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

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