Particle size segregation in granular avalanches: A brief review of recent progress

Hazardous natural flows such as snow avalanches, debris-flows, lahars and pyroclastic flows are part of a much wider class of granular avalanches, that frequently occur in industrial processes and in our kitchens! Granular avalanches are very efficient at sorting particles by size, with the smaller...

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Bibliographic Details
Published in:Proceedings of the IUTAM-ISIMM Symposium 2009-09, Vol.1227, p.343-362
Main Author: Gray, J M N T
Format: Article
Language:English
Subjects:
Avalanches
Breaking
Compressing
Computation
Computer simulation
Construction
Derivation
Diffusion
Diffusion layers
Exact solutions
Feedback
Geophysics
Grains
Hazardous
Joining
Links
Mass flow
Mathematical analysis
Mathematical models
Nonlinear dynamics
Nonlinearity
Particle size
Particle size distribution
Pyroclastic flow
Segregations
Snow avalanches
Sorting
Stratification
Transformations
Two phase
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Summary:Hazardous natural flows such as snow avalanches, debris-flows, lahars and pyroclastic flows are part of a much wider class of granular avalanches, that frequently occur in industrial processes and in our kitchens! Granular avalanches are very efficient at sorting particles by size, with the smaller ones percolating down towards the base and squeezing the larger grains up towards the free-surface, to create inversely-graded layers. This paper provides a short introduction and review of recent theoretical advances in describing segregation and remixing with relatively simple hyperbolic and parabolic models. The derivation from two phase mixture theory is briefly summarized and links are drawn to earlier models of Savage & Lun and Dolgunin & Ukolov. The more complex parabolic version of the theory has a diffusive force that competes against segregation and yields S-shaped steady-state concentration profiles through the avalanche depth, that are able to reproduce results obtained from particle dynamics simulations. Time-dependent exact solutions can be constructed by using the Cole-Hopf transformation to linearize the segregation-remixing equation and the nonlinear surface and basal boundary conditions. In the limit of no diffusion, the theory is hyperbolic and the grains tend to separate out into completely segregated inversely graded layers. A series of elementary problems are used to demonstrate how concentration shocks, expansion fans, breaking waves and the large and small particles paths can be computed exactly using the model. The theory is able to capture the key features of the size distribution observed in stratification experiments, and explains how a large particle rich front is connected to an inversely graded avalanche in the interior. The theory is simple enough to couple it to the bulk flow field to investigate segregation-mobility feedback effects that spontaneously generate self-channelizing leveed avalanches, which can significantly enhance the total run-out distance of geophysical mass flows.
ISSN:0094-243X