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The adsorption-desorption model and its application to vibrated granular materials

J. Talbot·G. Tarjus·P. Viot
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Abstract

We investigate both analytically and by numerical simulation the kinetics of a microscopic model of hard rods adsorbing on a linear substrate, a model which is relevant for compaction of granular materials. The computer simulations use an event-driven algorithm which 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 successive regimes: an algebraic one where the density varies as $1/t$, a logarithmic one where the density varies as $1/\ln(t)$, followed by a terminal exponential approach. The characteristic relaxation time of the final regime, though incorrectly predicted by a mean field arguments, can be obtained with a systematic gap-distribution approach. The density fluctuations at equilibrium are also investigated, and the associated time-dependent correlation function exhibits a power law regime followed by a final exponential decay. Finally, we show that denser particle packings can be obtained by varying the desorption rate during the process.

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J. Talbot, G. Tarjus, P. Viot. 1999-10-15. The adsorption-desorption model and its application to vibrated granular materials. https://doi.org/10.1103/physreve.61.5429

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