Fluid-Structure Interactions in Low-Reynolds-Number Flows PDF
Preview Fluid-Structure Interactions in Low-Reynolds-Number Flows
Fluid–StructureInteractionsinLow-Reynolds-NumberFlows RSCSoftMatterSeries SeriesEditors: ProfessorDrHans-Ju¨rgenButt,MaxPlanckInstituteforPolymerResearch, Germany ProfessorIanW.Hamley,UniversityofReading,UK ProfessorHowardA.Stone,PrincetonUniversity,USA ProfessorChiWu,TheChineseUniversityofHongKong,China TitlesinthisSeries: 1:FunctionalMolecularGels 2:HydrogelsinCell-BasedTherapies 3:Particle-StabilizedEmulsionsandColloids:FormationandApplications 4:Fluid–StructureInteractionsinLow-Reynolds-NumberFlows Howtoobtainfuturetitlesonpublication: Astandingorderplanisavailableforthisseries.Astandingorderwillbring deliveryofeachnewvolumeimmediatelyonpublication. Forfurtherinformationpleasecontact: BookSalesDepartment,RoyalSocietyofChemistry,ThomasGrahamHouse, SciencePark,MiltonRoad,Cambridge,CB40WF,UK Telephone:(cid:67)44(0)1223420066,Fax:(cid:67)44(0)1223420247 Email:[email protected] Visitourwebsiteatwww.rsc.org/books Fluid–Structure Interactions in Low-Reynolds-Number Flows Editedby CamilleDuprat E´colepolytechnique,Palaiseau,France Email:[email protected] and HowardA.Stone PrincetonUniversity,Princeton,NewJersey,USA Email:[email protected] RSCSoftMatterNo.4 PrintISBN:978-1-84973-813-2 PDFeISBN:978-1-78262-849-1 ISSN:2048-7681 AcataloguerecordforthisbookisavailablefromtheBritishLibrary (cid:13)C TheRoyalSocietyofChemistry2016 Allrightsreserved Apartfromfairdealingforthepurposesofresearchfornon-commercialpurposesorfor privatestudy,criticismorreview,aspermittedundertheCopyright,DesignsandPatents Act1988andtheCopyrightandRelatedRightsRegulations2003,thispublicationmay notbereproduced,storedortransmitted,inanyformorbyanymeans,withouttheprior permissioninwritingofTheRoyalSocietyofChemistryorthecopyrightowner,orinthe caseofreproductioninaccordancewiththetermsoflicencesissuedbytheCopyright LicensingAgencyintheUK,orinaccordancewiththetermsofthelicencesissuedbythe appropriateReproductionRightsOrganizationoutsidetheUK.Enquiriesconcerning reproductionoutsidethetermsstatedhereshouldbesenttoTheRoyalSocietyof Chemistryattheaddressprintedonthispage. TheRSCisnotresponsibleforindividualopinionsexpressedinthiswork. The authors have sought to locate owners of all reproduced material not in their ownpossessionandtrustthatnocopyrightshavebeeninadvertentlyinfringed. PublishedbyTheRoyalSocietyofChemistry, ThomasGrahamHouse,SciencePark,MiltonRoad, CambridgeCB40WF,UK RegisteredCharityNumber207890 Forfurtherinformationseeourwebsiteatwww.rsc.org PrintedintheUnitedKingdombyCPIGroup(UK)Ltd,Croydon,CR04YY,UK Preface CAMILLEDUPRATa ANDHOWARDA.STONEb aE´colepolytechnique,91128PalaiseauCedex,France;bDepartment ofMechanicalandAerospaceEngineering,PrincetonUniversity, Princeton,NJ08544,USA The topics in this book fall into the domain of fluid-structure interactions where the fluid flow is characterized by motions at low Reynolds num- bers.Ingeneral,theterm“fluid-structureinteraction”referstotheclassof mechanics problems where a flow field affects the position, orientation, and/orshapeofanobject,and,correspondingly,thestructuremodifiesthe flow field. Therefore, the rigid-body dynamics and/or elasticity problems associatedwithanobjectorwithsoftboundaries,andthedynamicsproblem ofthemotionofthefluidarecoupled.Notsurprisingly,thesekindsofprob- lemsintroducemanyvariablesandlinktwosetsofdynamicsquestionsthat, individually,aretypicallyrathercomplicated.Onefeaturethatwewillseein everychapterofthisbookisthatsimplifiedmodels,oftenonedimensional, and the use of dimensional analysis can go very far in providing physical insightandquantitativeestimatesformanyproblems. Thesubjectoffluid-structureinteractionsoccursinmanyguises,suchas thesloshingofliquidinatankrestingonanelasticfoundation,aerodynamic flutter of wings, hydroplaning of tires, acoustical effects triggered by flow- induced vibrations (think of a telephone line “singing” in the wind), and