Effect of inertia on the thermocapillary velocity of a drop

We consider the effects of inertia on the thermocapillary migration velocity of a small liquid droplet in a microgravity environment. The externally imposed temperature gradient is assumed to be constant, and the fluid surrounding the droplet is taken to be unbounded and otherwise quiescent. With the convective transfer of heat neglected, droplets with densities higher/lower than the outside liquid deform to prolate/oblate spheroidal shapes, at small values of the capillary and Reynolds numbers. The corrections to the temperature field and the migration velocity of the droplet, resulting from this deformation, are obtained using the so-called Lorentz reciprocal theorem. It is found that the migration velocity could increase, decrease, or remain unchanged depending on the value of certain controlling parameters. The results are presented in vector-invariant form.