Aoshima Masayuki, Satoh Akira, Chantrell Roy W, Coverdale Geoff N
Faculty of System Science and Technology, Akita Prefectural University, 84-4 Ebinokuchi, Tsuchiya-aza, Honjyo, Akita 015-0055, Japan.
J Colloid Interface Sci. 2002 Sep 15;253(2):455-64. doi: 10.1006/jcis.2002.8451.
We have investigated the orientational distributions and rheological properties of dilute colloidal dispersions, which consist of ferromagnetic spherocylinder particles. First, the governing equation of the orientational distribution function has been derived for the typical two cases of magnetic field directions: the direction parallel to the shear flow and the direction parallel to the angular velocity vector of the shear flow. The equation has been solved approximately by Galerkin's method. With these numerical solutions we have obtained the results of the orientational distribution and viscosity. The results obtained for the magnetic field in the shear flow direction are summarized as follows. In the case of a weak magnetic field, the particle tends to orient nearly toward the shear flow direction and its opposite direction. As the magnetic field increases, the orientation of the particle is restricted and the viscosity increases significantly. As the influence of the magnetic field becomes dominant, an overshoot in the viscosity curve appears. This is due to the fact that there is a maximum deviation of the averaged particle direction from the magnetic field direction. When the strength of the magnetic field increases significantly, the particle inclines close to the magnetic field direction and the viscosity converges to a constant value. Particles with a larger aspect ratio give rise to a larger increment in the viscosity since such elongated particles induce larger resistance in a flow field. We also have obtained results for the case of the magnetic field in the direction parallel to the angular velocity vector of the shear flow. When the flow field is dominant over both the rotational Brownian motion and the magnetic interaction, the particle rotates in the plane nearly perpendicular to the magnetic field direction. As the magnetic field increases, the particle inclines toward the magnetic direction. For this direction of field, the viscosity is independent of the magnetic field and is always zero.
我们研究了由铁磁球柱体颗粒组成的稀胶体分散体的取向分布和流变特性。首先，针对磁场方向的两种典型情况推导了取向分布函数的控制方程：平行于剪切流的方向和平行于剪切流角速度矢量的方向。该方程已通过伽辽金方法近似求解。利用这些数值解，我们得到了取向分布和粘度的结果。在剪切流方向施加磁场时得到的结果总结如下。在弱磁场情况下，颗粒倾向于几乎朝着剪切流方向及其相反方向取向。随着磁场增强，颗粒的取向受到限制，粘度显著增加。当磁场的影响占主导时，粘度曲线会出现一个峰值。这是由于平均颗粒方向与磁场方向存在最大偏差。当磁场强度显著增加时，颗粒接近磁场方向倾斜，粘度收敛到一个恒定值。长径比更大的颗粒会使粘度有更大的增量，因为这种细长颗粒在流场中会产生更大的阻力。我们还得到了磁场方向平行于剪切流角速度矢量情况下的结果。当流场比旋转布朗运动和磁相互作用都更占主导时，颗粒在几乎垂直于磁场方向的平面内旋转。随着磁场增强，颗粒向磁场方向倾斜。对于这个磁场方向，粘度与磁场无关且始终为零。
