On the theory of nucleation and nonstationary evolution of a polydisperse ensemble of crystals

The process of nucleation and unsteady-state growth of spherical crystals in a supersaturated solution is considered with allowance for the Weber-Volmer-Frenkel-Zel'dovich and Meirs kinetic mechanisms. The first two corrections to the steady-state growth rate of spherical crystals are found analytically as the solution of the moving boundary problem. On the basis of this solution, we formulate and solve the integro-differential model consisting of the Fokker-Planck type equation for the particle-size distribution function and of the balance equation for the system supersaturation. The distribution function dependent on the nucleation kinetics is found as a functional of the supersaturation. The integro-differential equation for the system supersaturation is solved by means of the saddle-point method. As a result, a complete analytical solution of the problem of nucleation and nonstationary evolution of a polydisperse ensemble of crystals in a metastable medium is constructed in a parametric form. How to use the obtained solutions for supercooled liquids is discussed.