A dynamical systems approach to mixing and segregation of granular materials in tumblers

Steven W. Meier, Richard M. Lueptow, Julio M. Ottino*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

127 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)757-827
Number of pages71
JournalAdvances in Physics
Issue number5
StatePublished - Sep 2007


  • Chaos
  • Dynamical systems
  • Granular flow
  • Granular matter
  • Mixing
  • Segregation

ASJC Scopus subject areas

  • Condensed Matter Physics


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