Evolution of Rayleigh equation in a problem with phase transition

In the Rayleigh equation, physical effects are included such as the reaction of recoil of molecules of the gaseous phase on the interface and the time variation of the density of the gaseous phase during a process with phase transition. A simultaneous analysis is performed of the modified Rayleigh equation and asymptotic representation of the self-similar solution of the problem formulated on the basis of the energy model with a variable temperature of the interface. An equation is obtained that defines the dynamics of motion of a spherically shaped interface. A comparison of the calculation results obtained in solving this equation with experimental data on boiling of highly superheated water and the $\mathrm{R}113$ refrigerant reveals their good agreement.