Abstract
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.
Highlights
Shielding problems of electromagnetic fields have been actively studied for solid thin-walled layers, see, e.g., references in [9], whereas a ferrofluid, as a softCopyright c 2022 The Author(s)
Made of a thick ferrofluid layer, in an externally applied uniform magnetic field is investigated in the current research via numerical modelling
Similar qualitative behavior is presented for three ferrofluids under consideration, whereas the moderately concentrated ferrofluid MF2 shows the strongest increase of the shielding effectiveness factor Kedfiff, compared with Kef
Summary
Shielding problems of electromagnetic fields have been actively studied for solid thin-walled layers, see, e.g., references in [9], whereas a ferrofluid, as a soft. Magnetic shielding of an external uniform magnetic field by ferrofluids is numerically studied in the current research, based on various mathematical models. When no external magnetic field is applied, the ferroparticles of a diameter about 10 nm are in Brownian motion inside the carrier-liquid. Once affected by an externally applied magnetic field, the particle diffusion in the direction of field gradient, named as magnetophoresis, occurs inside the ferrofluid as well. Made of a thick ferrofluid layer, in an externally applied uniform magnetic field is investigated in the current research via numerical modelling. 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. These ferrofluids are described in [21, Table II], with the volume fraction of the magnetic phase equaled to 0.05, 0.1 and 0.16, respectively
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