Velocity correlations in the dense granular shear flows: Effects on energy dissipation and normal stress

TL;DR

This study investigates how pre-collisional velocity correlations affect energy dissipation and normal stress in dense granular shear flows, revealing that these correlations cause deviations from kinetic theory predictions.

Contribution

The paper demonstrates that velocity correlations neglected in kinetic theory significantly influence energy dissipation and normal stress in dense granular flows.

Findings

Velocity correlations reduce relative normal velocities of colliding particles.

Discrepancies in dissipation and normal stress are corrected by introducing collisional temperature.

Correlation grows through multiple inelastic collisions during shear flow.

Abstract

We study the effect of pre-collisional velocity correlations on granular shear flow by molecular dynamics simulations of the inelastic hard sphere system. Comparison of the simulations with the kinetic theory reveals that the theory overestimates both the energy dissipation rate and the normal stress in the dense flow region. We find that the relative normal velocity of colliding particles is smaller than that expected from random collisions, and the discrepancies in the dissipation and the normal stress can be adjusted by introducing the idea of the collisional temperature, from which we conclude that the velocity correlation neglected in the kinetic theory is responsible for the discrepancies. Our analysis of the distributions of the pre-collisional velocity suggests that the correlation grows through multiple inelastic collisions during the time scale of the inverse of the shear rate. As for the shear stress, the discrepancy is also found in the dense region, but it depends strongly on the particle inelasticity.