Transport Processes at Fluidic Interfaces PDF
Preview Transport Processes at Fluidic Interfaces
Advances 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 quality monographs, or collections of works, on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. Its mathematical aimsandscopearesimilartothoseoftheJournalofMathematicalFluidMechanics. Inparticular,mathematicalaspectsofcomputationalmethodsandofapplicationsto scienceandengineeringarewelcomeasanimportantpartofthetheory.Soalsoare worksinrelatedareasofmathematicsthathaveadirectbearingonfluidmechanics. Themonographsandcollectionsofworkspublishedheremaybewritteninamore expositorystylethanisusualforresearchjournals,withtheintentionofreachinga wideaudience.Collectionsofreviewarticleswillalsobesoughtfromtimetotime. Moreinformationaboutthisseriesathttp://www.springer.com/series/5032 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 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisbookispublishedunderthetradenameBirkhäuser,www.birkhauser-science.com TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland 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
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