Flow of a Thin Magnetic Liquid Layer in a Magnetic Field

Abstract

The problem of flow of a thin layer of an incompressible magnetic liquid with a given dependence of the magnetization on the magnetic field strength is analytically solved in the lubrication theory approximation in the case of inhomogeneous magnetic field. A partial differential equation that describes time variation in the layer shape is obtained. The general formulation of the problem is considered. The solution of the problem of the behavior of a thin magnetic liquid layer in the magnetic field of a vertical infinite cylindrical conductor carrying a given sufficiently heavy electric current is written.