Highly accurate integral equation based methods for surfactant laden drops in two and three dimensions
Anna-Karin Tornberg, KTH


In micro-fluidics, at small scales where inertial effects become negligible, surface to volume ratios are large and the interfacial processes are extremely important for the overall dynamics.
Integral equation based methods are attractive for the simulations of e.g. droplet-based microfluidics, with tiny water drops dispersed in oil, stabilized by surfactants. 

We have developed highly accuracte numerical methods for drops with insoluble surfactants, both in two and three dimensions. In this talk I will discuss some fundamental challenges that we have addressed, that are also highly relevant to other applications: accurate quadrature methods for singular and nearly singular integrals, adaptive time-stepping, and reparameterization of time-dependent surfaces for high quality discretization of the drops throughout the simulations.