Drying flow in a thin film induced by the presence of alcohol vapour

Abstract

We consider a problem concerning the surface tension gradient driven flow induced in a thin water film by the presence of alcohol vapour above the film. We show that the basic evolution equation describing the movement of the water free surface is a first order nonlinear partial differential equation of kinematic wave type. Using the method of characteristics, we show that this equation has multivalued solutions in certain limiting cases and conclude that this effect can be traced back to the occurrence of a boundary layer and a subsequent need to modify the evolution equation. Finally we make some observations on a family of nonlinear equations of essentially similar structure to the basic evolution equation and seek travelling wave and soliton type solutions in certain limiting situations.