Pattern formation in flowing sand

Baxter, G. W.; Behringer, R. P.; Fagert, T; Johnson, G. Allan

doi:10.1103/physrevlett.62.2825

Cited by 228 publications

(109 citation statements)

References 11 publications

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“…Baxter et al found density waves in a hopper only if a certain amount of rough sands is mixed with smooth sands [28]. The role of the rough sands is not clearly established.…”

Section: Density Waves In Hoppersmentioning

confidence: 99%

Density waves in the flows of granular media

Lee

1994

Phys. Rev. E

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We study density waves in the flows of granular particles through vertical tubes and hoppers using both analytic methods and molecular dynamics (MD) simulations. We construct equations of motion for quasi one-dimensional systems. The equations, combined with the Bagnold's law for friction, are used to describe the time evolutions of the density and the velocity fields for narrow tubes and hoppers. The solutions of the equations can have two types of density waves, kinetic and dynamic. For tubes, we can show the existence of kinetic waves, and obtain the condition for dynamic waves for tubes from the equations. For hoppers, we obtain the solutions of the equations up to the first order of the opening angle, which also show the existence of kinetic waves. We reproduce density waves in the MD simulations for tubes. The waves are believed to be kinetic based on a few evidences, including a well defined flux-density curve. In MD simulations of flows in hoppers, we find density waves, which are also believed to be kinetic. 05.40+j, 46.10+z, 62.20-x Typeset using REVT E X 1

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“…Baxter et al found density waves in a hopper only if a certain amount of rough sands is mixed with smooth sands [28]. The role of the rough sands is not clearly established.…”

Section: Density Waves In Hoppersmentioning

confidence: 99%

Density waves in the flows of granular media

Lee

1994

Phys. Rev. E

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“…larger velocity above the orifice than near the stagnant region), as suggested by the shape of some experimental density waves (Baxter et al, 1989). The geometrical spot propagator, P s (x, |z, x 0 , z 0 ), is the conditional probability of finding a spot at horizontal position x once it has risen to a height z from an initial position (x 0 , z 0 ).…”

Section: Statistical Dynamics Of Spotsmentioning

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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“…Beverloo thoroughly investigated the relation between the orifice size and the mass flow rate in cylindrical silos and proposed a formula describing the observed dependence [6]. Using radiography, Baxter, et al observed the density wave in the hopper flow and showed various patterns of the wave depending on the particle roughness and the hopper angle [7].…”

Section: Introductionmentioning

confidence: 99%

Velocity profile of granular flows inside silos and hoppers

Choi

Kudrolli

Bazant

2005

J. Phys.: Condens. Matter

121

103

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Abstract. We measure the flow of granular materials inside a quasi-two dimensional silo as it drains and compare the data with some existing models. The particles inside the silo are imaged and tracked with unprecedented resolution in both space and time to obtain their velocity and diffusion properties. The data obtained by varying the orifice width and the hopper angle allows us to thoroughly test models of gravity driven flows inside these geometries. All of our measured velocity profiles are smooth and free of the shock-like discontinuities ("rupture zones") predicted by critical state soil mechanics. On the other hand, we find that the simple Kinematic Model accurately captures the mean velocity profile near the orifice, although it fails to describe the rapid transition to plug flow far away from the orifice. The measured diffusion length b, the only free parameter in the model, is not constant as usually assumed, but increases with both the height above the orifice and the angle of the hopper. We discuss improvements to the model to account for the differences. From our data, we also directly measure the diffusion of the particles and find it to be significantly less than predicted by the Void Model, which provides the classical microscopic derivation of the Kinematic Model in terms of diffusing voids in the packing. However, the experimental data is consistent with the recently proposed Spot Model, based on a simple mechanism for cooperative diffusion. Finally, we discuss the flow rate as a function of the orifice width and hopper angles. We find that the flow rate scales with the orifice size to the power of 1.5, consistent with dimensional analysis. Interestingly, the flow rate increases when the funnel angle is increased.

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Pattern formation in flowing sand

Cited by 228 publications

References 11 publications

Density waves in the flows of granular media

Density waves in the flows of granular media

The Spot Model for random-packing dynamics

Velocity profile of granular flows inside silos and hoppers

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