Unsteady Thermocapillary Drop Migration in a Uniform Temperature Gradient

A theoretical analysis of liquid drop unsteady migration under microgravity conditions is presented, if an interfracial tension gradient is generated on the drop surface by a uniform temperature gradient in the surrounding liquid. The effect of buoyancy due to a residual gravity vector aligned parallel to the temperature gradient is included. The relevant equations are solved in the creeping flow limit where in the convective transport of momentum as well as that of the energy is neglected, i.e. at low Reynolds and Marangoni numbers. The flow and the temperature field within and around the drop are obtained after transforming the results from the Laplace transform domain, in which they are derived, to the time domain. The time transient behaviour of the Migration speed depends strongly on the choice of the initial flow and temperature fields. The comparison with other initial conditions from the literature is performed.