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

Authors S.I. Denisov , T.V. Lyutyy , A.T. Liutyi

Sumy State University, Rymsky-Korsakov St., 2, 40007 Sumy, Ukraine

Е-mail denisov@sumdu.edu.ua
Issue Volume 12, Year 2020, Number 6
Dates Received 10 August 2020; revised manuscript received 15 December 2020; published online 25 December 2020
Citation S.I. Denisov, T.V. Lyutyy, A.T. Liutyi, J. Nano- Electron. Phys. 12 No 6, 06028 (2020)
DOI https://doi.org/10.21272/jnep.12(6).06028
PACS Number(s) 75.75.Jn, 47.65.Cb
Keywords Dilute ferrofluids, Single-domain nanoparticles, Gradient magnetic field, Balance equations, Translational and rotational dynamics.

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.

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