Model for dense granular flows down bumpy inclines

Abstract

We consider dense flows of spherical grains down an inclined plane on which spherical bumps have been affixed. We propose a theory that models stresses as the superposition of a rate-dependent contribution arising from collisional interactions and a rate-independent part related to enduring frictional contacts among the grains. We show that dense flows consist of three regions. The first is a thin basal layer where grains progressively gain fluctuation energy with increasing distance from the bottom boundary. The second is a core region where the solid volume fraction is constant and the production and dissipation of fluctuation energy are nearly balanced. The last is a thin collisional surface layer where the volume fraction abruptly vanishes as the free surface is approached. We also distinguish basal flows with the smallest possible height, in which the core and surface layers have disappeared. We derive simple closures of the governing equations for the three regions with insight from the numerical simulations of Silbert et al. [Phys. Rev. E64, 051302 (2001)] and the physical experiments of Pouliquen [Phys. Fluids 11, 542 (1999)]. The theory captures the range of inclination angles at which steady, fully developed flows are observed, the corresponding shape of the mean and fluctuation velocity profiles, the dependence of the flow rate on inclination, flow height, interparticle friction, and normal restitution coefficient, and the dependence of the height of basal flows on inclination.

A visco‐elasto‐plastic model for granular materials under simple shear conditions

“…In contrast, the theoretical constitutive model hereafter presented, as in Johnson and Jackson [34,35], Savage [36], Louge [37], Lee and Huang [38], Berzi et al [39] and Vescovi et al [40], assumes a parallel scheme according to which the stress tensor is evaluated as the sum of two contributions: one "ratedependent" and another "rate-independent". The model hereafter illustrated can be interpreted as the extension to unsteady conditions of the model discussed in Berzi et al [39] and Vescovi et al [40].…”

Velocity Correlations in Dense Granular Flows

“…The fact that the influence of θ on the flow velocity comes into play through the deposit function h stop (θ) is not straightforward and could be simply the result of a coincidence [7]. However, an interesting interpretation of relation 1 has been proposed by Ertas and Halsey [12].…”

“…Recent theoretical models try to take into account the existence of this contact network through different approaches. Some models describe the flow as a mixture of solid and liquid phases [5] or try to account for the frictional contacts by adding a frictional term in collisional theories [6,7]. Other models consider the presence of arches in the flow [8,9] or account for some non local propagation of momentum through the contact network [10,11].…”

Rheology of Confined Granular Flows : from Gas to Glass

“…Although kinetic theory captures the behavior of dilute granular flows, the theoretical attempts made to describe dense granular flows, and in particular the necessity to take into account enduring contacts [1,2] are still matter of debate. Pouring continuously grains at the top of a granular heap allows one to observe all the states of granular matter: from gaseous state (close the the free surface) to a quasistatic state (deep inside the flow).…”