Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow

TL;DR

This paper analyzes dense granular flow down a slope, demonstrating the applicability of Bagnold scaling and kinetic theory in the bulk, and compares simulation data with theoretical predictions revealing areas of agreement and discrepancy.

Contribution

It provides a detailed comparison of kinetic theory with simulation data for dense granular flow, highlighting where the theory succeeds and where it diverges.

Findings

Quantitative agreement in normal and shear stresses between theory and simulation.

Discrepancy in energy dissipation leads to large differences in flow analysis.

Bagnold scaling is valid in the bulk of dense granular flows.

Abstract

We investigate the bulk rheology of dense granular flow down a rough slope, where the density profile has been found to show a plateau except for the boundary layers in simulations [Silbert {\it et al.}, Phys. Rev. E {\bf 64}, 051302 (2001)]. It is demonstrated that both the Bagnold scaling and the framework of kinetic theory are applicable in the bulk, which allows us to extract the constitutive relations from simulation data. The detailed comparison of our data with the kinetic theory shows quantitative agreement for the normal and shear stresses, but there exists slight discrepancy in the energy dissipation, which causes rather large disagreement in the kinetic theory analysis of the flow.