Particle-size segregation in dense granular avalanches

Gray, J.O.; Gajjar, Parmesh; Kokelaar, Peter

doi:10.1016/j.crhy.2015.01.004

Cited by 42 publications

(30 citation statements)

References 98 publications

(153 reference statements)

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“…In many flows, this is small compared to the segregation (Gray & Hutter 1997;Dasgupta & Manna 2011;Wiederseiner et al 2011b;Thornton et al 2012b) and so the non-diffuse solution in which D r = 0 is a useful approximation, with (1.1) reducing to a scalar hyperbolic equation. A full review of the derivation, history and applications of (1.1) can be found in Gray, Gajjar & Kokelaar (2015).…”

Section: Continuum Segregation Equation For Bidisperse Mixturesmentioning

confidence: 99%

Asymmetric flux models for particle-size segregation in granular avalanches

2014

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Debris and pyroclastic flows often have bouldery flow fronts, which act as a natural dam resisting further advance. Counter intuitively, these resistive fronts can lead to enhanced run-out, because they can be shouldered aside to form static levees that self-channelise the flow. At the heart of this behaviour is the inherent process of size segregation, with different sized particles readily separating into distinct vertical layers through a combination of kinetic sieving and squeeze expulsion. The result is an upward coarsening of the size distribution with the largest grains collecting at the top of the flow, where the flow velocity is greatest, allowing them to be preferentially transported to the front. Here, the large grains may be overrun, resegregated towards the surface and recirculated before being shouldered aside into lateral levees. A key element of this recirculation mechanism is the formation of a breaking size-segregation wave, which allows large particles that have been overrun to rise up into the faster moving parts of the flow as small particles are sheared over the top. Observations from experiments and discrete particle simulations in a moving-bed flume indicate that, whilst most large particles recirculate quickly at the front, a few recirculate very slowly through regions of many small particles at the rear. This behaviour is modelled in this paper using asymmetric segregation flux functions. Exact non-diffuse solutions are derived for the steady wave structure using the method of characteristics with a cubic segregation flux. Three different structures emerge, dependent on the degree of asymmetry and the non-convexity of the segregation flux function. In particular, a novel 'lens-tail' solution is found for segregation fluxes that have a large amount of non-convexity, with an additional expansion fan and compression wave forming a 'tail' upstream of the 'lens' region. Analysis of exact solutions for the particle motion shows that the large particle motion through the 'lens-tail' is fundamentally different to the classical 'lens' solutions. A few large particles starting near the bottom of the breaking wave pass through the 'tail', where they travel in a region of many small particles with a very small vertical velocity, and take significantly longer to recirculate. † Email address for correspondence: parmesh.gajjar@alumni.manchester.ac.uk Asymmetric breaking size-segregation waves 461

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Section: Continuum Segregation Equation For Bidisperse Mixturesmentioning

confidence: 99%

Asymmetric flux models for particle-size segregation in granular avalanches

2014

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“…Theoretical comparison.-Current approaches to modeling size segregation use an advection-diffusion equation for φ [40]:…”

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confidence: 99%

Underlying Asymmetry within Particle Size Segregation

et al. 2015

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We experimentally study particle scale dynamics during segregation of a bidisperse mixture under oscillatory shear. Large and small particles show an underlying asymmetry that is dependent on the local particle concentration, with small particles segregating faster in regions of many large particles and large particles segregating slower in regions of many small particles. We quantify the asymmetry on bulk and particle scales, and capture it theoretically. This gives new physical insight into segregation and reveals a similarity with sedimentation, traffic flow, and particle diffusion.

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“…A review of this approach together with a detailed discussion of how it relates to earlier work is provided by Gray, Gajjar & Kokelaar (2015). Mixture theory provides a useful framework, with clear definitions of intrinsic and mixture quantities as well as individual mass and momentum conservation laws for each species of particle.…”

Section: Introductionmentioning

confidence: 99%

Particle-size and -density segregation in granular free-surface flows

Gray

Ancey

2015

J. Fluid Mech.

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When a mixture of particles, which differ in both their size and their density, avalanches downslope, the grains can either segregate into layers or remain mixed, dependent on the balance between particle-size and particle-density segregation. In this paper, binary mixture theory is used to generalize models for particle-size segregation to include density differences between the grains. This adds considerable complexity to the theory, since the bulk velocity is compressible and does not uncouple from the evolving concentration fields. For prescribed lateral velocities, a parabolic equation for the segregation is derived which automatically accounts for bulk compressibility. It is similar to theories for particle-size segregation, but has modified segregation and diffusion rates. For zero diffusion, the theory reduces to a quasilinear first-order hyperbolic equation that admits solutions with discontinuous shocks, expansion fans and one-sided semi-shocks. The distance for complete segregation is investigated for different inflow concentrations, particle-size segregation rates and particle-density ratios. There is a significant region of parameter space where the grains do not separate completely, but remain partially mixed at the critical concentration at which size and density segregation are in exact balance. Within this region, a particle may rise or fall dependent on the overall composition. Outside this region of parameter space, either size segregation or density segregation dominates and particles rise or fall dependent on which physical mechanism has the upper hand. Two-dimensional steady-state solutions that include particle diffusion are computed numerically using a standard Galerkin solver. These simulations show that it is possible to define a Péclet number for segregation that accounts for both size and density differences between the grains. When this Péclet number exceeds 10 the simple hyperbolic solutions provide a very useful approximation for the segregation distance and the height of rapid concentration changes in the full diffusive solution. Exact one-dimensional solutions with diffusion are derived for the steady-state far-field concentration.

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Particle-size segregation in dense granular avalanches

Cited by 42 publications

References 98 publications

Asymmetric flux models for particle-size segregation in granular avalanches

Asymmetric flux models for particle-size segregation in granular avalanches

Underlying Asymmetry within Particle Size Segregation

Particle-size and -density segregation in granular free-surface flows

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