Thermocapillary migration of bubbles: convective effects at low Peclet number

The effect of a weak convective heat transfer on the thermocapillary intera ction of two bubbles migrating in an externally imposed temperature gradien t is examined. It is shown that, for short and moderate separation distance s, the corrections to the individual migration velocities of the bubbles ar e of O(Pe), where Pe is Peclet number. For separation distances larger than O(Pe(-1/2)) the correction is of O(Pe(2)) as previously found for an isola ted drop. The perturbations to the bubble velocities have opposite signs: t he motion of the leading bubble is enhanced while the motion of the trailin g one is retarded. A newly found feature is that equal-sized bubbles, which otherwise would move with equal velocities, acquire a relative motion apar t from each other under the influence of convection. For slightly unequal b ubbles there are three different regimes of large-time asymptotic behaviour : attraction up to the collision, infinite growth of the separation distanc e, and a steady migration with equal velocities, the steady motion separati on distance being a function of the parameters of the problem. Sufficient c onditions for the realization of each regime are given in terms of the Pecl et number, initial separation and radii ratio.