Influence of surface tension on the conical miniscus of a magnetic fluid in the field of a current-carrying wire

TL;DR

This paper investigates how surface tension affects the shape of the conical meniscus of a magnetic fluid around a current-carrying wire, using numerical methods to analyze various influencing factors.

Contribution

It introduces a regularized numerical approach to model the magnetic fluid surface shape considering surface tension and other effects.

Findings

Surface tension significantly alters the conical meniscus shape.

The model accounts for nonlinear magnetization and multiple liquids.

Wire diameter impacts the free surface profile.

Abstract

We study the influence of surface tension on the shape of the conical miniscus built up by a magnetic fluid surrounding a current-carrying wire. Minimization of the total energy of the system leads to a singular second order boundary value problem for the function $\zeta(r)$ describing the axially symmetric shape of the free surface. An appropriate transformation regularizes the problem and allows a straightforward numerical solution. We also study the effects a superimposed second liquid, a nonlinear magnetization law of the magnetic fluid, and the influence of the diameter of the wire on the free surface profile.