Numerical study of the shielding properties of a ferrofluid taking into account magnitophoresis and particle interaction

    Olga Lavrova   Affiliation
    ; Viktor Polevikov   Affiliation


Shielding properties of a cylindrical thick-walled ferrofluid layer that protects against externally applied uniform magnetic fields are numerically investigated. We take into account the diffusion of magnetic nanoparticles in the ferrofluid with magnetic dipole-dipole, steric and hydrodynamic interactions between particles. Permeability of the ferrofluid is considered to be dependent on the magnetic-field strength and the particle concentration. A combined method of finite differences and boundary elements is applied to solve a nonlinear transmission problem of magnetostatics in the whole space, augmented by nonlinear algebraic equations based on the mass transfer equation for magnetic nanoparticles in ferrofluids. Numerical experiments revealed that the diffusion of particles has negligible influence on the shielding properties at weak and strong intensities of the applied magnetic field when comparing with the results of computations for a uniform particle distribution.

Keyword : magnetostatics problem, diffusion problem, finite-difference method, boundary element method, Newton’s method, ferrofluid, magnetic shielding

How to Cite
Lavrova, O., & Polevikov, V. (2022). Numerical study of the shielding properties of a ferrofluid taking into account magnitophoresis and particle interaction. Mathematical Modelling and Analysis, 27(1), 161–178.
Published in Issue
Feb 7, 2022
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B.M. Berkovsky and V. Bashtovoi. Magnetic fluids and applications handbook. Begell House Inc. Publ., New York, 1996.

B.M. Berkovsky, V.F Medvedev and M.S. Krakov. Magnetic fluids: engineering applications. Oxford University Press, Oxford, 1993.

A. Cebers, E. Blum and M.M. Maiorov. Magnetic fluids. Walter de Gruyter, Berlin, 1997.

S. Celozzi, R. Araneo and G. Lovat. Electromagnetic Shielding. John Wiley & Sons, 2008.

B. Dolník, M. Rajňák, R. Cimbala, I. Kolcunová, J. Kurimský, J. Balogh, J. Džmura, J. Petráš, P. Kopčanský, M. Timko, J. Briančin and M. Fabián. The response of a magnetic fluid to radio frequency electromagnetic field. Acta Physica Polonica A, 131(4):946–948, 2017.

B. Dolník, M. Rajňák, R. Cimbala, I. Kolcunová, J. Kurimský, J. Džmura, J. Petráš, J. Zbojovský, M. Kosterec, P. Kopčanský and M. Timko. The shielding effectiveness of a magnetic fluid in radio frequency range. Acta Physica Polonica A, 133(3):585–587, 2018.

V. Glyva, N. Kasatkina, V. Nazarenko, N. Burdeina, N. Karaieva, L. Levchenko, O. Panova, O. Tykhenko, B. Khalmuradov and O. Khodakovskyy. Development and study of protective properties of the composite materials for shielding the electromagnetic fields of a wide frequency range. Eastern-European Journal of Enterprise Technologies, 2(12):40–47, 2020.

A.O. Ivanov and O.B. Kuznetsova. Magnetic properties of dense ferrofluids: An influence of interparticle correlations. Physical Review E, 64:041405, 2001.

O. Lavrova, V. Polevikov and S. Polevikov. Numerical modelling of magnetic shielding by a cylindrical ferrofluid layer. Math. Model. Anal., 24(2):155–170, 2019.

O. Lavrova, V. Polevikov and L. Tobiska. Numerical study of diffusion of interacting particles in a magnetic fluid layer. In P. Miidla(Ed.), Numerical Modelling, pp. 183–202. IntechOpen, 2012.

O. Lavrova, V. Polevikov and L. Tobiska. Modeling and simulation of magnetic particles diffusion in a ferrofluid layer. Magnetohydrodynamics, 52(4):439–452, 2016.

M. Mishra, A.P. Singh, B.P. Singh, V.N. Singh and S.K. Dhawan. Conducting ferrofluid: a high-performance microwave shielding material. J. Mater. Chem. A, 2(32):13159–13168, 2014.

H. Mohseni. Dynamic magnetic shielding and beamforming using ferrofluid for compact magnetoencephalography (meg). US Patent US20200088811A1, 2019.

V. Polevikov and L. Tobiska. On the solution of the steady-state diffusion problem for ferromagnetic particles in a magnetic fluid. Math. Model. Anal., 13(2):233–240, 2008.

V.K. Polevikov and B.T. Erofeenko. Numerical modelling of the interaction of a magnetic field with a cylindrical magnetic-fluid layer. Informatika, 2(54):5–13, 2017. (in Russian)

A.F. Pshenichnikov. Equilibrium magnetization of concentrated ferrocolloids. J. Magn. Magn. Mater., 145(3):319–326, 1995.

A.F. Pshenichnikov, E.A Elfimova and A.O. Ivanov. Magnetophoresis, sedimentation, and diffusion of particles in concentrated magnetic fluids. J. Chem. Phys., 134:184508, 2011.

A.F. Pshenichnikov and A.V. Lebedev. Magnetic susceptibility of concentrated ferrocolloids. Colloid J., 67:189–200, 2005.

A.F. Pshenichnikov, V.V. Mekhonoshin and A.V. Lebedev. Magneto-granulometric analysis of concentrated ferrocolloids. J. Magn. Magn. Mater., 161:94– 102, 1996.

R.E. Rosensweig. Ferrohydrodynamics. Dover Pubns, New York, 1998.

A.Y. Solovyova, E.A. Elfimova, A.O. Ivanov and P.J. Camp. Modified mean-field theory of the magnetic properties of concentrated, highsusceptibility, polydisperse ferrofluids. Physical Review E, 96:052609, 2017.