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August 20, 1995 Press Contact: Steve Koppes
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Clues About How a Sand Pile Holds Itself Up:Scientists Get 3-D View of Force Chains in Granular Materials

Scientists at the University of Chicago and AT&T Bell Laboratories have for the first time gained an understanding of how forces are distributed in granular materials–how a sand pile holds itself up, or how stresses are distributed throughout grain in a silo, for example. The research was published in the Friday, July 28, issue of the journal Science.

Understanding the physics of the behavior of granular materials is of vital importance to industries ranging from agriculture and mining to construction and pharmaceuticals. “Granular materials are not exactly liquid and not exactly solid,” said Susan Coppersmith, one of the co-authors of the study. Coppersmith, formerly of AT&T Bell Laboratories, joined the University of Chicago faculty on Aug. 1. “You can pour sand like a liquid, but at the same time you can stand on the sand on a beach–most people have a hard time standing on the water. We wanted to know how the force is distributed when someone walks on a beach, or when you pile up grain in a silo, for example.”

Sidney Nagel, a co-author of the study and Professor of Physics at Chicago, said, “These questions are of crucial importance to industry, particularly in designing containers to hold and transport granular materials and for beginning to understand how materials flow–and even more importantly, why they stop flowing.”

Nagel and Coppersmith, along with their collaborators, conducted experiments and devised a model that clearly shows the forces are concentrated along lines called “force chains.” The researchers were also able to characterize the distribution of these forces and found that the frequency of very large forces falls off exponentially.

Nagel said, “In a solid crystal, the distribution of forces is homogenous–the same everywhere. If the distribution of forces in a granular material were fractal–that is, a sparse set of networks that go all the way to the bottom–you might find very large forces in one place and none next to it. What we found is that the force distribution is actually something in between those extremes.”

In one experiment, the scientists took advantage of the property that Plexiglas rotates polarized light when it is under pressure, called “stress-induced birefringence.” They placed Plexiglas beads in a fluid–a mixture of glycerol and water–that prevented the beads from scattering light randomly. The beads were placed in a cylinder with two crossed polarizers, one at either end. Without pressure on the cylinder, no light is transmitted through it. But under pressure, the beads rotate the polarized light proportionally to the amount of stress placed on them, and the force chains become visible.

To determine the distribution of forces, the physicists used carbon paper placed under a cylinder filled with beads. When pressure was applied to the top of the cylinder, the researchers found that the area of the mark left by a bead was roughly proportional to the weight supported by that bead.

They used these observations to construct a theoretical model of how the system behaved.

Nagel said, “What we would really like to understand, and what is absolutely crucial in industry, is how does granular material flow? But that is something that is more complicated than we have been able to look at so far. But understanding what the forces are that hold the pile stationary is a first step in beginning to understand the behavior when it’s flowing. And when material gets stuck in a hopper and clogs up, that is because of the force distribution in a stationary pack.”

Chu-Heng Liu, now at Exxon Research and Engineering Company, conducted the experiments under the direction of Nagel when he was a graduate student at the University of Chicago. Other collaborators include Satya Majumdar, now at Yale University, and Onuttom Narayan, now at the University of California at Santa Cruz–both of whom were postdoctoral fellows at AT&T Bell Laboratories–David Schecter, a Chicago undergraduate student, and Thomas Witten, Professor of Physics at Chicago.

The research was supported by the University of Chicago Materials Research Science & Engineering Center, sponsored by the National Science Foundation.
Last modified at 03:50 PM CST on Wednesday, June 14, 2000.

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