Shear bands in granular flow through a mixing length model.

We discuss the advantages and results of using a mixing-length, compressible model to account for the shear banding behaviour in granular flow. We formulate a general approach based on two functions of the solid fraction to be determined. Studying the vertical chute flow, we show that the shear band thickness is always independent of flow rate 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 on channel width, while the 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.