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The Quarterly Journal of Mechanics and Applied Mathematics 1991 44(3):471-486; doi:10.1093/qjmam/44.3.471
© 1991 by Oxford University Press
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A TRANSLATING DISK IN A SAMPSON FLOW; PRESSURE-DRIVEN FLOW THROUGH CONCENTRIC HOLES IN PARALLEL WALLS

A. M. J. DAVIS

( Mathematics Department, University of Alabama Tuscaloosa, Alabama 35487-0350, USA )

The concise analytical method developed for disks sedimenting in the presence of fixed boundaries is extended to several flows that may be regarded as perturbations of the well-known pressure-driven (Sampson) flow through a hole in a wall. The speed of translation of the disk may be chosen to achieve zero drag or zero flux through the wall. The presence of a second wall with a concentric hole allows comparison with the corresponding orifice flow and verification of the expected lubricating effect of the fluid between the walls. This comparison is extended to the Poiseuille flow by regarding the latter as the limit of pressure-driven flow through a periodic array of walls.


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