On the relevance of accounting for the evolution of the fractal dimension in aerosol process simulations

A population balance model is presented, which tracks particle growth in the gas phase and accounts for simultaneous agglomeration and sintering: Simulations reveal the evolution of the full distribution of a volume equivalent diameter and, amongst others, the evolution of the agglomerate collision diameter, a mean primary particle size and the number of primary particles per agglomerate. Furthermore, assuming fractal behaviour of the growing agglomerate particles—for the first time—a model for the evolution of a mean value of the fractal dimension based on physical and process parameters is proposed and incorporated into the simulation model. PARSIVAL, a commercial solver for integro-differential equations is employed to solve the equations involved. It is based on a generalised finite-element scheme with self-adaptive grid- and order construction. Calculations are performed to validate the model against monodisperse and sectional models published in literature for the exemplary case of Si production. The results are in good agreement if the same simplifying assumptions are made. However, results obtained from the new model for both—isothermal and non-isothermal process conditions—clearly show that it is important to consider the changing fractal dimension in many cases.