Density fluctuations in vibrated granular materials

Edmund R. Nowak, James B. Knight, Eli Ben-Naim, Heinrich M. Jaeger, and Sidney R. Nagel
Phys. Rev. E 57, 1971 – Published 1 February 1998
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Abstract

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.

  • Received 22 May 1997

DOI:https://doi.org/10.1103/PhysRevE.57.1971

©1998 American Physical Society

Authors & Affiliations

Edmund R. Nowak, James B. Knight*, Eli Ben-Naim, Heinrich M. Jaeger, and Sidney R. Nagel

  • The James Franck Institute and the Department of Physics, The University of Chicago, Chicago, Illinois 60637

  • *Present address: Department of Physics, Princeton University, Princeton, NJ 08540.
  • Present address: Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545.

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Vol. 57, Iss. 2 — February 1998

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