Slow axial drift in three-dimensional granular tumbler flow

TL;DR

This study investigates axial drift in three-dimensional granular tumblers, revealing that particles experience slow, geometry-dependent axial displacements driven by wall slope effects, challenging the assumption of negligible axial flow.

Contribution

It provides experimental and simulation evidence of slow axial drift in spherical and double cone tumblers, highlighting the influence of wall slope and tumbler geometry on particle movement.

Findings

Axial drift is 1-3% of tumbler diameter per pass.

Wall slope causes axial drift, increasing with equatorial diameter.

Axial drift varies with position, peaking away from the equator.

Abstract

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.