Stability analysis on the free surface phenomena of a magnetic fluid for general use

This paper presents an analysis for elucidating a variety of physical processes on the interface (free surface) of magnetic fluid. The present analysis is composed of the magnetic and the fluid analysis, both of which have no limitations concerning the interface elevation or its profile. The magnetic analysis provides rigorous interface magnetic field under arbitrary distributions of applied magnetic field. For the fluid analysis, the equation for interface motion includes all nonlinear effects. Physical quantities such as the interface magnetic field or the interface stresses, obtained first as the wavenumber components, facilitate confirming the relations with those by the conventional theoretical analyses. The nonlinear effect is formulated as the nonlinear mode coupling between the interface profile and the applied magnetic field. The stability of the horizontal interface profile is investigated by the dispersion relation, and summarized as the branch line. Furthermore, the balance among the spectral components of the interface stresses are shown, within the sufficient range of the wavenumber space.

Research Highlights
► General, rigorous but compact analysis for free surface phenomena is shown.
► Analysis is applied without limitations on the interface elevation or its profile.
► Nonlinear effects are formulated as the nonlinear mode coupling.
► Bifurcation of stability is summarized as the branch line.
► Balance among the interface stresses are shown in the wavenumber space.