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

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.