A frictional Cosserat model for the flow of granular materials through a vertical channel

TL;DR

This paper introduces a Cosserat continuum model incorporating a material length scale to accurately predict shear layer formation and velocity profiles in dense granular flows through a vertical channel, aligning well with experimental data.

Contribution

The paper develops a frictional Cosserat model that includes a material length scale, enabling prediction of shear layers in granular flow, which classical models fail to capture.

Findings

Velocity profiles match experimental data

Shear layer thickness depends on channel width

Shear layer thickness scales with particle diameter

Abstract

A rigid-plastic Cosserat model has been used to study dense, fully developed flow of granular materials through a vertical channel. Frictional models based on the classical continuum do not predict the occurrence of shear layers, at variance with experimental observations. This feature has been attributed to the absence of a material length scale in their constitutive equations. The present model incorporates such a material length scale by treating the granular material as a Cosserat continuum. Thus localised couple stresses exist and the stress tensor is asymmetric. The velocity profiles predicted by the model are in close agreement with available experimental data. The predicted dependence of the shear layer thickness on the width of the channel is in reasonable agreement with data. In the limit of the ratio of the particle diameter to the half-width of the channel being small, the model predicts that the shear layer thickness scaled by the particle diameter grows.