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We study theoretically the deterministic dynamics of single-domainferromagnetic nanoparticles in dilute ferrofluids, which is induced by atime-varying gradient magnetic field. Using the force and torque balanceequations, we derive a set of the first-order differential equations describingthe translational and rotational motions of such particles characterized bysmall Reynolds numbers. Since the gradient magnetic field generates both thetranslations and rotations of particles, these motions are coupled. Based onthe derived set of equations, we demonstrate this fact explicitly by expressingthe particle position through the particle orientation angle, and vice versa.The obtained expressions are used to show that the solution of the basic set ofequations is periodic in time and to determine the intervals, where theparticle coordinate and orientation angle oscillate. In addition, this set ofequations is solved approximately for the case of small characteristicfrequency of the particle oscillations. With this condition, we find that allparticles perform small translational oscillations near their initialpositions. In contrast, the orientation angle oscillates near the initial angleonly if particles are located in the vicinity of zero point of the gradientmagnetic field. The possible applications of the obtained results inbiomedicine and separation processes are also discussed.

Dynamics of Suspended Nanoparticles in a Time-varying Gradient Magnetic Field: Analytical Results