Dense, Rapid Flows of Inelastic Grains under Gravity

The standard hydrodynamic description does not apply to the rapid flow regime of inelastic grains in the dense limit. Emphasizing the role of inelastic loss and collapse, we propose a new approach relying on a nonlocal dissipation scheme. Our model succeeds in accounting qualitatively and quantitatively for the linear profile of velocity found in experiments on dense gravity-driven flows.

Figure 1

Flow of a collection of monodisperse aluminum spheres (restitution coefficient $e=0.6$, flow rate $\approx 1100\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{s}/\sec $, exposure time of the photograph: $1/125\sec $).

Figure 2

Flow of aluminum grains, flow rate $\approx 1100\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{s}/\sec $, averaged over 100 samplings. (○) Adimensioned velocity profile; (×) surface fraction.

Figure 3

Representation of an elementary shear transformation. The velocity of the upper layer ($i$) is ${\mathbf{v}}_i$, that of the layer ($i+1$) beneath is ${\mathbf{v}}_{i+1}$.