How granular vortices can help understanding rheological and mixing properties of dense granular flows

Abstract

Abstract. Dense granular flows exhibit fascinating kinematic patterns characterised by strong fluctuations in grain velocities. In this paper, we analyse these fluctuations and discuss their possible role on macroscopic properties such as effective viscosity, non-locality and shear-induced diffusion. The analysis is based on 2D experimental granular flows performed with the stadium shear device and DEM simulations. We first show that, when subjected to shear, grains self-organised into clusters rotating like rigid bodies. The average size of these so-called granular vortices is found to increase and diverge for lower inertial numbers, when flows decelerate and stop. We then discuss how such a microstructural entity and its associated internal length scale, possibly much larger than a grain, may be used to explain two important properties of dense granular flows: (i) the existence of shear-induced diffusion of grains characterised by a shear-rate independent diffusivity and (ii) the development of boundary layers near walls, where the viscosity is seemingly lower than the viscosity far from walls.

Relationship between vortex structures and shear localization in 3D granular specimens based on combined DEM and Helmholtz–Hodge decomposition

“…The 2D vortices were computed in the vertical cross-sectional slice with the area of 4 × 14 cm 2 and thickness of 5 × d 50 of Fig. 2c that was located at the specimen mid-depth l. The coordinates of each sphere (x, y, z) were projected onto the plane using the coordinates (x, y).…”

“…Note that the size of vortex structures could not be directly deduced from HHD since the vortex structures corresponded to points only that were associated with their rotational centres. The size of vortices may be detected with the aid of other methods, based on the vector displacement field of single particles [6,[50][51][52].…”

“…The procedure for determining the material parameters in DEM was described in detail by Kozicki et al [34,35]. The index properties of Karlsruhe sand are: mean grain diameter d 50 The following material constants were found in DEM by fitting numerical outcomes with experimental ones during homogeneous triaxial compression: 3 and a = 0.08. Note that the constants E c and v c do not correspond to the elastic constants of grains [34,35] M-contact moment vector, K s -tangential stiffness, K n -normal stiffness, K r -rolling stiffness, U -penetration depth, ω-tangential displacement vector, -angular rotation vector, μ-inter-particle friction angle, η-limit rolling coefficient grain diameter of d 50 = 2.5 mm.…”

“…Figure 3 demonstrates one typical evolution of the mobilized internal friction angle (calculated with principal stresses [7] (note that membrane is transparent to make granular specimen visible) from Mohr's equation) versus the vertical normal strain ε 1 = u 1 /h and volumetric strain ε v versus ε 1 for the granular specimen [7]. Figures 4 and 5 show the distribution of sphere rotations ω and void ratio e at four different values of axial strain in the vertical mid-section slice with the area of 4 × 14 cm 2 and thickness of 5 × d 50 (1.25 cm with d 50 = 2.5 mm) cut out from the granular specimen [7] (Fig. 2c).…”

“…2c). Both the quantities were calculated from the volumetric cell V c = 5d 50 × 5d 50 × 5d 50 moved by d 50 in two directions within the slice in order to create a 2D grid of the averaged values in the cell. The cell size, which was smaller than the shear zone thickness t s , was chosen with preliminary calculations.…”