Homogenization of a fluid problem with a free boundary

We study the interface between water and air in a porous medium. In order to simplify the geometry we assume the medium to consist of a periodic array of cylinders of size and distance $O(\text{eps})$. In between the cylinders there is fluid (lower part) or air (upper part). We apply the method of two-scale convergence to find limiting equations. Inside the (unknown) fluid-domain this is the Darcy-law. Along the interface we can derive a nonlinear pressure-condition that determines the position of the free boundary. We have to deal with the fact that the contact-angle equation introduces a capillary pressure of the order $1/\text{eps}$.