  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.
