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.