The kinetic rate equation (KRE) model, unlike the population balance equation model, can describe growth, nucleation, and even Ostwald ripening simultaneously. However, the KRE model cannot be applied in cooling crystallization systems. In this work, we propose a modified KRE model to describe cooling crystallization. The modified KRE model can successfully describe crystal growth and nucleation in cooling crystallization systems. In addition, the metastable zone width was simulated using the modified KRE model and compared with the experimental data in references. The results revealed that the modified KRE model could express the effect of overheating prior to cooling on the metastable zone width. As the extent of overheating increases, the metastable zone width becomes wider, which phenomenon can be clearly simulated by the modified KRE model. This modeling capability is attributed to the behavior of particle clusters that are sized less than the size of sub-nuclei. Because the population balance equation model cannot describe the metastable zone width, the modified KRE model has certain competitive advantages in its application to various crystallization systems.

中文翻译：

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冷却结晶的修正动力学速率方程模型

与种群平衡方程模型不同，动力学速率方程 (KRE) 模型可以同时描述生长、成核甚至 Ostwald 成熟。但是，KRE 模型不能应用于冷却结晶系统。在这项工作中，我们提出了一种改进的 KRE 模型来描述冷却结晶。修改后的 KRE 模型可以成功地描述冷却结晶系统中的晶体生长和成核。此外，使用改进的 KRE 模型模拟了亚稳区宽度，并与参考文献中的实验数据进行了比较。结果表明，修改后的 KRE 模型可以表达冷却前过热对亚稳区宽度的影响。随着过热程度的增加，亚稳区宽度变宽，这种现象可以通过修正的 KRE 模型清楚地模拟。这种建模能力归因于尺寸小于子核尺寸的粒子簇的行为。由于种群平衡方程模型不能描述亚稳区宽度，改进的KRE模型在应用于各种结晶体系时具有一定的竞争优势。