Definition of Helmholtz and Kelvin forces in magnetic fluids

Abstract

The Helmholtz and Kelvin forces for volume force density in magnetic fluids are valid only in some situations. Based on calculation of the volume force density in magnetic fluids, the origin for the Helmholtz and Kelvin forces in magnetic fluids is suggested, and the range of validity of them is analyzed in this paper. The calculation results show that the volume force density can be expressed in the form of Helmholtz force when the permeability of magnetic fluid is independent of the applied magnetic field, while the Kelvin force is valid when the average magnetic moment of magnetic particles in the magnetic fluid is independent of the specific volume of magnetic fluid. When the susceptibility is proportional to the density of magnetic fluid, the Helmholtz force is reduced to the Kelvin force.