Slow relaxation in granular compaction

Details Slow relaxation in granular compaction Slow relaxation in granular compaction

1996-03-25

arxiv.org/abs/cond-mat/9603150v1

Physica D 123, 380 (1998)

Physics

Condensed Matter

revtex, 4 pages, 3 figures, also available from http://arnold.uchicago.edu/~ebn/

Scientific paper

10.1016/S0167-2789(98)00136-5

Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density value follows an inverse logarithmic law. We propose a simple stochastic adsorption-desorption process which captures the essential mechanism underlying this remarkably slow relaxation. As the system approaches its final state, a growing number of beads have to be rearranged to enable a local density increase. In one dimension, this number grows as $N=\rho/(1-\rho)$, and the density increase rate is drastically reduced by a factor $e^{-N}$. Consequently, a logarithmically slow approach to the final state is found $\rho_{\infty}-\rho(t)\cong 1/\ln t$.

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