Coalescence of Particles by Differential Sedimentation |
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Authors: | P. Horvai S. V. Nazarenko T. H. M. Stein |
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Affiliation: | (1) Mathematics Institute, University of Warwick, CV4 7AL Coventry, UK |
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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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Keywords: | Coagulation Sedimentation Self-similarity |
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