manybiomechanicsproblemsinvolvingflowinandaroundsoftboundaries (e.g.elasticvalvesandwavepatternsinfieldsofwheat).Thegeneraltopichas been the subject of books,1,2 and even specific topics such as aeroelasticity RSCSoftMatterNo.4 Fluid–StructureInteractionsinLow-Reynolds-NumberFlows EditedbyCamilleDupratandHowardA.Stone (cid:13)C TheRoyalSocietyofChemistry2016 PublishedbytheRoyalSocietyofChemistry,www.rsc.org v vi Preface havetheirownextensivebooks.3,4 Thegreatmajorityofthesepresentations focus on high-Reynolds-number motion and highlight the various models andapproximationssuitableforinertia-dominatedfluidflow. Althoughthesetopicshavebeenstudiedformanyyears,twoareaswhich havereceivedmuchlessattentionconcernfluid–structureinteractionprob- lems where fluid-fluid interfaces are important (e.g. surface tension is capableofdeformingsoftsurfaces),andflowsituationswheretheReynolds number is less than unity, so that viscous effects are expected to dominate thefluidstresses.Thesetwotopicsformthemainthemesofthisbook.We hopetohighlightthemanydifferentkindsofproblemsthatfallunderthis umbrellaoffluid-structureinteractionsatlowReynoldsnumbers,including materialssciencequestions(e.g.theshapeoffibersdeformedbythesurface tensionexertedbyaliquiddrop,andthewrappingofliquidsheetsaround liquiddroplets),rheologyquestionsinspiredbytheslowflowofasuspension offlexiblefibers,andbiophysicsquestionssuchasthemotionofflagellaand thecorrespondingswimmingofmicroorganisms.Indeed,basicquestionsin embryology involve fluid that is stirred by the movement of flexible biofil- aments. Moreover, cells are soft and so, not surprisingly, the motion and deformationofcellsandvesiclesareimportantquestionsinphysiologythat involvetheinterplayofelasticityandfluiddynamics.Wehavebeenfortunate to get outstanding contributions from colleagues with expertise spanning thesedifferentsubjects. The chapters of the book have been written with a student or interested professional in mind, and we are hopeful that some if not all of the chap- terswillproveusefulasasourceofexamplesforuseincoursesorevenfor sectionsofacourse.Inparticular,webeginwithtwointroductorychapters highlightingimportantideasfromthetheoryofelasticityandlow-Reynolds- numberhydrodynamics.Thefirstofthese,Chapter1,waswrittenbyBasile Audoly,whointroducestheelasticamodelofafilament,whichplaysanim- portantroleinmanyofthelaterchapters.WehavewritteninChapter2about low-Reynolds-numberflows,highlightingseveralthemessuchaselementary channel flows, mathematical properties, particle motion, and slender-body theory,whichareallthemesthatrecurinlaterchapters. One of the great models of elasticity is the elastica, as mentioned above. The coupling of the elastica to a simplified form of viscous fluid motion, called resistive force theory or slender-body theory, forms the basisofChapter3,whichconsistsofasetofmodelproblems.Hereweguide the reader through various steps, including scaling of equations, identify- ingcharacteristicquantitiesofbeamdeformation,andsimilaritysolutions. Wehopethatthischapterwillprovideareadysourceofclassroomexamples orhomeworkproblemsthatcombinetheideaofbuildingphysicalintuition with the important steps of solving some fun but nontrivial fluid-structure interactionproblems.Thiscouplingoffluiddynamicswiththeelasticapro- videsanintroductiontothenexttwochapters.First,inChapter4,OnShun Pak and Eric Lauga provide an introduction to swimming microorganisms in a comprehensive survey that includes many important theoretical ideas Preface vii fromlow-Reynolds-numberhydrodynamics.Then,inChapter5,AnkeLind- ner and Mike Shelley describe fluid flows in the presence of flexible fibers fromtheperspectiveofmaterialsscienceandrheology,includingtheresults oftheoryandexperimentsonmodelflows. A widely applicable topic that combines elasticity and fluid mechanics is elastocapillarity, which brings in the topic of surface tension and is de- scribed in Chapter 6. We wrote this chapter with the idea of including a largeassortmentofgeometriesandconfigurations,sincethebreadthofthe