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).
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Funding
The work by Brilliantov, Zagidullin, and Smirnov (derivation of the equations, formulation of the problem, and the numerical computations) was supported by the Russian Science Foundation (project no. 21-11-00363) and the work by Matveev (construction of the rational approximation) was supported by the Russian Science Foundation (project no. 19-11-00338).
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Translated by I. Ruzanova
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Brilliantov, N.V., Zagidullin, R.R., Matveev, S.A. et al. Aggregation Kinetics in Sedimentation: Effect of Diffusion of Particles. Comput. Math. and Math. Phys. 63, 596–605 (2023). https://doi.org/10.1134/S096554252304005X
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DOI: https://doi.org/10.1134/S096554252304005X