Migration of a Pair of Bubbles under the Combined Action of Gravity and Thermocapillarity

TLDR: In this paper, the authors considered the migration of a pair of gas bubbles in an unbounded fluid subject to the combined action of gravity and a downward temperature gradient in the quasistatic limit of negligible Reynolds and Peclet numbers.

Abstract: The migration of a pair of gas bubbles in an unbounded fluid subject to the combined action of gravity and a downward temperature gradient is considered in the quasistatic limit of negligible Reynolds and Peclet numbers. The solution for the case when the line-of-centers is oriented arbitrarily with respect to the gravity vector is constructed by superposing solutions of the axisymmetric and asymmetric problems. In the axisymmetric problem, it is found that a pair of unequal bubbles can reach a stable critical separation at which both bubbles move at the same velocity, if the smaller bubble is on top of the larger one; at an appropriate balance of the relative strengths of the gravitational and thermocapillary effects, such a pair of bubbles also can reach a motionless state. It is also shown that a downward moving bubble can cause a small bubble which is nearby to move upward, opposite to the direction in which the small bubble would move if isolated. Finally, flow structures, computed by a boundary-collocation method, are illustrated via streamlines in an appropriate symmetry plane in the laboratory frame of reference or in a reference frame traveling with one of the bubbles as appropriate.