Marangoni meets Burgers: analytical solutions describing the formation of stagnant caps of surfactant

This talk will demonstrate the theoretical importance of a complex Burgers equation in describing unsteady surfactant evolution on interfaces at low Reynolds and capillary numbers. Methods familiar to fluid dynamicists from compressible gas dynamics, where the real Burgers equation is well known, are shown to be relevant also to Marangoni flows driven by surfactants. It will be shown that a nonlinear dynamical system governing insoluble surfactant evolution at an interface can be linearized, at arbitrary surface Peclet number, by a generalization of the Cole-Hopf transformation. And, at infinite surface Peclet number, exact solutions describing the time dependent formation of stagnant caps can be derived using a generalization of the method of characteristics.