Subsurface X-ray Visualization of Three-Dimensional Granular Tumbler Flow and Mixing

Granular flow and mixing experiments in rotating partially filled tumblers are often limited to visualization along walls or the free surface. To probe the dynamics deep inside the bed, a common approach is to experimentally utilize quasi-two-dimensional (quasi-2D) geometries and infer the three dimensional (3D) behavior by assuming that the flow is primarily 2D with diffusive spanwise particle motion. However, this model can miss subtle effects seen solely in 3D geometries. For example, we demonstrate that an axial drift of monodisperse particles exists in partially filled spherical and double cone tumblers using experiments and discrete element method (DEM) simulations. The drift is small (1-2 particle diameters or 1-3% of the tumbler diameter per flowing layer pass) relative to streamwise displacements, whose speed depends on the flowing layer length.

To further our understanding of 3D flow and mixing in tumblers, we designed and built an X-ray imaging system that provides subsurface imaging of the tumbler during flow. Tracer (X-ray opaque) particles in a bed of X-ray translucent particles are tracked to construct trajectories through the particle bed. Stroboscopic imaging of the tumbler can provide Poincaré sections to determine regions of good mixing and regions of segregation. Current work involves providing experimental support for the existence of persistent segregated regions for a two axis tumbling protocol, as predicted by a dynamical systems theoretical model. Ultimately, the verification of the model will allow for informed design of tumbling protocols. Funded by NSF Grant CMMI-1000469.