Simulation of hydrostatical equilibrium of ferrofluid subject to magneto-static field

In this paper, a numerical scheme for obtaining ferrofluid shape formation is presented using the revisited Kelvin's force formula. The formula adopts the newly appreciated field intensity from the original Kelvin's concept and the virtual air gap scheme. For the hydrostatic equilibrium subject to magneto-static field, both electromagnetic and gravitational body forces should be considered. The free surface profile of ferrofluid can be obtained through numerical iterations based on the fact that the pressures on the free surface should be the same. Test models are presented as validations of the proposed scheme. Index Terms--Ferrofluid, hydrostatics, Kelvin's formula, magnetic body force, virtual air gap.