Thermocapillary Motion of Bubbles Inside Drops

A quasi-static analysis is performed for the thermocapillary motion of a bubble located inside a drop in free fall, with arbitrary axisymmetric temperature fields prescribed on the drop surface. It is shown that in the case of an axially symmetric temperature field, the bubble moves along the axis of symmetry toward the nearest warm pole. The bubble velocity as well as the velocity and temperature fields in the drop can be predicted on the basis of the quasi-static assumptions. An approximation is presented which adequately describes bubble migration velocities in the case where the ratio of the bubble radius to the drop radius is relatively small.