An integral equation method for closely interacting surfactant-covered droplets in wall-confined Stokes flow

TL;DR

This paper introduces a highly accurate boundary integral method with specialized quadrature and spectral acceleration for simulating closely interacting surfactant-covered droplets in wall-confined Stokes flow, applicable to complex geometries.

Contribution

It develops a novel integral equation approach with advanced quadrature and spectral methods for high-accuracy simulation of surfactant-covered droplets near boundaries and other droplets.

Findings

Method achieves high accuracy in close interactions

Handles complex geometries with solid boundaries

Validated through convergence studies and challenging examples

Abstract

A highly accurate method for simulating surfactant-covered droplets in two-dimensional Stokes flow with solid boundaries is presented. The method handles both periodic channel flows of arbitrary shape and stationary solid constrictions. A boundary integral method together with a special quadrature scheme is applied to solve the Stokes equations to high accuracy, also for closely interacting droplets. The problem is considered in a periodic setting and Ewald decompositions for the Stokeslet and stresslet are derived. Computations are accelerated using the spectral Ewald method. The time evolution is handled with a fourth order, adaptive, implicit-explicit time-stepping scheme. The numerical method is tested through several convergence studies and other challenging examples and is shown to handle drops in close proximity both to other drops and solid objects to high accuracy.