An exact solution for stokes flow in a channel with arbitrarily large wall permeability


Journal Article

© 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.

Full Text

Duke Authors

Cited Authors

  • Herschlag, G; Liu, JG; Layton, AT

Published Date

  • January 1, 2015

Published In

Volume / Issue

  • 75 / 5

Start / End Page

  • 2246 - 2267

International Standard Serial Number (ISSN)

  • 0036-1399

Digital Object Identifier (DOI)

  • 10.1137/140995854

Citation Source

  • Scopus