(21c) Surface Flow of Granular Materials in Non-Circular Rotating Cylinders

Rotating cylinders are
commonly used in many industrial applications -- mixing, coating,
grinding etc. The flow of particles in such cylinders is limited to a
shallow flowing layer at the free surface with most of the particles
following a solid-body rotation. Most of the mixing or segregation is
limited to this thin layer.

We studied experimentally
the flow of granular particles in cylinders with non-circular
cross-sections using flow visualization. Cylinders with square and
star cross-sections are considered for the study. We observed that
the flow of particles is time-periodic and the length and thickness
of the flowing layer vary periodically with time. The angle of the
free surface increases and decreases with the length of the flowing
layer. However, the length of the free surface is not very sensitive
to the changing free surface angle. The measured values are
well-predicted by the geometric considerations at a constant value of
the surface angle even at the highest rotational speed of the mixer
(5 rpm). The layer thickness profiles of the flowing layer are
qualitatively similar to those for a circular cross-section. However,
the thickness is larger in non-circular cross-sections for larger
particle size (3 mm). The measured layer profiles scaled with L(t),
half length of the free surface, and averaged over different
orientations of the mixer show large deviations from a mean value,
especially at higher rotational speeds of the mixer.

At low rotational speeds,
a pseudo-steadystate solution of the depth averaged mass balance
equation has been shown to match well with the measured mean layer
thickness profiles. We also show that the depth-averaged flow model
with an assumption of constant shear rate predicts the varying layer
thickness profiles at different orientations of the geometry to a
reasonably good accuracy. The variation of scaled midlayer thickness
is also well predicted by the model.