(163f) Predicting Non-Mixing Regions of Granular Flows in a Spherical Tumbler

Mixing of granular materials is a key element in ensuring product uniformity in various industrial processes. However, the design of solids mixers has not changed significantly over the years due to under-developed theories and experimental approaches for studying three-dimensional (3D) granular flows. We consider the simple flow geometry of a half-filled spherical tumbler rotated by less than 90° alternately about two perpendicular horizontal axes as a prototype to investigate mixing behaviors under competing influences of both stretching (during flow) and cutting & shuffling (upon changing the axis of rotation). From experiments utilizing x-ray subsurface visualization, we identify persistent non-mixing regions, whose properties are surprisingly consistent with predictions of a continuum model simulation and an idealized model based on the mathematics of piecewise isometries in which an object is cut, rearranged, and then reassembled into the original shape. Combining experiment, mathematical modelling and simulation, we aim to resolve the formation of non-mixing regions, and ultimately to predict non-mixing regions for a given protocol. The mechanisms of mixing and non-mixing behaviors of granular materials in this simple 3D geometry provide significant insights for mixer design in more complicated geometries. Funded by NSF Grants CMMI-1000469 and CMMI-1435065.