A microscopic 2D lattice model of dimer granular compaction with friction

TL;DR

This paper models the compaction of 2D granular dimers under shaking and friction using Monte Carlo simulations, revealing different density evolution regimes and the impact of friction on compaction dynamics.

Contribution

It introduces a microscopic lattice model incorporating friction and analyzes how shaking duration and friction influence granular compaction behaviors.

Findings

Density follows stretched exponential or power-law decay depending on shaking duration.

A critical shaking time $ au^*$ marks a transition in density scaling behavior.

Friction reduces the final density proportionally to the friction coefficient.

Abstract

We study by Monte Carlo simulation the compaction dynamics of hard dimers in 2D 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.