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

Article type: Research Article

Authors: Baňas, Ľubomír^{a; *} | Mahato, Hari Shankar^b

Affiliations: [a] Department of Mathematics, Bielefeld University, 33501 Bielefeld, Germany. E-mail: banas@math.uni-bielefeld.de | [b] College of Engineering, University of Georgia, 30602 Athens, USA. E-mail: hsmahato@uga.edu

Correspondence: [*] Corresponding author. E-mail: banas@math.uni-bielefeld.de.

Abstract: 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.

Keywords: Stokes–Cahn–Hilliard equations, phase-field models, multiphase porous media flow, periodic homogenization, two-scale convergence

DOI: 10.3233/ASY-171436

Journal: Asymptotic Analysis, vol. 105, no. 1-2, pp. 77-95, 2017