(518i) Analysis of Orientational Characteristics of Disk-like Hematite Particles in a Simple Shear Flow (For the Case of an External Magnetic Field in the Angular Velocity Direction)

We discuss the orientational properties of an oblate spheroidal hematite particle in a simple shear flow under the situation of an 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. For instance, a rod-like hematite particle suspension exhibits negative viscosity characteristics in a certain direction of an applied magnetic field, however, in a different direction, does not exhibit negative viscosity, but ordinary positive viscosity. Hence, 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 in order to discuss orientational characteristics. These characteristics are dependent on a variety of factors such as shear rate and applied magnetic field strength. It is noted that an oblate spheroidal hematite particle has an important characteristic that it is magnetized in a direction normal to the particle axis, so that the present analysis takes into account spin rotational Brownian motion about the particle axis. The basic equation of the orientational distribution function, which is derived from the balance of the torques acting on a particle, has been numerically solved in order to investigate the dependence of the orientational distribution on the above-mentioned factors. 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 rotate 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, which is in contrast to the other field directions, where the viscosity significantly increases with increasing applied magnetic field strength.