On a multivariate population balance model to describe the structure and composition of silica nanoparticles

The aim of this work is to present the mathematical description of a detailed multivariate population balance model to describe the structure and composition of silica nanoparticles. A detailed numerical study of a stochastic particle algorithm for the solution of the multidimensional population balance model is presented. Each particle is described by its constituent primary particles and the connectivity between these primaries. Each primary in turn has internal variables that describe its chemical composition. The algorithms used to solve the population balance equations and to couple the population balance model to gas-phase chemistry are described. Numerical studies are then performed for a number of functionals calculated from the model to establish the convergence with respect to the numerical parameter that determines the number of computational particles in the system. The computational efficiency of the model is found to render it applicable to the simulation of industrial scale systems.

► Detailed model for synthesis of silica nanoparticles (SiNP) is presented.
► Consists of kinetic model (KM) and a multidimensional population balance model (PBM).
► KM and PBM describe the gas-phase and structure/composition of SiNP, respectively.
► KM and PBM solution algorithms described along with their coupling algorithm.
► Convergence of various functionals with respect to different parameters reported.