A finite-element method for interfacial surfactant transport, with application to the flow-induced deformation of a viscous drop

A Galerkin finite-element method is developed for solving the transport equation governing the evolution of the surface concentration of an insoluble surfactant over a stationary or evolving fluid interface. The numerical procedure is implemented on an unstructured three-dimensional surface grid consisting of six-node curved triangular elements. Numerical investigations show that the finite-element method is superior to a previously developed finite-volume method for both convection- and diffusion-dominated transport, and especially when the interfacial grid is coarse and steep gradients arise due to local accumulation. The numerical methods for surface transport are combined with a boundary-element method for Stokes flow, and dynamical simulations are performed to illustrate the possibly significant effect of the surface equation of state relating the surface tension to the surfactant concentration on the deformation of a viscous drop in simple shear flow.