Ferrohydrodynamics: Retrospective and Issues

Abstract

Two basic sets of hydrodynamic equations for magnetic colloids (so-called ferrofluids) are reviewed. Starting from the quasistationary ferrohydrodynamics, we then give a particular attention to an expanded model founded on the concept of internal rotation. A specific relation between magnetic and rotational degrees of freedom of suspended grains provides a coupling of the fluid magnetization with the fluid dynamics. Hence a complete set of constitutive equations consists of the equation of ferrofluid motion, the Maxwell equations, and the magnetization equation. There are three kinds of the latter. Two of them were derived phenomenologically as a generalization of the Debye relaxation equation in case of spinning magnetic grains, while one of them was derived microscopically from the Fokker-Planck equation. Testing the magnetization equations, we compare their predictions about the dependence of the rotational viscosity on the magnetic field and the shear rate.