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Numerical modelling of magnetic shielding by a cylindrical ferrofluid layer. (English) Zbl 1473.35530

Summary: 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.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
65N06 Finite difference methods for boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs

References:

[1] H. Altenbach and G.I. Mikhasev(Eds.). Shell and Membrane Theories in Me-chanics and Biology: From Macro-to Nanoscale Structures. Advanced structured materials. Springer, 2015. https://doi.org/10.1007/978-3-319-02535-3. · Zbl 1306.74002 · doi:10.1007/978-3-319-02535-3
[2] 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. · Zbl 0862.65080 · doi:10.1006/jcph.1996.0181
[3] B.M. Berkovsky and V. Bashtovoi. Magnetic fluids and applications handbook. Begell House Inc. Publ., New York, 1996.
[4] B.M. Berkovsky, V.F Medvedev and M.S. Krakov. Magnetic fluids: engineering applications. Oxford University Press, Oxford, 1993.
[5] C.A. Brebbia, J.C.F. Telles and L.C. Wrobel. Boundary element tech-niques: theory and application in engineering. Springer-Verlag, Berlin, 1984. https://doi.org/10.1007/978-3-642-48860-3. · Zbl 0556.73086 · doi:10.1007/978-3-642-48860-3
[6] A. Cebers, E. Blum and M.M. Maiorov. Magnetic fluids. Walter de Gruyter, Berlin, 1997.
[7] S. Celozzi, R. Araneo and G. Lovat. Electromagnetic Shielding. John Wiley & Sons, 2008. https://doi.org/10.1002/9780470268483. · doi:10.1002/9780470268483
[8] Ya.G. Dorfman. Magnetic properties and structure of matter. Izdatelstvo LKI, Moscow, 2010. (in Russian)
[9] 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)
[10] V.T. Erofeenko, G.F. Gromyko and G.M. Zayats. Boundary value prob-lems 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. · Zbl 1456.74040 · doi:10.1134/S0012266117070102
[11] U.V. Glonyagin. Elements of the theory and calculation of magnetostatic fields of ferromagnetic bodies. Sudostroenie, Leningrad, 1967. (in Russian)
[12] 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. · doi:10.1016/j.jmmm.2015.08.122
[13] 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.
[14] 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. · doi:10.1103/PhysRevE.64.041405
[15] L.V. King. Electromagnetic shielding at radio frequencies. Phil. Mag. J. Sci., 15(97):201-223, 1933. https://doi.org/10.1080/14786443309462178. · Zbl 0006.27602 · doi:10.1080/14786443309462178
[16] 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. · doi:10.1088/0953-8984/18/38/S09
[17] 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.
[18] 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. · Zbl 1426.76169 · doi:10.3846/1392-6292.2010.15.223-233
[19] O. Lavrova, V. Polevikov and L. Tobiska. Modeling and simulation of magnetic particles diffusion in a ferrofluid layer. Magnetohydrodynamics, 52(4):417-430, 2016.
[20] A.V. Lebedev. Dipole interparticle interaction in magnetic fluids. Colloid Jour-nal, 76(3):334-341, 2014. https://doi.org/0.1134/S1061933X14030107.
[21] G. Mikhasev, I. Mlechka and H. Altenbach. Soft suppression of traveling lo-calized vibrations in medium-length thin sandwich-like cylindrical shells con-taining magnetorheological layers via nonstationary magnetic field. In J. Awre-jcewicz(Ed.), Dynamical Systems: Theoretical and Experimental Analysis, vol-ume 182 of Springer Proceedings in Mathematics & Statistics, pp. 241-260, Switzerland, 2016. Springer. · Zbl 1397.74141
[22] G.I. Mikhasev, H. Altenbach and E.A. Korchevskaya. On the influence of the magnetic field on the eigenmodes of thin laminated cylindrical shells contain-ing magnetorheological elastomer. Composite Structures, 113:186-196, 2014. https://doi.org/10.1016/j.compstruct.2014.02.031. · doi:10.1016/j.compstruct.2014.02.031
[23] 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. · Zbl 1221.76128 · doi:10.2478/cmam-2004-0005
[24] 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)
[25] 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. · Zbl 1255.76127 · doi:10.3846/1392-6292.2008.13.233-240
[26] 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. · doi:10.1063/1.1778135
[27] 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. · doi:10.1007/s10595-005-0080-x
[28] R.E. Rosensweig. Ferrohydrodynamics. Dover Pubns, New York, 1998.
[29] A.N. Tikhonov and A.A. Samarskii. Equations of Mathematical Physics. Perga-mon, Oxford, 1963. · Zbl 0111.29008
[30] 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. · doi:10.1016/j.jallcom.2018.03.288
[31] 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 ad-ditives on the structure of Bi films. J. Alloys Compd., 735:1943-1948, 2018. https://doi.org/10.1016/j.jallcom.2017.11.329. · doi:10.1016/j.jallcom.2017.11.329
[32] 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. · doi:10.1016/j.jmmm.2017.07.053
[33] 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 electrode-posited Ni-Fe nanogranular films. CrystEngComm, 20:2306-2315, 2018. https://doi.org/10.1039/C8CE00310F. · doi:10.1039/C8CE00310F
[34] T.I. Zubar, S.A. Sharko, D.I. Tishkevich, N.N. Kovaleva, D.A. Vin-nik, S.A. Gudkova, E.L. Trukhanova, E.A. Trofimov, S.A. Chizhik, L.V. Panina, S.V. Trukhanov and A.V. Trukhanov. Anomalies in Ni-Fe nanogranular films growth. J. Alloys Compd., 748:970-978, 2018. https://doi.org/10.1016/j.jallcom.2018.03.245. · doi:10.1016/j.jallcom.2018.03.245
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