From the orderly flow of sand through an hourglass to the unpredictable nature of an avalanche, much of the behavior of flowing solidsgranular flowsremains a mystery. 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 (Urbana-Champaign, IL) have cast serious doubt on this hypothesis.
Lead researcher Eliot Fried, professor of theoretical and applied mechanics at Illinois, found that very uniform spherical particles develop fingers as they flow, just as they do when mixed with a small amount of larger, irregularly-shaped particles.
"There has to be some other mechanism at work here," said Fried. "Our results show that even when the medium consists of nearly spherical particles, its leading edge may still develop fingers." To examine the influence of particle segregation on the formation of frontal fingers, Fried, 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, researchers began with industrial-grade blasting powder consiting 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.
Micrographs of granular media used: (a) small, spherical material; (b) larger, coarse material.
"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.
Stationary fingering pattern at the granular front for w = 14.5 rad/s and a filling percentage of h = 1.6%. (a) Full cylinder span; (b) closeup of fingers, showing the segregation bands and the distribution of larger, coarse material (see figure 1) within the fingers.
"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. "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. Although granular media are commonly thought to be incapable of sustaining surface tension, we can't rule out the possibility that the fingering patterns result from a similar competition between the viscosity of the bulk medium and effective surface tension."
Fried's ultimate goal is to understand the mechanisms that drive pattern formation, including patterns that reflect (but are not limited to) the separations of different species in flowing granular materials. "Such an understanding should aid in the design of equipment and processes," Fried stated, "that enhance mixing or, if so required, separation."
For more information: Eliot Fried, Professor, Dept. of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, 216 Talbot Laboratory, 104 South Wright St., Urbana, IL 61801-2935. Tel: 217-333-0966. Fax: 217-244-5707. Email: firstname.lastname@example.org.
By Angelo DePalma