A highly accurate boundary integral equation method for surfactant-laden drops in 3D

摘要

The presence of surfactants alters the dynamics of viscous drops immersed inan ambient viscous fluid. This is specifically true at small scales, such as inapplications of droplet based microfluidics, where the interface dynamicsbecome of increased importance. At such small scales, viscous forces dominateand inertial effects are often negligible. Considering Stokes flow, a numericalmethod based on a boundary integral formulation is presented for simulating 3Ddrops covered by an insoluble surfactant. The method is able to simulate dropswith different viscosities and close interactions, automatically controllingthe time step size and maintaining high accuracy also when substantial dropdeformation appears. To achieve this, the drop surfaces as well as thesurfactant concentration on each surface are represented by spherical harmonicsexpansions. A novel reparameterization method is introduced to ensure ahigh-quality representation of the drops also under deformation, specializedquadrature methods for singular and nearly singular integrals that appear inthe formulation are evoked and the adaptive time stepping scheme for thecoupled drop and surfactant evolution is designed with a preconditionedimplicit treatment of the surfactant diffusion.