Gray, JMNT and Shearer, M and Thornton, AR
(2006)
*Time-dependent solutions for particle size segregation in shallow granular avalanches.*
Proceedings of the Royal Society A, 462.
pp. 947-972.
ISSN 1364-5021

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## Abstract

Rapid shallow granular free-surface flows develop in a wide range of industrial and geophysical flows, ranging from rotating kilns and blenders to rock-falls, snow slab-avalanches and debris-flows. Within these flows, grains of different sizes often separate out into inversely graded layers, with the large particles on top of the fines, by a process called kinetic sieving. In this paper, a recent theory is used to construct exact time-dependent two-dimensional solutions for the development of the particle-size distribution in inclined chute flows. The first problem assumes the flow is initially homogeneously mixed and is fed at the inflow with homogeneous material of the same concentration. Concentration shocks develop during the flow and the particles eventually separate out into inversely graded layers sufficiently far downstream. Sections with a monotonically decreasing shock height, between these layers, steepen and break in finite time. The second problem assumes that the material is normally graded, with the small particles on top of the coarse ones. In this case, shock waves, concentration expansions, non-centred expanding shock regions and breaking shocks develop. As the parameters are varied, nonlinearity leads to fundamental topological changes in the solution, and, in simple-shear, a logarithmic singularity prevents a steady-state solution from being attained.

Item Type: | Article |
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Uncontrolled Keywords: | particle-size segregation; kinetic sieving; inverse-grading; shocks |

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: | Prof JMNT Gray |

Date Deposited: | 24 Mar 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/196 |

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