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A thermodynamic theory of powder endures

24 July 2017

Three decades after the theory debuted, researchers have finally tested its premise: that all possible arrangements of grains in a packing are equally probable.

Granular material
Credit: Mattie Hagedorn, CC BY-SA 2.0

The properties of a granular material depend intimately on how the grains are prepared. The mechanical strength of a powder that’s been gently piled into a heap, for instance, differs from that of an identical powder that’s been tamped down into a container. Some 30 years ago, Cambridge University’s Sam Edwards proposed a theoretical framework to capture that behavior. He drew an analogy between a packing of grains and an ensemble of atoms: The volume of the packing is to the grains as energy is to the atoms, and the number of ways the grains can fill the volume—more precisely, the logarithm of that number—constitutes a sort of entropy. From those pseudothermodynamic properties followed others, including the granular equivalents of temperature, free energy, and specific heat.

Edwards’s model yielded valuable insights into granular behavior. It helped explain, for example, the density fluctuations of powder shaken in a container. But it was premised on what seemed like an untestable conjecture: All possible configurations for a given packing volume are equally probable.

Now researchers led by Daan Frenkel at Cambridge and Bulbul Chakraborty at Brandeis University have tested the Edwards conjecture and shown that it holds true—but only under certain conditions. The group repeatedly simulated the packing of 64 grains and determined the probabilities of obtaining various stable packing configurations. At the so-called jamming limit, which corresponds to the loosest possible mechanically stable packing, all configurations emerged with equal probability. However, when the slightly squishy particles were compressed to smaller volumes, the grains seemed to prefer configurations that minimized the pressure. The authors suggest that the discrepancy can be explained with a generalized formulation of the Edwards conjecture that incorporates pressure terms. (S. Martiniani et al., Nat. Phys., in press.)

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