A highly accurate boundary integral equation method for surfactant-laden drops in 3D
For researchers in droplet microfluidics and multiphase flow, this method enables accurate simulation of surfactant effects on drop dynamics, addressing a known bottleneck in handling deformation and close interactions.
The paper presents a boundary integral method for simulating 3D surfactant-laden drops in Stokes flow, achieving high accuracy even under large deformations and close interactions. The method uses spherical harmonics and novel reparameterization to maintain surface quality, with adaptive time stepping and implicit surfactant diffusion treatment.
The presence of surfactants alters the dynamics of viscous drops immersed in an ambient viscous fluid. This is specifically true at small scales, such as in applications of droplet based microfluidics, where the interface dynamics become of increased importance. At such small scales, viscous forces dominate and inertial effects are often negligible. Considering Stokes flow, a numerical method based on a boundary integral formulation is presented for simulating 3D drops covered by an insoluble surfactant. The method is able to simulate drops with different viscosities and close interactions, automatically controlling the time step size and maintaining high accuracy also when substantial drop deformation appears. To achieve this, the drop surfaces as well as the surfactant concentration on each surface are represented by spherical harmonics expansions. A novel reparameterization method is introduced to ensure a high-quality representation of the drops also under deformation, specialized quadrature methods for singular and nearly singular integrals that appear in the formulation are evoked and the adaptive time stepping scheme for the coupled drop and surfactant evolution is designed with a preconditioned implicit treatment of the surfactant diffusion.