Flow at the interface of a model fibrous porous medium

Planar flow in the interfacial region of an open porous medium is investiga ted 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 squ are array oriented across the flow and are widely spaced, so that the solid volume fraction phi is 0.1 or less. For this spacing, singularity methods are appropriate and so they are used to find solutions for both planar Coue tte flow and Poiseuille flow in the open portion of the channel. The soluti ons, accurate to O(phi), are used to calculate the apparent slip velocity a t the interface, U-s, and results obtained for U-s are presented in terms o f a dimensionless slip velocity. For shear-driven flow, this dimensionless quantity is found to depend only weakly on phi 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-dr iven flow, U-s is found to be less than that under comparable shear-flow co nditions, and dependent on cylinder size and filling fraction in this case. Calculations also show that the external how penetrates the porous medium very little, even for sparse arrays, and that U-s is about one quarter of t he velocity predicted by the Brinkman model.