Technical Report 19, c4e-Preprint Series, Cambridge

Authors: Neal M. Morgan, Clive G. Wells, Markus Kraft*, and Wolfgang Wagner

Reference: Technical Report 19, c4e-Preprint Series, Cambridge, 2003

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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 SiO₂ and TiO₂. 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 TiCl₄ to TiO₂ 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.

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