Shear flow of dense granular materials near smooth walls. I. Shear localization and constitutive laws in the boundary region

Abstract

We report on a numerical study of the shear flow of a simple two-dimensional model of a granular material under controlled normal stress between two parallel smooth, frictional walls, moving with opposite velocities ±V . Discrete simulations, which are carried out with the contact dynamics method in dense assemblies of disks, reveal that, unlike rough walls made of strands of particles, smooth ones can lead to shear strain localization in the boundary layer. Specifically, we observe, for decreasing V , first a fluid-like regime (A), in which the whole granular layer is sheared, with a homogeneous strain rate except near the walls; then (B) a symmetric velocity profile with a solid block in the middle and strain localized near the walls and finally (C) a state with broken symmetry in which the shear rate is confined to one boundary layer, while the bulk of the material moves together with the opposite wall. Both transitions are independent of system size and occur for specific values of V . Transient times are discussed. We show that the first transition, between regimes A and B, can be deduced from constitutive laws identified for the bulk material and the boundary layer, while the second one could be associated with an instability in the behavior of the boundary layer. The boundary zone constitutive law, however, is observed to depend on the state of the bulk material nearby.

Unsteady granular flows down an inclined plane

“…Φ s is uniform with depth [2] and constant (a very week dependence on flow velocity has been found [1,6,7,12]). As a result, the normal stress N (y, t) is lithostatic: N = Φ s ρg cos θy.…”

“…[12] and used to determine transient time to obtain steady Couette flow in a simple shear cell. Note that for a flow under gravity investigated here, the diffusion coefficient is non-uniform.…”

“…Steady granular flows have been investigated for more than a half a century, resulting in good knowledge of their rheology [5][6][7][8], flow regimes [2,3,33], scaling [9,10] and effects of boundary conditions [11,12]. On the other hand, unsteady flows have been discussed much less and have been described only approximately using depth-averaged models, a.k.a "shallow water models", or computer simulations.…”

“…Neither of the approaches has established analytical forms of velocity and stress profiles, which are required to access energy dissipation, or the associated destructive potential of the flow. In addition, friction coefficient is known from physics and geophysics to depend on shear rate or relative sliding velocity between two surfaces [6][7][8][12][13][14]. Knowledge of shear rate could thus facilitate development of theoretical friction models.…”

Sliding Friction on Wet and Dry Sand

“…If adding water to sand has an effect on friction, this should have consequential repercussions for, e.g., sand transport through pipes [6]. This is an important issue, since the transport and handling of granular materials is responsible for around 10% of the world energy consumption [7], and optimizing granular transport ultimately relies on understanding the friction between the granular system and the walls [8][9][10].…”