Ostwald ripening is a main phenomenon responsible for growth of particles manufactured using colloidal methods. This paper considers mathematical description of the process using population balance approach solved by method of moments. However, in the case of particles’ dissolution which is a part of the process a closure problem is generated. A novel closure method for the moment – transformed population balance equations based on Gram – Charlier expansions is introduced. Due to its simplicity it allows to reconstruct the full particle size distribution in a stepwise manner giving an access to the pointwise values of the density function required to close the model. The introduced numerical scheme is further used to simulate several carefully chosen test cases including dissolution of solid particles and ageing of particles’ population. The mathematical model presented in the paper is then applied to interpret experimental results for batch precipitation of silica.

奥斯特瓦尔德熟化是导致使用胶体方法制造的颗粒生长的主要现象。本文考虑采用矩量法求解的总体平衡法对过程进行数学描述。然而，在作为过程一部分的颗粒溶解的情况下，产生了封闭问题。目前介绍了一种新颖的闭合方法-基于Gram-Charlier展开的变换的人口平衡方程。由于其简单性，它允许以逐步的方式重建完整的粒度分布，从而可以访问关闭模型所需的密度函数的逐点值。引入的数值方案还用于模拟几个精心选择的测试案例，包括固体颗粒的溶解和颗粒总体的老化。