Aggregation kinetics at sedimentation: the impact of particles diffusion

We investigate the aggregation kinetics of sedimenting particles theoretically and numerically, using the advection-diffusion equation. Agglomeration, caused by both transport mechanisms (diffusion and advection), is important for small particles, like primary ash or soot particles in atmosphere, and large particles of equal or close size, where the advection mechanism is weak. For small Peclet numbers, which quantify the relative importance of diffusion and advection, we obtain the aggregation rates, as an expansion in Peclet numbers. For large Peclet numbers we use purely ballistic aggregation rates. Combining these results we obtain the rational approximant for the whole range of Peclet numbers. We also compute the aggregation rates by numerically solving the advection-diffusion equation. The results of the numerical simulations are in excellent agreement with the analytical theory for the studied Peclet numbers, varying by four orders of magnitude.