Granular beads in a vibrating, quasi two-dimensional cell: The true shape of the effective pair potential

TL;DR

This study demonstrates that steady-state pair correlations in vibrated granular beads can be effectively mapped onto an equilibrium fluid model, revealing simpler conservative interactions and a smooth, concave effective potential.

Contribution

It shows that granular bead correlations can be modeled by a simpler equilibrium reference system using Ornstein--Zernike inversion across various conditions.

Findings

Effective potential is a smooth, concave function of particle distance.

At low packing fractions, the potential fits an $r^{-2}$ dependence.

Mapping applies across a wide range of packing fractions and restitution coefficients.

Abstract

Steady-state pair correlations between inelastic granular beads in a vertically shaken, quasi two-dimensional cell can be mapped onto the particle correlations in a truly two-dimensional reference fluid in thermodynamic equilibrium. Using Granular Dynamics simulations and Iterative Ornstein--Zernike Inversion, we demonstrate that this mapping applies in a wide range of particle packing fractions and restitution coefficients, and that the conservative reference particle interactions are simpler than it has been reported earlier. The effective potential appears to be a smooth, concave function of the particle distance $r$. At low packing fraction, the shape of the effective potential is compatible with a one-parametric fit function proportional to $r^{-2}$.