We 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.

We study an instability of thin liquid-vapor layers bounded by rigid parallel walls from both below and above. In this system, the interfacial instability is induced by lateral vapor pressure fluctuation, which is in turn attributed to the effect of phase change: evaporation occurs at a hotter portion of the interface and condensation at a colder one. The high vapor pressure pushes the interface downward and the low one pulls it upward. A set of equations describing the temporal evolution of the interface of the liquid-vapor layers is derived. This model neglects the effect of mass loss or gain at the interface and guarantees the mass conservation of the liquid layer. The result of linear stability analysis of the model shows that the presence of the pressure dependence of the local saturation temperature mitigates the growth of long-wave disturbances. The thinner vapor layer enhances the vapor pressure effect.We find the stability criterion, which suggests that only slight temperature gradients are sufficient to overcome the gravitational effect for a water/vapor system. The same holds for the Rayleigh-Taylor unstable case, with a possibility that the vapor pressure effect may be weakened if the accommodation coefficient is below a certain critical value.

We examine the droplet motion in one-component fluids in a small temperature gradient by solving linearized hydrodynamic equations supplemented with appropriate surface boundary conditions. We show that the velocity field and the temperature around the droplet are strongly influenced by first-order phase transition taking place at the interface. Latent heat released or absorbed at the interface drastically changes the hydrodynamic flow around the droplet. As a result, the temperature becomes almost homogeneous inside the droplet and the Marangoni effect arising from the surface tension gradient is much suppressed. The droplet velocity is also much decelerated.

We numerically investigate the nonlinear evolution of the interface of a thin liquid-vapor bilayer system confined by rigid horizontal walls from both below and above. The lateral variation of the vapor pressure arising from phase change is taken into account in the present analysis. When the liquid ͑vapor͒ is heated ͑cooled͒ and gravity acts toward the liquid, the deflection of the interface monotonically grows, leading to a rupture of the vapor layer, whereas nonruptured stationary states are found when the liquid ͑vapor͒ is cooled ͑heated͒ and gravity acts toward the vapor. In the latter case, vapor-flow-driven convective cells are found in the liquid phase in the stationary state. The average vapor pressure and interface temperature deviate from their equilibrium values once the interface departs from the flat equilibrium state. Thermocapillarity does not have a significant effect near the thermodynamic equilibrium, but becomes important if the system significantly deviates from it.

We study stability of a condensing liquid film of a binary vapor mixture. When a binary vapor mixture of some kind is cooled on a substrate, a condensing liquid film emerges to take an inhomogeneous form such as a droplet one due to the solutal Marangoni effect. In order to analyze this phenomenon, we apply the long-wave approximation to the condensing liquid film and derive a nonlinear partial differential equation describing the spatio-temporal evolution of the film thickness. An interfacial boundary condition taking account of an effect of mass gain of the liquid film is adopted. Based on this model, we perform a linear stability analysis around a flat-film solution. We obtain an evolution equation of the amplitude of a disturbance, from which the cutoff and fastest growth wavenumbers are deduced. The maximum value of the cutoff wavenumber relative to the film thickness and its film thickness are estimated for water-ethanol mixture at atmospheric pressure. We numerically verify the long-wave nature of the instability of the condensate liquid film in this system. A significant difference in their values is found for low-ethanol fractions of the ambient vapor whether or not the temperature dependence of the mass transfer coefficient is considered. The wavenumber of a pattern of the liquid film observed in the experiment has the same parameter dependence as that of the fastest growth wavenumber.