In this talk, I will present a homogenization result concerning the flow of a viscous fluid through a permeable membrane containing perforations with random sizes and shapes distributed along it. Leak boundary conditions of threshold type are considered on the membrane, the normal velocity of the fluid is zero until the jump of the normal component of the stress acting on the membrane reaches a certain limit, and the fluid may pass freely through the holes.
 
The description of the perforations is given in terms of a random set-valued variable defined on a probability space and a dynamical system acting on it. Effective boundary conditions for the fluid are derived. Depending on the relative size of the holes, there are two cases. In the first case we obtain a homogenized equation of the same type and in the second case a slip boundary condition of Navier type is obtained. If the dynamical system is assumed to be ergodic, the limiting behaviour of the fluid is deterministic.
 
The method of proof is based on the Mosco convergence, which allows us to pass from the stationary case to the time dependent case through the convergence of associated semigroups.