Oscillatory motion in a ferromagnetic fluid

V. I. Yakushin

Abstract
We consider the motion of a suspension of ferromagnetic particles produced by an unbounded plane surface which performs (in its plane) harmonic oscillatory motion at a frequency ω. It is assumed the intensity of the external magnetic field is less than the anisotropy field of the particles so that they can be regarded as rigid magnetic dipoles. The solution of the equations of motion for such a medium in terms of velocity and densities of mechanical and magnetic moments is given in the form of expansions in powers of the volume concentration c of the solid phase and of a small parameter which represents the deviation of the densities of both moments from their equilibrium values. It is shown that in a ferrofluid magnetization waves which are propagated with the same phase velocity are possible in addition to viscous shear waves. The excitation of oscillatory motions in a ferrofluid (in the plane xy⊥H) leads to the appearance of a z-component of the magnetization oscillating at twice the frequency and to a reduction in the constant component of the magnetic moment. We propose to use the change in the constant magnetization for detection of oscillatory motions. Nonuniformity in the density of the mechanical moment leads to the presence of secondary viscous waves the amplitudes of which are not maximum in the oscillating plane but at some distance from it. There is a phase shift, which varies with an increase in ω, between the main and secondary flows. During oscillatory motions, the effective viscosity of the suspension depends not only on H, but also on ω.