Hydrodynamic Torques and Rotations of Superparamagnetic Bead Dimers

Chains of micro-magnetic particles are often rotated with external magnetic fields for many lab-on-a-chip technologies such as transporting beads or mixing fluids. These applications benefit from faster responses of the actuated particles. In a rotating magnetic field, the magnetization of superparamagnetic beads, created from embedded magnetic nano-particles within a polymer matrix, is largely characterized by induced dipoles $m_{ip}$ along the direction of the field. In addition there is often a weak dipole $m_{op}$ that orients out-of-phase with the external rotating field. On a two-bead dimer, the simplest chain of beads, $m_{op}$ contributes a torque $\Gamma_m$ in addition to the torque from $m_{ip}$. For dimers with beads unbound to each other, $m_{op}$ rotates individual beads which generate an additional hydrodynamic torque on the dimer. Whereas, $m_{op}$ directly torques bound dimers. Our results show that $\Gamma_m$ significantly alters the average frequency-dependent dimer rotation rate for both bound and unbound monomers and, when $m_{op}$ exceeds a critical value, increases the maximum dimer rotation frequency. Models that include magnetic and hydrodynamics torques provide good agreement with the experimental findings over a range of field frequencies.