On the Behavior of an Oblate Spheroidal Hematite Particle in a Simple Shear Flow Under a Uniform Magnetic Field Applied in the Flow Direction

Abstract

We discuss the orientational properties of an oblate spheroidal hematite particle and also its influence on the rheological characteristics of a dilute suspension of these magnetic particles, by means of an analytical approach based on the orientational distribution function. An oblate spheroidal hematite particle has an important characteristic that it is magnetized in a direction normal to the particle axis. This particle is assumed to conduct the rotational Brownian motion including both the usual and spin Brownian motion in a simple shear flow under a uniform magnetic field applied in the shear flow direction. In the present analysis, we have taken into account only the friction force (torque) with neglecting the hydrodynamic interactions among particles. From the balance of the torques acting on a particle, we have developed the basic equation of the orientational distribution function. This basic equation has been numerically solved in order to investigate the dependence of the orientational distribution on the magnetic field strength, shear rate and rotational Brownian motion, and also the relationship between the orientational distribution and the transport coefficients such as viscosity and diffusion coefficient. The results obtained here are summarized as follows. If both the magnetic field and the shear flow are weak, the particle does not exhibit specific directional characteristics under the influence of rotational Brownian motion. If the magnetic field is more dominant, the particle inclines such that the oblate surface is parallel to the magnetic field direction. If the Peclet number increases and the shear flow becomes more dominant, the particle shows a sharper peak of the orientational distribution in the shear flow direction. The viscosity due to the magnetic torque increases and finally converges to a constant value as the magnetic field increases. The viscosity curve has an overshoot profile and this overshoot appears at a larger value of the magnetic field strength for the case of a larger Peclet number. Moreover, the viscosity increases more significantly for a larger aspect ratio or for a more oblate hematite particle. In a sedimentation process under the gravitational field, the translational diffusion coefficient decreases with increasing magnetic field strength in the present case of the magnetic field direction.