Density fluctuations in vibrated granular materials,
E.R. Nowak, J.B. Knight, E. Ben-Naim, H.M. Jaeger, and S.R. Nagel
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 G. 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.
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