Magnetoviscosity in dilute ferrofluids from rotational Brownian dynamics simulations

Ferrofluids are suspensions of magnetic nanoparticles which respond to imposed magnetic fields by changing their viscosity without losing their fluidity. Prior work on modeling the behavior of ferrofluids has focused on using phenomenological suspension-scale continuum equations. A disadvantage of this approach is the controversy surrounding the equation describing the rate of change of the ferrofluid magnetization, the so-called magnetization relaxation equation. In this contribution the viscosity of dilute suspensions of spherical magnetic nanoparticles suspended in a Newtonian fluid and under applied shear and constant magnetic fields is studied through rotational Brownian dynamics simulations. Simulation results are compared with the predictions of suspension-scale models based on three magnetization relaxation equations. Excellent agreement is observed between simulation results and the predictions of an equation due to Martsenyuk, Raikher, and Shliomis. Good qualitative agreement is observed with predictions of other equations, although these models fail to accurately predict the magnitude and shear rate dependence of the magnetic-field-dependent effective viscosity. Finally, simulation results over a wide range of conditions are collapsed into master curves using a Mason number defined based on the balance of hydrodynamic and magnetic torques.