Periodic and chaotic orbits of plane-confined micro-rotors in creeping flows

TL;DR

This paper investigates the complex behaviors of spinning micro-rotors in viscous fluids, revealing intricate periodic and chaotic trajectories influenced by initial conditions and interactions.

Contribution

It introduces a theoretical model of plane-confined micro-rotors in creeping flows, highlighting emergent complex dynamics and drawing parallels to 2D vortex systems.

Findings

Emergence of periodic and chaotic trajectories

Dependence of dynamics on initial positions and separations

Insights into interactions in denser rotor populations

Abstract

We explore theoretically the complex dynamics and emergent behaviors of spinning spheres immersed in viscous fluid. The particles are coupled to each-other via the fluid in which they are suspended: each particle disturbs the surrounding fluid with a rotlet field and that fluid flow affects the motion of the other particles. We notice the emergence of intricate periodic or chaotic trajectories that depend on the rotors initial position and separation. The point-rotor motions confined to a plane bear similarities the classic 2D point-vortex dynamics. Our analyses highlight the complexity of the interaction between just a few rotors and suggest richer behavior in denser populations. We discuss how the model gives insight into more complex systems and suggest possible extensions for future theoretical studies.