Adaptive time-stepping for surfactant-laden drops

An adaptive time-stepping scheme is presented aimed at computing the dynam- ics of surfactant-covered deforming droplets. This involves solving a coupled system, where one equation corresponds to the evolution of the drop interfaces and one to the surfactant concentration. The first is discretised in space using a boundary integral formulation which can be treated explicitly in time. The latter is a convection-diffusion equation solved with a spectral method and is advantageously solved with a semi-implicit method in time. The scheme is adaptive with respect to drop deformation as well as surfactant concentration and the adjustment of time-steps takes both errors into account. It is applied and demonstrated for simulation of the deformation of surfactant-covered droplets, but can easily be applied to any system of equations with similar structure. Tests are performed for both 2D and 3D formulations and the scheme is shown to meet set error tolerances in an efficient way.