  A mean-field Fokker-Planck equation approach to the dynamics of ferrofluids
in the presence of a magnetic field and velocity gradients is proposed that
incorporates magnetic dipole-dipole interactions of the colloidal particles.
The model allows to study the combined effect of a magnetic field and dipolar
interactions on the viscosity of the ferrofluid. It is found that dipolar
interactions lead to additional non-Newtonian contributions to the stress
tensor, which modify the behavior of the non-interacting system. The
predictions of the present model are in qualitative agreement with experimental
results, such as presence of normal stress differences, enhancement and
different anisotropy of magnetoviscous effect and the dependence of the
viscosity on the hydrodynamic volume fraction. A quantitative comparison of the
concentration dependence of the magnetoviscosity shows good agreement with
experimental results for low concentrations.
