Modeling of silica synthesis in a laminar flame by coupling an extended population balance model with computational fluid dynamics

In the present study, we propose a novel extended population balance equation (PBE) model for aggregation and sintering and couple it with computational fluid dynamics (CFD) to investigate synthesis of silica nanoparticles in a laminar diffusion flame. The extended PBE includes finite-rate sintering of primary particles by solving the PBE together with a transport equation for the number concentration of primary particles. In the process simulated, the particles are formed via the oxidation of a vapor precursor, hexamethyldisiloxane (HMDSO), and the aerosol processes include nucleation, condensation, aggregation and sintering. The model is validated with detailed experimental in-situ SAXS data found in the literature and is also compared with a monodisperse and a two-PBE approach. Good agreement is found between the extended one-PBE and two-PBE models, while both of them provide a substantial improvement over the monodisperse one. Furthermore, the coupled CFD-PBE simulation with the extended one-PBE model reduces substantially the computational time as compared with the two-PBE model and requires less than twice the time needed for the monodisperse model. Excellent agreement is found between numerical predictions and experimental data for temperature along the centerline and reasonably good agreement is found between numerical predictions and SAXS data for primary particle diameters. While results for the particle number concentration are in qualitative agreement with the experimental data, the particle formation rate is overpredicted, leading to an overestimation of the number concentration of the primary particles. This is attributed to uncertainties in the experimental data and precursor decomposition kinetics.