Logarithmic density relaxation in compaction of granular materials

TL;DR

This paper introduces a one-dimensional lattice model for granular material compaction, demonstrating logarithmic density relaxation consistent with experiments, and analytically explains the origin of this anomalous behavior.

Contribution

The paper presents a novel lattice model and analytical approach to explain the logarithmic relaxation in granular compaction.

Findings

Logarithmic time-dependence of density relaxation observed

Model aligns with experimental results by Knight et al.

Analytical solution elucidates the origin of anomalous relaxation

Abstract

On the basis of physical considerations we propose a one-dimensional discrete lattice model for the density relaxation of granular materials under tapping. Solving the difference equation numerically, we find a logarithmic time-dependence of the density relaxation. This is in agreement with experimental results of Knight et al. [Phys. Rev. E 51, 3957(1995)]. The origin of this anomalous relaxation is elucidated analytically by solving the equation of its continuum version asymptotically in time.