Adsorption-desorption model and its application to vibrated granular materials

We investigate both analytically and by numerical simulation the kinetics o f a microscopic model of hard rods adsorbing on a linear substrate, a model that is relevant for compaction of granular materials. The computer simula tions use an event-driven algorithm that is particularly efficient at very long times. For a small, but finite desorption rate, the system reaches an equilibrium state very slowly, and the long-time kinetics display three suc cessive regimes: an algebraic one where the density varies as lit, a logari thmic one where the density varies as 1/ln(t), followed by a terminal expon ential approach. The characteristic relaxation time of the final regime, th ough incorrectly predicted by mean field arguments, can be obtained with a systematic gap-distribution approach. The density fluctuations at equilibri um are also investigated, and the associated time-dependent correlation fun ction exhibits a power law regime followed by a final exponential decay. Fi nally, we show that denser particle packings can be obtained by varying the desorption rate during the process.