Slow relaxation in granular compaction

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 follows an inverse logarithmic law. As the system approaches its final state, a growing number of beads have to be rearranged to enable a local density increase. A free volume argument shows that this number grows as N = ρ/(1−ρ). The time scale associated with such events increases exponentially ∼ e , and as a result a logarithmically slow approach to the final state is found ρ∞ − ρ(t) ∼ 1/ ln t . Furthermore, a onedimensional toy model that captures this relaxation dynamics as well as the observed density fluctuations is discussed. Copyright © 1998 Published by Elsevier Science B.V. PACS:05.40. +j; 81.20.Ev; 82.65.My