Darren Crowdy

Marangoni meets Burgers in the complex plane: new mathematics for surfactant dynamics

This talk will survey a number of new mathematical results on insoluble surfactant dynamics, and the resulting Marangoni effects, on the free surface of a viscous fluid. Starting with a discussion of some basic transport problems involving “viscous Marangoni propulsion” (or “Marangoni surfers”) we will build up the theoretical approach to describe the unsteady formation of “stagnant caps” when surface diffusion is negligible. The effects of reaction kinetics are also incorporated into the model. All this leads up to the main aim of the talk: to show the surprising relevance of the complex Burgers equation to the dynamics of insoluble surfactants at arbitrary surface Péclet numbers – when surface diffusion and advection are both present – leading to a remarkable linearization of this nonlinear problem having a number of mathematical, and physical, ramifications only so far partially explored.