Theoretical description of the Free surface shapes of the magnetic fluid surrounding the magnetizable plate in external magnetic field

V. V. Gogosov¹ - O. A. Grishanina² - V. V. Kiryushin¹ - A. Ya. Simonovskii²

¹ Institute of Mechanics of the M.V.Lomonosov Moscow State University, 117192, Moscow, Russia
² Academy of Stavroplol, 355014 Stavroplol, Russia

Abstract
The theory allowing to describe possible free surface shapes of the magnetic fluid surrounding the thin flat magnetizable plate with infinite magnetic susceptibility is presented. In order to solve the Maxwell s equations and hydrostatics equation for magnetic fluid together with appropriate boundary conditions at the magnetic fluid free surface the methods of the theory of complex variable are used. Distribution of the magnetic field and pressure in the magnetic fluid surrounding the plate are found. The equation describing the free surface shapes of the magnetic fluid is derived. The graphs of the free surface shapes of the magnetic fluid near the plate are given for various values of the volume of the fluid surrounding the plate. The angle between the plate and the applied external magnetic field vector in infinity is supposed to be equal to zero, 90o, 45o and 135o. The free surface shapes are shown to be dependent on the plate size, its orientation relative to the applied magnetic field vector, magnitude of the magnetic field and the magnetic fluid volume surrounding the plate. Itis shown that the small volumes of the magnetic fluid is concentrated near the edges of the plate in the form of drops. As the fluid volume increases the size of the drops increases too. At the certain critical magnetic fluid volume the drops are linked at the certain distance from the plate. Near the central part of plate the vapour cavities are being formed. The size of the cavities Is decreasing when the fluid volume is increasing. Figs 3, Refs 8.