Effective boundary conditions for dense granular flows

Abstract

We derive an effective boundary condition for dense granular flow taking into account the effect of the heterogeneity of the force network on sliding friction dynamics. This yields an intermediate boundary condition which lies in the limit between no slip and Coulomb friction; two simple functions relating wall stress, velocity, and velocity variance are found from numerical simulations. Moreover, we show that this effective boundary condition corresponds to Navier slip condition when the model of G. D. R. Midi, Eur. Phys. J. E 14, 3412004 is assumed to be valid, and that the slip length depends on the length scale that characterizes the system, viz. the particle diameter

Effective Wall Friction in Wall-Bounded 3D Dense Granular Flows

“…Conclusions.-Results presented in this work confirm for 3D flows the conceptual framework which was suggested in Ref. [17]; at flat frictional walls, force fluctuations trigger slip events even if the system is globally below the slip threshold. These stick-slip events produce (i) a nonzero average slip velocity and (ii) a variable effective wall friction coefficient which scales on a dimensionless slip parameter.…”

Scaling Laws for the Slip Velocity in Dense Granular Flows

“…The main point of the theory is that the stronger the phenomenon of force chains breaking and forming in the material, the larger will be the deviation from the condition of steady sliding for the particles at a boundary, implying generally that µ w < µ pw , where µ pw is the particle-wall friction coefficient, and suggesting the emergence of a dependence of the effective wall friction coefficient on the flow properties. In this Letter we prove the evidence of these flow dependent boundary conditions, and extend the scaling proposed in [5]. In the following, the dense flow of granular materials composed of irregular particles down a flat frictional inclined plane (as sketched in Fig.…”

“…From the practical point of view, in the dense flow of granular materials in silos and hoppers, wall friction is usually described by means of the effective wall friction coefficient µ w = σT σN , which is a bulk, not a particle property, where σ T is the shear stress and σ N is the normal stress in the direction perpendicular to the wall. Such a coefficient, often presented as the angle of wall friction (defined as tan −1 µ w ), is not necessarily a constant property of the couple of particle and wall materials [4,5]. In presence of shear, in a recent work we argued [5] that shear-induced fluctuations of the force network could determine a dependence of the effective wall friction coefficient on flow properties, such as slip velocity, shear rate and stresses.…”

Rheological properties of dense granular flows

“…Even though the link with the bulk inertial number is still lacking, an interesting step has been made to relate the slip velocity to the physical properties. Artoni et al studied the movement of a grain submitted to a stochastic force from an imaginary bulk and inferred a scaling law for the slip velocity [87]. This empirical scaling has been confirmed analyzing flows of angular grains down frictional smooth plane numerically [85].…”