A multidimensional population balance model to describe the aerosol synthesis of silica nanoparticles

The aim of this work is to present a new detailed multivariate population balance model to describe the aerosol synthesis of silica nanoparticles from tetraethoxysilane (TEOS). The new model includes a chemical representation of the silica particles to facilitate a detailed chemical description of particle processes. Silica nanoparticles are formed by the interaction of silicic acid monomers (Si(OH)4) in the gas-phase as reported in a previous study. A multidimensional population balance model is developed where 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, i.e., the number of Si, free O and OH units. Different particle processes, such as inception, surface reaction, coagulation, sintering, and intra-particle reactions, are formulated from first-principles that alter the particle ensemble and are two-way coupled to the gas-phase. The free parameters in the model are estimated by fitting the model response to experimental values of collision and primary particle diameters using low discrepancy Sobol sequences followed by the simultaneous perturbation stochastic approximation algorithm. The simulation results are finally presented at different process conditions. A strong dependence of particle properties on process temperature and inlet concentration is observed. The desirable operating conditions for different industrial applications are also highlighted. This work illustrates the significance of adopting a multidimensional approach to understand, and hence control, complex nanoparticle synthesis processes.