Second order effects in fluidmagnetic buoyancy

Abstract

A non-magnetic solid object placed in a magnetically responsive fluid in the presence of a magnetic field gradient experiences a net buoyancy force of magnetic origin. A procedure is developed to account for the effects of magnetic field distortion due to the difference of magnetic permeability between the fluid and the solid and non-zero dependence of fluid magnetization on magnetic field strength. This procedure gives an expression for the magnetic buoyancy force correct to first order in the dimensionless magnetization of the fluid and in the dimensionless variation of fluid magnetization across the object. Calculations are performed for a sphere, cylinder and plate in an applied magnetic field where the field and field gradient are either aligned or at right angles in order to give an indication of the range of force variation due to a change of shape and due to a change of applied field geometry. Variations on the order of 10% can be expected in typical applications.