Degenerate states, emergent dynamics and fluid mixing by magnetic rotors

Abstract

We investigate the collective motion of magnetic rotors suspended in a viscous fluid under an uniform rotating magnetic field. The rotors are positioned on a square lattice, and low Reynolds hydrodynamics is assumed. For a 3 × 3 array of magnets, we observe three characteristic dynamical patterns as the external field strength is varied: a synchronized pattern, an oscillating pattern, and a chessboard pattern. The relative stability of these depends on the competition between the energy due to the external magnetic field and the energy of the magnetic dipole-dipole interactions among the rotors. We argue that the chessboard pattern can be understood as an alternation in the stability of two degenerate states, characterized by striped and spin-ice configurations, as the applied magnetic field rotates. For larger arrays, we observe propagation of slip waves that are similar to metachronal waves. The rotor arrays have potential as microfluidic devices that can mix fluids and create vortices of different sizes.

Diffusion and collective motion of rotlets in 2D space*

“…Recently, we reported that the magnetic rotors that are placed in a square grid show interesting rotational patterns. [9,10] We found a quarter pattern, in which the rotors undergo full rotations with different quadrants of the array turning in different directions when the external magnetic field is dominant. When the dipolar interaction between the rotors is dominant, a stripe pattern in which the rotors swing upwards or downwards in alternating stripes emerges.…”