New aspects for friction coefficients of finite granular avalanche down a flat narrow reservoir
Journal
Granular Matter
Journal Volume
18
Journal Issue
4
Date Issued
2016
Author(s)
Huang, Y.-T.
Abstract
This work examines the bulk internal friction coefficient, μ, and effective wall friction coefficient, μw, for finite number of nearly identical dry glass spheres in avalanche down a narrow inclined reservoir of smooth frictional bed using a validated discrete element scheme. Instantaneous deviatoric strain rate tensor γ˙ijd and stress tensor τi j are computed locally to evaluate a three-dimensional constitutive model developed based on the rheology of steady homogeneous surface flows. On one side, the algebraic μ- I relation conforms to conventional relation for glass beads, μ= 0.34 + 0.31 / (1 + 0.15 / I) (Jop et al. in J. Fluid Mech. 541:167–192, 2005, Midi in Eur. Phys. J. E 14:341–365, 2004, Jop in Comptes Rendus Phys. 16:62–72, 2015), when the inertial number I> Ic= 2 × 10 - 2. The assumption of collinear τi j and γ˙ijd, however, does not hold and such misalignment agrees to the findings in non-uniform inhomogeneous flows (Cortet et al. in Europhys. Lett. 88(1):14001, 2009). Below Ic, we observe a decaying μ- I as found in slowly deforming rheology tests and a simplified model is developed in view of shear-induced dilatation upon yielding. Non-constant effective wall friction coefficient is measured to grow in time and with I towards the sphere-wall sliding friction coefficient in the contact model while preserving the depth-weakening feature as in confined steady surface flows (Richard et al. in Phys. Rev. Lett. 101:248002, 2008, Brodu et al. in Phys. Rev. E 87:022202, 2013). The fact that rotation at one sphere center can divert surface relative velocity across the contact area to render lower sliding friction is considered to develop a model describing how μw drops with the ratio between rotation-induced velocity and sliding velocity, Ω. The simulation data compares fairly well to the predicted monotonic decay of μw with Ω.
SDGs
Type
journal article