We discuss the orientational properties of an oblate spheroidal hematite particle in a simple shear flow under the situation of a uniform external magnetic field, by means of an analytical approach based on the orientational distribution function. Magneto-rheological properties are strongly dependent on the direction of an applied magnetic field. In the present study, we consider the case of an external magnetic field applied in the direction of the angular velocity vector of a simple shear flow. An oblate spheroidal hematite particle is magnetized in a direction normal to the particle axis. The basic equation of the orientational distribution function has been numerically solved. If the rotational Brownian motion is much more dominant, the particle does not exhibit specific directional characteristics. If the magnetic field is much more dominant, the particle inclines such that the particle almost freely rotates with the magnetic moment inclining in the magnetic field direction. If the shear flow becomes a significantly governing factor, the particle exhibits a usual single peak-type orientational distribution similar to that of a polymer molecule in a strong shear flow. The viscosity due to the magnetic particle-field interaction does not arise in the present magnetic field direction.
