A mesoscopic approach to the “negative” viscosity effect in ferrofluids

We present a mesoscopic approach to analyse the dynamics of a single magnetic dipole under the influence of an oscillating magnetic field, based on the formulation of a Fokker–Planck equation. The dissipated power and the viscosity of a suspension of such magnetic dipoles are calculated from non-equilibrium thermodynamics of magnetized systems. By means of this method we have found a non-monotonous behaviour of the viscosity as a function of the frequency of the field which has been referred to as the “negative” viscosity effect. Moreover, we have shown that the viscosity depends on the vorticity field thus exhibiting non-Newtonian behaviour. Our analysis is complemented with numerical simulations which reproduce the behaviour of the viscosity we have found and extend the scope of our analytical approach to higher values of the magnetic field.