Instability and breakup of a thick layer of a viscous magnetic fluid in a tilted magnetic field

A linear partial differential equation describing the evolution of an initial disturbance of a flat free surface of a thin layer of a viscous magnetic fluid covering a horizontal plate in the presence of a uniform magnetic field, is derived within a system of ferrohydrodynamic and magnetostatic equations. The effect of magnetizing the plate on the stability of the flat free surface is investigated. An estimate is obtained for the minimum value of the tangential component of the magnetization vector of the fluid sufficient to radically alter the pattern of the final breakup of the continuous layer.