Abstract
A complete analytical solution of an integro-differential model describing the transient nucleation of solid particles and their subsequent growth at the intermediate stage of phase transitions in metastable systems is constructed. A functional Fokker–Plank type equation for the density distribution function is solved by the separation of variables method for the Weber–Volmer–Frenkel–Zeldovich nucleation kinetics. A non-linear integral equation with memory kernel connecting the density distribution function and the system supercooling/supersaturation is analytically solved on the basis of the saddle point method for the Laplace integral. The analytical solution obtained shows that the transient phase transition process attains its steady-state solution at large times. An exact analytical solution for the steady-state problem is found too. It is demonstrated that the crystal-size distribution function increases with increasing the intensity of external sources. In addition, the number of larger (smaller) particles decreases (increases) with increasing the withdrawal rate of crystals from a metastable liquid.
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