An integral equation method for closely interacting surfactant-covered droplets in wall-confined Stokes flow
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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 droplets in close interaction. The problem is considered in a periodic setting and an Ewald decomposition for the Stokeslet and stresslet is derived to make the periodic sums convergent. Computations are sped up 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 a high accuracy.
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