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

被引：51

作者：

Alexandrov, D. V. ^{[1
]}

Nizovtseva, I. G. ^{[2
]}

Alexandrova, I. V. ^{[1
]}

机构：

[1] Ural Fed Univ, Dept Theoret & Math Phys, Lab Multiscale Math Modeling, Ekaterinburg 620000, Russia

[2] Friedrich Schiller Univ Jena, Phys Astron Fak, D-07743 Jena, Germany

来源：

INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER | 2019年 / 128卷

基金：

俄罗斯科学基金会;

关键词：

Growth models; Nucleation; Phase transformations; INTERMEDIATE STAGE; DIFFUSION-COEFFICIENTS; NONLINEAR DYNAMICS; UNSTEADY PROCESSES; AQUEOUS-SOLUTIONS; CRYSTALLIZATION; KINETICS; GROWTH;

D O I：

10.1016/j.ijheatmasstransfer.2018.08.119

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

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.

引用

页码：46 / 53

页数：8

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