Abstract
This paper presents an analytical study of the thermocapillary motion of an adiabatic gas bubble and a liquid drop with constant temperature by using the method of reflections. The particles are allowed to differ in radius, and the droplet viscosity is arbitrary, which can be limited to a solid sphere. The Peclet and Reynolds numbers are assumed small, so that the temperature and flow fields are governed, respectively, by the Laplace and Stokes equations. The method of reflections is based on an analysis of the thermal and hydrodynamic disturbances produced by an insulated gas bubble and by a single drop with constant temperature, placed in an arbitrarily Laplacian temperature field. The results for two-sphere interactions are correct to O(r12-7), where r12 is the distance between the particle centers. The thermocapillary interactions between a gas bubble and a thermally uniform droplet are discussed in the situations of the prescribed temperature gradient parallel and/or normal to the particles' center line. In addition, the axisymmetric particle interactions in a medium with uniform applied temperature are formulated. The effect of interactions on thermocapillary migrations of an insulated gas bubble and a thermally uniform droplet is generally stronger than that on the motions influenced by the interaction of two gas bubbles or droplets. Meanwhile, the particle behaviors are quite different from those we know.
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