Thermocapillary phoresis of inclusions with interphase surfactant

The motion of a spherical inclusion (gaseous, liquid or solid) submerged in an infinite (continuous) viscous media with a constant temperature gradient is considered. The analysis is carried out by considering negligible values of the Reynolds and Marangoni (Peclet) numbers and some other certain assumptions. The formulae for the thermocapillary phoresis velocity of the inclusions with the surfactant films are derived and can be applied for emulsions containing spherical drops, systems of liquids with solid or gaseous inclusions, e.g. at flotation, metal foaming, steel refining from the inclusions.