The dynamics of granular flow in an hourglass

We present experimental investigations of flow in an hourglass with a slowly narrowing elongated stem. The primary concern is the interaction between grains and air. For large grains the flow is steady. For smaller grains we find a relaxation oscillation (ticking) due to the counterflow of air, as previously reported by Wu et al. [Phys. Rev. Lett. 71, 1363 (1993)]. In addition, we find that the air/grain interface in the stem is either stationary or propagating depending on the average grain diameter. In particular, a propagating interface results in power-law relaxation, as opposed to exponential relaxation for a stationary interface. We present a simple model to explain this effect. We also investigate the long-time properties of the relaxation flow and find, contrary to expectations, that the relaxation time scale is remarkably constant. Finally, we subject the system to transverse vibrations of maximum acceleration Gamma. Contrary to results for non-ticking flows, the average flow rate increases with Gamma. Also, the relaxation period becomes shorter, probably due to the larger effective permeability induced by the vibrations.