Numerical modelling of magnetic shielding by a cylindrical ferrofluid layer
Abstract
A coupled method of finite differences and boundary elements is applied to solve a nonlinear transmission problem of magnetostatics. The problem describes an interaction of a uniform magnetic field with a cylindrical ferrofluid layer. Ferrofluid magnetisations, based on expansions over the Langevin law, are considered to model ferrofluids with a different concentration of ferroparticles. The shielding effectiveness factor of the cylindrical thick-walled ferrofluid layer is calculated depending on intensities of the uniform magnetic field and on thickness of the ferrofluid layer.
Keyword : transmission magnetostatics problem, finite difference method, boundary element method, magnetic fluid, shielding
How to Cite
Lavrova, O., Polevikov, V., & Polevikov, S. (2019). Numerical modelling of magnetic shielding by a cylindrical ferrofluid layer. Mathematical Modelling and Analysis, 24(2), 155-170. https://doi.org/10.3846/mma.2019.011
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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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)
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D.I. Tishkevich, S.S. Grabchikov, L.S. Tsybulskaya, V.S. Shendyukov, S.S. Perevoznikov, S.V. Trukhanov, E.L. Trukhanova, A.V. Trukhanov and D.A.
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A.V. Trukhanov, S.S. Grabchikov, A.A. Solobai, D.I. Tishkevich, S.V. Trukhanov and E.L. Trukhanova. AC and DC-shielding properties for the Ni80Fe20/Cu film structures. J. Magn. Magn. Mater., 443:142–148, 2017. https://doi.org/10.1016/j.jmmm.2017.07.053.
T.I. Zubar, L.V. Panina, N.N. Kovaleva, S.A. Sharko, D.I. Tishkevich, D.A. Vinnik, S.A. Gudkova, E.L. Trukhanova, E.A. Trofimov, S.A. Chizhik, S.V. Trukhanov and A.V. Trukhanov. Anomalies in growth of electrodeposited Ni-Fe nanogranular films. CrystEngComm, 20:2306–2315, 2018. https://doi.org/10.1039/C8CE00310F.
T.I. Zubar, S.A. Sharko, D.I. Tishkevich, N.N. Kovaleva, D.A. Vinnik, S.A. Gudkova, E.L. Trukhanova, E.A. Trofimov, S.A. Chizhik, L.V. Panina, S.V. Trukhanov and A.V. Trukhanov. Anomalies in NiFe nanogranular films growth. J. Alloys Compd., 748:970–978, 2018. https://doi.org/10.1016/j.jallcom.2018.03.245.
J.-P. Berenger. Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J. of Computational Physics, 127(2):363–379, 1996. https://doi.org/10.1006/jcph.1996.0181.
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.
C.A. Brebbia, J.C.F. Telles and L.C. Wrobel. Boundary element techniques: theory and application in engineering. Springer-Verlag, Berlin, 1984. https://doi.org/10.1007/978-3-642-48860-3.
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. https://doi.org/10.1002/9780470268483.
Ya.G. Dorfman. Magnetic properties and structure of matter. Izdatelstvo LKI, Moscow, 2010. (in Russian)
E.A. Elfimova. Statistical thermodynamics and physical properties of magnetic fluids: influence of interparticle correlations. Dissertation for a degree of doctor, Ekaterinburg, 2016. (in Russian)
V.T. Erofeenko, G.F. Gromyko and G.M. Zayats. Boundary value problems with integral boundary conditions for the modelling of magnetic fields in cylindrical film shells. Differential Equations, 53(7):935–948, 2017.https://doi.org/10.1134/S0012266117070102.
U.V. Glonyagin. Elements of the theory and calculation of magnetostatic fields of ferromagnetic bodies. Sudostroenie, Leningrad, 1967. (in Russian)
S.S. Grabchikov, A.V. Trukhanov, S.V. Trukhanov, I.S. Kazakevich, A.A. Solobay, V.T. Erofeenko and N.V. Vasilenkov. Effectiveness of the magnetostatic shielding by the cylindrical shells. J. Magn. Magn. Mater., 398(15):49–53, 2016.https://doi.org/10.1016/j.jmmm.2015.08.122.
G.F. Gromyko, S.S. Grabchikov, V.T. Erofeenko and G.M. Zayats. The shielding effectiveness of static magnetic fields by cylindrical screen taking into account nonlinear effects. Physical Bases of Instrumentation, 4(4):30–39, 2015.
A.O. Ivanov and O.B. Kuznetsova. Magnetic properties of dense ferrofluids: An influence of interparticle correlations. Physical Review E, 64:041405, 2001.https://doi.org/10.1103/PhysRevE.64.041405.
L.V. King. Electromagnetic shielding at radio frequencies. Phil. Mag. J. Sci., 15(97):201–223, 1933. https://doi.org/10.1080/14786443309462178.
O. Lavrova, G. Matthies, T. Mitkova, V. Polevikov and L. Tobiska. Numerical treatment of free surface problems in ferrohydrodynamics. Journal of Physics: Condensed Matter, 18(38):S2657–S2669, 2006. https://doi.org/10.1088/0953-8984/18/38/S09.
