Abstract
An exact solution, using pairs of dual integral equations that arise from mixed boundary conditions, is presented for the interaction, due to a circular hole in the bounding wall, of a shear flow with otherwise stationary fluid. Together with a suction-driven flow through the hole, this flow has been used by Yan, Acrivos, and Weinbaum [J. Fluid. Mech. (in press)] to asymptotically model fluid skimming and particle entrainment into a small circular side pore. The Cartesian velocity components and dynamic pressure can be quite simply expressed in terms of toroidal coordinates.
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