  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.
