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

Gregory J. Herschlag Duke University Jian-Guo Liu Duke University Anita T. Layton Duke University

Analysis of PDEs mathscidoc:1702.03029

Siam Journal on Applied Mathematics, 75, (5), 2015.12
We derive an exact solution for Stokes flow in an in a channel with permeable walls. We assume that 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 non-dimensional 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.
filtration, permeable boundaries, Stokes flow
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@inproceedings{gregory2015an,
  title={An exact solution for Stokes flow in a channel with arbitrarily large wall permeability},
  author={Gregory J. Herschlag, Jian-Guo Liu, and Anita T. Layton},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207232544020717274},
  booktitle={Siam Journal on Applied Mathematics},
  volume={75},
  number={5},
  year={2015},
}
Gregory J. Herschlag, Jian-Guo Liu, and Anita T. Layton. An exact solution for Stokes flow in a channel with arbitrarily large wall permeability. 2015. Vol. 75. In Siam Journal on Applied Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207232544020717274.
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