Image: F. ROUYER/University of Massachusetts |
How granular material behaves--shifting and sifting and sliding around in miniature avalanches--may not seem like the most fascinating subject, but it is of vital importance in the real world: understanding such mechanics helps physicists model how grains move in silos, how soils collapse in earthquakes, and how certain materials and food products mix. And researchers from the University of Massachusetts at Amherst have now come up with an elegant way of describing grains that are shaken, drawing a direct analogy to the century-old kinetic theory of gases. Narayanan Menon and Florence Rouyer describe their work in the October 23 issue of the Physical Review Letters.
In an ideal gas, the individual molecules are at equilibrium with their environment; when one hits the wall of its container, energy is exchanged. As a result, it is possible by way of kinetic theory to derive, based only on the average temerature of the gas, a distribution of all the velocities of the molecules. Because grains that are shaken are not at equilibrium--they absorb energy in the form of heat by way of interparticle collisions caused by the shaking--it wasn't clear that a kinetic-type theory might apply, Menon explained.
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Even so, he and Rouyer measured the velocities of steel beads, 1.6 millimeters in diameter, in an enclosed space shaken vertically at speeds up to 1.8 meters per second. A high-speed video camera captured the motions (shown above) over a period of 5.5 milliseconds. They found that the probability of the horizontal velocities fell neatly into a bell-shaped distribution--not identical to, but not unlike the Gaussian curve of kinetic theory. This distribution remained the same when they changed the rate and amount of shaking, the density of the particles and the shape of the container. But its width varied with the average speed of a particle--the granular equivalent of temperature in gases. It is a preliminary result at the moment, but just perhaps a fundamental theory of grains is in the making.
