Math @ Duke

Publications [#316991] of Gregory J. Herschlag
Papers Published
 Herschlag, G; Liu, JG; Layton, AT, An exact solution for stokes flow in a channel with arbitrarily large wall permeability,
Siam Journal on Applied Mathematics, vol. 75 no. 5
(January, 2015),
pp. 22462267, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361399 [3672], [doi]
(last updated on 2019/02/23)
Abstract: © 2015 Society for Industrial and Applied Mathematics. We derive an exact solution for Stokes flow in a channel with permeable walls. At the channel walls, the normal component of the fluid velocity is described by Darcy's law, and the tangential component of the fluid velocity is described by the no slip condition. The pressure exterior to the channel is assumed to be constant. Although this problem has been well studied, typical studies assume that the permeability of the wall is small relative to other nondimensional parameters; this work relaxes this assumption and explores a regime in parameter space that has not yet been well studied. A consequence of this relaxation is that transverse velocity is no longer necessarily small when compared with the axial velocity. We use our result to explore how existing asymptotic theories break down in the limit of large permeability for channels of small length.
Keywords: filtration • permeable boundaries • Stokes flow


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