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 and Paul B. Umbanhowar ()
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Zafir Zaman: Northwestern University
Mengqi Yu: Northwestern University
Paul P. Park: Northwestern University
Julio M. Ottino: Northwestern University
Richard M. Lueptow: Northwestern University
Paul B. Umbanhowar: Northwestern University

Nature Communications, 2018, vol. 9, issue 1, 1-9

Abstract: Abstract 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.

Date: 2018
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DOI: 10.1038/s41467-018-05508-7

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