Mathematical modeling of micropolar fluid flows through a thin porous medium

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