O. Lavrova, V. Polevikov and L. Tobiska. Instability of a magnetic fluid drop in a capillary: a numerical study. Magnetohydrodynamics, 44(2):183–189, 2008
O. Lavrova, V. Polevikov and L. Tobiska. Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles. Math. Model. Anal., 15(2):223–233, 2010. https://doi.org/10.3846/1392-6292.2010.15.223-233.
O. Lavrova, V. Polevikov and L. Tobiska. Modeling and simulation of magnetic particles diffusion in a ferrofluid layer. Magnetohydrodynamics, 52(4):417–430, 2016.
A.V. Lebedev. Dipole interparticle interaction in magnetic fluids. Colloid Journal, 76(3):334–341, 2014. https://doi.org/10.1134/S1061933X14030107.
G. Mikhasev, I. Mlechka and H. Altenbach. Soft suppression of traveling localized vibrations in medium-length thin sandwich-like cylindrical shells containing magnetorheological layers via nonstationary magnetic field. In J. Awrejcewicz(Ed.), Dynamical Systems: Theoretical and Experimental Analysis, volume 182 of Springer Proceedings in Mathematics & Statistics, pp. 241–260, Switzerland, 2016. Springer.
G.I. Mikhasev, H. Altenbach and E.A. Korchevskaya. On the influence of the magnetic field on the eigenmodes of thin laminated cylindrical shells containing magnetorheological elastomer. Composite Structures, 113:186–196, 2014.https://doi.org/10.1016/j.compstruct.2014.02.031.
V.K. Polevikov. Methods for numerical modeling of two-dimensional capillary surfaces. Computational Methods in Applied Mathematics, 4(1):66–93, 2004.https://doi.org/10.2478/cmam-2004-0005.
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)
V.K. Polevikov and L. Tobiska. On the solution of the steady-state diffusion problem for ferromagnetic particles in a magnetic field. Math. Model. Anal., 13(2):233–240, 2008. https://doi.org/10.3846/1392-6292.2008.13.233-240.
A.F. Pshenichnikov and A.V. Lebedev. Low-temperature susceptibility of concentrated magnetic fluids. J. Chem. Phys., 121(11):5455–5467, 2004. https://doi.org/10.1063/1.1778135.
A.F. Pshenichnikov and A.V. Lebedev. Magnetic susceptibility of concentrated ferrocolloids. Colloid Journal, 67(2):189–200, 2005.https://doi.org/10.1007/s10595-005-0080-x.
R.E. Rosensweig. Ferrohydrodynamics. Dover Pubns, New York, 1998.
A.N. Tikhonov and A.A. Samarskii. Equations of Mathematical Physics. Pergamon, Oxford, 1963.
D.I. Tishkevich, S.S. Grabchikov, S.B. Lastovskii, S.V. Trukhanov, T.I. Zubar, D.S. Vasin and A.V. Trukhanov. Correlation of the synthesis conditions and microstructure for Bi-based electron shields production. J. Alloys Compd., 749:1036–1042, 2018. https://doi.org/10.1016/j.jallcom.2018.03.288.
D.I. Tishkevich, S.S. Grabchikov, L.S. Tsybulskaya, V.S. Shendyukov, S.S. Perevoznikov, S.V. Trukhanov, E.L. Trukhanova, A.V. Trukhanov and D.A.
Vinnik. Electrochemical deposition regimes and critical influence of organic additives on the structure of Bi films. J. Alloys Compd., 735:1943–1948, 2018. https://doi.org/10.1016/j.jallcom.2017.11.329.
A.V. Trukhanov, S.S. Grabchikov, A.A. Solobai, D.I. Tishkevich, S.V. Trukhanov and E.L. Trukhanova. AC and DC-shielding properties for the Ni80Fe20/Cu film structures. J. Magn. Magn. Mater., 443:142–148, 2017. https://doi.org/10.1016/j.jmmm.2017.07.053.
T.I. Zubar, L.V. Panina, N.N. Kovaleva, S.A. Sharko, D.I. Tishkevich, D.A. Vinnik, S.A. Gudkova, E.L. Trukhanova, E.A. Trofimov, S.A. Chizhik, S.V. Trukhanov and A.V. Trukhanov. Anomalies in growth of electrodeposited Ni-Fe nanogranular films. CrystEngComm, 20:2306–2315, 2018. https://doi.org/10.1039/C8CE00310F.
T.I. Zubar, S.A. Sharko, D.I. Tishkevich, N.N. Kovaleva, D.A. Vinnik, S.A. Gudkova, E.L. Trukhanova, E.A. Trofimov, S.A. Chizhik, L.V. Panina, S.V. Trukhanov and A.V. Trukhanov. Anomalies in NiFe nanogranular films growth. J. Alloys Compd., 748:970–978, 2018. https://doi.org/10.1016/j.jallcom.2018.03.245.