The influence of evaporation on long-wavelength instabilities in liquid layer with insoluble surfactant

We investigate the long-wavelength Marangoni instability in an evaporating horizontal liquid layer with insoluble surfactant absorbed on the free deformable surface. The insoluble surfactant hinders the evaporation of the liquid into a vapor. The mass flux depends on the difference between the actual surface temperature and the equilibrium one. Different kinetics limited regimes of evaporation are considered. Density, viscosity, and thermal conductivity of the vapor are smaller than those of the liquid, and a one-sided model is applied. The layer is subjected to a heat flux at its bottom. We assume a small heat transfer coefficient at the interface. The linear stability analysis of this system for different values of kinetic resistance parameter is performed. Instability thresholds are determined and critical Marangoni numbers for monotonic, as well as for oscillatory mode, are found.