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

In this paper we investigated a stochastic particle method (SPM) for solving an extension to the sintering–coagulation equation and modelled two particle systems: the production of SiO₂ and TiO₂. A new mass-flow stochastic algorithm to find numerical solutions to the particle model is stated. The stochastic method calculates fully the evolution of the bivariate particle size distribution (PSD) and is computationally very efficient in comparison to traditional finite element methods. The SPM was compared to a bivariate sectional method for a system with coagulation and sintering as the only mechanisms. The results obtained agree closely to those in the literature and were obtained in a small fraction of the time. An extended model with particle inception and surface growth was then used to model the TiCl₄ → TiO₂ system under various conditions. At low precursor concentration the effect of varying temperature was investigated, whilst at high precursor concentration the effect of surface growth on the system was explored. The results agree well with the conclusions reached previously in the literature.

Keywords: :

• Nanoparticles
• Particle size distribution
• Stochastic processes
• Flame synthesis

Acknowledgments

The authors would like to thank the EPSRC (grant number GR/R85662/01) for the financial support of Neal Morgan under the title ‘Mathematical and Numerical Analysis of Coagulation-Diffusion Processes in Chemical Engineering' and the Oppenheimer Fund for the support of Clive Wells.