Thermocapillary motion of a fluid droplet normal to a plane surface

Abstract

The thermocapillary motion of a fluid droplet in a constant applied temperature gradient perpendicular to a plane surface is analyzed. The exact solution for the temperature and velocity fields in the quasisteady situation is obtained by using spherical bipolar coordinates, and the asymptotic formulas for the droplet velocity are derived from a method of reflections. The boundary effect on the thermocapillary motion is found to be weaker than that on the motion driven by a gravitational force. Even so, the interaction between the plane surface and the droplet can be very strong when the gap thickness approaches zero. For the motion of a droplet normal to a solid plane, the effect of the plane surface is to reduce the migration velocity of the droplet. For the case of droplet migration toward a free fluid 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 of the droplet and its relative distance from the plane. In general, a free surface exerts less influence on droplet movement than a solid surface docs.