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Coalescence of particles by differential sedimentation | | P. Horvai
; S. V. Nazarenko
; T. H. M. Stein
; | | Date: |
18 May 2007 | | Subject: | Statistical Mechanics (cond-mat.stat-mech) | | 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, 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. | | Source: | arXiv, arxiv.0705.2618 | | Services: | Forum | Review | PDF | Favorites | |
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