Filtration of highly miscible liquids based on two-scale homogenization of the Navier-Stokes and Cahn-Hilliard equations (Q6552842)

This brief study looks into the formal two-scale homogenization of an incompressible mixture of two fluids travelling through a porous media. The main aim is to describe displacement in which mixing of fluids occurs. Essentially, one looks at a Cahn-Hilliard system coupled with the Navier-Stokes equations posed in a two-dimensional periodically perforated set. The asymptotic results are complemented with numerical simulations.