Boundary integral method for deformable interfaces in the presence of insoluble surfactants

A 3D boundary-integral/finite-volume method is presented for the simulation of drop dynamics in viscous flows in the presence of insoluble surfactants. The concentration of surfactant on the interfaces is governed by a convection-diffusion equation, which takes into account an extra tangential velocity. The spatial derivatives are discretized by a finite-volume method with second-order accuracy on an unstructured triangular mesh. Either an Euler explicit or Crank-Nicolson scheme is used for time integration. The convection-diffusion and Stokes equations are coupled via the interfacial velocity and the gradient in surfactant concentration. The coupled velocity - surfactant concentration system is solved in a semi-implicit fashion. Tests and comparisons with an analytical solution, as well as with simulations in the 2D axisymmetric case, are shown