Density fluctuations in vibrated granular materials

We report systematic measurements of the density of a vibrated granular material as a function of time. Monodisperse spherical beads were confined to a cylindrical container and shaken vertically. Under vibrations, the density of the pile slowly reaches a final steady-state value about which the density fluctuates. We have investigated the frequency dependence and amplitude of these fluctuations as a function of vibration intensity Γ. The spectrum of density fluctuations around the steady state value provides a probe of the internal relaxation dynamics of the system and a link to recent thermodynamic theories for the settling of granular material. In particular, we propose a method to evaluate the compactivity of a powder, first put forth by Edwards and co-workers, that is the analog to temperature for a quasistatic powder. We also propose a stochastic model based on free volume considerations that captures the essential mechanism underlying the slow relaxation. We compare our experimental results with simulations of a one-dimensional model for random adsorption and desorption.