Alexandrov Dmitri V, Alexandrova Irina 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. 2020 May 15;378(2171):20190247. doi: 10.1098/rsta.2019.0247. Epub 2020 Apr 13.
The transition of a metastable liquid (supersaturated solution or supercooled melt) occurring from the intermediate stage (where the crystals nucleate and grow) to the concluding stage (where the larger particles evolve at the expense of the dissolution of smaller particles) is theoretically described, with allowance for various mass transfer mechanisms (reaction on the interface surface, volume diffusion, grain-boundary diffusion, diffusion along the dislocations) arising at the stage of Ostwald ripening (coalescence). The initial distribution function (its 'tail') for the concluding stage (forming as a result of the evolution of a particulate assemblage during the intermediate stage) is taken into account to determine the particle-size distribution function at the stage of Ostwald ripening. This modified distribution function essentially differs from the universal Lifshitz-Slyozov (LS) solutions for several mass transfer mechanisms. Namely, its maximum lies below and is shifted to the left in comparison with the LS asymptotic distribution function. In addition, the right branch of the particle-size distribution lies above and is shifted to the right of the LS blocking point. It is shown that the initial 'tail' of the particle-size distribution function completely determines its behaviour at the concluding stage of Ostwald ripening. The present theory agrees well with experimental data. This article is part of the theme issue 'Patterns in soft and biological matters'.
从中间阶段（晶体成核并生长的阶段）到结束阶段（较大颗粒以较小颗粒溶解为代价而演化的阶段）发生的亚稳态液体（过饱和溶液或过冷熔体）的转变，在理论上进行了描述，其中考虑了在奥斯特瓦尔德熟化（聚结）阶段出现的各种传质机制（界面表面反应、体积扩散、晶界扩散、沿位错的扩散）。考虑了结束阶段的初始分布函数（其“尾部”，这是由于中间阶段颗粒聚集体的演化而形成的），以确定奥斯特瓦尔德熟化阶段的粒度分布函数。这种修正后的分布函数与几种传质机制的通用利夫希茨 - 斯廖佐夫（LS）解有本质区别。具体而言，与LS渐近分布函数相比，其最大值位于下方且向左移动。此外，粒度分布的右支位于LS阻塞点上方且向右移动。结果表明，粒度分布函数的初始“尾部”完全决定了其在奥斯特瓦尔德熟化结束阶段的行为。本理论与实验数据吻合良好。本文是主题为“软物质和生物物质中的模式”的一部分。
