Scalar Conservation Laws with Nonconstant Coefficients with Application to Particle Size Segregation in Granular Flow

May, Lindsay B. H.; Shearer, Michael; Daniels, Karen E.

doi:10.1007/s00332-010-9069-7

Cited by 26 publications

(10 citation statements)

References 17 publications

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“…Bridgwater, Foo & Stephens 1985;Savage & Lun 1988;Bridgwater 1994;Dolgunin & Ukolov 1995;Gray & Thornton 2005;Gray & Chugunov 2006;Thornton et al 2006;May, Shearer & Daniels 2010) all share a similar advection-diffusion structure…”

Section: Continuum Segregation Equation For Bidisperse Mixturesmentioning

confidence: 99%

Asymmetric breaking size-segregation waves in dense granular free-surface flows

et al. 2016

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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. †

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Section: Continuum Segregation Equation For Bidisperse Mixturesmentioning

confidence: 99%

Asymmetric breaking size-segregation waves in dense granular free-surface flows

et al. 2016

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“…13,28,29 In the papers cited the segregation rate is assumed to be proportional to the local shear rate and the experimentally determined velocity profiles are used to solve the continuum model. In these experiments it was not possible to monitor the local volume fraction of the small particles directly, and it had to be inferred via the measured expansion and compaction of the sample.…”

Section: Previous Comparison To the Theorymentioning

confidence: 99%

Modeling of Particle Size Segregation: Calibration Using the Discrete Particle Method

Thornton

Weinhart

Luding

et al. 2012

Int. J. Mod. Phys. C

136

160

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Over the last 25 years a lot of work has been undertaken on constructing continuum models for segregation of particles of different sizes. We focus on one model that is designed to predict segregation and remixing of two differently sized particle species. This model contains two dimensionless parameters, which in general depend on both the flow and particle properties. One of the weaknesses of the model is that these dependencies are not predicted; these have to be determined by either experiments or simulations.We present steady-state simulations using the discrete particle method (DPM) for bi-disperse systems with different size ratios. The aim is to determine one parameter in the continuum model, i.e., the segregation Péclet number (ratio of the segregation velocity to diffusion) as a function of the particle size ratio.Reasonable agreement is found; but, also measurable discrepancies are reported; 1 October 21, 2011 10:39 2 Thornton, Weinhart, Luding and Bokhove mainly, in the simulations a thick pure phase of large particles is formed at the top of the flow. In the DPM contact model, tangential dissipation was required to obtain strong segregation and steady states. Additionally, it was found that the Péclet number increases linearly with the size ratio for low values, but saturates to a value of approximately 7.35.

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“…Golick and Daniels [72] and May et al [104] performed ring shear segregation experiments which showed that under a confining pressure both the velocity profile, u = u(z), and the segregation rate, q = q(z), could have a strong height dependence and exact solutions for this case have been constructed [104,105]. Another interesting feature of these experiments is that they measured the degree of segregation based on the rise and fall of the top plate, which was caused by the grains packing denser in a mixed state than in a pure phase.…”

Section: Segregation In Bidisperse Mixturesmentioning

confidence: 99%