Homogenization of evolutionary Stokes-Cahn-Hilliard equations for two-phase porous media flow

We consider homogenization of a phase-field model for two-phase immiscible, incompressible porous media flow with surface tension effects. The pore-scale model consists of a strongly coupled system of time-dependent Stokes-Cahn-Hilliard equations. In the considered model the fluids are separated by an evolving diffuse interface of a finite width, which is assumed to be independent of the scale parameter ε. We obtain upscaled equations for the considered model by a rigorous two-scale convergence approach.