Simulation and validation of surfactant-laden drops in two-dimensional Stokes flow

Highlights: • Formulates a boundary integral method for surfactant-laden deforming drops that is highly accurate, also for drops in very close proximity. • Derives estimates of the numerical errors when evaluating the near-singular boundary integrals using standard Gauss-Legendre quadrature. • Extends semi-analytical solutions for a pair of deforming bubbles in extensional flow to include also surfactants. • Presents exact and semi-analytical solutions as easily accessible algorithms for validation of numerical methods for droplets in Stokes flow. -- Abstract: Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method for computing the evolution of surfactant-covered droplets in 2D Stokes flow. The method has spectral accuracy in space and the adaptive time-stepping scheme allows for control of the temporal errors. Previously available semi-analytical solutions (based on conformal-mapping techniques) are extended to include surfactants, and a set of algorithms is introduced to detail their evaluation. These semi-analytical solutions are used to validate and assess the accuracy of the boundary integral method, and it is demonstrated that the presented method maintains its high accuracy even when droplets are in close proximity.