CiteULike: dchens Bazant

Diffusion and Mixing in Gravity-Driven Dense Granular Flows

Jaehyuk Choi — 2008-01-23T19:08:39-00:00

Physical Review Letters, Vol. 92, No. 17. (27 April 2004), 174301.

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 superdiffusion 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 long-lasting contacts but not thermal collisions; as in normal fluids.

Dynamics of random packings in granular flow

Chris Rycroft — 2008-04-26T23:45:29-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 73, No. 5. (2006)

We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed spot model, where particles in a dense random packing undergo chainlike collective displacements in response to diffusing "spots" of influence, carrying a slight excess of interstitial free volume. We reconstruct the microscopic dynamics of particles from the "coarse grained" dynamics of spots by introducing a localized particle relaxation step after each spot-induced block displacement, simply to enforce packing constraints with a (fairly arbitrary) soft-core repulsion. To test the model, we study to what extent it can describe the dynamics of up to 135 000 frictional, viscoelastic spheres in granular drainage simulated by the discrete-element method (DEM). With only five fitting parameters (the radius, volume, diffusivity, drift velocity, and injection rate of spots), we find that the spot simulations are able to largely reproduce not only the mean flow and diffusion, but also some subtle statistics of the flowing packings, such as spatial velocity correlations and many-body structural correlations. The spot simulations run over 100 times faster than the DEM and demonstrate the possibility of multiscale modeling for amorphous materials, whenever a suitable model can be devised for the coarse-grained spot dynamics.

Analysis of granular flow in a pebble-bed nuclear reactor

Chris Rycroft — 2008-04-26T23:14:59-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 74, No. 2. (2006)

Pebble-bed nuclear reactor technology, which is currently being revived around the world, raises fundamental questions about dense granular flow in silos. A typical reactor core is composed of graphite fuel pebbles, which drain very slowly in a continuous refueling process. Pebble flow is poorly understood and not easily accessible to experiments, and yet it has a major impact on reactor physics. To address this problem, we perform full-scale, discrete-element simulations in realistic geometries, with up to 440 000 frictional, viscoelastic 6-cm-diam spheres draining in a cylindrical vessel of diameter 3.5 m and height 10 m with bottom funnels angled at 30° or 60°. We also simulate a bidisperse core with a dynamic central column of smaller graphite moderator pebbles and show that little mixing occurs down to a 1:2 diameter ratio. We analyze the mean velocity, diffusion and mixing, local ordering and porosity (from Voronoi volumes), the residence-time distribution, and the effects of wall friction and discuss implications for reactor design and the basic physics of granular flow.

A Theory of Cooperative Diffusion in Dense Granular Flows

Martin Bazant — 2007-04-05T21:54:49-00:00

(8 May 2004)

Dilute granular flows are routinely described by collisional kinetic theory, but dense flows require a fundamentally different approach, due to long-lasting, many-body contacts. In the case of silo drainage, many continuum models have been developed for the mean flow, but no realistic statistical theory is available. Here, we propose that particles undergo cooperative displacements in response to diffusing “spots” of free volume. The typical spot size is several particle diameters, so cages of nearest neighbors tend to remain intact over large distances. The spot hypothesis relates diffusion and cage-breaking to volume fluctuations and spatial velocity correlations, in agreement with new experimental data. It also predicts density waves caused by weak spot interactions. Spots enable fast, multiscale simulations of dense flows, in which a small, internal relaxation enforces packing constraints during spot-induced motion. In the continuum limit of the model, tracer diffusion is described by a new stochastic differential equation, where the drift velocity and diffusion tensor are coupled non-locally to the spot density. The same mathematical formalism may also find applications to glassy relaxation, as a compelling alternative to void (or hole) random walks.

Velocity profile of granular flows inside silos and hoppers

Jaehyuk Choi — 2008-03-24T22:32:04-00:00

Journal of Physics: Condensed Matter, Vol. 17, No. 24. (2005), pp. S2533-S2548.

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 allow 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 are 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.

The Spot Model for random-packing dynamics

Martin Bazant — 2008-03-24T22:29:29-00:00

Mechanics of Materials, Vol. 38, No. 8-10. ( 2006), pp. 717-731.

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.