Steady Granular Flow in a Rotating Drum: Universal description of stress, velocity and packing fraction profiles covering grain shape effects from convex to very concave

TL;DR

This paper presents a universal analytical model for steady granular flow in a rotating drum that accounts for particle shape effects, from convex to highly concave, and accurately predicts stress, velocity, and packing fraction profiles.

Contribution

The work introduces a comprehensive analytical framework incorporating particle shape effects, extending Bagnold scaling with a non-local fluidity relation, validated through experiments and simulations.

Findings

Model accurately predicts velocity and packing fraction profiles.

Particle shape significantly influences flow characteristics.

Characteristic length captures shape and speed effects on flow behavior.

Abstract

The flow behavior of granular matter is significantly influenced by the shape of constituent particles. This effect is particularly pronounced for very concave particles, which exhibit unique flow characteristics such as higher porosity and sharper phase transitions between jamming and unjamming states. Despite the richness and ubiquitousness of these systems, our understanding of their intricate flow behavior and the local mechanisms driving these behaviors remains incomplete. In this work, we investigate the effect of particle shape, ranging from spherical to highly concave, on steady flows in a rotating drum - a system that facilitates a continuous phase transition from a jamming state at greater depths to an unjamming state at shallower regions. We develop an analytical model to elucidate granular behavior within the rotating drum: (i) Firstly, by decomposing the shear stress, we reconcile the discrepancy between simulation data and theoretical predictions, establishing a relationship with the angle of repose. (ii)Secondly, we extend the generalized Bagnold scaling , coupled with a non-local fluidity relation based on packing fraction, providing a framework for a correlation between shear stress, shear rate, and packing fraction. Additionally, we introduce a characteristic length to quantify the influence of particle shape and drum speed. This analytical model offers explicit functional forms for physical quantity profiles, which are validated experimentally in a thin rotating drum and numerically in a two-dimensional rotating drum. Our results demonstrate that this model accurately describes the change of velocity due to the phase transition of granular flow within a rotating drum. Moreover, for different shapes of particle and drum speeds, the characteristic length captures the interplay between shear stress, shear rate, and the variation of packing fraction.