Thermocapillary motion of a drop near a plane interface between liquids

The thermocapillary motion of a liquid drop immersed into another liquid near an infinite plane interface between two liquids is theoretically analyzed. The motion is considered under the conditions of a constant temperature gradient normal to the interface at infinity and small Reynolds and Peclet numbers. The problem is solved in bispherical coordinates. The analysis takes into consideration the thermal conductivity of the liquids and the thermocapillary motion of the liquids due to a nonuniform temperature distribution over the plane interface.