Segregation modeling of particle rapid gravity flow

Dolgunin, V. N.; Ukolov, A. A.

doi:10.1016/0032-5910(94)02954-m

Cited by 124 publications

(144 citation statements)

References 8 publications

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“…This is a significant advantage over other segregation theories (e.g. Savage & Lun 1988;Dolgunin & Ukolov 1995) which are independent of gravity. The theory is designed to be compatible with the assumptions of shallowness, incompressibility and bulk lithostatic pressure, that are made by almost all current avalanche models (e.g.…”

Section: Discussionmentioning

confidence: 94%

“…Not only are these the simplest non-trivial functions that satisfy the constraints (2.10) and (2.11), but, as will be shown in § 2.4, they lead to the same segregation flux function as used by Savage & Lun (1988) and Dolgunin & Ukolov (1995). The second key assumption in Gray & Thornton's (2005) size-segregation model was the form of the interaction drag β µ .…”

Section: Governing Equationsmentioning

confidence: 97%

“…By varying the length of the chute they were able to build up a detailed spatial picture of the size distribution and the evolution towards a fully segregated state, although the binning procedure did not have enough resolution to determine the position of the concentration shocks that they observed through the sidewall. Dolgunin & Ukolov (1995) binned samples from the cascading jet of material as it exited the chute. They claimed that their procedure could measure the outflow velocity, the particle concentration and the solids volume fraction.…”

Section: Comparison With Particle Dynamics Simulationsmentioning

confidence: 99%

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Particle-size segregation and diffusive remixing in shallow granular avalanches

2006

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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.

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Section: Discussionmentioning

confidence: 94%

Section: Governing Equationsmentioning

confidence: 97%

Section: Comparison With Particle Dynamics Simulationsmentioning

confidence: 99%

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Particle-size segregation and diffusive remixing in shallow granular avalanches

2006

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“…(4) combines the particle transport by the bulk velocity and the form of the segregation flux in the dilute limit used in Savage and Lun's [10] formulation, with Bridgwater et al's [49] diffusion and time-dependent term. Dolgunin and Ukolov's [60] model therefore contains all the essential ingredients of the bidisperse segregation models that are used today. Eq.…”

Section: R é S U M émentioning

confidence: 99%

Debris flows: Experiments and modelling

Turnbull

Bowman

McElwaine

2014

Comptes Rendus. Physique

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“…Vallance and Savage [14] showed that solutions to this theory were consistent with experiments on an inclined chute. Dolgunin and Ukolov [35] also wrote down this equation, based on the simple insight that the segregation flux −S ls φ s (1 − φ s ) must shut off, when there are either all small particles, or all large ones. The equation is closely related to Burgers' equation, which Gray and Chugunov [20] exploited, by means of the Cole-Hopf transformation, to construct exact solutions for time-dependent segregation with diffusion.…”

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

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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.

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Segregation modeling of particle rapid gravity flow

Cited by 124 publications

References 8 publications

Particle-size segregation and diffusive remixing in shallow granular avalanches

Particle-size segregation and diffusive remixing in shallow granular avalanches

Debris flows: Experiments and modelling

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

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