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

Abstract

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.

Author Grzegorz Tyl (FCPE / DCRED)
Grzegorz Tyl,,
- Department of Chemical Reactor Engineering and Dynamics
, Jerzy Robert Bałdyga (FCPE / DCRED)
Jerzy Robert Bałdyga,,
- Department of Chemical Reactor Engineering and Dynamics
, Mounir Bouaifi
Mounir Bouaifi,,
-
, Magdalena Jasińska (FCPE / DCRED)
Magdalena Jasińska,,
- Department of Chemical Reactor Engineering and Dynamics
Journal seriesChemical Engineering Research & Design, [Chemical Engineering Research and Design], ISSN 0263-8762, e-ISSN 1744-3563
Issue year2020
Vol159
Pages491-504
Keywords in Englishpopulation balance, Ostwald ripening, colloid, silica, method of moments, Gram-Charlier expansion
ASJC Classification1500 General Chemical Engineering; 1600 General Chemistry
DOIDOI:10.1016/j.cherd.2020.05.007
URL https://reader.elsevier.com/reader/sd/pii/S0263876220302148?token=AC848E48A29F4CE19B02FE4E76BD942A9C1AA801FB348224D282584EDDFE526A48AA35BE68D031E154AB2B4712102308
Languageen angielski
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Tyl G. (i in.) - Population balance approach...pdf 1.89 MB
Score (nominal)140
Score sourcejournalList
ScoreMinisterial score = 140.0, 15-06-2020, ArticleFromJournal
Publication indicators Scopus Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 1.296; WoS Impact Factor: 2018 = 3.073 (2) - 2018=3.23 (5)
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