Watching how beads collide in space may help quantify how grains of wheat, plastic pellets, pharmaceutical capsules, and avalanches all flow on Earth.

They're all composed of moving chunks of material, large and small. They're all subject to gravity. Their behaviors are all important to understand for reasons ranging from safety to health to commercial profit. And those behaviors are all the province of a field of physics known as granular flow.

"Granular flows are essential to many industrial processes on Earth," explains James T. Jenkins, professor of theoretical and applied mechanics at Cornell University, Ithaca, New York. "In the production of plastic toys, for example, the raw material is handled as pellets until it's melted and formed into the final product. In a coal-fired power station, fully 60 percent of the cost is sunk in transporting coal in a freight train, onto a conveyor belt, or into a boiler. And for predicting natural phenomena such as avalanches of rock or snow, you must understand granular flow."

It's a Solid! It's a Liquid! It's Both!

Problem is, granular flow is so complex it's poorly understood.

Physicists have long had neat mathematical equations that fully describe the behavior of bulk solids like bricks, liquids like water, and gases like air. But granular materials "sometimes act like solids and sometimes like fluids," Jenkins points out, "and the transition from one behavior to the other is very rapid." For example, gravel in the back of a dump truck sits virtually unmoving in a solid pile, even as the truck bed begins to tilt — until a certain angle is reached, and then suddenly it all tumbles downward in a thundering river of rock.

While industries have studied the behavior of specific types of granular materials so as to design efficient materials-handling systems for individual applications, no one has yet devised a mathematically precise description of granular flows in general. That's now Jenkins's aim: "I'm a theoretician, trying to come up with continuum equations for grain flows," that is, equations for when moving grains of solid materials behave like fluids.

Why is that such a desideratum?

Fluids can be completely described by partial differential equations — essentially, mathematical averages of the behaviors of the millions of molecules that make up the flowing liquid. Partial differential equations not only accurately predict how liquids flow depending on such numerical characteristics as viscosity, pressure, and temperature; they are also so computationally efficient that they are easy for desktop computers to solve. Thus, they are highly practical for helping to, say, design injection-molding systems.

Granular flows, however, so far have resisted adequate description by partial differential equations. Averaging the velocities of discrete particles loses essential detail about differences in velocities of individual grains — velocity fluctuations that near boundaries tend to segregate particles by size and/or mass. For example, seemingly in blithe disregard of the laws of entropy that claim the universe is growing ever more disordered, crumbs simply insist on filtering to the bottom of a cereal box (dust at the very bottom of all), while larger flakes and dried fruits congregate near the top. "Typically you want particles to stay mixed," Jenkins explains, "so you need to understand the mechanisms of spontaneous de-mixing." Other times, spontaneous segregation in granular flows causes clumping that can quickly halt an entire flow — a perpetual nuisance in industrial applications wherever a granular flow must be funneled down from a large river to a thin stream. Thus, in any continuum equations for granular flows, segregation and clumping are essential to understand and to model mathematically.

So far, the only successful simulations of granular flows have relied on treating each individual grain as a discrete particle — each having a certain mass, subject to Newton's laws of motion, the force of gravity, frequency and amplitude of agitation, and coefficients of friction and "restitution" (the elasticity of collisions between particles at different angles). But such brute-force simulations are so computationally demanding that even a supercomputer can't simulate the behavior of many more than 10,000 particles — not very representative of the millions or even billions of grains flowing in real-life corn elevators or landslides.

Getting Rid of Gravity

On Earth, segregation in every granular flow is influenced by at least two distinct types of interactions: gravitational and collisional. (For very small grains and powders, electrostatic interactions also become important; but, for simplicity, Jenkins is concentrating on large grains.) On Earth, though, gravity so dominates the physics of granular flows that it's virtually impossible to isolate and quantify the contribution of collisional interactions.

