Derivation of a quasi-stationary coupled Darcy-Reynolds equation for incompressible viscous fluid flow through a thin porous medium with a fissure

We consider a non-stationary Stokes system in a thin porous medium of thickness epsilon that is perforated by periodically distributed solid cylinders of size epsilon, and containing a fissure of width eta(epsilon). Passing to the limit when epsilon goes to zero, we find a critical size eta(epsilon) approximate to epsilon(2/3) in which the flow is described by a 2D quasi-stationary Darcy law coupled with a 1D quasi-stationary Reynolds problem. Copyright (c) 2017 John Wiley & Sons, Ltd.