Gray, J.M.N.T. (2001) Granular flow in partially filled slowly rotating drums. Journal of Fluid Mechanics, 441. pp. 1-29. ISSN 0022-1120

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Abstract

In many industrial processes granular materials are mixed together in partially filled slowly rotating drums. In this paper a general theoretical framework is developed for the quasi-two-dimensional motion of granular material in a rotating drum. The key assumption is that the body can be divided into a fluid-like and a solid-like region, that are separated by a non-material singular surface at which discontinuities occur. Experiments show that close to the free surface there is a thin rapidly moving fluid-like avalanche that flows downslope, and beneath it there is a large region of slowly rotating solid-like material. The solid region provides a net transport of material upslope and there is strong mass transfer between the two regions. In the theory the avalanche is treated as a shallow incompressible Mohr–Coulomb or inviscid material sliding on a moving bed at which there is erosion and deposition. The solid is treated as a rigid rotating body, and the two regions are coupled together using a mass jump condition. The theory has the potential to model time-dependent intermittent flow with shock waves, as well as steady-state continuous flow. An exact solution for the case of steady continuous flow is presented. This demonstrates that when the base of the avalanche lies above the axis of revolution a solid core develops in the centre of the drum. Experiments are presented to show how a mono-disperse granular material mixes in the drum, and the results are compared with the predictions using the exact solution.

Item Type: Article
Additional Information: © 2001 Cambridge University Press
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 > 86 Geophysics
Depositing User: Ms Lucy van Russelt
Date Deposited: 04 Aug 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/432

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