Ferrofluid hydrostatics according to classical and recent theories of the stresses

The hydrostatics of soft polarisable liquids is examined in the context of four `classical¿ theories of the stresses in fluids, and of recent theoretical work which has resolved the controversy surrounding those theories. The classical stress systems predict various different internal pressures and magnetostrictive density changes, and only the stress system, based on energy, correctly gives the density change. The energy-based stresses proposed by Gans in 1904 generalise for nonlinear fluids the stress system of Helmholtz. All the stress systems predict the same surface variation of the pressure to contain a liquid, and they lead to a common surface-integral method useful for computing force on saturable iron bodies. The modern theories are represented, for equilibrium conditions, by a single and unique stress system which gives no information on internal forces. The meaning of the various `pressures¿ found in the recent literature is discussed, and the role of density, rather than pressure, as the predictable mechanical variable inside a liquid is illustrated by a thought experiment.