Population balance approach to model Ostwald ripening of silica using Gram – Charlier series expansion based closure
Grzegorz Tyl , Jerzy Robert Bałdyga , Mounir Bouaifi , Magdalena Jasińska
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.
|Journal series||Chemical Engineering Research & Design, [Chemical Engineering Research and Design], ISSN 0263-8762, e-ISSN 1744-3563|
|Keywords in English||population balance, Ostwald ripening, colloid, silica, method of moments, Gram-Charlier expansion|
|Score||= 140.0, 15-06-2020, ArticleFromJournal|
|Publication indicators||= 0; : 2018 = 1.296; : 2018 = 3.073 (2) - 2018=3.23 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.