The thermocapillary migrations of two bubbles in microgravity environment

The thermocapillary motion of two bubbles along their line of centers in a uniform temperature gradient is investigated theoretically. The bubbles are moving in the direction of the temperature gradient. And the interaction between the leading bubble and the trailing one becomes significant as the separation distance between them is decreased greatly so that the bubble interaction is considered in this case. The appropriate equations of momentum and energy are solved using the method of reflections. In order to proceed analytically, sets of transformations between two coordinates are obtained. By using these transformations and the reflection process, accurate migration velocities of these two bubbles in the microgravity environment are derived for the limit of small Marangoni and Reynolds numbers. These results are employed to describe the thermocapillary motion of two bubbles and to estimate the effects of bubble size and the thermal gradient on the interaction between two bubbles. All of our results for the migration of the two bubbles demonstrate that the approach of the second bubble to the first one intensifies the mutual interaction between these two bubbles and yields some interesting thermocapillary motions.