Evolution of dry patches in evaporating liquid films

We investigate evolution of dry patches in a thin film of a volatile liquid on a heated plate in the framework of a model that accounts for the effects of surface tension, evaporation, thermocapillarity, and disjoining pressure. Dry areas on the plate are modeled by isothermal microscopic films which are in thermodynamic equilibrium with the vapor. For nonpolar liquids such equilibrium is achieved due to van der Waals forces, well-defined capillary ridges are formed around growing dry patches, contact line speed increases with time. For polar liquids the microscopic film is formed by combined action of van der Waals and electrical double layer forces, capillary ridge is small, and contact line speed quickly approaches a constant value. Thermocapillary stresses tend to increase the height of the capillary ridges formed around expanding patches. Numerical simulations demonstrate that the proposed model is capable of describing a number of complicated phenomena observed in experimental studies of evaporating films including fingering instabilities and merger of growing dry patches.