A mixing procedure of two viscous fluids using some homogenization tools

A mathematical mixing procedure of two homogeneous viscous fluids is proposed. These fluids are separated by a rapidly oscillating interface of period ϵ and constant amplitude. The mixture is obtained in a region around the interface as ϵ tends to zero. The so-called homogenization equation, which governs the mixture behavior, is presented. Using standard homogenization tools and a compactness result, the convergence of the fluid velocity to the corresponding homogenized solution is proved. An analogous result for the fluid pressure is also studied.