The aim of this talk is to present the derivation of the new effective boundary condition for the fluid flow in a domain with porous boundary. Starting from the Stokes system in a domain with an array of small holes on the boundary and using the homogenization and the boundary layers, we find an effective law in the form of the generalized Darcy law. If the pores geometry is isotropic, then the condition splits in Beavers-Joseph type condition for the tangential flow and the standard Darcy condition for the normal flow. We will also study the roughness-induced effects on the proposed Darcy-type boundary condition.

This is a joint work with Eduard Marusic-Paloka (University of Zagreb).