  We study theoretically the deterministic dynamics of single-domain
ferromagnetic nanoparticles in dilute ferrofluids, which is induced by a
time-varying gradient magnetic field. Using the force and torque balance
equations, we derive a set of the first-order differential equations describing
the translational and rotational motions of such particles characterized by
small Reynolds numbers. Since the gradient magnetic field generates both the
translations and rotations of particles, these motions are coupled. Based on
the derived set of equations, we demonstrate this fact explicitly by expressing
the particle position through the particle orientation angle, and vice versa.
The obtained expressions are used to show that the solution of the basic set of
equations is periodic in time and to determine the intervals, where the
particle coordinate and orientation angle oscillate. In addition, this set of
equations is solved approximately for the case of small characteristic
frequency of the particle oscillations. With this condition, we find that all
particles perform small translational oscillations near their initial
positions. In contrast, the orientation angle oscillates near the initial angle
only if particles are located in the vicinity of zero point of the gradient
magnetic field. The possible applications of the obtained results in
biomedicine and separation processes are also discussed.
