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

Abstract

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.

Bézier Curve Method to Compute Various Meniscus Shapes

“… 12 Eißman et al presented three-dimensional calculations of the meniscus of a magnetic fluid placed around a current-carrying vertical and cylindrical wire. 13 Liu et al computed the meniscus shape around a fiber vertically piercing into the water surface to mimic the strider leg on the water surface. 14 Liu et al also computed the meniscus of a pendant droplet.…”

“…Tang and Cheng systematically studied the meniscus on the outside of a small circular cylinder immersed vertically in a liquid bath in a cylindrical container using the Young–Laplace equation . Eißman et al presented three-dimensional calculations of the meniscus of a magnetic fluid placed around a current-carrying vertical and cylindrical wire . Liu et al computed the meniscus shape around a fiber vertically piercing into the water surface to mimic the strider leg on the water surface .…”