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

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.

28 pages, 7 figures

Cited by in corpus (9)

• Numerical model for granular compaction under vertical tapping
• Glassy systems under time-dependent driving forces: application to slow granular rheology
• Orientational correlations and the effect of spatial gradients in the equilibrium steady state of hard rods in 2D : A study using deposition-evaporation kinetics
• Edwards-like statistical mechanical description of the parking lot model for vibrated granular materials
• Response properties in a model for granular matter
• Phenomenological glass model for vibratory granular compaction
• Linear response of vibrated granular systems to sudden changes in the vibration intensity
• A microscopic 2D lattice model of dimer granular compaction with friction
• Slow relaxation due to optimization and restructuring: Solution on a hierarchical lattice