Simulation and validation of surfactant-laden drops in two-dimensional Stokes flow

TL;DR

This paper introduces a boundary integral method with spectral accuracy for simulating surfactant-covered droplets in 2D Stokes flow, validated against semi-analytical solutions and effective even at close droplet proximity.

Contribution

The paper develops a high-accuracy boundary integral method for surfactant-laden droplet simulation in 2D Stokes flow, extending semi-analytical solutions for validation.

Findings

Method maintains high accuracy near droplet contact

Spectral accuracy in space with adaptive time-stepping

Validated against extended semi-analytical solutions

Abstract

Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method for computing the evolution of surfactant-covered droplets in 2D Stokes flow. The method has spectral accuracy in space and the adaptive time-stepping scheme allows for control of the temporal errors. Previously available semi-analytical solutions (based on conformal-mapping techniques) are extended to include surfactants, and a set of algorithms is introduced to detail their evaluation. These semi-analytical solutions are used to validate and assess the accuracy of the boundary integral method, and it is demonstrated that the presented method maintains its high accuracy even when droplets are in close proximity.