Rolling and propulsion of self-assembled magnetic clusters in confined environments

We investigate the dynamics of magnetic particles subjected to rotating magnetic fields, focusing on the influence of confinement geometry on their collective motion. Two experimental configurations were studied: two-dimensional (2D) confinement, where particles move freely on a flat solid–liquid interface, and one-dimensional (1D) confinement within narrow microchannels. In both cases, external magnetic actuation leads to the formation of self-assembled elongated clusters that exhibit directed motion. We perform detailed particle tracking and propose a scaling analysis of the translational velocity normalized by the angular frequency ($v/\omega$) as a function of cluster length. Our results demonstrate that, under 2D confinement, clusters display rolling-like behavior consistent with theoretical predictions for non-slipping elongated bodies. In contrast, the introduction of geometric constraints in 1D confinement significantly reduces locomotion efficiency, as evidenced by lower $v/\omega$ values. These findings highlight the critical role of morphology and environmental constraints in the magnetic actuation and transport of microstructured aggregates. The proposed framework provides information for optimizing design principles in magnetically driven microrobotics operating in restricted environments.