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

• Published in: Nature communications Vol. 9; no. 1; pp. 3122 - 9
• Main Authors: Zaman, Zafir, Yu, Mengqi, Park, Paul P., Ottino, Julio M., Lueptow, Richard M., Umbanhowar, Paul B.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 07.08.2018; Nature Publishing Group; Nature Portfolio
• Subjects: 639/638/898; 639/705/1041; 639/766/189; 639/766/530/2803; Collision dynamics; Computational fluid dynamics; Cutting fluids; Cuttings; Dynamical systems; Folding; Humanities and Social Sciences; multidisciplinary; Science; Science (multidisciplinary); Spherical shells; Stretching; Three dimensional flow
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-018-05508-7

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. Understanding mixing in yield stress materials, such as paint and sand, is complicated due to the coexistence of solid-like and fluid-like regimes. Zaman et al. examine mixing in a granular material in three dimensions and find persistent complex non-mixing structures within the chaotic flowing regime.