Long Range Correlation in Granular Shear Flow II: Theoretical Implications

TL;DR

This paper investigates the limitations of kinetic theory in predicting granular shear flow, revealing the importance of force networks and elastic deformations in dense regimes, and proposes an analytical model that accurately predicts stress.

Contribution

It introduces a new analytical model accounting for non-collisional forces from force networks, improving predictions in dense granular flows.

Findings

Kinetic theory accurately predicts dilute granular flow.

Discrepancies in dense regimes are due to force networks.

The proposed model matches simulation results across regimes.

Abstract

Numerical simulations are used to test the kinetic theory constitutive relations of inertial granular shear flow. These predictions are shown to be accurate in the dilute regime, where only binary collisions are relevant, but underestimate the measured value in the dense regime, where force networks of size $\xi$ are present. The discrepancy in the dense regime is due to non-collisional forces that we measure directly in our simulations and arise from elastic deformations of the force networks. We model the non-collisional stress by summing over all paths that elastic waves travel through force networks. This results in an analytical theory that successfully predicts the stress tensor over the entire inertial regime without any adjustable parameters.