Meniscus of a ferrofluid around a vertical cylindrical wire carrying electric current.

We study the meniscus profiles of ferrofluids in the magnetic field of a vertical current-carrying wire. Measurements of the free ferrofluid surface profile are quantitatively compared with numerical calculations. The theoretical model leads to a second-order ordinary differential equation. All material parameters are determined in independent experiments, therefore no fitting parameters are involved in the calculations. The experimental results can be modeled by the equilibrium of magnetic, gravitational, and interface tension forces. The classical model that neglects interface tension yields significant deviations from the experimental profiles in the parameter range studied.