Stability of wall bounded, shear flows of dense granular materials: the role of the Couette gap, the wall velocity and the initial concentration

Abstract

In this paper, the stability of a plane, unidirectional Couette flow of a dense granular material is investigated via the means of a normal mode stability analysis. Our studies are based on a continuum mechanical model for the flows of interest coupled with the constitutive expressions for the normal and the shear stresses of the granular material induced by the µ(I)-rheology. According to our analysis, both the Couette gap and the wall velocity play a destabilizing role in the flows of interest as opposed to the initial concentration that acts as stabilizer. For sufficiently high Couette gaps and wall velocities, unstable modes are recovered. The predicted instability manifests itself through shear-induced dilatancy that, in turn, engenders particle migration and the formation of bulbs, similar to the ones that have been acquired through molecular dynamics simulations.

Application of the compressible -dependent rheology to chute and shear flow instabilities

“…This is referred to as a temporal stability analysis, which contrasts with a spatial stability analysis in which a pulsation σ = −iω for ω ∈ R is specified and k ∈ C is the eigenvalue of interest (see Schmid & Henningson 2001, Chapter 7). A spatial stability analysis is carried out in Forterre (2006); Gray & Edwards (2014) in order to compare their results directly with the spatial stability data of Forterre & Pouliquen (2003), however we avoid this approach given that the eigenvalue k appears quadratically in the stability problem, which is typically more difficult to handle numerically (Malik 1990;Varsakelis & Papalexandris 2016). In any case, we discuss in §3.4 how the temporal analysis can be used to compare against the spatial stability data.…”