Drift of suspended single-domain nanoparticles in a harmonically oscillating gradient magnetic field

We study the nonlinear dynamics of single-domain ferromagnetic nanoparticles in a viscous liquid induced by a harmonically oscillating gradient magnetic field in the absence and presence of a static uniform magnetic field. Under some physically reasonable assumptions, we derive a coupled set of stiff ordinary differential equations for the magnetization angle and particle coordinate describing the rotational and translational motions of nanoparticles. Analytical solutions of these equations are determined for nanoparticles near and far from the coordinate origin, and their correctness is confirmed numerically. We show that if a uniform magnetic field is absent, the magnetization angle and particle coordinate of each nanoparticle are periodic functions of time. In contrast, the presence of a uniform magnetic field makes these functions aperiodic. In this case, we perform a detailed analysis of the nanoparticle dynamics and predict the appearance of the drift motion (directed transport) of nanoparticles. We calculate both analytically and numerically the drift velocity, study its dependence on time and model parameters, analyze the physical origin of the drift phenomenon and discuss its potential biomedical applications.