X-ray movies reveal sand flow patterns.

X-ray movies reveal sand flow patterns

Coal tumbling out the bottom of a silo can literally shake the silo apart, causing it to collapse. The same kind of potentially destructive vibrations occur when sand and other granular materials flow out of a hopper. The causes of such vibrations have long mystified researchers, but now they have a clue in the form of X-ray images showing the spontaneous development of density fluctuations that propagate like waves within flowing sand.

"As far as I know, no one has ever seen this before," says physicist Robert P. Behringer of Duke University in Durham, N.C. "What goes on inside a hopper as the sand comes out is really quite intriguing. There is a great deal of structure." Behringer reported his findings last week at an American Physical Society meeting in Baltimore.

Behringer and graduate student G. William Baxter did their experiments using a flat, acrylic plastic hopper containing a wedge of sand 1.27 centimeters thick and about 30 cm high. By placing the hopper in front of a hospital X-ray machine, they could study what happens inside the hopper as sand flows out.

"We were fortunate enough to use a fancy X-ray machine capable of taking 10 pictures per second, which allowed us to follow the details of the flow," Behringer says. The pictures were then pieced together into a movie.

The X-ray pictures show distinctive patterns of dark, sloping bands, which correspond to areas where the sand is more loosely packed, or less dense, than elsewhere in the hopper. The bands form within a well-defined, narrow central region extending from the hopper opening to the top of the sand wedge. As sand flows out, these bands gradually move upward while new bands form just above the outlet.

Behringer and Baxter studied the effects of changing the flow rate, the width of the bottom opening and the hopper angle, but the most striking differences appeared when they tried different types of sand. They found that propagating patterns form in flowing sand consisting of rough, faceted grains but not in sand consisting of smooth, rounded grains of the same size.

"what matters is the orientability of the particles," Behringer says. In other words, patterns form when sand particles are more like rice grains, which tend to align themselves, than smooth spheres, which have no preferred orientation. By experimenting with mixtures of faceted and smooth sand, the researchers determined the threshold at which propagating patterns begin to form.

Their work demonstrates how little is known about granular flows despite the need to understand such flows in solving a variety of problems encountered in the storage and handling of bulk materials. The new research furnishes important clues useful for developing mathematical equations for describing and predicting granular flow.

"the theoretical understanding of granular flow is really very limited," says Duke mathematician David G. Schaeffer. Such flows differ considerably from those of ordinary liquids such as water. "even a very fine powder doesn't behave like a fluid," he says.

New mathematical models may, in turn, help researchers interpret experimental results. "We're trying to understand where the propagating modes come from," Behringer says. "We hope part of that understanding will come from mathematical analysis."