Nizovtseva Irina G, Alexandrov Dmitri V
Physikalisch-Astronomische Fakultät, Friedrich-Schiller-Universität Jena, Jena 07743, Germany.
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. 2020 May 15;378(2171):20190248. doi: 10.1098/rsta.2019.0248. Epub 2020 Apr 13.
A nonlinear problem with two moving boundaries of the phase transition, which describes the process of directional crystallization in the presence of a quasi-equilibrium two-phase layer, is solved analytically for the steady-state process. The exact analytical solution in a two-phase layer is found in a parametric form (the solid phase fraction plays the role of this parameter) with allowance for possible changes in the density of the liquid phase accordingly to a linearized equation of state and arbitrary value of the solid fraction at the boundary between the two-phase and solid layers. Namely, the solute concentration, temperature, solid fraction in the mushy layer, liquid and solid phases, mushy layer thickness and its velocity are found analytically. The theory under consideration is in good agreement with experimental data. The obtained solutions have great potential applications in analysing similar processes with a two-phase layer met in materials science, geophysics, biophysics and medical physics, where the directional crystallization processes with a quasi-equilibrium mushy layer can occur. This article is part of the theme issue 'Patterns in soft and biological matters'.
一个具有两个相变移动边界的非线性问题描述了在准平衡两相层存在下的定向结晶过程，本文针对稳态过程给出了该问题的解析解。考虑到液相密度可能根据线性化状态方程发生变化以及两相层与固相层边界处固相分数的任意值，在两相层中找到了以参数形式（固相分数作为该参数）表示的精确解析解。具体而言，解析得到了溶质浓度、温度、糊状层中的固相分数、液相和固相、糊状层厚度及其速度。所考虑的理论与实验数据吻合良好。所得解在分析材料科学、地球物理学、生物物理学和医学物理学中遇到的具有两相层的类似过程时具有很大的潜在应用价值，这些领域可能会出现具有准平衡糊状层的定向结晶过程。本文是主题为“软物质和生物物质中的模式”的一部分。
