Modelling nanoparticle dynamics: coagulation, sintering, particle inception and surface growth

Abstract

In this paper we investigate a new stochastic particle method (SPM) for solving an extension to the sintering-coagulation equation and model two particle systems: the production of SiO 2 and TiO 2 . A model which includes both a particle source and an area dependent surface growth term as well as coagulation and sintering is presented. A new mass-flow stochastic algorithm to solve the model is stated. The stochastic method is able to recover fully the evolution the bivariate particle size distribution function (PSDF) and is computationally very efficient when compared to traditional finite element methods. The SPM is compared to a bivariate sectional method for a system with coagulation and sintering as the only mechanisms. Despite using a different form of coagulation kernel to the sectional investigation, the results obtained agree closely to those in the literature and were obtained in a small fraction of the time. The full model with particle inception and surface growth was then used to model the TiCl 4 → TiO 2 system under various conditions. At low precursor concentration we investigate the effect of changing temperature, whilst at high precursor concentration we investigate the effect of surface growth on the system. The results agree with many of the conclusions reached in the literature.

Analytical technology aided optimization and scale‐up of impinging jet mixer for reactive crystallization process

“…Based on the adsorption layer theory, particle growth occurs on pre‐existing layers of atoms or molecules that adsorbed on crystal faces. Besides these theories, another phenomenon which causes the size to increase is aggregation . Solution hydrodynamics, static forces, and particle structures may all have effects on crystal aggregation.…”

Continuous reactive crystallization of pharmaceuticals using impinging jet mixers

“…Adsorption layer theory suggests that particle growth happens on pre‐exist layers of atoms or molecules that adsorbed on crystals faces. For rapid reactive crystallization it was thought that in addition surface growth, aggregation of small particles including nuclei is another factor causing crystal size growth …”

Image Analysis and Computer Simulation of Nanoparticle Clustering in Combustion Systems

“…Other researchers have explored hybrid solution methods, for example integrating discrete relations for small clusters (i = 1 to 20) with sectional relations for the larger clusters (Gelbard et al 1980;Wu and Flagan 1988;Langrebe and Pratsinis 1990). Mathematical modeling of agglomeration has also been carried out using finite element (Das and Bhattacharjee 2003), Monte Carlo (Sinyagin et al 2005;Balthasar et al 2005), and stochastic methods (Morgan et al 2005(Morgan et al , 2007.…”