A fast numerical method for the interfacial motion of a surfactant-laden bubble in creeping flow

Numerical simulation is an important contemporary tool used to investigate interfacial motion in complex fluids. Even with increasing computer speed and memory, fast, efficient and highly accurate algorithms that are able to handle large-scale long-time simulations, are needed. We present a new robust numerical method for computing the motion of a two-dimensional bubble interface in a straining Stokes Flow laden with surfactants, which induce nonuniform surface tension. This consists of evolving a convective-diffusive equation describing the surfactant dynamics, coupled with the interface motion equations. The interface velocity is found by solving an integral equation derived from the complex variable theory of the biharmonic equation. The numerical method solving the integral equations is spectrally accurate and employs a Fast Multipole-based iterative method. We investigate an Implicit-Explicit time-stepping method to ease the stability constraint. By maintaining an equal arclength point spacing, we maximize the time-stepping scheme's efficiency.