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

• Published in: International journal of heat and mass transfer 2019-01, Vol.128, p.46-53
• Main Authors: Alexandrov, D.V., Nizovtseva, I.G., Alexandrova, I.V.
• Format: Article
• Language: English
• Subjects: Crystal growth; Differential equations; Distribution functions; Evolution; Growth models; Nucleation; Particle size; Particle size distribution; Phase transformations; Saddle points; Supersaturation
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2018.08.119

•Processes of nucleation and growth of crystals in metastable liquids are studied.•Unsteady-state effects in the growth rates of crystals are taken into account.•Kinetic and balance equations are solved on the basis of the saddle-point technique. 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.