Abstract
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.
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Horvai, P., Nazarenko, S.V. & Stein, T.H.M. Coalescence of Particles by Differential Sedimentation. J Stat Phys 130, 1177–1195 (2008). https://doi.org/10.1007/s10955-007-9466-y
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DOI: https://doi.org/10.1007/s10955-007-9466-y