AbstractWe propose a novel model of a pure liquid film evaporating into an inert gas, taking into account an effect of convection of the vapour by the evaporation flow of the gas. For the liquid phase, the long-wave approximation is applied to the governing equations. Assuming that fluctuations of the vapour concentration in the gas phase are localized in the vicinity of the liquid–gas interface, we consider only the limit of the mass transport equation at the interface. The diffusion term in the vertical direction of the mass transport equation is modelled by introducing the concentration boundary layer above the liquid film and solving the stationary convection–diffusion equation for the concentration inside the boundary layer. We investigate the linear stability of a flat film based on our model. The effect of vapour diffusion along the interface mitigates the Marangoni effect for short-wavelength disturbances. The local variation of vertical advection is found to be negligible. A critical thickness above which the film is stable exists under the presence of gravity. The effect of fluctuation of mass loss of the liquid induced by horizontal vapour diffusion becomes the primary instability mechanism in a very thin region. The effects of the resistance of phase change and the time derivative of the interface concentration are also examined.
A complex definite integral used in the semi-analytical solution of the mass transport equation in an unbounded two- or three-dimensional domain
