Boundary interactions for two-dimensional granular flows. Part 1. Flat boundaries, asymmetric stresses and couple stresses

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Abstract
The behaviour of a granular flow at a boundary cannot be specified independently of what is happening in the rest of the flow field. This paper describes a study of two fictitious, but instructive, flat boundary types using a computer simulation of a two-dimensional granular flow with the goal of trying to understand the possible effects of the boundary on the flow. The two boundary conditions, Type A and Type B, differ largely in the way that they apply torques to the flow particles. During a particle–wall collision, the Type A boundary applies the force at the particle surface, thus applying the largest mechanistically possible torque to the particle, while the Type B boundary applies the force directly to the particle centre, resulting in the application of zero torque. Though a small change on continuum scales (i.e. the point at which the force is applied has only been moved by a particle radius) it makes a huge difference to the macroscopic behaviour of the system. Generally, it was found that, near boundaries, large variations in continuum properties occur over distances of a particle diameter, a non-continuum scale, throwing into doubt whether boundaries may be accurately modelled via continuum mechanics. Finally, the large torques applied to the particles by the Type A boundary induce asymmetries in the stress tensor, which, in these steady flows, are balanced by gradients in a couple stress tensor. Thus, near boundaries, a frictional granular material must be modelled as a polar fluid.