Diffuse interface modelling of soluble surfactants in two-phase flow

TL;DR

This paper develops thermodynamically consistent diffuse interface models for soluble surfactants in two-phase flows, connecting them to sharp interface models and demonstrating their effectiveness through numerical simulations.

Contribution

It introduces a flexible, thermodynamically consistent diffuse interface framework for soluble surfactants, covering dynamic and instantaneous adsorption, with connections to sharp interface models.

Findings

Models are thermodynamically consistent and derived from fundamental principles.

Asymptotic analysis relates diffuse interface models to sharp interface limits.

Numerical simulations confirm the approach's effectiveness.

Abstract

Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are related to sharp interface models. Both cases of dynamic as well as instantaneous adsorption are covered. Flexibility with respect to the choice of bulk and surface free energies allows to realise various isotherms and relations of state between surface tension and surfactant. Some numerical simulations display the effectiveness of the presented approach.