Autocorrelation spectra of an air-fluidized granular system measured by NMR

A novel insight into the dynamics of a fluidized granular system is given by a nuclear magnetic resonance method that yields the spin-echo attenuation proportional to the spectrum of the grain positional fluctuation. Measurements of the air-fluidized oil-filled spheres and mustard seeds at different degrees of fluidization and grain volume fractions provide the velocity autocorrelation that differs from the commonly anticipated exponential Enskog decay. An empiric formula, which corresponds to the model of grain caging at collisions with adjacent beads, fits well to the experimental data. Its parameters are the characteristic collision time, the free path between collisions and the cage-breaking rate or the diffusion- like constant, which decreases with increasing grain volume fraction. Mean-squared displacements calculated from the correlation spectrum clearly show transitions from ballistic, through sub-diffusion and into diffusion regimes of grain motion.