Microscopic two-dimensional lattice model of dimer granular compaction with friction.

We study by Monte Carlo simulation the compaction dynamics of hard dimers in two dimensions under the action of gravity, subjected to vertical and horizontal shaking, considering also the case in which a friction force acts for horizontal displacements of the dimers. These forces are modeled by introducing effective probabilities for all kinds of moves of the particles. We analyze the dynamics for different values of the time tau during which the shaking is applied to the system and for different intensities of the forces. It turns out that the density evolution in time follows a stretched exponential behavior if tau is not very large, while a power law tail develops for larger values of tau. Moreover, in the absence of friction, a critical value tau(*) exists, which signals the crossover between two different regimes: for tau<tau(*) the asymptotic density scales with a power law of tau, while for tau>tau(*) it reaches logarithmically a maximal saturation value. Such behavior smears out when a finite friction force is present. In this situation the dynamics is slower and lower asymptotic densities are attained. In particular, for significant friction forces, the final density decreases linearly with the friction coefficient. We also compare the frictionless single tap dynamics to the sequential tapping dynamics, observing in the latter case an inverse logarithmic behavior of the density evolution, as found in the experiments.