Mixing of granular materials in slowly rotated containers

Abstract

AbstractNoncohesive granular materials in slowly rotated containers mix by discrete avalanches; such a process can be described mathematically as a mapping of avalanching wedges. A natural decomposition is thus proposed: a geometrical part consisting of a mapping wedge → wedge, which captures large‐scale aspects of the problem; a dynamical part confined to the avalanche itself, which captures details emanating from differences in size/density/morphology. Both viewpoints are developed and comparisons with experiments are used to verify the predictions of the models. In this article, we develop a model of granular mixing and show how to extend the model in order that it may: (1) handle complicated geometries, (2) be applicable for 3‐D mixers, (3) rapidly test mixing enhancement strategies, and (4) incorporate differences in particle properties. In addition, an optimal fill level is determined for several 2‐D mixing geometries, and a novel hybrid—geometrical/dynamical—computational technique is proposed. By merging the geometrical and dynamical viewpoints, this technique reduces the computational time of a typical molecular‐dynamics‐type simulation by a factor of 15. The ultimate goal is to provide fundamental understanding and tools for the rational design and optimization of granular mixing devices.