Makoveeva Eugenya V, Alexandrov Dmitri V
Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg 620000, Russian Federation.
Philos Trans A Math Phys Eng Sci. 2019 Apr 22;377(2143):20180210. doi: 10.1098/rsta.2018.0210.
In this paper, we show that the nonlinear growth rate of particles in a supersaturated solution or supercooled melt, as well as the rate of removal of crystals from the metastable liquid of a crystallizer, significantly change the size-distribution function of crystals. Taking these rates into account, we present a complete analytical solution of the integro-differential model describing the transient nucleation of solid particles and their evolution in a metastable liquid. The distribution function and metastability degree (supersaturation or supercooling) are found by means of the separation of variables and saddle-point methods. The nonlinear growth rates of crystals in supersaturated solutions and supercooled melts (single-component and binary) are summarized and compared with experimental data. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.
在本文中，我们表明，过饱和溶液或过冷熔体中颗粒的非线性生长速率，以及结晶器亚稳液体中晶体的去除速率，会显著改变晶体的尺寸分布函数。考虑到这些速率，我们给出了一个积分 - 微分模型的完整解析解，该模型描述了固体颗粒的瞬态成核及其在亚稳液体中的演化。通过变量分离和鞍点方法得到了分布函数和亚稳度（过饱和度或过冷度）。总结了过饱和溶液和过冷熔体（单组分和二元）中晶体的非线性生长速率，并与实验数据进行了比较。本文是主题为“异质材料：亚稳和非遍历内部结构”的一部分。
