THE SPREADING OF HEAT OR SOLUBLE SURFACTANT ALONG A THIN LIQUID-FILM

The spreading of a localized distribution of surfactant on a thin viscous film is considered, in the situation in which the surfactant is soluble in the bulk layer and the boundary beneath the fluid is impermeable to surfactant. The surfactant distribution is controlled by advection and diffusion both at the surface of the film, where the surfactant forms a monolayer, and in the bulk. The bulk and surface surfactant concentrations are related by linearized sorption kinetics. The surfactant diffuses rapidly across the thin fluid layer, and lubrication theory is used to derive evolution equations for the film height and the surface and cross-sectionally averaged bulk surfactant concentrations. A special case of the governing equations describes the Marangoni flow induced by a locally hot region of the layer. It is shown that in comparison to the spreading of insoluble surfactant, transient desorption of surfactant from the monolayer to the bulk causes the spreading rate to diminish, although once the bulk and surface concentrations are locally in equilibrium, film deformations are more severe, with a sharp pulse in the film height created just upstream of the leading edge of the surfactant distribution.