Relaxation dynamics of a vibro-fluidized granular pile

Relaxation is one of the phenomena lying at the center of soft matter physics. As for granular media, heap structure (e.g. sand pile) shows relaxation toward a horizontally-flat surface in gravitational field when subjected to perturbations such as vibration. The complete understanding of this dynamics has not yet been achieved, although this kind of relaxation has been observed in broad research fields from general soft matter physics to civil engineering and geophysics. Motivated by this fact, in this study nonlinear relaxation dynamics of a vertically-vibrated granular pile is experimentally studied. In the experiment, the flux and slope on a vibro-fluidized pile are measured by using a high-speed laser profiler. To explain the relation of these quantities, we propose the nonlinear transport law based on the assumption that an entire pile is uniformly fluidized by vibration. By the continuity equation with this proposed model, the actual relaxation is successfully reproduced. The fitting parameter of the model is only the relaxation efficiency, which characterizes the energy conversion rate from vertical vibration into horizontal transport. We finally demonstrate that this value is a universal constant independent of experimental conditions.