Duke physicists reveal new insights into stresses between sliding grains

Densely packed granular particles that inch past each other under tension interact in ways more complex and surprising than previously believed, two Duke University physicists have discovered.

Their observations, described in the Thursday, February 27, 2003, issue of the research journal Nature, could provide new insight into such geophysical processes as the behavior of a slowly moving glacier or an active earthquake fault, said Robert Behringer, a Duke physics professor who is one of the Nature article’s authors. The physicists’ findings could also have implications for industrial problems, such as how the contents of a hopper holding granular materials such as grain or coal flow, he added.

By using plastic beads made of a material that affects light differently when under stress, Behringer and graduate student Robert Hartley have for the first time shown what happens to grains in a granular network subjected to frictional or “shear” forces that may build slowly.

Their work, supported by the National Science Foundation and NASA, constitutes a new scientific view of phenomena that are difficult to visualize or measure, and for which there is no established theory, Behringer said. Granular materials interest scientists particularly because the materials behave in some ways like solids and in others like liquids.

According to the scientists, tensions in granular materials obviously increase when densely packed grains in close contact with each other seek to move in opposite directions. But nothing apparent happens to these grain collections until forces build enough to cause the grains to begin slipping past each other, the authors noted in their Nature report.

Physicists from the 1770s to recent times had believed that after sliding begins, frictional forces between the grains remain constant even as sliding speeds slowly increase. “This is still routinely taught in introductory physics courses,” Behringer said in an interview.

Various experiments, particularly since the early 1980s, however, have suggested that frictional forces between the grains do not remain the same but instead appear to decrease as sliding speeds inch upwards, Behringer added. Such a weakening is no surprise, according to Behringer. “With increasing speed, the contacts between individual grains should be weakening,” he said.

The surprises came when Hartley and Behringer explored in unprecedented detail what is happening within such systems. Their article illustrated how they were able to “zoom in uniquely” on individual beads, which served as laboratory surrogates for granular particles in nature.

In their experiments, they studied how the plastic beads interacted in a confined space between an outer ring and an inner rotating wheel. Using that apparatus, they demonstrated that built-up frictional stresses are actually transferred into jagged networks of “force chains” that some contacting grains develop within the tight networks.

So, although forces between individual grains drop overall as sliding speeds grow, the scientists found that the force chains reorganize and proliferate at the same time to sop up what are increasing stresses to the system. “The force network increases in strength with increasing speed,” Behringer said.

In these experiments, speeds are relatively slow — the fastest being one revolution of the wheel every 30 seconds.

Another surprise occurred when the researchers halted the grain interaction by stopping the rotating wheel. With the tightly packed grains no longer sliding past one another but instead remaining in constant contact, forces between individual grains should freeze in place, Behringer said.

Instead, the researchers found that stresses within the force chains began dropping, rapidly initially and slowly thereafter over periods of many hours. “Those contacts should remain exactly as they are over time. But nature does something different,” he said.

These surprises “indicate that newly found and possibly subtle processes are at work that make collections of grains behave in a way that appears to be the reverse of what would be expected,” he added.

“Our observations have important implications for modeling the internal stress states of geophysical systems,” Behringer said. Examples might include California’s notorious San Andreas Fault, in which two rock faces move in opposite directions deep underground. In some places, the rock faces slowly creep past each other. In others, the rock faces bind, causing pressures to build up until the faces suddenly snap apart in an earthquake that is sometimes catastrophic.

There may also be lessons for the design of industrial devices, such as hoppers, he said. In the flow of coal or of wheat in hoppers, “there could be a large range of velocities in different parts of the hopper, from very fast near its outlet to very slow at the top,” he said. “The stresses are likely to behave very differently for these different flow speeds.”

Hoppers have been known to self-destruct because of hard to decipher changes inside.