Granular Convection Observed by Magnetic Resonance Imaging

Ehrichs, E. E.; Jaeger, Heinrich M.; Karczmar, G. S.; Knight, James B.; Kuperman, Vadim; Nagel, Sidney R.

doi:10.1126/science.267.5204.1632

Cited by 267 publications

(142 citation statements)

References 24 publications

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“…Nakagawa et al [11] first applied MRI to study the dynamics of granular flow in a rotating cylinder and recorded velocity and density profiles along and perpendicular to the flowing layer of particles. Using a spin-tagging sequence, the flow and diffusion in a vertically shaken container of poppy seeds was recently measured and convection rolls found [12]. Most recently, the shape of the radially and axially segregated core were also investigated by MRI [9,13].…”

Section: Introductionmentioning

confidence: 99%

Shape dynamics of interfacial front in rotating cylinders

Ristow

Nakagawa

1999

Phys. Rev. E

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Section: Introductionmentioning

confidence: 99%

Shape dynamics of interfacial front in rotating cylinders

Ristow

Nakagawa

1999

Phys. Rev. E

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“…Ultimately this can significantly degrade the quality of the resulting products and in some circumstances it can have serious safety implications. There are a number of mechanisms for segregation of dissimilar grains including particle size (Bridgwater 1976), particle density (Drahun & Bridgwater 1983), convection (Ehrichs et al 1995), differential fluid drag (Zhang & Reese 2000), inertia (Thomas 2000;Mobius et al 2001) and collisional condensation (Jenkins 1998). This paper focuses on the competition between gravity-driven size-segregation by kinetic sieving (Bridgwater 1976; Savage & Lun 1988) and diffusive remixing (e.g.…”

Section: Introductionmentioning

confidence: 99%

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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“…Shaking sand may result in size segregation, rich pattern formation [2,3], or creation of convection rolls [4]. Adding a few grains to a sand pile leads to avalanches [5][6][7].…”

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confidence: 99%

Slow relaxation in granular compaction

Ben‐Naim

Knight

Nowak

et al. 1998

Physica D: Nonlinear Phenomena

111

109

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Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density value follows an inverse logarithmic law. We propose a simple stochastic adsorption-desorption process which captures the essential mechanism underlying this remarkably slow relaxation. As the system approaches its final state, a growing number of beads have to be rearranged to enable a local density increase. In one dimension, this number grows as N = ρ/(1 − ρ), and the density increase rate is drastically reduced by a factor e −N . Consequently, a logarithmically slow approach to the final state is found ρ∞ − ρ(t) ∼ = 1/ ln t.

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Granular Convection Observed by Magnetic Resonance Imaging

Cited by 267 publications

References 24 publications

Shape dynamics of interfacial front in rotating cylinders

Shape dynamics of interfacial front in rotating cylinders

Particle-size segregation and diffusive remixing in shallow granular avalanches

Slow relaxation in granular compaction

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