We use a recently introduced[[i]] hybrid particle-number and detailed particle model for the Monte Carlo simulation of particle formation and growth in the combustion synthesis of titanium dioxide. In the hybrid model, the particle type space is split to facilitate resolving the particle size distribution under conditions where the process rates are large, such as those used for industrial synthesis[[ii]]. A particle-number model is used to track small primary particles formed through rapid inception, and a discrete ensemble of particles, described by a detailed particle model, is used to track high-dimensional aggregate morphology. The new model solves numerical problems in the Monte Carlo algorithm caused by rapid growth of the small particles. We show that this new method can be applied to study aggressive process conditions, allowing mapping of interesting regions of the process rates space.
[i] Boje, A., Akroyd, J., Kraft, M, A hybrid particle-number and particle model for efficient solution of population balance equations, Journal of Computational Physics, in press (2019).
[ii] Boje, A., Akroyd, J., Sutcliffe, S., Edwards, J., Kraft, M, Detailed Population Balance Modelling of TiO2 Synthesis in an Industrial Reactor, Chemical Engineering Science 164 (2017) 219–231.