Shear rate dependence o f viscosity and normal stress differences in ferrofluids

In this work we investigate numerically the viscosity and normal stress differences of mono and polydisperse ferrofluids undergoing a simple shear flow in the presence of a transverse applied magnetic field. The simulations are carried out by means of a Brownian Dynamics integration algorithm. For all simulations we assume that the dipole moments are fixed to the magnetic particles. In the case of polydisperse suspensions the particles present a typical log-normal distribution of magnetic diameters which are covered with a layer of surfactant of constant width. The long-range dipolar interaction between the magnetic moments are computed by Ewald summation technique and the surfactant influence is modeled as a steric repulsive force between pairs of particles. The attractive van der Waals force is also incorporated in the numerical simulations. The numerical procedure is validated by comparing the simulation results of the non-dimensional relative viscosity increase as a function of the magnetic field intensity with experimental data. The present numerical simulations show that the non-dimensional relative viscosity increment as a function of the non-dimensional shear rate is strongly influenced by the particle volume fraction and the strength of the dipolar interactions parameter. By examining the suspension microstructure into the numerical box, we can see anisotropic structures like chains of particles for the low shear rate regimes, specially in the polydisperse cases. The results also indicate the presence of a suspension shear-thinning behavior with two different non-dimensional shear rate dependence. In addition, non-dimensional normal stress differences are observed even in the absence of dipolar interactions, as a consequence of stress anisotropy produced by the repulsive forces during the particle collisions induced by the imposed steady-shear flow. The dipolar interactions increase these non-dimensional normal stress differences and make their dependence on the non-dimensional shear rate non-monotonic. For low non-dimensional shear rates, the dipolar interactions dominate and the formation of large-structures like chains oriented in the direction of the magnetic fields leads to an increase in the non-dimensional first normal stress difference. For very high non-dimensional shear rates, the flow breaks the anisotropic structures and the effects of polydispersity and dipolar interactions become unimportant. The numerical simulations provide a useful tool for understanding the complex microphysical and rheology of real ferrofuids under shear flows.