Theoretical study of the dynamic magnetic response of ferrofluid to static and alternating magnetic fields / Batrudinov T.M., Ambarov A.V., Elfimova E.A., Zverev V.S., Ivanov A.O. // Journal of Magnetism and Magnetic Materials. - 2017. - V. 431, l. . - P. 180-183.

ISSN:

03048853

Type:

Article

Abstract:

The dynamic magnetic response of ferrofluid in a static uniform external magnetic field to a weak, linear polarized, alternating magnetic field is investigated theoretically. The ferrofluid is modeled as a system of dipolar hard spheres, suspended in a long cylindrical tube whose long axis is parallel to the direction of the static and alternating magnetic fields. The theory is based on the Fokker-Planck-Brown equation formulated for the case when the both static and alternating magnetic fields are applied. The solution of the Fokker-Planck-Brown equation describing the orientational probability density of a randomly chosen dipolar particle is expressed as a series in terms of the spherical Legendre polynomials. The obtained analytical expression connecting three neighboring coefficients of the series makes possible to determine the probability density with any order of accuracy in terms of Legendre polynomials. The analytical formula for the probability density truncated at the first Legendre polynomial is evaluated and used for the calculation of the magnetization and dynamic susceptibility spectra. In the absence of the static magnetic field the presented theory gives the correct single-particle Debye-theory result, which is the exact solution of the Fokker-Planck-Brown equation for the case of applied weak alternating magnetic field. The influence of the static magnetic field on the dynamic susceptibility is analyzed in terms of the low-frequency behavior of the real part and the position of the peak in the imaginary part. © 2016 Elsevier B.V.

Author keywords:

Dynamic magnetic susceptibility spectra; Ferrofluid; The Fokker-Planck-Brown equation

Index keywords:

Computational mechanics; Fokker Planck equation; Magnetic fields; Magnetic fluids; Magnetic susceptibility; Polynomials; Probability; Probability density function; Alternating magnetic field; Analytic

DOI:

10.1016/j.jmmm.2016.09.094

Смотреть в Scopus:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85001610070&doi=10.1016%2fj.jmmm.2016.09.094&partnerID=40&md5=8a6f1dcb646c1918d4921eec3a0a6d07

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Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-85001610070&doi=10.1016%2fj.jmmm.2016.09.094&partnerID=40&md5=8a6f1dcb646c1918d4921eec3a0a6d07
Affiliations	Institute of Mathematics and Computer Sciences, Ural Federal University, Lenin Avenue 51, Ekaterinburg, Russian Federation
Author Keywords	Dynamic magnetic susceptibility spectra; Ferrofluid; The Fokker-Planck-Brown equation
Funding Details	15-12-10003, RSF, Russian Science Foundation
Funding Text	This research was supported by Russian Science Foundation, Grant no. 15-12-10003.
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Correspondence Address	Elfimova, E.A.email: Ekaterina.Elfimova@urfu.ru
Publisher	Elsevier B.V.
CODEN	JMMMD
Language of Original Document	English
Abbreviated Source Title	J Magn Magn Mater
Source	Scopus