Technical Report 23, c4e-Preprint Series, Cambridge

Bivariate Stochastic Modelling of Nanoparticles

ref: Technical Report 23, c4e-Preprint Series, Cambridge

Associated Themes: Numerics and Nanoparticles

Abstract

In this paper we find numerical solutions to a generalization of Smoluchowski's coagulation equation using a bivariate massflow stochastic algorithm. Specifically we simulate the growth and morphology of nanoparticles in premixed laminar flames. The our model includes terms for particle inception, surface growth and particle sintering. A test simulation was implemented to examine the stochastic algorithm under various simple starting conditions. The production of SiO2 from a low-pressure premixed laminar flame doped with SiH4 was investigated. A free-molecular kernel was used for the coagulation terms and a grain boundary diffusion model implemented for the particle sintering. The flame itself was simulated using a skeletal H2/O2/Ar mechanism including the SiH4 oxidation reactions. We were able to simulate the transition from a bimodal particle size distribution to a unimodal particle size distribution for the silica particles produced, and predict a value for an effective fractal dimension of silica particles in a flame close to those reported in the experimental literature.

Material from this preprint has been published in: Chemical Engineering Science 61 (1), 158-166, (2006)

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