Granular Physics
With this powerful code, I have studied a number of granular systems. Because of a lack of a general theory of granular materials, we have turned to simulation to elucidate the essential characteristics of various types of granular flow.
Our model hopper system is pictured here. It is a
periodic system with initially cylindrical walls that eventually form a
funnel. Gravity is in the downward direction. Particles flow out
through the funnel at the bottom and settle on the top of the pile at
the top. We can thus easily attain steady state in this geometry. The
example on the left is for 40,000 particles of diameter d in a cylinder
of radius 10d that narrows to an opening of radius 3d.
We are principally interested in exploring the characteristics of the flow in this geometry. We observe plug flow as particles flow through the system, but the specifics of this flow are dependent on the particle-wall friction. This system has been used as a model system to study the approach to jamming in 2D, and we wish to do the same in 3D. We have studied P(f) force distributions for a range of flow rates and compared the result to the jammed case. We find that while there is a significant difference between the jammed system and the flowing system, the distribution of forces in the flowing system is insensitive to the flow rate. By contrast, the distribution of impulses, P(i), is very sensitive to the flow rate, but in a manner opposed to the theoretical prediction. We have also studied the stress distribution in the flow.
We plan to measure the distribution of impulses between particles and between particles and the wall. Because the system undergoes plug flow in the upper part of the silo, the initial mixing is very small, but this increases as the radius of the container changes in the funnel region.
Hopper flow has also been studied in depth in two dimensions by several other groups. Longhi et al (Smith and UMass Amherst) performed experiments in a 2D hopper system to measure the impulse as the system approaches jamming. Ferguson et al (Brandeis) performed 2D simulations and found a changing impulse distribution as the system approaches jamming. Other work by Denniston and Li has also studied this problem.
We have recently begun a collaboration with Martin Bazant and Ruben Rosales of MIT and Arshad Kudrolli of Clark University to study the physics of hopper flow. We are exploring in detail the physical characteristics of hopper flow and comparing them to theoretical models. This has many applications, one of which is the pebble bed nuclear reactor.
"Forces in Granular Hopper Flow"; APS March Meeting; Austin, TX; March 3, 2003 (pdf, html)
Here is a sample packing in a cylindrical container
of 20,000 particles. The container has radius 10d, where d is the
diameter of a particle. We can construct these packings in a variety of
ways, from pouring to sedimentation to arrest of flowing piles.
There are a number of issues associated with packings. One important issue is the form of the vertical stress distribution in a packing. Janssen in 1895 predicted a simple exponential form with one free parameter. We showed that this form is not appropriate for packings constructed in a general manner: there is a hydrostatic-like region of linear stress with depth at the top of the pile that does not follow the Janssen form.
Other issues we have considered are the effects of dimension on granular packs. Fully two-dimensional packings have different properties than three-dimensional packings, though quasi two-dimensional packings (packings constructed between sheets of glass) rapidly become very similar to three-dimensional packings as one increases the separation between the plates.
There has also been a lot of interest in the force distribution in a granular packing. Numerous experiments have measured P(f), the distribution of forces in a packing. We measured this for our simulations and showed the effects on small forces of friction.
"Dimensionality effect on stress in granular packings"; JWL, G. S. Grest, and S. J. Plimpton; submitted to Powder Technology; cond-mat/0302115
"Confined granular packings: structure, stress, and forces"; JWL, G. S. Grest, L. E. Silbert, and S. J. Plimpton; accepted for Phys. Rev. E; cond-mat/0211218
"Statistics of the contact network in frictional and frictionless granular packings"; L. E. Silbert, G. S. Grest, and JWL; Phys. Rev. E 66, 061303 (2002); cond-mat/0208462
Chute flow has been extensively studied by the
granular physics group at Sandia, by both myself and others. My
contribution to this large effort focused on understanding the behavior
of the flow at both initiation and cessation of flow. In both cases,
the flow is controlled by actions at the base of the pack. In
initiation of flow, the packing first breaks at the bottom, causing the
upper parts of the packing to ride along as a plug that is eventually
broken up. In cessation of flow, the pack freezes first at the bottom
of the pack, and this trapping front propagates up to the top of the
pile.
Recently we have been investigating the role of clusters in chute flow. There are a variety of cluster definitions, ranging from number of contacts to Voronoi constructions, and we have been using these to more completely characterize the rheology of the flow. The precise definition of clusters in a granular flow is a very complicated problem.
"Granular flow down a rough inclined plane: transition between thin and thick piles"; L. E. Silbert, JWL, and G. S. Grest; Phys. Fluids 15, 1, (2003); cond-mat/0206188
This work was supported by the Division of Materials Science and Engineering, Basic Energy Sciences, Office of Science, U.S. Department of Energy. This collaboration was performed under the auspices of the DOE Center of Excellence for the Synthesis and Processing of Advanced Materials. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.