On diffuse interface modeling and simulation of surfactants in two-phase fluid flow

TL;DR

This paper critically analyzes a phase-field model for surfactants in two-phase flows, revealing ill-posedness issues and proposing modifications to improve its mathematical and physical robustness, supported by numerical simulations.

Contribution

It identifies ill-posedness in an existing model and introduces modifications to enhance its validity and applicability in simulating surfactant-laden flows.

Findings

Original model is mathematically ill-posed for many parameters.

Modified model shows improved well-posedness and physical accuracy.

Numerical simulations validate theoretical insights and demonstrate complex flow effects.

Abstract

An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and the qualities of the physical model. A fully coupled hydrodynamic test-case demonstrates the potential to capture also non-trivial effects on the overall flow.