Boundary conditions for stokes flows near a porous membrane |
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Authors: | Kek-Kiong Tio and Satwindar Singh Sadhal |
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Institution: | (1) Department of Applied Mechanics and Engineering Sciences, University of California, 92093-0411 San Diego, La Jolla, CA, USA;(2) Department of Mechanical Engineering, University of Southern California, 90089-1453 Los Angeles, CA, USA |
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Abstract: | A theoretical development is carried out to model the boundary conditions for Stokes flows near a porous membrane, which, in general, allows non-zero slip as well as normal flow at the surface. Two types of models are treated: an infinitesimally thin plate with a periodic array of circular apertures and a series of parallel slits. For Stokes flows, the mean normal flux and slip velocity are proportional to the pressure difference across the membrane and the average shear stress at the membrane, respectively. The appropriate proportionality constants which depend on the membrane geometry are calculated as functions of the porosity. An interesting feature of the results is that the slip at the membrane has, in general, a direction different from that of the applied shear for these models. |
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Keywords: | Stokes flow porous membrane |
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