Influence of insoluble surfactants on shear flow over a surface in Cassie state at large Peclet numbers

Surfactants can immobilize fluid-liquid interfaces under shear stress. We investigate the impact of insoluble surfactants on shear flow along a superhydrophobic surface in Cassie state, with gas trapped in grooves oriented perpendicular to the flow direction. Assuming convection-dominated transport along the gas-liquid interface, analytical results for the surfactant distribution on a groove and the corresponding flow field in its vicinity are derived both for a single groove and for an array of evenly spaced grooves. The results are elaborated for the case where the surface tension depends linearly on the surfactant concentration, which is characteristic for dilute coverage of the gas-liquid interface. For an array of grooves, the relation between the applied shear stress and the effective slip length on the microstructured surface is investigated.