Surface Tension May Explain Fingering Patterns In Granular Flows

One poorly understood characteristic of granular flows is the frequent formation of "fingers" at the leading edge. While some researchers have suggested that these patterns are created by the segregation of coarse, irregularly shaped particles, recent experiments at the University of Illinois have cast serious doubt on the validity of this explanation.

"There has to be some other mechanism at work here," said Eliot Fried, a U. of I. professor of theoretical and applied mechanics. "Our results show that even when the medium consists of nearly spherical particles, its leading edge may still develop fingers."

To examine the influence that particle segregation plays on the formation of frontal fingers, Fried and his colleagues -- theoretical and applied mechanics professor Sigurdur Thoroddsen and graduate student Amy Shen -- performed a series of experiments by rotating an acrylic cylinder containing a small amount of granular material around its horizontal axis of symmetry.

For the granular medium, the researchers started with industrial-grade blasting powder -- which consisted of tiny, fairly uniform glass beads. The motion of the granules was recorded on videotape with a CCD (charge-coupled device) camera and then analyzed one frame at a time.

"Initially, there is a stick-slip motion of the layer as a whole, as it is dragged up the rising side of the cylinder to a critical angle where it falls back to the bottom," Fried said. "But as the angular velocity is increased, a wave-motion sets in, which creates a span-wise variation in the thickness of the layer -- visible as bright and dark bands of light transmitted through the granular material. The frontal patterns resemble fingers."

Next, the researchers added some coarse sand to the glass beads. The resulting fingers and wave patterns did not differ substantially from what had been observed with the beads alone.

"Our results clearly demonstrate that fingers can form at the front of a flowing granular medium even in the absence of segregation induced by coarse, irregularly shaped particles," said Fried, who presented his team's findings at the American Physical Society meeting, held March 21-26, in Atlanta. "This suggests that some other mechanism is responsible. " Because the fingering patterns are similar to those seen in conventional viscous fluids, Fried said, the explanation may lie in an effective surface tension generated by cohesive forces between grains. "In fluids, the frontal fingering instability is driven by a competition between viscosity and surface tension," Fried said.

"Although granular media are commonly thought to be incapable of sustaining surface tension, we cannot rule out the possibility that the fingering patterns result from a similar competition between the viscosity of the bulk medium and effective surface tension."