Hydrodynamic coupling of magnet-induced swarming disks on free surface

Artificial swarm systems inspired by swarming animals in nature have been developed recently. These engineered swarms are utilized for various applications, including surgical procedures, targeted drug delivery, and contactless micro-assembly. Since the swarms utilized in these applications are likely to operate in fluid environments, they experience strong hydrodynamic coupling, making it essential to understand their hydrodynamic responses and stability. We investigate the fundamental dynamic response of a magnetically controlled swarm system using two-dimensional magnetic disks floating on free surface. Floating magnetic disks are towed at a constant speed, using an external control magnet mounted on a linear guide above the free surface. The height from the free surface to the control magnet and the towing speed are varied to change the magnetic force strength and hydrodynamic loading, respectively, while the number of magnetic disks ranges from one to ten. The balance between magnetic control force and hydrodynamic loading determines swarming modes. Flow visualization reveals that the stability and dynamics of the magnetic swarms are correlated with flow structures. This research provides insights into designing externally controlled artificial swarm systems operating in dense fluid environments.