On the orientational characteristics and transport coefficients of an oblate spheroidal hematite particle in a simple shear flow

Abstract

We have developed the basic equation of the orientational distribution function of oblate spheroidal hematite particles with rotational Brownian motion in a simple shear flow under an applied magnetic field. An oblate spheroidal hematite particle has an important characteristic in that it is magnetized in a direction normal to the particle axis. Since a dilute dispersion is addressed in the present study, we have taken into account only the friction force (torque) whilst neglecting the hydrodynamic interactions among the particles. This basic equation has been solved numerically in order that we may investigate the dependence of the orientational distribution on the magnetic field strength, shear rate and rotational Brownian motion and the relationship between the orientational distribution and the transport coefficients such as viscosity and diffusion coefficient. We found that if the effect of the magnetic field is more dominant, the particle inclines in such a way that the oblate surface aligns in the magnetic field direction. If the Peclet number increases and the effect of the shear flow becomes more dominant, the particle inclines such that the oblate surface tilts in the shear flow direction. The viscosity due to the magnetic torque is shown to increase as the magnetic field increases, since the magnetic torque due to the applied magnetic field becomes the more dominant effect. Moreover, the viscosity increase is shown to be more significant for a larger aspect ratio or for a more oblate hematite particle. We have applied the analysis to the problem of particle sedimentation under gravity in the presence of a magnetic field applied in the sedimentation direction. The particles are found to sediment with the oblate surface aligning more significantly in the sedimentation direction as the applied magnetic field strength increases.

Control of the orientational characteristics of disk-like hematite particles by a simple shear flow

“…This linear peak-type distribution along the φ-direction implies that the particle almost freely rotate about the z-axis with the magnetic moment maintaining inclining in the magnetic filed direction in the situation of a weak shear flow. This orientational characteristic is in significantly contrast to that for the previous other field directions where the distribution shows only a single peak-type distribution with a high peak (Satoh, 2012;Satoh and Yokoyama, 2014). …”

“…(4) gives rise to such an important result regarding the viscosity that, in the case of an external magnetic field applied in the direction of the angular velocity vector of the simple shear flow, the viscosity due to the magnetic particle-field interaction gives rise to zero. This is quite in contrast to the results for the previous cases of the different directions of an external magnetic field, where large viscosity significantly arises in strong magnetic field situations (Satoh, 2012;Satoh and Yokoyama, 2014). Satoh, Mechanical Engineering Letters, Vol.2 (2016) [DOI: 10.1299/mel.16-00314]…”

“…As in the previous study (Satoh, 2012;Satoh and Yokoyama, 2014), we consider a suspension composed of disk-like hematite particles in order to investigate the behavior of these particles in a simple shear flow. A uniform external magnetic field is here assumed to be applied in the direction of the angular velocity vector of a simple shear flow.…”

“…A uniform external magnetic field is here assumed to be applied in the direction of the angular velocity vector of a simple shear flow. The situations of the different field directions had already been focused on in the previous studies (Satoh, 2012;Satoh and Yokoyama, 2014), so that we here mainly focus on the control of the orientational characteristics by the simple shear flow, which may be a different aspect of a series of studies regarding a disk-like hematite particle suspension. The theory based on the orientational distribution function is basically the same as in the previous studies (Satoh, 2012;Satoh and Yokoyama, 2014), and therefore, in this brief report, we concentrate on the main characteristic results with summarized descriptions of the particle model and the basic equation of the rotational distribution function.…”