Numerical studies of cusp formation at fluid interfaces in Stokes flow

Numerical studies are performed addressing the development of regions of high curvature and the spontaneous occurrence of cusped interfacial shapes in two-dimensional and axisymmetric Stokes flow. In the numerical simulations, the velocity field is computed using a boundary-integral method, and the evolution of the concentration of an insoluble surfactant over an evolving interface is computed using an implicit finite-volume method. Three configurations are considered in detail, and the results are used to elucidate three different aspects of cusp formation