The Effect of the Medium on the Thermocapillary Force of a Heated Droplet Drifting in a Viscous Liquid in the Field of External Temperature Gradient

The Stokes approximation is used to theoretically investigate the effect of the medium on the thermocapillary drift of a heated droplet inside which nonuniformly distributed heat sources are operative. The droplet drift proceeds in a viscous incompressible liquid under conditions of arbitrary temperature differences between the particle surface and a region away from it. The problem is solved in view of the exponential-power form of the temperature dependence of viscosity. In the process of solving the hydrodynamic equations, analytical expressions are derived for the thermocapillary force acting on the droplet. It is demonstrated that, in the approximation applied, the droplet retains its spherical shape. Numerical estimates indicate that the motion of the medium affects considerably the magnitude of the thermocapillary force.