A discontinuous Galerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant

TL;DR

This paper develops a discontinuous Galerkin numerical method for simulating two-phase flows with soluble surfactants using a phase-field model, capturing complex flow dynamics and adsorption phenomena.

Contribution

It introduces a novel discontinuous Galerkin scheme that accurately models immiscible fluids with surfactants, including adsorption effects and real pore geometries.

Findings

The scheme recovers Langmuir adsorption isotherms at equilibrium.

Simulations demonstrate flow dynamics in porous media with surfactants.

The method effectively captures complex flow behaviors in micro-CT images.

Abstract

A numerical method using discontinuous polynomial approximations is formulated for solving a phase-field model of two immiscible fluids with a soluble surfactant. The scheme recovers the Langmuir adsorption isotherms at equilibrium. Simulations of spinodal decomposition, flow through a cylinder and flow through a sequence of pore throats show the dynamics of the flow with and without surfactant. Finally the numerical method is used to simulate fluid flows in the pore space of Berea sandstone obtained by micro-CT imaging.