Surface flow on a granular pile inside a rotating drum (photo Hubert Raguet)
We investigate steady granular surface flows in a rotating drum, measuring the velocity profile in the flowing layer at the center of the drum, the flowing layer thickness and the static/flowing boundary profiles. The velocity varies linearly with depth, with a gradient independent of both the flowing layer thickness and the static/flowing boundary local slope. Then, writing the depth averaged conservation equations for granular surface flows, it was possible to find experimentally the constitutive relations needed to close these equations. Altogether it has brought the evidence that the relation between stress and strain is non local:
(i) the velocity gradient is found to be constant in the flowing layer whereas momentum balance predicts a linear variation of the shear stress with depth;
(ii) the velocity gradient presents a different scaling with the depth for dense granular flows down a rough inclined plane indicating the non local influence of boundary conditions on internal rheology inside the flowing layer;
(iii) the velocity gradient does not vanish at the free surface at variance with typical fluids.
Measuring correlations among moving grains in the flowing layer, we could observe the first experimental evidence of rigid clusters of grains embedded in the flow and characterize their geometrical and statistical properties.. Although clustering instabilities driven by the inelasticity of grain collision are well known in granular gases, they have never been observed in dense surface flows. We find that these clusters are fractal and their size is power-law distributed from the microscopic scale - the diameter of a grain - up to the macroscopic scale - the flowing layer thickness. Therefore, no characteristic correlation length can be defined in the flowing layer. These results clearly call for further work in modelizing non-local effects in granular flows. A collective paper on the subject of granular flows is currently being written by the participants to the GDR Milieux Divisés.