Controlling pair dynamics of rotating magnetic microparticles through radial and transverse interactions

RESUMO

Rotating magnetic microparticles are building blocks for field-driven assembly and microrobotic control. As the elementary interaction rule for larger assemblies, pair motion in these systems is governed not only by magnetic forcing, but also by hydrodynamic coupling and other long-range interactions. Here we develop a reduced framework for two synchronized rotating magnetic particles by resolving the interactions into radial components that change the interparticle distance and transverse components that rotate the line of centers. The competition between magnetic dipolar interaction, additional radial repulsion, and rotation-induced transverse coupling selects three pair-motion modes: rigid-body rotation, contact-separation rotation, and irreversible separation. We derive transition criteria for the rigid-body state, reversed orbital motion, and the separation boundary, and obtain an asymptotic solution for the separation dynamics. Lattice Boltzmann simulations of particles rotating near a wall provide a hydrodynamic realization of the model, in which inertial secondary flow generates radial repulsion and rotational flow produces transverse coupling. The resulting phase diagram in the physical $(\mathrm{Re},C_m)$ plane is consistent with the reduced-model predictions. These results provide design rules for programming elementary pair interactions in rotating magnetic-particle systems and may help guide the control of microrobotic assemblies.