Axisymmetric thermal wake interaction of two bubbles in a uniform temperature gradient at large Reynolds and Marangoni numbers

An analysis is performed on the thermocapillary motion of two bubbles in a continuous phase in which a linear temperature field is imposed in the undisturbed state. The bubbles are moving in the direction of the temperature gradient and are assumed to interact axisymmetrically via the influence of the thermal wake of the leading bubble on the trailing bubble. The flow-field interaction of the bubbles is neglected. The Reynolds number of the motion is assumed to be sufficiently large that a potential flow field prevails around each bubble. The energy equation for the temperature field around the trailing bubble is solved by matched asymptotic expansions for large values of the Marangoni number. It is shown that the thermal wake of the leading bubble induces a nonmonotonic temperature field on the surface of the trailing bubble. The effective temperature gradient on the trailing bubble is weakened. Hence its migration speed is reduced compared to the case when it is isolated. This result is in qualitative agreement with experimental results for a pair of interacting drops obtained from a space flight experiment that has been reported in the literature.