Instabilities in evaporating liquid layer with insoluble surfactant

Abstract

The stability of an evaporating liquid layer with insoluble surfactant distributed over the free deformable surface is studied theoretically. The insoluble surfactant hinders the evaporation, and mass flux through the interface is a decreasing function of surfactant concentration. Density, viscosity, and thermal conductivity of the gaseous phase are assumed to be small compared with those of the liquid phase, and a one-sided model is applied. A system of nonlinear equations is obtained using the long-wave approximation and the assumption of a slow time evolution. These equations incorporate basic physical effects which take place in the system. Linear stability analysis of the base state is performed for long-wave disturbances in the framework of the frozen interface approximation. The cases of quasi-equilibrium evaporation (when the interfacial temperature equals the equilibrium one) and nonequilibrium evaporation are considered. In addition to a monotonic instability mode, an oscillatory mode has been found.