Planar flow in the interfacial region of an open porous medium is investigated by
finding solutions for Stokes flow in a channel partially filled with an array of circular
cylinders beside one wall. The cylinders are in a square array oriented across the flow
and are widely spaced, so that the solid volume fraction ϕ is 0.1 or less. For this
spacing, singularity methods are appropriate and so they are used to find solutions
for both planar Couette flow and Poiseuille flow in the open portion of the channel.
The solutions, accurate to O(ϕ), are used to calculate the apparent slip velocity at the
interface, Us, and results obtained for Us are presented in terms of a dimensionless
slip velocity. For shear-driven flow, this dimensionless quantity is found to depend
only weakly on ϕ and to be independent of the height of the array relative to the
height of the channel and independent of the cylinder size relative to the height of the
channel. For pressure-driven flow, Us is found to be less than that under comparable
shear-flow conditions, and dependent on cylinder size and filling fraction in this case.
Calculations also show that the external flow penetrates the porous medium very little,
even for sparse arrays, and that Us is about one quarter of the velocity predicted by
the Brinkman model.