Interfacial instability induced by lateral vapor pressure fluctuation in bounded thin liquid-vapor layers

摘要

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 by applying long-wave approximation to both layers. 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.