Flow rule of dense granular flows down a rough incline
T. Börzsönyi and R.E. Ecke
[Phys.Rev.E. 76, 031301 (2007).]
We present experimental findings on the flow rule for granular flows on a rough inclined plane using various materials including sand and glass beads of various sizes and four types of copper particles with different shapes. We characterize the materials by measuring h_s (the thickness at which the flow subsides) as a function of the plane inclination on various surfaces. Measuring the surface velocity u of the flow as a function of flow thickness h, we find that for sand and glass beads the Pouliquen flow rule (PFR) (see Fig. 1) provides reasonable but not perfect collapse of the u(h) curves measured for various plane inclinations and mean particle diameter d. Improved collapse is obtained for sand and glass beads by using a recently proposed scaling referred to as Pouliquen-Jenkins flow rule (PJFR) (see Fig. 2.). Measuring the slope \beta of the PJFR for ten different sizes of sand and glass beads, we find a systematic, strong increase of \beta with the divergence angle \theta_1 of h_s (see Fig. 3.). The copper materials with different shapes are not well described by either flow rule.
 

Sketch of the experimental setup:





Fig. 1. Normalized surface velocity as a function of the normalized flow thickness (PFR) for sand and glass beads of various sizes.


Fig. 2. Normalized surface velocity as a function of the normalized flow thickness (PJFR) for the same set of data as Fig. 1.



Fig. 3. The slope \beta of the  Pouliquen-Jenkins flow rule for for various materials as a function of the divergence angle \theta_1 of h_s.