A hybrid numerical method for interfacial fluid flow with soluble surfactant

We address a significant difficulty in the numerical computation of fluid interfaces with soluble surfactant that occurs in the physically representative limit of large bulk Peclet number Pe. At the high values of Pe in typical fluid-surfactant systems, there is a transition layer near the interface in which the surfactant concentration varies rapidly, and large gradients at the interface must be resolved accurately to evaluate the exchange of surfactant between the interface and bulk flow. We use the slenderness of the layer to develop a fast and accurate ‘hybrid’ numerical method that incorporates a separate, singular perturbation analysis of the dynamics in the transition layer into a full numerical solution of the interfacial free boundary problem. The accuracy and efficiency of the method is assessed by comparison with a more ‘traditional’ numerical approach that uses finite differences on a curvilinear coordinate system exterior to the bubble, without the separate transition layer reduction. The traditional method implemented here features a novel fast calculation of fluid velocity off the interface.