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. Introduction. – Sand dunes, grain silos, building materials, catalytic beds, filtration towers, riverbeds, snowfields, and many foods are granular systems consisting of a large number of randomly arranged macroscopic grains. Despite their apparent simplicity, granular materials exhibit a host of unusual behaviors, whose unraveling more often than not appears to challenge the existing wisdom of science [1, 2]. A fluidized granular bed is a system of randomly arranged, macroscopic grains in which the driving force of motion is the shaking of a container or gas flow through the granular system. Although, these systems are of tremendous technological importance in the catalysis of gas-phase reactions, transport of powders, combustion of ores, and several other industrial processes, we do not have sufficient understanding of the fluid state of a granular medium that is analogous to macroscopic properties of liquids. Two particularly important aspects contribute to the unique properties of granular materials: thermodynamics plays no role, and interactions between the grains are dissipative, because of static friction and inelasticity of collisions. Several theoretical efforts start towards building granular fluid mechanics by considering the medium as a dense, inelastic gas with the temperature defined by induced local velocity fluctuations [3, 4]. The autocorrelation function of a single-particle velocity