Generalized Rayleigh-Lamb equation

The dynamics of the vapor-liquid interface when a solid particle heated to a high temperature comes into contact with a cold liquid is analyzed. The generalized Rayleigh-Lamb equation taking into account temperature changes in the liquid and the vapor, the saturation vapor pressure change associated with it, and the emergence of the mass flux due to liquid evaporation at the interface is deduced. At medium parameters far from the critical point, the generalized Rayleigh-Lamb equation reduces to its well-known form. Around the critical point, the difference between the obtained equation and arising modes of changes of the vapor-liquid interface can be rather considerable. Unlike the well-known Stefan problem, far from the critical liquid temperature, the phase transition temperature and, respectively, the saturation vapor pressure change with the vapor-liquid interface movement, which yields various modes of dynamics of the vapor cavity. In the special case of small variations from the stationary mode, an analytical solution for the problem on a small change in the vapor cavity radius with time was developed.