Magnetostatic buoyancy force acting on a non-magnetic sphere immersed in a ferrofluid magnetized by a gradient field

Abstract

A buoyancy force that acts on the solid non-magnetic sphere immersed in a ferrofluid magnetized by a gradient magnetic field is considered in the framework of 5 physical approaches. The paper overviews (i) the effective magnetic moment and (ii) the antimatter hole concepts, (iii) the excess polarization approach (Pohl), and (iv) the Maxwell stress tensor analysis (Naletova). We propose (v) the ponderomotive buoyancy force decomposition developed according to the general Rosensweig formula which distinguishes between volume and surface effects. Our approach shows the physical background of the buoyancy force, gives estimates of the ratio of surface-to-volume forces and allows to calculate the pressure, which deforms (squeezes) the sphere. All analytical formulas were compared and verified by applying direct numerical simulations to the problem of a small non-magnetic sphere immersed in a ferrofluid characterized by the linear magnetization law. The applied gradient field was assumed to be generated by two coaxial permanent ring magnets. It is shown that the proposed formula (v) is equivalent to (iii) (numerical matching), although they differ by a coefficient that equals 1 in case of the non-magnetic sphere. For the magnetic body, these expressions differ quantitatively, because formula (iii) gives the resultant magnetic force, while formula (v) describes only the action of the ferrofluid.