Persistent structures in a three-dimensional dynamical system with flowing and non-flowing regions

Zafir Zaman, Mengqi Yu, Paul P. Park, Julio M. Ottino, Richard M. Lueptow, Paul B. Umbanhowar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Mixing of fluids and mixing of solids are both relatively mature fields. In contrast, mixing in systems where flowing and non-flowing regions coexist remains largely unexplored and little understood. Here we report remarkably persistent mixing and non-mixing regions in a three-dimensional dynamical system where randomness is expected. A spherical shell half-filled with dry non-cohesive particles and periodically rotated about two horizontal axes generates complex structures that vary non-trivially with the rotation angles. They result from the interplay between fluid-like mixing by stretching-and-folding, and solids mixing by cutting-and-shuffling. In the experiments, larger non-mixing regions predicted by a cutting-and-shuffling model alone can persist for a range of protocols despite the presence of stretching-and-folding flows and particle-collision-driven diffusion. By uncovering the synergy of simultaneous fluid and solid mixing, we point the way to a more fundamental understanding of advection driven mixing in materials with coexisting flowing and non-flowing regions.

Original languageEnglish (US)
Article number3122
JournalNature communications
Issue number1
StatePublished - Dec 1 2018

ASJC Scopus subject areas

  • General Physics and Astronomy
  • General Chemistry
  • General Biochemistry, Genetics and Molecular Biology


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