A theory for particle size segregation in shallow granular free-surface flows

Gray, J.M.N.T. and Thornton, A.R. (2005) A theory for particle size segregation in shallow granular free-surface flows. Proceedings of the Royal Society A, 461. pp. 1447-1473. ISSN 1364-5021

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Abstract

Granular materials composed of a mixture of grain sizes are notoriously prone to segregation during shaking or transport. In this paper, a binary mixture theory is used to formulate a model for kinetic sieving of large and small particles in thin, rapidly flowing avalanches, which occur in many industrial and geophysical free-surface flows. The model is based on a simple percolation idea, in which the small particles preferentially fall into underlying void space and lever large particles upwards. Exact steady-state solutions have been constructed for general steady uniform velocity fields, as well as time-dependent solutions for plug-flow, that exploit the decoupling of material columns in the avalanche. All the solutions indicate the development of concentration shocks, which are frequently observed in experiments. A shock-capturing numerical algorithm is formulated to solve general problems and is used to investigate segregation in flows with weak shear.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics MSC 2010, the AMS's Mathematics Subject Classification > 86 Geophysics PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 46 Continuum mechanics of solids
Depositing User:	Prof JMNT Gray
Date Deposited:	28 May 2010
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1462

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A theory for particle size segregation in shallow granular free-surface flows. (deposited 24 Mar 2006)
- A theory for particle size segregation in shallow granular free-surface flows. (deposited 28 May 2010) [Currently Displayed]

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