Hence Jenkins's desire to study how BB-sized multicolored beads of ceramic, steel, and acrylic collide with one another when "weightless" in space. "We have to get Earth's gravity out of the picture," he declares, "to create a simpler system where segregation in granular flows is dominated by collisions."

Jenkins's experimental apparatus is conceptually simple. The heart of it is a shearing cell: a doughnut-shaped chamber that is really a gap between two concentric counter-rotating cylinders within a close-fitting stationary housing [see figure]. The outer wall of the inner cylinder and the inner wall of the outer cylinder are separated by about an inch, equivalent to about 10 diameters of the beads used in the experiment. The walls are also machined with parallel, hemispherical corrugations 2 to 4 mm across — roughly the size of the beads used in the experiment.

Above: Schematic detail of a small segment of the shearing cell chamber shows its rectangular cross section and counter-rotating corrugated boundaries. Not shown is the stationary clear window on top (parallel with the stationary floor) through which a camera photographs beads in the chamber. Credit: Jacky Edwards.

When an experiment begins, the chamber between the two cylinders is partially filled (anywhere from 15 to 40 percent full) with two different species of beads — either ones of different sizes but the same mass, or ones of different masses but the same size. Then the inner and outer walls of the chamber are set to rotate in opposite directions up to 90 revolutions per minute. The speed-bump-like corrugations knock against beads nearest the walls, causing them to collide with ones closer to the center of the chamber, transferring both momentum and a shearing force across the width of the chamber. Through a transparent window that forms the stationary housing's top wall, a high-speed camera photographs the colliding beads at 1,000 frames per second for the duration of each experimental run — ideally several minutes, depending on the specific experiment.

Then begins the tough slogging. Special software developed by Jenkins's Cornell colleagues analyzes each photographic frame, mapping the tiny displacement of each individual bead from one frame to the next and diligently tracking how beads tend to segregate themselves by type toward the inner or outer wall. From these quantitative measurements of the motions of different types of beads at different wall speeds, Jenkins and his colleagues compare the observations with what is predicted by their theory.

Now, when the chamber runs on the ground, two forces act on the beads: the horizontal momentum transfer caused by the chamber's rotating walls and the vertical force of Earth's gravity (perpendicular to the toroidal chamber). In microgravity, however, the beads would freely float in the chamber during the experiment; thus, their segregation would be determined only by collisions among one another and with the chamber's inner and outer walls. In other words, in space Jenkins would have just the "simpler system" he needs to understand the respective contributions of collisions and gravity, and to formulate equations to describe segregation and clumping.

So far, early prototypes of Jenkins's shearing cell have flown on NASA's KC-135 aircraft, which soars up in a high parabola to yield about 20 seconds of microgravity in freefall.

Such brief periods are not enough to obtain scientific data useful for Jenkins's theoretical goals. ("It takes minutes of microgravity for the segregation of the beads to achieve a steady state," Jenkins explains.) Also, unavoidable air turbulence and engine vibrations add unwanted mixing of the beads. Nonetheless, the airborne tests have validated the basic experimental setup, tantalizing Jenkins with what the shearing cell might reveal in orbit.

The shearing cell is undergoing airborne flight tests and refinements of its design and data-collection software in anticipation of its scheduled launch to the International Space Station in 2007.

Left: A prototype of James T. Jenkins's shearing cell apparatus for investigating granular flows in microgravity, designed by Research Technician Stephen Keast at Cornell University, has been tested in NASA's KC-135 aircraft. The shearing cell itself is inside the large aluminum block at the left near the man's feet. The bank of electronics on the right controls the experiment's operation as well as the camera recording data. On the space station, a similar cell will run eight different experiments using three different species of beads (different sizes and masses). Credit: Michel Louge, Cornell University.

Jenkins's research team on the shearing cell includes Professors Michel Louge and Anthony Reeves at Cornell. Jenkins's collaborators on research on sand dunes include Professor Daniel Hanes at the University of Florida and Professor Daniel Bideau at the University of Rennes 1 in France.