Influence of the Spin Rotational Brownian Motion on the Negative Magneto-Rheological Effect in a Dispersion Composed of Rod-Like Hematite Particles

Abstract

We have shown the basic equation of the orientational distribution function of prolate spheroidal hematite particles that conduct the rotational Brownian motion in a simple shear flow under an applied magnetic field. The equation has been solved numerically in order to investigate mainly the influence of the spin rotational Brownian motion on the orientational distribution, the negative magneto-rheological effect and the characteristics of magnetization. A prolate spheroidal hematite particle has an important characteristic that it is magnetized in a direction normal to the particle axis. The main results obtained in the present study are summarized as follows. The present results are in good agreement with those of the theory without that motion in that the position and the height of a peak of the orientational distribution and also the whole distribution shape agree significantly well with each other. Hence, it is seen that the spin rotational Brownian motion does not significantly influence the orientational distribution. In contrast, the spin rotational Brownian motion has a quantitative effect on the negative viscosity, although the dependence of the negative viscosity on the magnetic field strength is in qualitatively good agreement with that of the theory without the spin rotational Brownian motion: the effect of the spin rotational Brownian motion quantitatively appears as a significant decrease in the negative viscosity effect. Moreover, the negative magneto-rheological effect can be obtained for a larger aspect ratio or for a more prolate hematite particle. Since the magnetization has a strong relationship with the orientation of the magnetic moment, the effect of the spin rotational Brownian motion appears in this characteristic more significantly.