Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres

TL;DR

This study shows that in dense sheared inelastic hard sphere flows, the velocity autocorrelation function decays much faster than in elastic fluids, suggesting different underlying physics and implications for kinetic theory.

Contribution

It provides experimental and simulation evidence that velocity autocorrelation decays rapidly in sheared inelastic granular flows, challenging previous elastic fluid models.

Findings

Velocity autocorrelation decays faster than t^{-3/2}

Diffusive behavior observed at long times, except with layering effects

Rapid decay is independent of particle arrangement details

Abstract

We find in complementary experiments and event driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function $\psi(t)$ decays much faster than $t^{-3/2}$ obtained for a fluid of elastic spheres at equilibrium. Particle displacements are measured in experiments inside a gravity driven flow sheared by a rough wall. The average packing fraction obtained in the experiments is 0.59, and the packing fraction in the simulations is varied between 0.5 and 0.59. The motion is observed to be diffusive over long times except in experiments where there is layering of particles parallel to boundaries, and diffusion is inhibited between layers. Regardless, a rapid decay of $\psi(t)$ is observed, indicating that this is a feature of the sheared dissipative fluid, and is independent of the details of the relative particle arrangements. An important implication of our study is that the non-analytic contribution to the shear stress may not be present in a sheared inelastic fluid, leading to a wider range of applicability of kinetic theory approaches to dense granular matter.