  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.
