Time-dependent solutions for particle-size segregation in shallow granular avalanches

Gray, J.O.; Shearer, Michael; Thornton, Anthony Richard

doi:10.1098/rspa.2005.1580

Cited by 53 publications

(38 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Both Savage and Lun [10] and Bridgwater et al [49] tried to construct exact solutions in the absence of diffusion using the method of characteristics. These were only partially successful, although later attempts have generated complete time and spatially dependent exact solutions in both uniform and non-uniform flows [54][55][56][57][58]. A review of the results in the absence of diffusion is provided in [47].…”

Section: R é S U M émentioning

confidence: 99%

“…When D r = 0 it is possible to use the method of characteristics to construct two-dimensional steady-state [54,55,71] as well as fully time-dependent solutions [56,57], which have evolving expansion fans and concentration shocks. Asymmetric flux functions [49,69,71,73,77] give rise to additional one-sided shocks (or semi-shocks) and adjacent expansion fans [62,71], which significantly enhance the distance over which segregation occurs.…”

Section: Segregation In Bidisperse Mixturesmentioning

confidence: 99%

See 1 more Smart Citation

Debris flows: Experiments and modelling

Turnbull

Bowman

McElwaine

2014

Comptes Rendus. Physique

View full text Add to dashboard Cite

Section: R é S U M émentioning

confidence: 99%

Section: Segregation In Bidisperse Mixturesmentioning

confidence: 99%

Debris flows: Experiments and modelling

Turnbull

Bowman

McElwaine

2014

Comptes Rendus. Physique

View full text Add to dashboard Cite

“…When there is no diffusive remixing (z 0 = 0), the particles separate out to form two distinct inversely graded layers with all the large particles on top of all the fines and a sharp concentration jump at z = φ m . This is the case that Savage & Lun (1988), Gray & Thornton (2005), Thornton et al (2006) and Gray, Shearer & Thornton (2006) investigated theoretically and experimentally. At the opposite extreme, when there is no segregation (z 0 −→ ∞), the particles are uniformly distributed with concentration φ = φ m throughout the depth of the avalanche.…”

Section: Steady-state Solutions For Uniform Flowsmentioning

confidence: 99%

Particle-size segregation and diffusive remixing in shallow granular avalanches

2006

View full text Add to dashboard Cite

Segregation and mixing of dissimilar grains is a problem in many industrial and pharmaceutical processes, as well as in hazardous geophysical flows, where the sizedistribution can have a major impact on the local rheology and the overall run-out. In this paper, a simple binary mixture theory is used to formulate a model for particlesize segregation and diffusive remixing of large and small particles in shallow gravitydriven free-surface flows. This builds on a recent theory for the process of kinetic sieving, which is the dominant mechanism for segregation in granular avalanches provided the density-ratio and the size-ratio of the particles are not too large. The resulting nonlinear parabolic segregation-remixing equation reduces to a quasi-linear hyperbolic equation in the no-remixing limit. It assumes that the bulk velocity is incompressible and that the bulk pressure is lithostatic, making it compatible with most theories used to compute the motion of shallow granular free-surface flows. In steady-state, the segregation-remixing equation reduces to a logistic type equation and the 'S'-shaped solutions are in very good agreement with existing particle dynamics simulations for both size and density segregation. Laterally uniform time-dependent solutions are constructed by mapping the segregation-remixing equation to Burgers equation and using the Cole-Hopf transformation to linearize the problem. It is then shown how solutions for arbitrary initial conditions can be constructed using standard methods. Three examples are investigated in which the initial concentration is (i) homogeneous, (ii) reverse graded with the coarse grains above the fines, and, (iii) normally graded with the fines above the coarse grains. Time-dependent twodimensional solutions are also constructed for plug-flow in a semi-infinite chute.

show abstract

“…A range of two-dimensional steady-state [19,39] and timedependent [40,41,42] exact solutions have been constructed. A highlight of the theory is its ability to predict the formation of breaking size segregation waves, which form whenever small particles are sheared over large ones [43,29,44] as shown in the sequence of images in figure 5.…”

Section: Segregation In Two-component Mixturesmentioning

confidence: 99%

A hierarchy of particle-size segregation models: From polydisperse mixtures to depth-averaged theories

Gray¹

2013

AIP Conference Proceedings

View full text Add to dashboard Cite

Numerical study on the axial segregation dynamics of a binary-size granular mixture in a three-dimensional rotating drum Physics of Fluids 29, 103302 (2017) Abstract.Particle size segregation in granular avalanches occurs due to inter-particle percolation and squeeze expulsion. The general theory for a polydisperse mixture yields a segregation equation for each grain size class. For a three constituent mixture of large, small and medium sized particles there are three segregation equations, one of which can be eliminated, since the concentrations of all the species necessarily sums to unity. The remaining two coupled parabolic equations can be solved using a standard Galerkin finite element method. Numerical solutions show that small particles percolate to the base of the avalanche, large particles are squeezed to the surface and the medium sized grains are sandwiched in between. For certain choices of the segregation parameters it is possible to generate instabilities that lead to saw-tooth segregation in the threephase mixture, but these die off as the grains separate into bi-disperse sub-mixtures. In general, all the grains contribute to the segregation process and develop an inversely graded particle size distribution, that coarsens upwards. This is known as reverse distribution grading. Sometimes, however, the fine particles may not segregate readily, leading to reverse coarse tail grading. For a bi-disperse mixture, the general theory yields one independent segregation equation, which always seeks to drive the particles into an inversely graded state. However, when the bulk flow shears small particles over the top of large, a breaking size-segregation wave is created. Such waves are important close to flow fronts, because they allow large particles that are over-run to rise up to the surface again and be recirculated. Computing the evolving particle-size distribution in a three-dimensional flow is still a challenge. However, it is possible to obtain a simplified representation by integrating the segregation equation through the avalanche depth. This fits naturally into the depth-averaged framework of avalanche models and opens the door to fully couple calculations to study levee formation and segregation induced flow fingering.

show abstract

Time-dependent solutions for particle-size segregation in shallow granular avalanches

Cited by 53 publications

References 20 publications

Debris flows: Experiments and modelling

Debris flows: Experiments and modelling

Particle-size segregation and diffusive remixing in shallow granular avalanches

A hierarchy of particle-size segregation models: From polydisperse mixtures to depth-averaged theories

Contact Info

Product

Resources

About