Local film thinning due to concentration gradient of an insoluble surfactant at an interface

The local thinning of a viscous liquid film on a substrate driven by a surface (or interfacial) tension gradient due to a concentration gradient of a monolayer of an insoluble surfactant initially non-uniformly distributed at a liquid interface relevant to chemical engineering, biomedical and other applications is investigated. A simple model is presented for the temporal evolution of the profiles of radial variation in the thickness of a thin liquid film, the effects of gravity and capillarity due to deformation of the interface in slowing down the film thinning process being allowed. As time increases, the surfactant spreads and the radius of its front increases inversely with decrease in the two-third power of the film thickness at the center. The model describes well not only the published experimental results but also those obtained by other authors using numerical simulations of a set of coupled partial differential equations.