Homogenization of a micropolar fluid past a porous media with nonzero spin boundary condition

We consider a micropolar fluid flow in a media perforated by periodically distributed obstacles of size epsilon. A nonhomogeneous boundary condition for microrotation is considered: The microrotation is assumed to be proportional to the rotation rate of the velocity on the boundary of the obstacles. The existence and uniqueness of solution are analyzed. Moreover, passing to the limit when epsilon tends to zero, an analog of the classical micropolar Darcy's law in the theory of porous media is derived.

Automated summary

This study examines the flow of a micropolar fluid in a medium perforated by periodically distributed obstacles of size epsilon. A nonhomogeneous boundary condition for microrotation is considered, with microrotation assumed to be proportional to the rotation rate of the velocity on the boundary of the obstacles. The existence and uniqueness of solution are analyzed, and an analog of the classical micropolar Darcy's law in the theory of porous media is derived in the limit as epsilon tends to zero.