rangeofapplicationsisinspiring.Also,inChapter7,LudovicPauchardand Fr´ed´eriqueGiorgiuttiprovideafascinatingdescriptionofthedryingof(soft) suspensions and polymer solutions. Again, the important ideas of elastic- ity and capillarity occur throughout, and the authors even link these ideas to paintings, including the Mona Lisa! Although some of the problems in thesetwochaptersinvolvestaticsonly,othersincludethedynamicsofavis- cous fluid flow. We think the reader will be amazed by the wide range of elastocapillaryproblemsandhowfarelementaryphysicalbalancescangoin illuminatinginterestingphysicalproblems. Biophysical ideas provide the motivation for three other chapters in the book, which deal with topics including internal flows, where the motions are typically within soft boundaries, and external flows, where the motions arearoundsoftobjects,suchasvesiclesandcells.Theformertopicofflows inflexiblechannelsispresentedinChapter8byMatthiasHeilandAndrew Hazel, who make stimulating connections to applications of elasticity and fluid dynamics in physiology. In Chapter 9, Petia Vlahovska describes the theoryandmathematicalmodelingofthelow-Reynolds-numbermotionand deformation of vesicles and polymer capsules in simple model flows and in applied electric fields. Vesicles are liquid drops bound by a lipid mem- brane and so have similarities to biological cells. Finally, in Chapter 10, Manouk Abkarian and Annie Viallat discuss the motion and deformation ofredbloodcellsinlow-Reynolds-numberflows.Theycharacterizetheme- chanicalpropertiesofthecells,highlightingmechanicalfeaturesatdifferent lengthscales,andsummarizeexperimentalandtheoreticalunderstanding. TherearemanysynergiesbetweenthethemesdiscussedinChapters8–10. Inordertotrytohelpthereader,wehaveencouragedalloftheauthorsto adoptaconsistentschemeofnotation,andthedefinitionsaresummarized in the following pages. Given the wide range of physical problems that ap- pearandthelargenumberofphysicalvariables,however,thereareinevitable conflictsinthechoiceofnotationinsomeofthechapters,andinthosecases wehavetriedtoindicatetherelevantdefinitionsclearlyineachchapter. We hope that you enjoy this tour of fluid-structure interactions in low- Reynolds-numberflows. We thank our many colleagues, at our home institutions and elsewhere, fortheircollaborationandintellectualsupport.Weappreciatetheuniversal- ityoftheideasthatwehavebeenabletopursue. CamilleDupratandHowardA.Stone viii Preface References 1. M.Pa¨ıdoussis,S.PriceandE.deLangre,Fluid-StructureInteractions:Cross- flow-inducedInstabilities,CambridgeUniversityPress,NewYork,2011. 2. M. Pa¨ıdoussis, Fluid-Structure Interactions: Slender Structures and Axial Flow,AcademicPress,SanDiego,2ndedn,2014. 3. R.Bisplinghoff,H.AshleyandH.Halfman,Aeroelasticity,Dover,1996. 4. AModernCourseinAeroelasticity,ed.E.Dowell,KluwerAcademicPublish- ers,4thedn,2004. Nomenclature Quantities B Bendingmodulus(beam) C Capillarynumber a D Deborahnumber E Youngmodulus E Freeenergy (cid:51)(cid:51)(cid:51) Straintensor f Forceperunitlength F Force G Shearmodulus (cid:103) Surfacetension (cid:103)˙ Shearrate K Bulkmodulus (cid:107) Meancurvature (cid:96) (cid:90)((cid:103)/(cid:114)g)1/2 Capillarylength c (cid:109) Dynamicviscosity n Unitnormalvector (cid:110)(cid:90)(cid:109)/(cid:114) Kinematicviscosity (cid:110) Poisson’sratio p (cid:117)(cid:117)(cid:117) Vorticity p Pressure rorx(cid:90)(x,y,z) Positionvector (cid:114) Density Re Reynoldsnumber (cid:115)(cid:115)(cid:115) Stresstensor RSCSoftMatterNo.4 Fluid–StructureInteractionsinLow-Reynolds-NumberFlows EditedbyCamilleDupratandHowardA.Stone (cid:13)C TheRoyalSocietyofChemistry2016 PublishedbytheRoyalSocietyofChemistry,www.rsc.org ix x Nomenclature t Time T Temperature t Unittangentvector Acronyms 2D two-dimensional 3D three-dimensional BC boundarycondition(s) Operators ∧ crossproduct (cid:86) gradient (cid:86)·f divergenceofavectorfieldf (cid:86)∧f curlofavectorfieldf (cid:86)2 Laplacian
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