Wall roughness and nonlinear velocity profiles in granular shear flows

Paul Schuhmacher,Farhang Radjai,Stéphane Roux

doi:10.1051/epjconf/201714003090

Abstract

Inhomogeneous velocity profiles in granular flows are well known from both experiments and simulations, and considered as a hallmark of nonlocal behavior. By means of extensive contact dynamics simulations, we show that the sigmoidal velocity profiles in 2D flows of rigid disks are controlled by the roughness of driving boundary walls. We find that the velocity profile becomes linear for a critical value of wall roughness up to an exponential decay close to the walls with a characteristic length that does not depend on the flow thickness and rate. We describe the velocity profiles by introducing a state parameter that carries wall perturbation. By assuming that the local shear rate is a linear function of the state parameter, we obtain an analytical expression that fits velocity profiles. In this model, the nonlinear velocity profiles are explained in terms of the effects of wall roughness as boundary condition for the state parameter.

Highlights

Many natural processes, such as debris flows [1, 2], and industrial operations in powder technology [3], involve granular flows with various particle properties, boundary geometries and driving mechanisms
This model was later supplemented in soil mechanics with a flow rule by considering dilatancy as a function of a state variable measuring the distance to the critical state and a phenomenological evolution rule of the state variable [5]
The shear strain is uniform across the flow. We show that this observation can be rationalized in a model accounting for a state parameter as carrier of perturbation introduced by wall roughness

Summary

Introduction

Many natural processes, such as debris flows [1, 2], and industrial operations in powder technology [3], involve granular flows with various particle properties, boundary geometries and driving mechanisms. In the classical Mohr-Coulomb model, only quasi-static deformations and limit states are considered and the behavior is modeled in terms of a yield surface characterized by an isotropic effective (or internal) friction coefficient μ = σt/σn, where σt is the shear stress and σn is the normal stress [4] This model was later supplemented in soil mechanics with a flow rule by considering dilatancy as a function of a state variable measuring the distance to the critical state (steady isochor flow) and a phenomenological evolution rule of the state variable [5]. Independently of the inertial number, wall roughness controls the velocity profile as long as the flow thickness is below 130d, where d is mean particle size. This thickness, the shear strain is uniform across the flow. We show that this observation can be rationalized in a model accounting for a state parameter as carrier of perturbation introduced by wall roughness

Numerical procedures

Velocity profiles

Perturbation model

Conclusion