Asymptotic Theory for Directed Transport of Suspended Ferromagnetic Nanoparticles

Using the rigid dipole model, we study the translational and rotational motions of single-domain fer-romagnetic nanoparticles in a dilute suspension induced by the harmonically oscillating gradient magnetic field in the presence of a time-independent uniform magnetic field. Our approach is based on a set of the first-order differential equations that describe the time dependencies of the particle coordinate and mag-netization angle. We find the asymptotic solutions of this set of equations at small and large times and, by applying the matched asymptotic expansions for discrete times, derive analytical expressions for the aver-age particle coordinate and velocity.