Coalescence of particles by differential sedimentation

Details Coalescence of particles by differential sedimentation Coalescence of particles by differential sedimentation

2007-05-18

arxiv.org/abs/0705.2618v2

Physics

Condensed Matter

Statistical Mechanics

26 pages, 7 figures. Accepted by J.Stat.Phys., 12 November 2007. Sections 2.4 and 3.1 expanded for more elaborate derivation o

Scientific paper

10.1007/s10955-007-9466-y

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, used to study e.g. rain initiation and particle distributions in the atmosphere. We solve the kinetic equation analytically to obtain steady state and self-similar solutions in time and in height, 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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