Authors: Meier, Steven¹; Lueptow, Richard²; Ottino, Julio³

Source: Advances In Physics, Volume 56, Number 5, September 2007 , pp. 757-827(71)

Publisher: Taylor and Francis Ltd

Abstract:

The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.

Keywords: Chaos; Granular matter; Mixing; Segregation; Dynamical systems; Granular flow

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00018730701611677

Affiliations: 1: Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA 2: Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA 3: Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA,Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA

Publication date: 2007-09-01

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