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.

Numerical Study of the Shielding Properties of a Ferrofluid Taking Into Account Magnitophoresis and Particle Interaction

“…The geometry for the problem under consideration is similar to the one in [9,15], see Figure 1. The two-dimensional geometry description is possible due to the assumptions that a cylindrical ferrofluid layer is infinitely long in the z-direction and that an applied magnetic field is uniform with the only non-zero component h 0 = const > 0 in the y-direction, see Figure 1.…”

“…To investigate the magnetic shielding by weakly, moderately and highly concentrated ferrofluids, the mathematical models in the form of the Maxwells equations for different magnetization laws of ferrofluids are considered in [9] under an assumption of a uniform particle distribution inside the ferrofluid. These mathematical models, formulated in the polar coordinates (r, ϕ) in terms of magnetostatic potentials u i (r, ϕ) :…”

“…Numerical investigations of magnetic shielding by a cylindrical thick-walled ferrofluid layer have their origins in [9,15]. Mathematical models in [9,15] were constructed on the basis of Maxwell's equations under the assumption that the magnetic particles inside the ferrofluid are uniformly distributed for any intensities of the externally applied field, thereby excluding the effects of magnetophoresis.…”

“…Numerical investigations of magnetic shielding by a cylindrical thick-walled ferrofluid layer have their origins in [9,15]. Mathematical models in [9,15] were constructed on the basis of Maxwell's equations under the assumption that the magnetic particles inside the ferrofluid are uniformly distributed for any intensities of the externally applied field, thereby excluding the effects of magnetophoresis. The present study continues research in [9,15] by taking into account the diffusion of nanosized ferroparticles (magnetophoresis) and particle interactions in the carrier-liquid, in order to estimate an influence of the steady-state particle redistribution on the degree of shielding.…”

“…Three mathematical models are constructed in which the magnetostatics equations in [9] and the diffusion equations are coupled with each other. Computations are made for three differently concentrated ferrofluids.…”