Homogenization of a coupled incompressible Stokes-Cahn-Hilliard system modeling binary fluid mixture in a porous medium

TL;DR

This paper derives homogenized equations for a coupled Stokes-Cahn-Hilliard system modeling binary fluid flow in porous media, capturing surface tension and interface evolution at the pore scale.

Contribution

It introduces a rigorous homogenization approach for a complex coupled micro-scale model of two-phase flow in porous media, including well-posedness and derivation of effective equations.

Findings

Homogenized equations for the Stokes-Cahn-Hilliard system are obtained.

The pore-scale model is well-posed.

The approach uses unfolding operator and two-scale convergence methods.

Abstract

A phase-field model for two-phase immiscible, incompressible porous media flow with surface tension effects is considered. The pore-scale model consists of a strongly coupled system of Stokes-Cahn-Hilliard equations. The fluids are separated by an evolving diffuse interface of a finite width depending on the scale parameter $\varepsilon$ in the considered model. At first the well-posedness of a coupled system of partial differential equations at micro scale is investigated. We obtained the homogenized equations for the microscopic model via unfolding operator and two-scale convergence approach.