Simulations of the magnetization and magnetoviscosity of dilute magnetic fluids

Abstract

In this work was studied the rotational Brownian motion of magnetic spherical and tri-axial ellipsoidal particles suspended in a Newtonian fluid, in the dilute suspension limit, under applied shear and magnetic fields by Brownian dynamics simulation to determine the magnetization and magnetoviscosity of the suspension. The algorithm describing the change in the magnetization and magnetoviscosity of the suspension was derived from the stochastic angular momentum equation using the fluctuation-dissipation theorem and a quaternion formulation of orientation space. Results are presented for the response of dilute suspensions of magnetic nanoparticles to constant and transient magnetic fields with and without simple shear flow fields. Simulation results are in agreement with the Langevin function for equilibrium magnetization and with single-exponential relaxation from equilibrium at small fields using Perrin’s effective relaxation time. Dynamic susceptibilities for ellipsoidal particles of different aspect ratios were obtained from the response to oscillating magnetic fields of different frequencies and described by Debye’s model for the complex susceptibility using Perrin’s effective relaxation time. Suspensions of ellipsoidal particles show a significant effect of aspect ratio on the intrinsic magnetoviscosity of the suspension, and this effect is more pronounced as the aspect ratio becomes more extreme. The use of an effective rotational diffusion coefficient Dr,eff collapses the normalized intrinsic magnetoviscosity of all suspensions to a master curve as a function of Péclet number and the Langevin parameter a=(µ0µH)/kBT), up to a critical value of a for which the results for suspensions of spherical particles deviate from those of suspensions of ellipsoids. This discrepancy is attributed to the action of the shear-torque on the ellipsoidal particles, which tends to orient the particles in the direction of maximum deformation of the simple shear flow. On the other hand, for suspensions of spherical particles a decrease to negative values in the intrinsic magnetoviscosity is observed for oscillating and co-rotating magnetic fields whereas an increase is observed for counter-rotating magnetic fields. The frequency corresponding to zero viscosity and the minimum value in the negative viscosity is lower for co-rotating magnetic fields than for oscillating magnetic fields. In the negative magnetoviscosity regions the particles in a co-rotating magnetic field rotate faster than in an oscillating magnetic field. It is estimated that the flow due to co-rotating particles could be strong enough to obtain a negative effective viscosity in dilute suspension. Moreover, it is shown that the commonly accepted constitutive equation for the antisymmetric stress describes well the intrinsic magnetoviscosity of the suspension.