Magnetoviscosity in suspensions of grains with finite magnetic anisotropy

Coupling between magnetic and mechanical rotational degrees of freedom of fine ferromagnetic grains is provided by the energy of their magnetic anisotropy. In the limiting case of strong anisotropy, an applied stationary magnetic field induces the greatest obstacles to the "rigid dipole" spin in a vortex ferrofluid flow, while in the opposite ideal case, the "soft dipoles" twist freely with the liquid. As a result, the field-dependent part of the ferrofluids viscosity depends not only on the external magnetic field strength but also on the particle magnetic anisotropy. An explicit expression coming from simple physical arguments and describing both these dependencies of magnetoviscosity is derived and discussed.