Enhanced numerical approaches for modeling insoluble surfactants in two-phase flows with the diffuse-interface method

TL;DR

This paper introduces two improved diffuse-interface methods for accurately simulating insoluble surfactants in two-phase flows, enhancing conservation and computational efficiency.

Contribution

The study proposes two novel approaches to enhance the accuracy and practicality of interfacial transport models for insoluble surfactants without increasing computational costs.

Findings

The new methods preserve mass conservation of fluid and surfactant.

Numerical tests demonstrate improved accuracy and efficiency.

A challenging benchmark case is proposed for method evaluation.

Abstract

Surfactants reside at the interface of two-phase flows and significantly influence the flow dynamics. Numerical simulations are essential for a comprehensive understanding of such surfactant-laden flows and require a method that can accurately simulate surfactant transport along the interface. In this study, we focus on interfacial transport models for insoluble surfactants based on the diffuse-interface method and propose two approaches to improve their accuracy: (a) adopting a formulation that avoids the spatial derivatives of variables with sharp gradients and (b) allowing the width of the delta function to be specified independently of the interface width. These approaches are simple and practical in that they do not lead to significant increases in computational cost, implementation complexity, or degradation of interface-capturing accuracy. Moreover, they preserve the discrete conservation of both fluid and surfactant mass. We conduct a series of numerical tests to demonstrate the effectiveness of the proposed approaches. Finally, we present a challenging test case that is difficult to solve accurately and has not been previously discussed. We expect this case to serve as a valuable benchmark for evaluating and comparing the performances of various methods proposed in the literature.