Movement of a fluid sphere in the vicinity of a flat plane with constant temperature gradient

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. (C) 2000 Academic Press.