Viscoelasticity reshapes the frequency response of a rotating magnetic particle

RESUMO

A magnetic particle driven by a rotating magnetic field undergoes a transition from synchronous to asynchronous rotation at a critical driving frequency. The asynchronous dynamics is well understood in Newtonian fluids but remains unclear in viscoelastic media. Here, we develop a theoretical description of the asynchronous rotation of a magnetic particle in a Jeffreys-type viscoelastic fluid. The particle's time-averaged angular velocity exhibits a nontrivial frequency dependence that changes from non-monotonic to monotonic as the polymer relaxation time increases. This behavior is explained by the interplay among magnetic driving, viscoelastic relaxation, and frequency-dependent viscous dissipation. We further derive an asymptotic expression that captures the non-monotonic dependence. These results clarify how solvent and polymer contributions jointly control asynchronous rotation and provide a physical basis for guiding relevant applications in complex fluids.