Remobilizing a stagnant cap of surfactant through fast kinetic exchange and surface diffusion

Explicit solutions are presented describing the steady remobilization of a planar interface between two viscous fluids laden with surfactant soluble to the upper fluid. In the presence of a linear extensional flow, steady stagnant caps of surfactant form resulting in an immobilized interface. We show analytically that both fast kinetic exchange with the bulk fluid and surface diffusion can mollify these sharp surfactant gradients, thereby reducing the interfacial Marangoni stresses. The case of insoluble surfactant on an interface between a viscous fluid and a constant pressure region is also treated equivalently.