Measurements of Grain Motion in a Dense, Three-Dimensional Granular Fluid

We have used an NMR technique to measure the short-time, three-dimensional displacement of grains in a system of mustard seeds vibrated vertically at $15g$. The technique averages over a time interval in which the grains move ballistically, giving a direct measurement of the granular temperature profile. The dense, lower portion of the sample is well described by a recent hydrodynamic theory for inelastic hard spheres. Near the free upper surface the mean free path is longer than the particle diameter and the hydrodynamic description fails.