  Models of monodisperse particle flow in partially filled three-dimensional
tumblers often assume that flow along the axis of rotation is negligible. We
test this assumption, for spherical and double cone tumblers, using experiments
and discrete element method simulations. Cross sections through the particle
bed of a spherical tumbler show that, after a few rotations, a colored band of
particles initially perpendicular to the axis of rotation deforms: particles
near the surface drift toward the pole, while particles deeper in the flowing
layer drift toward the equator. Tracking of mm-sized surface particles in
tumblers with diameters of 8-14 cm shows particle axial displacements of one to
two particle diameters, corresponding to axial drift that is 1-3% of the
tumbler diameter, per pass through the flowing layer. The surface axial drift
in both double cone and spherical tumblers is zero at the equator, increases
moving away from the equator, and then decreases near the poles. Comparing
results for the two tumbler geometries shows that wall slope causes axial
drift, while drift speed increases with equatorial diameter. The dependence of
axial drift on axial position for each tumbler geometry is similar when both
are normalized by their respective maximum values.
