Size segregation of granular matter in silo discharges

Samadani, Azadeh; Pradhan, Arpan; Kudrolli, Arshad

doi:10.1103/physreve.60.7203

Cited by 98 publications

(64 citation statements)

References 23 publications

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“…Segregation has been observed in most flows of granular mixtures, including granular convection (Knight et al, 1993), hopper flows (Gray and Hutter, 1997a;Makse et al, 1997b;Samadani et al, 1999;Samadani and Kudrolli, 2001), flows in rotating drums (Choo et al, 1997;Hill, 1997;Zik et al, 1994), and even in freely cooling binary granular gases (Catuto and Marconi, 2004). Segregation among large and small particles due to shaking has been termed "Brazil nut effect" (Rosato et al, 1987).…”

Section: Models Of Granular Segregationmentioning

confidence: 99%

Patterns and collective behavior in granular media: Theoretical concepts

2006

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Granular materials are ubiquitous in our daily lives. While they have been a subject of intensive engineering research for centuries, in the last decade granular matter attracted significant attention of physicists. Yet despite a major efforts by many groups, the theoretical description of granular systems remains largely a plethora of different, often contradicting concepts and approaches. Authors give an overview of various theoretical models emerged in the physics of granular matter, with the focus on the onset of collective behavior and pattern formation. Their aim is two-fold: to identify general principles common for granular systems and other complex non-equilibrium systems, and to elucidate important distinctions between collective behavior in granular and continuum pattern-forming systems.

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Section: Models Of Granular Segregationmentioning

confidence: 99%

Patterns and collective behavior in granular media: Theoretical concepts

2006

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“…2 and Eq. (4) applied to granular drainage in a quasitwo-dimensional silo with a narrow opening, far from the side walls, as in the experiments of Samadani et al (1999) and Choi et al (2004). For simplicity, we simulate the model in two dimensions (d h = 1) using uniform spots with the parameters determined from experiments above (w = 0.0024, d s = 5d, b = 1.3d).…”

Section: Spot Simulationsmentioning

confidence: 99%

The Spot Model for random-packing dynamics

Bazant

2006

Mechanics of Materials

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The diffusion and flow of amorphous materials, such as glasses and granular materials, has resisted a simple microscopic description, analogous to defect theories for crystals. Early models were based on either gas-like inelastic collisions or crystal-like vacancy diffusion, but here we propose a cooperative mechanism for dense random-packing dynamics, based on diffusing "spots" of interstitial free volume. Simulations with the Spot Model can efficiently generate realistic flowing packings, and yet the model is simple enough for mathematical analysis. Starting from a non-local stochastic differential equation, we derive continuum equations for tracer diffusion, given the dynamics of free volume (spots). Throughout the paper, we apply the model to granular drainage in a silo, and we also briefly discuss glassy relaxation. We conclude by discussing the prospects of spot-based multiscale modeling and simulation of amorphous materials.Dedicated to Prager Medalist, Salvatore Torquato.

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“…On the other hand, the diffusive void model [4,5] takes a particle approach, in which 'voids' injected at the orifice cause drainage by diffusing upward and exchanging position with particles along the way. Averaging over the void trajectories yields the same continuum velocity field for particles as the 'kinematic model' [6,8], which provides a reasonable fit to experimental data with only one fitting parameter (the diffusion length, b) [5,6,9,10], although the void model on a regular lattice (as in Ref. [11]) underpredicts its value [12].…”

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Diffusion and Mixing in Gravity-Driven Dense Granular Flows

et al. 2004

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We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from super-diffusion to normal diffusion, as a function of the distance fallen, independent of the flow speed. In the superdiffusive (but sub-ballistic) regime, which occurs before a particle falls through its diameter, the displacements have fat-tailed and anisotropic distributions. In the diffusive regime, we observe very slow cage breaking and Péclet numbers of order 100, contrary to the only previous microscopic model (based on diffusing voids). Overall, our experiments show that diffusion and mixing are dominated by geometry, consistent with fluctuating contact networks but not thermal collisions, as in normal fluids.PACS numbers: PACS number(s): 45.70.Mg, Granular flow is an attractively simple and yet surprisingly complex subject [1]. Fast, dilute flows are known to obey classical hydrodynamics (with inelastic collisions), but slow, dense flows pose a considerable challenge to theorists, due to many-body interactions and non-thermal fluctuations. Beyond their fundamental scientific interest, such flows have important engineering applications [2], e.g. to new pebble-bed nuclear reactors [3], whose efficiency and safety depend on the degree of mixing in very slow granular drainage (< 1 pebble/min).Although dense granular drainage is very familiar (e.g. sand in an hourglass), it is far from fully understood. Over the past forty years, a number of theoretical approaches have been proposed for steady state flow [4,5,6,7,8]. Continuum approaches are based on the critical-state theory of soil mechanics and yield only mean velocity fields [7,8]. On the other hand, the diffusive void model [4, 5] takes a particle approach, in which 'voids' injected at the orifice cause drainage by diffusing upward and exchanging position with particles along the way. Averaging over the void trajectories yields the same continuum velocity field for particles as the 'kinematic model ' [6, 8], which provides a reasonable fit to experimental data with only one fitting parameter (the diffusion length, b) [5,6,9,10], although the void model on a regular lattice (as in Ref. [11]) underpredicts its value [12]. Remarkably, these models depend only on geometry and not on momentum, energy, etc.In spite of the success of the kinematic model, however, its only microscopic basis, the void model, greatly overpredicts diffusion. To see this, consider the Péclet number, Pe x = v z d/D x , the dimensionless ratio of advection in uniform downward flow of speed, v z , to diffusion with a horizontal diffusivity, D x , at the scale of a particle diameter, d. In the void model, when a particle falls a distance ∆h, Pe x = (∆h/∆t)d/( ∆x 2 /2∆t) = ∆h 2d/ ∆x 2 , is of order one for any conceivable packing since ∆h ≈ ∆x ≈ d, and therefore it diffuses horizontally by roughly √ ∆h. This prediction is contradicted by ev- eryday experience and our experiments below, which exhibit far less mixing. ...

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Size segregation of granular matter in silo discharges

Cited by 98 publications

References 23 publications

Patterns and collective behavior in granular media: Theoretical concepts

Patterns and collective behavior in granular media: Theoretical concepts

The Spot Model for random-packing dynamics

Diffusion and Mixing in Gravity-Driven Dense Granular Flows

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