Collisional Dynamics in Granular Flow

Granular materials can exhibit a static, solid-like character because thermal energies are not sufficient to move grains around one another. Granular materials can also exhibit a liquid-like character in which they flow and deform smoothly when acted on by large external forces. A central questions in understanding such flows, then, is the fate of the energy supplied by the driving forces. Rather than shake or tilt a sandpile, we have thus created two dynamical systems in which energy is supplied continuously and homogeneously throughout the medium at a known rate. The first consists of a rectangular hopper, or hourglass, with uniform cross section [1], while the second is a gas-fluidized bed in which motion is excited by an upward flow of gas [2]. In both cases we probe the resulting grain dynamics via diffusing-wave spectroscopy (DWS). We find that grains fly ballistically between collisions with the typical mean free times and paths being far too short to be measured by conventional imaging techniques: 10^-5 s and 10 nm, respectively, for 0.1 mm diameter grains. Though surprising, these scales are in rough accord with energy conservation, showing that random collisions (the so-called ``granular temperature'') rather than kinetic friction, can dominate the dissipation even in slow dense flows. This phenomenon is intrinsically nonlinear: the collisional dynamics are determined by the hydrodynamic flow, rather than KbT, while the hydrodynamic flow itself is determined by the collisional dynamics.

[1] N. Menon and D. J. Durian, "Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow," Science 275, 1920-1922 (1997).
[2] N. Menon and D. J. Durian, "Particle motion in a gas-fluidized bed of sand," Phys. Rev. Lett. 79, 3407-3410 (1997).