Thermocapillary alignment of gas bubbles induced by convective transport

The effect of a weak convective heat transfer on the thermocapillary intera ction of two bubbles with an arbitrary orientation relative to an externall y imposed temperature gradient is examined. Asymptotic analysis of the case of large separation distances, Z, suggests that the corrections to the bub bles' velocities are of O(Pe/Z(2)), rather than O(Pe(2)) previously found f or an isolated bubble. Equal-sized bubbles are known to move with the same velocities, as if they were isolated, when heat conduction is the only tran sport mechanism. However, the convective transport results in a relative mo tion of the bubbles. The tendency of equal bubbles to line up in a plane pe rpendicular to the applied thermal gradient is shown analytically in the we akly nonlinear limit of small Pe numbers, and an interesting interaction be havior in the case of unequal bubbles is discussed. (C) 2001 Academic Press .