  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.
