integral equation based methods for surfactant laden drops in
two and three dimensions
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.