Planar thermocapillary migration of two bubbles in microgravity environment

A theoretical investigation is performed on the thermocapillary motion of two bubbles in arbitrary configuration in microgravity environment under the assumption that the surface tension is high enough to keep the bubbles spherical. The two bubbles are driven by the surface tension gradient due to temperature nonuniformity on the surfaces. The bubble interaction is considered for the limit of small Marangoni and Reynolds numbers in the present paper. In order to solve the problem analytically, the method of successive reflections is employed, and then accurate migration velocities of two arbitrarily oriented bubbles in the planar thermocapillary motions are derived. The results demonstrate that two equal-size bubbles exert no influence on the thermocapillary migration of each other at any separation because of the thorough cancellation of the thermal and fluid mechanical interaction effects, and the effect of the large bubble on the motion of the smaller one becomes significant with the two bubbles approaching each other, while the effect of the smaller one on the large remains weak. Moreover, three typical kinds of trajectories of the smaller bubble are identified.