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

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This study reveals persistent mixing and non-mixing regions in particle systems, driven by a synergy of fluid and solid dynamics. Understanding these complex interactions is key for materials science.

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Area of Science:

  • Physics
  • Materials Science
  • Complex Systems

Background:

  • Mixing of fluids and solids are mature fields.
  • Mixing in systems with coexisting flowing and non-flowing regions is poorly understood.

Purpose of the Study:

  • Investigate mixing phenomena in a 3D dynamical system with both fluid-like and solid-like behaviors.
  • Uncover the interplay between different mixing mechanisms in complex materials.

Main Methods:

  • Utilized a 3D dynamical system involving a spherical shell half-filled with dry particles.
  • Periodically rotated the shell about two horizontal axes to induce mixing.
  • Employed a cutting-and-shuffling model to predict non-mixing regions.

Main Results:

  • Observed remarkably persistent mixing and non-mixing regions, contrary to expectations of randomness.
  • Demonstrated that fluid-like stretching-and-folding and solid-like cutting-and-shuffling interplay to create complex structures.
  • Found that non-mixing regions, predicted by the solids mixing model, can persist despite fluid flows and diffusion.

Conclusions:

  • The synergy between fluid and solid mixing mechanisms governs advection-driven mixing in systems with coexisting flowing and non-flowing regions.
  • Highlights the need for a more fundamental understanding of mixing in such complex materials.
  • Provides insights into controlling mixing in granular materials and multiphase systems.