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Asymmetric flux models for particle-size segregation in granular avalanches

Published online by Cambridge University Press:  19 September 2014

P. Gajjar  and
J. M. N. T. Gray
P. Gajjar*
Affiliation:
School of Mathematics and Manchester Centre for Nonlinear Dynamics, University of Manchester, Manchester M13 9PL, UK
J. M. N. T. Gray
Affiliation:
School of Mathematics and Manchester Centre for Nonlinear Dynamics, University of Manchester, Manchester M13 9PL, UK
*
†Email address for correspondence: [email protected]
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Abstract

Particle-size segregation commonly occurs in both wet and dry granular free-surface flows through the combined processes of kinetic sieving and squeeze expulsion. As the granular material is sheared downslope, the particle matrix dilates slightly and small grains tend to percolate down through the gaps, because they are more likely than the large grains to fit into the available space. Larger particles are then levered upwards in order to maintain an almost uniform solids volume fraction through the depth. Recent experimental observations suggest that a single small particle can percolate downwards through a matrix of large particles faster than a large particle can be levered upwards through a matrix of fines. In this paper, this effect is modelled by using a flux function that is asymmetric about its maximum point, differing from the symmetric quadratic form used in recent models of particle-size segregation. For illustration, a cubic flux function is examined in this paper, which can be either a convex or a non-convex function of the small-particle concentration. The method of characteristics is used to derive exact steady-state solutions for non-diffuse segregation in two dimensions, with an inflow concentration that is (i) homogeneous and (ii) normally graded, with small particles above the large. As well as generating shocks and expansion fans, the new asymmetric flux function generates semi-shocks, which have characteristics intersecting with the shock just from one side. In the absence of diffusive remixing, these can significantly enhance the distance over which complete segregation occurs.

JFM classification

Mixing: Mixing Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 757 , 25 October 2014 , pp. 297 - 329
Copyright
© 2014 Cambridge University Press 

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