Granular cooling of hard needles

TL;DR

This paper develops a kinetic theory and simulations for granular hard needles, revealing a two-stage cooling process with exponential and algebraic decay, supported by simulations at various densities.

Contribution

It introduces a new kinetic theory for granular hard needles and validates it with simulations, highlighting the two-stage cooling process and density-dependent behaviors.

Findings

Cooling proceeds in two stages: exponential then algebraic decay.

Theory aligns well with simulations at low and moderate densities.

High densities lead to clustering and shear band formation.

Abstract

We have developed a kinetic theory of hard needles undergoing binary collisions with loss of energy due to normal and tangential restitution. In addition, we have simulated many particle systems of granular hard needles. The theory, based on the assumption of a homogeneous cooling state, predicts that granular cooling of the needles proceeds in two stages: An exponential decay of the initial configuration to a state where translational and rotational energies take on a time independent ratio (not necessarily unity), followed by an algebraic decay of the total kinetic energy $\sim t^{-2}$. The simulations support the theory very well for low and moderate densities. For higher densities, we have observed the onset of the formation of clusters and shear bands.