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We investigate theoretically on the basis of the steady Stokes equations fora viscous incompressible fluid the flow induced by a Stokeslet located on thecentre axis of two coaxially positioned rigid disks. The Stokeslet is directedalong the centre axis. No-slip boundary conditions are assumed to hold at thesurfaces of the disks. We perform the calculation of the associated Green'sfunction in large parts analytically, reducing the spatial evaluation of theflow field to one-dimensional integrations amenable to numerical treatment. Tothis end, we formulate the solution of the hydrodynamic problem for the viscousflow surrounding the two disks as a mixed-boundary-value problem, which we thenreduce into a system of four dual integral equations. We show the existence ofviscous toroidal eddies arising in the fluid domain bounded by the two disks,manifested in the plane containing the centre axis through adjacentcounterrotating eddies. Additionally, we probe the effect of the confiningdisks on the slow dynamics of a point-like particle by evaluating thehydrodynamic mobility function associated with axial motion. Thereupon, weassess the appropriateness of the commonly-employed superposition approximationand discuss its validity and applicability as a function of the geometricalproperties of the system. Additionally, we complement our semi-analyticalapproach by finite-element computer simulations, which reveals a goodagreement. Our results may find applications in guiding the design ofmicroparticle-based sensing devices and electrokinetic transport in small scalecapacitors.

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