Interface magnetic field analysis for free surface phenomena of magnetic fluid

Y. Mizuta

Department of Applied Physics, Hokkaido University, Kita-13, Nishi-8, Kita-ku, Sapporo 060-8628, Japan

Abstract
For three-dimensional analysis of free surface phenomena of magnetic fluid, a rigorous method to obtain interface magnetic fields is presented. The profile of the interface (free surface) and the distribution of the applied magnetic field are allowed to be arbitrary. A set of łqłq three-dimensional interface magnetic field equations" derived from the harmonic property of the magnetic field and the interface conditions are closed with the interface fields (tangential magnetic field and normal magnetic flux density). Interface fields are expanded into series of periodic functions, and the operation of the łqłq three-dimensional Hilbert transform" on periodic functions compactly determines a set of linear algebraic equations for the expansion coefficients of the interface fields. This set of equations is solved simultaneously. For different horizontal scales, we calculated the disturbance in a simply distributed magnetic field caused by the interface of a triangular lattice, and the magnetic stress difference. From these results, we deduce that the interaction between the surface profile and the applied magnetic field is important for the formation of surface patterns of magnetic fluid before the surface tension dominates. Figs 8, Refs 13.