Pattern generation and motion control of a vortex-like paramagnetic nanoparticle swarm

Controlling a swarm of microrobots with external fields is one of the major challenges for untethered microrobots. In this work, we present a new method to generate a vortex-like paramagnetic nanoparticle swarm (VPNS) from dispersed nanoparticles with a diameter of 500 nm, using rotating magnetic fields. The VPNS exhibits a dynamic-equilibrium structure, in which the nanoparticles perform synchronized motions. The mechanisms of the pattern-generation process are analyzed, simulated, and validated by experiments. By tuning the rotating frequency of the input magnetic field, the pattern of a VPNS changes accordingly. Analytical models for estimating the areal change of the pattern are proposed, and they have good agreement with the experimental data. Moreover, reversible merging and splitting of vortex-like swarms are demonstrated and investigated. Serving as a mobile robotic end-effector, a VPNS is capable of making locomotion by tuning the pitch angle of the actuating rotating field. With a small pitch angle, e.g. 2°, the whole swarm moves as an entity, and the shape of the pattern remains intact. In addition, the trapping forces of VPNSs are verified, showing the critical input parameters of the magnetic field that affect the morphology of the swarm. Finally, we demonstrate that VPNSs pass through curved and branched channels with high positioning precision, and the access rates for targeted delivery are over 90%, which are significantly higher than those in the cases of particle swarms moving with tumbling motions.