Shear bands in granular flow through a mixing length model

TL;DR

This paper presents a mixing-length model for granular flow that captures shear banding behavior, showing how shear band thickness depends on channel width and wall roughness, with implications for understanding granular flow dynamics.

Contribution

It introduces a general mixing-length approach with functions of solid fraction to model shear bands, predicting their dependence on channel width and wall roughness, aligning with experimental observations.

Findings

Shear band thickness is independent of flow rate in the quasistatic limit.

Shear band thickness scales linearly with channel width.

Wall roughness influences shear band thickness as predicted by the model.

Abstract

We discuss the advantages and results of using a mixing-length, compressible model to account for shear banding behaviour in granular flow. We formulate a general approach based on two function of the solid fraction to be determined. Studying the vertical chute flow, we show that shear band thickness is always independent from flowrate in the quasistatic limit, for Coulomb wall boundary conditions. The effect of bin width is addressed using the functions developed by Pouliquen and coworkers, predicting a linear dependence of shear band thickness by channel width, while literature reports contrasting data. We also discuss the influence of wall roughness on shear bands. Through a Coulomb wall friction criterion we show that our model correctly predicts the effect of increasing wall roughness on the thickness of shear bands. Then a simple mixing-length approach to steady granular flows can be useful and representative of a number of original features of granular flow.