Thermocapillary migration of bubbles and droplets

The migration of a droplet in a large liquid body possessing a uniform temperature gradient is analyzed in the creeping flow limit for small values of the Marangoni number (ε). The method of matched asymptotic expansions is used for the solution of the field equations. The migration velocity is calculated to 0(ε²) and the result reduces to that of Young, Goldstein and Block 10] in the limit of zero Marangoni number.