Journal
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
Volume 128, Issue -, Pages 46-53Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijheatmasstransfer.2018.08.119
Keywords
Growth models; Nucleation; Phase transformations
Categories
Funding
- Russian Science Foundation [18-19-00008]
- Russian Science Foundation [18-19-00008] Funding Source: Russian Science Foundation
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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. (C) 2018 Elsevier Ltd. All rights reserved.
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