Flow-induced shear instabilities of cohesive granulates

In this work we use a multiscale framework to calculate the fluidization threshold of three-dimensional cohesive granulates under shear forces exerted by a creeping flow. A continuum model of flow through porous media provides an analytical expression for the average drag force on a single grain. The balance equation for the forces and a force propagation model are then used to investigate the effects of porosity and packing structure on the stability of the pile. We obtain a closed-form expression for the instability threshold of a regular packing of monodisperse frictionless cohesive spherical grains in a planar fracture. Our result quantifies the compound effect of structural (packing orientation and porosity) and dynamical properties of the system on its stability.

Figure 1

Schematic of the domain on the left, and shape of the average velocity profile through the channel on the right. The grains are assumed to be cohesive.

Figure 2

(a) Top view of the structure of a two-layer 3-dimensional pile of spheres of dimensionless diameter $\epsilon$. (b) Sketch of the tetrahedron obtained by connecting the centers of the 4-sphere structure (left). The intralayer and iterlayer distances between sphere centers belonging to either the same or adjacent layers are $\ell$ and $h$, respectively. The unit vectors of the canonical orthonormal basis of the Euclidean space are ${\mathbf{e}}_{\alpha }$, $\alpha =\{1,2,3\}$. The unit vectors along the lattice directions connecting the center of the supported sphere with the centers of the supporting spheres are ${\mathbf{b}}_{\alpha }$, $\alpha =\{1,2,3\}$.

Figure 3

Schematics of the layer enumeration. The dashed horizontal lines represent the location of the contacts between two adjacent layers of grains.

Figure 4

Top view of the bottom two layers of a regular isostatic packing of monodisperse spheres before (a) and after (b) a counterclockwise rotation $\theta$ of the packing.

Figure 5

Fluidization threshold of a wet granulate under flow-induced shear in terms of packing orientation $\theta$ and capillary number ${\mathrm{Ca}}^{☆}$.