Correlation of spin and velocity in granular gases

TL;DR

This paper develops an analytical theory and numerical simulations to study how spin and velocity are correlated in granular gases of rough particles, revealing the conditions under which these correlations occur and their dependence on particle properties.

Contribution

It introduces a new analytical framework for understanding spin-velocity correlations in granular gases and compares predictions with simulations across various parameters.

Findings

Correlations depend on particle roughness and system parameters.

Perpendicular spin and velocity orientation is most common.

Smooth spheres exhibit no translation-rotation correlations.

Abstract

In a granular gas of rough particles the spin of a grain is correlated with its linear velocity. We develop an analytical theory to account for these correlations and compare its predictions to numerical simulations, using Direct Simulation Monte Carlo as well as Molecular Dynamics. The system is shown to relax from an arbitrary initial state to a quasi-stationary state, which is characterized by time-independent, finite correlations of spin and linear velocity. The latter are analysed systematically for a wide range of system parameters, including the coefficients of tangential and normal restitution as well as the moment of inertia of the particles. For most parameter values the axis of rotation and the direction of linear momentum are perpendicular like in a sliced tennis ball, while parallel orientation, like in a rifled bullet, occurs only for a small range of parameters. The limit of smooth spheres is singular: any arbitrarily small roughness unavoidably causes significant translation-rotation correlations, whereas for perfectly smooth spheres the rotational degrees of freedom are completely decoupled from the dynamic evolution of the gas.