Phase field modelling of surfactants in multi-phase flow

TL;DR

This paper develops a thermodynamically consistent diffuse interface model for surfactants in multi-phase flows with three or more fluids, incorporating complex boundary conditions at triple junctions and supported by numerical simulations.

Contribution

It introduces a novel phase field model for surfactants in multi-phase flow that accounts for triple junction dynamics and local chemical equilibrium, derived from first principles.

Findings

Model aligns with sharp interface limit through asymptotic analysis.

Numerical simulations validate the theoretical model.

Surfactant flow through triple junctions is effectively captured.

Abstract

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions.