一种基于元胞自动机的介观尺度模拟方法及其在磷酸二氢钾结晶过程中的应用

A Meso-Scale Simulation Method Based on Cellular Automata and Its Application in the Crystallization Process of Potassium Dihydrogen Phosphate

建立了一种介观尺度元胞自动机模拟方法,并应用于溶液冷却结晶过程。根据由经典扩散理论得到的晶体生长规律来制定元胞自动机演化规则,并利用晶体生长速度和蒙特卡洛方法实现了对溶液是否转换为晶体的描述。建立了能够模拟晶体在微米数量级的非均一生长过程的介观元胞自动机模型,并以磷酸二氢钾溶液间歇冷却结晶过程为例验证了该方法的可行性,不仅能展示模拟范围内每个晶体的简化形貌,而且可以统计得到不同时间时晶体尺寸和形貌的分布信息。该方法可以强化结晶过程的模拟结果,同时还避免了复杂的计算过程,减少了计算时间,为结晶过程的建模和分析提供了一个新的研究思路。

Crystallization is a widely used separation and purification technique. In the crystallization process, the change of growth conditions, such as temperature and supersaturation, may lead to changes in the size and morphology of the crystallized product, which not only affects the crystal quality, but also affects the subsequent process operations.In this work, cellular automata were used to simulate the batch crystallization process of the solution at the meso-scale.The method was built in a two-dimensional space, in which each cell was represented by a square, and neighbors adopt Moore’s law, that was, eight cells around the central cell were regarded as neighbors. The evolution rule was based on the crystal classical diffusion theory, and the state of each cell was described by two parameters, i.e., concentration and crystal state(crystal or solution). The change of concentration was determined by Fick’s law. For simplicity, the concentration of cell was the average of its neighbors. Whether the solution was converted into crystals was measured by the Monte Carlo method. By simulation, the size distribution and morphology of the crystal at the mesoscale were obtained. At the same time, the crystallization process was visualized, which gave an intuitive understanding of the morphological feature of each crystalline state during the crystallization. The validity of our method was compared to the high-resolution finite volume method. This work provides a theoretical reference for the identification, modeling and analysis of crystallization, facilitating the industrial practice of specific crystals, and providing new insights into fine-controlling crystal morphology.