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Nonequilibrium dynamics and magnetoviscosity of moderately concentrated magnetic liquids: A dynamic mean--field study

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.