Authors: Astrid Boje and Markus Kraft*

• Particle models are compared, highlighting models that resolve structure
• Numerical methods for solving the population balance equation are discussed
• Detailed population balance modelling using Monte Carlo methods is reviewed
• Developments in coupling the gas and particle phases are described

Particle formation and growth by chemical reactions and physical processes has implications spanning properties of industrial chemicals, human health, and environmental impact. It has been the subject of scientific scrutiny for many years with incremental developments in understanding driven by both experimental and numerical characterisation. Of the developed numerical methods, this review paper will focus on Monte Carlo methods, which are best suited to simultaneous, extensive characterisation of both chemistry and particle geometry in organic and inorganic systems, with other population balance modelling strategies discussed to contextualise the stochastic approach. We outline the high-dimensional particle models used to resolve the typically fractal-like, complex aggregate structure of particles produced by flame synthesis, and describe key features, advancements and limitations of the stochastic numerical methods that can accommodate practically arbitrarily many internal particle coordinates. We summarise a decade of our work in this area, and show how this so-called detailed population balance modelling approach provides close agreement with experimental flame measurements under a range of conditions and enables study of industrially relevant systems. Challenges remain, for example in treating flow-chemistry-particle coupling, and these are discussed in the context of the existing simulation strategies and future directions.

• This paper draws from preprint 278: Detailed modelling of aerosol growth dynamics
• Access the article at the publisher: DOI: 10.1016/j.jaerosci.2021.105895

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