Superstable Granular Heap in a Thin Channel

We observed experimentally a new regime for granular flows in an inclined channel with a flow-rate-controlled system. For high flow rates, the flow occurs atop a static granular heap whose angle is considerably higher than those usually exhibited by granular heaps. The properties of such superstable heaps (SSH) are drastically affected by a change in the channel width $W$. This indicates that the unusual stability of these heaps can be accounted for by the flowing layer and its friction on the sidewalls. A simple depth-averaged model, assuming Coulomb friction, shows that the SSH angle scales as $h/W$ ($W$ being the channel width), and that grain size plays no part.

Figure 1

(a) Snapshot of flowing sand taken with a regular video camera with $1/30\mathrm{s}$ exposure time. The blurry part corresponds to flowing grains and the sharp part is static. (b) Sketch of the experimental setup. The granular material is poured from a hopper onto a rough bottom between two vertical plates.

Figure 2

Sketches of the flow. (a) Velocity profiles within the granular material. (b) Simple picture of the flow.

Figure 3

Velocity profile at the wall for glass beads taken at $x=-20\mathrm{c}\mathrm{m}$ for $W=12.5\mathrm{m}\mathrm{m}$, $Q=90\mathrm{g}{\mathrm{s}}^{-1}{\mathrm{c}\mathrm{m}}^{-1}$, $\theta =40°$. The inset presents the velocity profile at the free surface.

Figure 4

Phase diagrams obtained with sand. (a) This phase diagram realized for $W=10\mathrm{m}\mathrm{m}$ shows two phases: (I) flow on the rough bottom and (II) flow atop a SSH. (b) Boundary lines between regions I and II [i.e., $\phi (Q)$] observed for different values of the channel width $W$.

Figure 5

The tangent of the angle $\phi$ is plotted as a function of the ratio $h/W$, for different values of the channel width $W$ using polydisperse beach sand.