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Axisymmetric Stokes flow due to a point-force singularity acting between two coaxially positioned rigid no-slip disks

hal.structure.identifierInstitut fur Theoretische Physik
dc.contributor.authorDADDI-MOUSSA-IDER, Abdallah
hal.structure.identifierInstitut fur Theoretische Physik
dc.contributor.authorSPRENGER, Alexander
hal.structure.identifierLaboratoire Ondes et Matière d'Aquitaine [LOMA]
dc.contributor.authorAMAROUCHENE, Yacine
hal.structure.identifierLaboratoire Ondes et Matière d'Aquitaine [LOMA]
dc.contributor.authorSALEZ, Thomas
hal.structure.identifierTechnische Universität Kaiserslautern [TU Kaiserslautern]
dc.contributor.authorSCHÖNECKER, Clarissa
hal.structure.identifierInstitut für Analysis und Numerik
dc.contributor.authorRICHTER, Thomas
hal.structure.identifierInstitut fur Theoretische Physik
dc.contributor.authorLÖWEN, Hartmut
hal.structure.identifierInstitut fur Theoretische Physik
dc.contributor.authorMENZEL, Andreas
dc.date.issued2020
dc.identifier.issn0022-1120
dc.description.abstractEnWe investigate theoretically on the basis of the steady Stokes equations for a viscous incompressible fluid the flow induced by a Stokeslet located on the centre axis of two coaxially positioned rigid disks. The Stokeslet is directed along the centre axis. No-slip boundary conditions are assumed to hold at the surfaces of the disks. We perform the calculation of the associated Green's function in large parts analytically, reducing the spatial evaluation of the flow field to one-dimensional integrations amenable to numerical treatment. To this end, we formulate the solution of the hydrodynamic problem for the viscous flow surrounding the two disks as a mixed-boundary-value problem, which we then reduce into a system of four dual integral equations. We show the existence of viscous toroidal eddies arising in the fluid domain bounded by the two disks, manifested in the plane containing the centre axis through adjacent counterrotating eddies. Additionally, we probe the effect of the confining disks on the slow dynamics of a point-like particle by evaluating the hydrodynamic mobility function associated with axial motion. Thereupon, we assess the appropriateness of the commonly-employed superposition approximation and discuss its validity and applicability as a function of the geometrical properties of the system. Additionally, we complement our semi-analytical approach by finite-element computer simulations, which reveals a good agreement. Our results may find applications in guiding the design of microparticle-based sensing devices and electrokinetic transport in small scale capacitors.
dc.language.isoen
dc.publisherCambridge University Press (CUP)
dc.subject.enStokes flow
dc.subject.ensingularity methods
dc.subject.enlow-Reynolds-number hydrodynamics
dc.title.enAxisymmetric Stokes flow due to a point-force singularity acting between two coaxially positioned rigid no-slip disks
dc.typeArticle de revue
dc.subject.halPhysique [physics]/Matière Condensée [cond-mat]/Matière Molle [cond-mat.soft]
dc.subject.halPhysique [physics]/Physique [physics]/Dynamique des Fluides [physics.flu-dyn]
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
dc.identifier.arxiv2006.05715
bordeaux.journalJournal of Fluid Mechanics
bordeaux.pageA34
bordeaux.volume904
bordeaux.peerReviewedoui
hal.identifierhal-02860235
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02860235v1
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