A complete analytical solution to the integro-differential model describing the nucleation and evolution of ellipsoidal particles

被引：1

作者：

Nikishina, Margarita A. ^{[1
]}

Alexandrov, Dmitri V. ^{[1
]}

机构：

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

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2022年 / 45卷 / 13期

基金：

俄罗斯科学基金会;

关键词：

applied mathematical modeling; integro-differential equations; phase transformations; saddle-point method; supersaturated solutions; INTERMEDIATE STAGE; PHASE-TRANSITION; CRYSTAL-GROWTH; NONLINEAR DYNAMICS; KINETICS; CRYSTALLIZATION; SOLIDIFICATION; CANAVALIN; MECHANISM;

D O I：

10.1002/mma.7927

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a complete analytical solution to the integro-differential model describing the nucleation and growth of ellipsoidal crystals in a supersaturated solution is obtained. The asymptotic solution of the model equations is constructed using the saddle-point method to evaluate the Laplace-type integral. Numerical simulations carried out for physical parameters of real solutions show that the first four terms of the asymptotic series give a convergent solution. The developed theory was compared with the experimental data on desupersaturation kinetics in proteins. It is shown that the theory and experiments are in good agreement.

引用

页码：8032 / 8044

页数：13

共 63 条

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