Number of Neighbors Determines Granular Structure
Grains, powders, and soils can support weight because of stable arrangements of particles within them called bridges. In the 15 July Physical Review Letters, a team shows that these structures are not due to applied forces, gravity, or the details of particle interactions, but instead depend only on the mean number of neighbors each particle has. The researchers imaged the 3-D structures of colloids–small particles suspended in liquid–because their conditions can be varied more widely than those of granular systems. The results should help researchers better understand how soils and other granular matter support weight and also address the process of “jamming” in chutes.
Granular materials seem like they should be homogeneous, but they aren’t. For example, the pressure on the walls of a grain silo varies significantly from place to place. Sometimes the particles jam in a chute, essentially turning the material into a solid. Efforts to understand these complex systems remain heavily reliant on approximations and experimental determinations of critical factors, rather than theoretical derivations of them. A long standing question is whether the arrangement of particles in three dimensions is heavily dependent on the details of each system, such as the type of particles, the force of gravity compacting them in a certain way, or how they fell into a heap in the first place.
One way to address this question is through measuring the particles that allow a granular material to bear weight. The weight of an object sitting on top of a pile of sand, for example, is not born by every particle in the pile, but only by those grains that are members of “bridges,” sets of grains that mutually stabilize one another against a force from a specific direction. They could be arranged like the bricks in an arch, for example, where each one is essential for stability, but there are many other arrangements as well.
To look for similarities among bridges under a wide range of conditions, Stefan Egelhaaf of the Heinrich Heine University in Düsseldorf, Germany, and his colleagues, used 2-micron-diameter, transparent spheres suspended in several different transparent fluids. These colloids allowed the researchers to see inside them with a microscope and to widely vary the conditions by changing the fluid, the particles, and the packing fraction (the percentage of space filled by particles). Reducing the particles’ buoyancy increased the effect of gravity and moved the system from a traditional colloid, which can’t resist any force applied to it, toward a classical granular system, which can sometimes support loads.
Egelhaaf and his colleagues have recently developed an algorithm for assigning particles to bridges based on the 3-D map of particle positions measured in the lab [1]. The algorithm needs to be told the direction of gravity, since an arch is only stable if gravity points down, for example. After finding the bridges, the team looked at the bridge distribution, a plot giving the fraction of particles that are members of bridges of each size. The distribution depended on the parameters the team varied, but they were surprised that they could also predict the distribution with just a single parameter–the coordination number, which is the average number of neighbors for each particle. The team says this seems reasonable, as the coordination number reflects the connectivity of particles, critical for load-bearing ability, whereas other properties, like the packing fraction, measure space filling, which has less relevance.
The researchers investigated the effect of gravity on the bridges by reassigning them assuming gravity pointed sideways or upward for the same particle configurations. The distribution of bridges remained the same, suggesting that bridge structures can form without an outside force being applied, answering a long-standing question. In yet another variant, both amorphous and partially crystalline samples showed the same distributions. Simulations of granular systems showed distributions of bridges that agreed with the experimental observations.
Bob Behringer of Duke University in Durham, North Carolina, says the paper asks whether bridges are “virtual and in the shadows lurking” or assembled entirely in response to an outside force. “This [work] gives a good indication that there are structures not quite at the right place to form bridges, but just a little nudge will let them bear loads.”
–David Harris
David Harris is a freelance science writer in Palo Alto, California.
References
- M. C. Jenkins, M. D. Haw, G. C. Barker, W. C. K. Poon, and S. U. Egelhaaf, “Finding Bridges in Packings of Colloidal Spheres,” Soft Matter 7, 684 (2011)