A Mesoscopic Approach to the ``Negative'' Viscosity Effect in Ferrofluids

TL;DR

This paper introduces a mesoscopic model using a Fokker-Planck framework to analyze the non-monotonous viscosity behavior, including negative viscosity effects, in ferrofluids under oscillating magnetic fields, revealing non-Newtonian characteristics.

Contribution

It presents a novel mesoscopic approach to understand the negative viscosity effect in ferrofluids, combining analytical and numerical methods to explore frequency-dependent viscosity behavior.

Findings

Viscosity exhibits non-monotonous dependence on magnetic field frequency.

Identifies negative viscosity effect at certain frequencies.

Viscosity depends on vorticity, indicating non-Newtonian behavior.

Abstract

We present a mesoscopic approach to analyze 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.