Aggregation kinetics at sedimentation: the impact of particles diffusion

TL;DR

This paper develops a theoretical and numerical framework to analyze how particles aggregate during sedimentation, considering both diffusion and advection, across different regimes characterized by Peclet numbers.

Contribution

It introduces a combined analytical and numerical approach to determine aggregation rates over the full range of Peclet numbers, bridging diffusion-dominated and advection-dominated regimes.

Findings

Analytical expressions for aggregation rates at small and large Peclet numbers.

Numerical simulations agree well with theoretical predictions across four orders of magnitude.

Provides a comprehensive model for particle aggregation during sedimentation.

Abstract

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.