Meniscus of a magnetic fluid in the field of a current-carrying wire: two-dimensional numerical simulations

Eißmann, P.-B.; Lange, Adrian; Odenbach, S.

doi:10.22364/mhd.47.2.6

Cited by 8 publications

(7 citation statements)

References 14 publications

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“…Extending the simulations in [19], the numerics here is done in three dimensions. The numerical calculations were conducted with the commercial software package ANSYS FLUENT 13.0 using the finite volume method for the two phases fluid and air.…”

Section: Methodsmentioning

confidence: 99%

“…For all calculated menisci of Figures 6 and 9, it is noticeable that the numerical values underestimate the experimental data. In principle, higher calculated surfaces would appear for smaller angles of contact at the wire, but a test in [19] showed that the effect of angles smaller than the measured ones is negligible. Therefore, the assumption of isothermal condition deserves a consideration in more detail.…”

Section: Menisci Of the Magnetic Fluidsmentioning

confidence: 96%

“…The overall picture is that three-dimensional calculations generate a clear smaller relative deviation, i.e., the experimental menisci are better matched. For r > 4 mm, the deviation of two-dimensional calculations [19] starts to become rather large. This is because these calculations are much less able to fashion tiny surface elevations compared to three-dimensional calculations.…”

Section: Menisci Of the Magnetic Fluidsmentioning

confidence: 96%

“…The experiments were performed with the magnetic fluid EMG 909 (APG S21) having the material parameters ρ = 1020 kg/m 3 (1140 kg/m 3 ), σ = 0.0258 N/m (0.0331 N/m) and χ = 0.61 (0.65) [17]. The dynamical viscosity is set to η = 10 −3 kg/(m•s) since all tested values of η including the values given by the producer [18] lead to identical menisci [19]. The magnetic fluid EMG 909 (APG S21) is a light hydrocarbon oil-based (synthetic ester oil based) ferrofluid [18] with a saturation magnetisation of M sat 13.4 kA/m (M sat 16.4 kA/m) and particles with a mean diameter ofd 7.1 nm (d 7.0 nm) [20].…”

Section: Governing Equationsmentioning

confidence: 99%

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Meniscus of a Magnetic Fluid in the Field of a Current-Carrying Wire: Three-Dimensional Numerical Simulations

2020

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Three-dimensional calculations of the meniscus of a magnetic fluid placed around a current carrying vertical and cylindrical wire are presented. Based on the material properties of experimentally used magnetic fluids, the numerically determined menisci are compared with the experimentally measured ones reported by May. The comparison is made for a linear law of magnetisation as well as for the experimentally measured nonlinear magnetisation curve. Up to moderate strengths of the applied current ( I < = 45 A), i.e., up to moderate strengths of the magnetic field close to the wire, the calculated profiles agree satisfyingly with the experimentally measured ones for a linear as well as for a nonlinear law of magnetisation. At a great strength of the applied current ( I = 70 A), i.e., at a large strength of the magnetic field close to the wire, the agreement is less good than in the range up to moderate strengths. Our analysis revealed that the numerically assumed isothermal conditions are not present in the experiment, particularly at the great strength of the applied current. A control of the temperature in the experiment and the implementation of a coupled thermal model in the numerics are considered the most relevant future steps for an improved agreement.

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Section: Methodsmentioning

confidence: 99%

Section: Menisci Of the Magnetic Fluidsmentioning

confidence: 96%

Section: Menisci Of the Magnetic Fluidsmentioning

confidence: 96%

Section: Governing Equationsmentioning

confidence: 99%

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Meniscus of a Magnetic Fluid in the Field of a Current-Carrying Wire: Three-Dimensional Numerical Simulations

2020

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“…Some studies have used numerical simulations and measurements of ferrofluid meniscus shape along vertical cylindrical wires carrying electrical currents, observing the influence of viscosity, contact angle and surface tension in the meniscus shape. Eissmann et al [14] showed that ferrofluids' viscosity has no influence on the final shape of the meniscus around the wire. Conversely, large changes in the wire contact angle as well as moderate modifications in the contact angle at the edge of the container can influence the meniscus over the entire container.…”

Section: Introductionmentioning

confidence: 99%

Analysis of magnetic fluid displacement in capillaries

Carvalho

Cunha

Gontijo

2019

J Braz. Soc. Mech. Sci. Eng.

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This work presents a theoretical, numerical and experimental investigation on the shape and vertical displacement of a free surface formed in the interface between a magnetic fluid and a non-magnetic one. The magnetic fluid is confined between two parallel vertical flat plates. The presence of an external magnetic field applied by a permanent magnet arbitrarily positioned in space is considered. A new mathematical model is proposed, leading to a nonlinear differential equation that governs both the shape and the vertical displacement of the free surface due to capillary and magnetic effects. The applied field considered in this work satisfies the Ampère-Maxwell equation in the magnetostatic limit. This equation is numerically solved by direct integration using a fourth-order Runge-Kutta method coupled with a Newton-Raphson scheme. The numerical code is validated by means of some analytical solutions valid on specific asymptotic limits and by experimental results. Experimental measurements of surface tension, density and vertical displacement of Newtonian fluids in capillaries are also presented in order to provide a new methodology to estimate the contact angle combining experiments and numerical integration results. The influence of the variation of the physical variables concerning the physics of the problem on the shape and on the vertical displacement is evaluated. An increase in the intensity of the magnetic effects resulting in an increase in the vertical displacement and in the asymmetry degree of the free surfaces is observed. Finally, relevant physical discussions exploring how this long range interaction between the applied field and the magnetic liquid could be applied to promote fluid displacement in capillaries are presented.

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Chaotic convection in a ferrofluid

Laroze

Siddheshwar

Pleiner

2013

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tWe report theoretical and numerical results on thermally driven convection of a magnetic suspension. The magnetic properties can be modeled as those of electrically non-conducting superparamagnets. We perform a truncated Galerkin expansion finding that the system can be described by a generalized Lorenz model. We characterize the dynamical system using different criteria such as Fourier power spectrum, bifurcation diagrams, and Lyapunov exponents. We find that the system exhibits multiple transitions between regular and chaotic behaviors in the parameter space. Transient chaotic behavior in time can be found slightly below their linear instability threshold of the stationary state.

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Meniscus of a magnetic fluid in the field of a current-carrying wire: two-dimensional numerical simulations

Cited by 8 publications

References 14 publications

Meniscus of a Magnetic Fluid in the Field of a Current-Carrying Wire: Three-Dimensional Numerical Simulations

Meniscus of a Magnetic Fluid in the Field of a Current-Carrying Wire: Three-Dimensional Numerical Simulations

Analysis of magnetic fluid displacement in capillaries

Chaotic convection in a ferrofluid

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