Chen SH
Department of Chemical Engineering, Hwa Hsia College of Technology and Commerce, Taipei, Taiwan, 235, Republic of China
J Colloid Interface Sci. 2000 Apr 1;224(1):63-75. doi: 10.1006/jcis.1999.6641.
An analytical study is presented for the thermophoresis of a sphere in a constant applied temperature gradient parallel to an adiabatic plane. The Knudsen number is assumed to be small so that the fluid flow can be described by a continuum model with a thermal creep and a hydrodynamic slip at the particle surface. A method of reflections is used to obtain the asymptotic formulas for the temperature and velocity fields in the quasisteady situation. The thermal insulated plane may be a solid wall (no-slip) and/or a free surface (perfect-slip). The boundary effect on the thermophoretic motion is found to be weaker than that on the axisymmetric thermophoresis of a sphere normal to a plane with constant temperature. In comparison with the motion driven by gravitational force, the interaction between the particle and the boundary is less significant under thermophoresis. Even so, the interaction between the plane and the particle can be very strong when the gap thickness approaches zero. For the thermophoretic motion of a particle parallel to a solid plane, the effect of the plane surface is to reduce the translational velocity of the particle. In the case of particle migration parallel to a free surface due to thermophoresis, the translating velocity of a particle can be either greater or smaller than that which would exist in the absence of the plane surface, depending on the relative thermal conductivity and the surface properties of the particle and its relative distance from the plane. Not only the translational velocity but also the rotational velocity of the thermophoretic sphere near the plane boundary is formulated analytically. The rotating direction of the particle is strongly dominated by its surface properties and the internal-to-external thermal conductivity. Besides the particle motion, the thickness of the thermophoretic boundary layer is evaluated by considering the thermophoretic mobility. Generally speaking, a free surface exerts less influence on the particle movement than a solid wall. Copyright 2000 Academic Press.
本文针对球体在平行于绝热平面的恒定外加温度梯度中的热泳现象进行了分析研究。假设克努森数较小，以便流体流动可以用连续介质模型来描述，该模型考虑了热蠕变以及颗粒表面的流体动力滑移。采用反射法来获得准稳态情况下温度场和速度场的渐近公式。绝热平面可以是固体壁面（无滑移）和/或自由表面（完全滑移）。发现边界对热泳运动的影响比对球体垂直于恒温平面的轴对称热泳的影响要弱。与重力驱动的运动相比，在热泳作用下颗粒与边界之间的相互作用不太显著。即便如此，当间隙厚度趋近于零时，平面与颗粒之间的相互作用可能会非常强烈。对于颗粒平行于固体平面的热泳运动，平面表面的作用是降低颗粒的平移速度。在颗粒因热泳而平行于自由表面迁移的情况下，颗粒的平移速度可能大于或小于无平面表面时的速度，这取决于颗粒的相对热导率、表面性质以及它与平面的相对距离。不仅颗粒的平移速度，而且平面边界附近热泳球体的旋转速度也通过解析方法进行了公式化。颗粒的旋转方向强烈地由其表面性质和内外热导率决定。除了颗粒运动外，还通过考虑热泳迁移率来评估热泳边界层的厚度。一般来说，自由表面对颗粒运动的影响比固体壁面小。版权所有2000年学术出版社。
