Transport Coefficients and Orientational Distributions of a Hematite Particle under Circumstances of a Simple Shear Flow (Analysis for an Applied Magnetic Field Normal to the Shear Plane)

Abstract

We have investigated the influences of the magnetic field strength, shear rate, and rotational Brownian motion on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. This rodlike particle is modeled as a magnetic spheroidal particle which has a magnetic moment normal to the particle axis ; such a particle may typically be a hematite particle. In the present study, an external magnetic field is applied in the direction normal to the shear plane of a simple shear flow. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. Although the orientational distribution function shows a sharp peak in the flow direction for a very strong magnetic field, such a peak is not restricted to the flow direction, but continues in every direction of the shear plane. This is due to the characteristic particle motion that the particle can rotate around the axis of the magnetic moment in the shear plane, although the magnetic moment nearly points to the magnetic field direction. This particle motion in the shear plane causes negative values of the viscosity due to the magnetic field. The viscosity decreases, attains a minimum value, and then converges to zero as the field strength increases. Additionally, the diffusion coefficient is significantly influenced by such characteristic particle motion in the shear plane for a strong magnetic field.