Transient dynamics of density-driven particle segregation in a rotating drum

The shearing of a particle bed composed of two or more species results in spontaneous segregation. This poses problems in many industries, where the mixing of granules and powders is a common process and a homogeneous product is desired. In this work, the segregation dynamics occurring in a horizontal rotating drum filled with two granular species that only differ in density is investigated. In this system, radial segregation is relatively fast and occurs over the course of a few drum rotations. State-of-the art techniques allow the study of segregation dynamics at the end walls of a drum, as well as the observation of slow axial dynamics and the steady state of radial mixing inside the drum bulk. They do not allow, however, continuous observation of the transient radial mixing in the bulk. Using the ultrafast X-ray computer tomography it is possible to to take cross-sectional images through the opaque granular systems at 1000 frames per second. The high-speed image sequences from intermediate planes of the drum can reveal the segregation dynamics in the bulk. Here we present experimental results from the transient state of radial mixing for a binary granular system with density difference (density ratio 2.8) and equal size (4 mm) spherical beads in a half-filled drum. Using a dimensionless mixing index (M), we compare the dynamics of radial mixing and segregation in transverse planes in the bulk of the drum, captured with UFXCT, with the dynamics from the circular end caps to highlight wall effects. We also compare two dynamic models for radial mixing and consider the effect of flow on mixing dynamics. We find that second-order dynamics fit better the data than the commonly used first-order, since it accounts for the overshooting mixing dynamics occurring at higher drum speeds. We also find that, compared to the end cap, the dense particle segregation core is larger in the bulk plane and the overshooting in the mixing index is smaller, suggesting a correlation between mixing and flow characteristics, such as the dynamic angle of repose. Our results, because of better describing overmixing, are highly relevant to the pharmaceutical, food and cement industries.