Superhydrophobic surface immobilization by insoluble surfactant

The effect of insoluble surfactants on Stokes flows over transverse-ridge-type superhydrophobic surface with flat menisci is discussed. The focus is on surface immobilization, where surfactant-induced surface tension forces, here modelled using a Langmuir equation of state, can severely retard menisci. At the core of this work is a novel numerical scheme constructed around a complex variable formulation of the problem. This scheme allows exploration of surfactant effects for the full range of surface Péclet numbers, Marangoni numbers, and surfactant loads. Perturbation theory solutions at the small Péclet and Marangoni number limits are used to validate the numerical results. The results reveal a yet unexplored mechanism for surface immobilization where flow retardation can occur at quite low Péclet and Marangoni numbers. This occurs for high values of surfactant load and is purely a consequence of the non-linearity of the equation of state.