Trickling grains, sandpiles, and avalanches.

The slow trickle of sand through an hourglass produces more than just a neat, conical sandpile. Close observation reveals a rich array of phenomena, among them the occurrence of miniature avalanches triggered by newly fallen grains and the seemingly automatic settling of particles into a pile with a characteristic slope.

To help illuminate the details of sandpile formation, physicist Franco M. Nori and his co-workers at the University of Michigan in Ann Arbor devised an apparatus that considerably reduces the speed at which grains of sand arrive at a pile's surface. Such a deposition strategy allows the researchers to concentrate on the subtle rearrangements and tiny avalanches that occur when grains arrive at very low speeds.

The apparatus they use to demonstrate "two-dimensional" sandpile formation consists of a strip of sand at the top, a layer of air bubbles in the middle, and a liquid at the bottom, all sandwiched between two parallel, vertical glass plates. The air bubbles act as a valve, trapping the sand so that only a few grains at a time can escape through a small gap among the bubbles into the liquid layer. The released grains then drift slowly down through the liquid and gradually build up into a sandpile.

As shown in the photograph, the deposited sand grains (of two different colors) rearrange themselves and settle so that the angle of the sandpile slope maintains a characteristic value.

To track avalanches, Nori's group used another apparatus, consisting of a high-walled acrylic tray containing a thick layer of tiny beads, that operates somewhat like the back of a dump truck. By electronically recording any changes in the appearance of the bead surface, the researchers could monitor the movement of even one or two beads as the tray's tilt angle slowly increased and the beads rearranged themselves.

As reported in a paper scheduled for the Oct. 12 PHYSICAL REVIEW LETTERS, Nori and his colleagues obtained clear evidence that grain rearrangements occur via avalanches of varying sizes. Large slides involving most or all of the upper grain layer periodically "reset" the bead bed to its characteristic slope. But a sequence of smaller, "precursor" avalanches -- most of which take place on the slope's upper half -- also occurs between these large slides.

Previous experiments by other groups had produced contradictory or inconclusive results on the distribution and size of avalanches in the formation of sandpiles (SN: 7/15/89, p.40). However, such factors as humidity, the types of grains used, and the speed and rate of deposition apparently influenced the findings. Moreover, most earlier experiments measured only those avalanches in which grains moved all the way down and off a slope.

"Results are often hard to reproduce because there are so many different variables involved," Nori says. "There's nothing simple about a sandpile."