Theoretical analysis on the orientational characteristics and rheological properties of a rod-like hematite particle suspension in a simple shear flow

We have theoretically investigated the particle orientational and rheological properties of a dilute suspension composed of spindle-like hematite particles under a simple shear flow. In the present study, we have derived the basic equation of the orientational distribution function by taking into account the spin Brownian motion about the particle axis. The basic equation has been solved numerically in order to investigate the influence of the shear rate, the magnetic field strength, and the rotational Brownian motion on the orientational distribution and rheological properties. For a very strong magnetic field applied in the shear flow direction, the rotational motion of the particle is restricted in a plane normal to the shearing plane due to the spin rotational Brownian motion. Although the negative viscosity was observed in the previous study, in the present case the orientational properties of the particle give rise to positive viscosity. The viscosity becomes large with increasing magnetic field strength. The viscosity due to magnetic properties does not occur in the situation of a magnetic field applied in the direction of the angular velocity vector of a simple shear flow.