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 undi sturbed state. The bubbles are moving in the direction of the temperature g radient and are assumed to interact axisymmetrically via the influence of t he thermal wake of the leading bubble on the trailing bubble. The flow-fiel d interaction of the bubbles is neglected. The Reynolds number of the motio n is assumed to be sufficiently large that a potential flow field prevails around each bubble. The energy equation for the temperature field around th e trailing bubble is solved by matched asymptotic expansions for large valu es of the Marangoni number. It is shown that the thermal wake of the leadin g bubble induces a nonmonotonic temperature field on the surface of the tra iling 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 res ults for a pair of interacting drops obtained from a space flight experimen t that has been reported in the literature. (C) 1999 American Institute of Physics. [S1070-6631(99)03010-X].