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We study the deterministic dynamics of single-domain ferromagneticnanoparticles in a viscous liquid induced by the joint action of the gradientand uniform magnetic fields. It is assumed that the gradient field depends ontime harmonically and the uniform field has two components, perpendicular andparallel to the gradient one. We also assume that the anisotropy magnetic fieldis so strong that the nanoparticle magnetization lies along the anisotropyaxis, i.e., the magnetization vector is "frozen" into the particle body. Withthese assumptions and neglecting inertial effects we derive the torque andforce balance equations that describe the rotational and translational motionsof particles. We reduce these equations to a set of two coupled equations forthe magnetization angle and particle coordinate, solve them numerically in awide range of the system parameters and analyze the role of the parallelcomponent of the uniform magnetic field. It is shown, in particular, thatnanoparticles perform only periodic rotational and translational motions if theperpendicular component of the uniform magnetic field is absent. In contrast,the nanoparticle dynamics in the presence of this component becomesnon-periodic, resulting in the drift motion (directed transport) ofnanoparticles. By analyzing the short and long-time dependencies of themagnetization angle and particle coordinate we show that the increase in theparallel component of the uniform magnetic field decreases both the particledisplacement for a fixed time and its average drift velocity on each period ofthe gradient magnetic field.

Numerical Analysis of the Nanoparticle Dynamics in a Viscous Liquid: Deterministic Approach