Chen SH
Department of Chemical Engineering, Hwa Hsia College of Technology and Commerce, Taipei, 235, Taiwan, Republic of China
J Colloid Interface Sci. 2000 Oct 1;230(1):157-170. doi: 10.1006/jcis.2000.7087.
An analytical study is presented on the thermocapillary migration of a fluid sphere within a constant applied temperature gradient in an arbitrary direction with respect to a plane surface. The Peclet and Reynolds numbers are assumed to be small so that the Laplace and Stokes equations, respectively, govern the temperature distributions and fluid velocities inside and outside the droplet. The asymptotic formulas for the temperature and the velocity fields in the quasi-steady situation are obtained by using a method of reflections. The plane surface can be a no-slip solid wall and/or a perfect-slip free surface. The boundary effect on the thermocapillary migration is found to be weaker than that on the motion driven by a body force. Even so, the interaction between the plane and the droplet can be very significant when the gap thickness approaches zero. For the motion of a droplet normal to a solid wall, the effect of the plane surface reduces the translational velocity of the droplet; however, this solid wall can be an enhancement factor on the particle migration as it is translating parallel to the wall. On the other hand, in case of a droplet migrating close to a free surface due to thermocapillarity, the droplet velocity 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. Furthermore, the interacting thickness of the affected region by the presence of the plane is discussed by considering the droplet mobility. Generally speaking, a free surface exerts less influence on the particle movement than does a solid surface. Copyright 2000 Academic Press.
本文针对在任意方向上相对于平面存在恒定外加温度梯度的情况下，流体球的热毛细迁移进行了分析研究。假设佩克莱数和雷诺数较小，使得拉普拉斯方程和斯托克斯方程分别用于描述液滴内部和外部的温度分布及流体速度。通过反射法得到了准稳态下温度场和速度场的渐近公式。平面可以是无滑移固体壁和/或完全滑移自由表面。发现热毛细迁移的边界效应比体力驱动运动的边界效应弱。即便如此，当间隙厚度趋近于零时，平面与液滴之间的相互作用可能会非常显著。对于液滴垂直于固体壁的运动，平面的作用会降低液滴的平移速度；然而，当固体壁平行于液滴平移时，它可能会增强粒子的迁移。另一方面，对于由于热毛细作用而靠近自由表面迁移的液滴，其速度可能大于或小于不存在平面时的速度，这取决于粒子的相对热导率、表面性质及其与平面的相对距离。此外，通过考虑液滴迁移率讨论了平面存在时受影响区域的相互作用厚度。一般来说，自由表面对粒子运动的影响比固体表面小。版权所有2000年学术出版社。
