Mathematical modeling of micropolar fluid flows through a thin porous medium

We study the flow of a micropolar fluid in thin domain with microstructure, i.e., thickness $$\varepsilon $$ which is perforated by periodically distributed solid cylinders size $$a_\varepsilon . A main feature this dependence characteristic length on small parameters describing geometry porous medium under consideration. Depending ratio respect to , we derive three different generalized Darcy equations where interaction between velocity and microrotation fields preserved.