Numerical simulation of formation and growth of fractal-like aggregates in a tubular aerosol reactor

Ceramic powders produced by gas phase synthesis frequently consist of non-spherical, fractal-like particle aggregates. Their shape is a result of the simultaneous action of particle coagulation and sintering. Coagulation describes the process of particle agglomeration, e.g. due to ballistic or diffusion-limited collisions, whereas sintering stands for coalescence of primary particles and acts to create denser aggregates. A low density aggregate has a larger collisional cross-section and thus is more likely to collide with other particles or aggregates, which is reflected in the development of the aggregate size distribution and should be taken into account when modeling the process. To this end, a class method based population balance modeling approach available in OpenFOAM was extended to allow for a simplified bivariate treatment. Among the many shape-characterizing parameters, the average surface-area-to-volume ratio of each size class is tracked by a separate transport equation. Together with a fixed fractal dimension, it can be translated into a collisional diameter and further used when calculating coagulation rates. The functionality is showcased by a simulation of the vapor synthesis of Titania in a tubular aerosol reactor [Akhtar et al., AlChE J., 37(10): 1561-1570, 1991]. Data from a differential mobility sizer is used to validate the approach.