Thermocapillary motion of a drop in a fluid under external gradients. Faxén theorem

We have studied the thermocapillary motion of a drop in a fluid under nonequilibrium conditions, in the presence of velocity and temperature gradients. After reformulating the boundary value problem in terms of an induced force and an induced heat source densities, we have derived the Faxén theorem for the drop. The theorem gives the hydrodynamic force exerted on the drop as a function of its velocity and of the unperturbed velocity and temperature fields. From it we infer expressions for the mobility and thermocapillary coefficients. Our general result then permits us to analyze a number of particular situations of interest which have been reported by other authors.