and Flow Analysis
withExperimentalValidation............................................. 663
Holger Marschall, Carlos Falconi, Christoph Lehrenfeld,
RufatAbiev,MartinWörner,ArnoldReusken,andDieterBothe
