MIGRATION OF A PAIR OF BUBBLES UNDER THE COMBINED ACTION OF GRAVITY AND THERMOCAPILLARITY

The migration of a pair of gas bubbles in an unbounded fluid subject t o the combined action of gravity and a downward temperature gradient i s considered in the quasistatic limit of negligible Reynolds and Pecle t numbers. The solution for the case when the line-of-centers is orien ted arbitrarily with respect to the gravity vector is constructed by s uperposing solutions of the axisymmetric and asymmetric problems, In t he axisymmetric problem, it is found that a pair of unequal bubbles ca n 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 m otionless state. It is also shown that a downward moving bubble can ca use a small bubble which is nearby to move upward, opposite to the dir ection in which the small bubble would move if isolated. Finally, flow structures, computed by a boundary-collocation method, are illustrate d via streamlines in an appropriate symmetry plane in the laboratory f rame of reference or in a reference frame traveling with one of the bu bbles as appropriate. (C) 1995 Academic Press, Inc.