Aggregation Kinetics in Sedimentation: Effect of Diffusion of Particles

N. V.  Brilliantov; Бриллиантов Н. В.; R. R. Zagidullin; Загидуллин Р. Р.; S. A. Matveev; Матвеев С. А.; A. P. Smirnov; Смирнов А. П.

doi:10.31857/S0044466923040051

Aggregation Kinetics in Sedimentation: Effect of Diffusion of Particles

Authors: Brilliantov N.V.¹^,2, Zagidullin R.R.¹^,3, Matveev S.A.³^,4, Smirnov A.P.³
Affiliations:
1. Skolkovo Institute of Science and Technology
2. University of Leicester
3. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
4. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences
Issue: Vol 63, No 4 (2023)
Pages: 629-638
Section: МАТЕМАТИЧЕСКАЯ ФИЗИКА
URL: https://journals.rcsi.science/0044-4669/article/view/136166
DOI: https://doi.org/10.31857/S0044466923040051
EDN: https://elibrary.ru/IPBWKP
ID: 136166

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Abstract
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References
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Abstract

The aggregation kinetics of settling particles is studied theoretically and numerically using the advection–diffusion equation. Agglomeration caused by these mechanisms (diffusion and advection) is important for both small particles (e.g., primary ash or soot particles in the atmosphere) and large particles of identical or close size, where the spatial inhomogeneity is less pronounced. Analytical results can be obtained for small and large Péclet numbers, which determine the relative importance of diffusion and advection. For small numbers (spatial inhomogeneity is mainly due to diffusion), an expression for the aggregation rate is obtained using an expansion in terms of Péclet numbers. For large Péclet numbers, when advection is the main source of spatial inhomogeneity, the aggregation rate is derived from ballistic coefficients. Combining these results yields a rational approximation for the whole range of Péclet numbers. The aggregation rates are also estimated by numerically solving the advection–diffusion equation. The numerical results agree well with the analytical theory for a wide range of Péclet numbers (extending over four orders of magnitude).

Keywords

coagulation kernel, spatial inhomogeneity, Péclet number

References

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