Modelling of particulate processes
We review models and numerical methods used in flame synthesis of organic and inorganic nanoparticles. We discuss a general model in which particles form in the gas phase and grow through mass-adding surface reactions, condensation, and coagulation. They shrink or reshape by sintering and mass-abstracting surface reactions. The model is formulated in terms of a population balance which can incorporate a range of levels of detail, i.e. a varying number of internal coordinates. These coordinates can not only describe the geometry of a particle but also its chemical composition or age. In the simplest version a particle is modelled as a sphere whereas in the most complicated form a particle is modelled as an agglomerate of smaller or primary particles where the geometrical shape is known exactly. For these population balance models a number of different numerical approaches exist. We review the method of moments, sectional, finite element, and Monte Carlo methods and give examples of their applications in flame synthesis. Different strategies for coupling a population balance to laminar and turbulent flows are reviewed. For turbulent flows the closure problems arising from chemical reactions and the population balance are briefly discussed. We then summarize the literature on nanoparticle modelling from laboratory to industrial scale and highlight important areas for future research.