Coalescence of particles by differential sedimentation
Horvai, P., Nazarenko, S. V. and Stein, T. H. M. (2008) Coalescence of particles by differential sedimentation. Journal of Statistical Physics, 130 (6). pp. 1177-1195. ISSN 1572-9613
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To link to this article DOI: 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. 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.