Theoretical derivation of Darcy's law for fluid flow in thin porous media

Abstract In this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is a bounded perforated 3 D domain confined between two parallel plates. The description of the domain includes two small parameters: ε representing the distance between plates and connected to the microstructure of the domain such that . We consider the classical setting of perforated media, i.e. ‐periodically distributed solid (not connected) obstacles of size . The goal of this paper is to introduce a version of the unfolding method, depending on both parameters ε and , and then to derive the corresponding 2 D Darcy law.