Hydrodynamic interaction of a nonvolatile droplet with a planar surface of evaporating liquid

Hydrodynamic interaction between a nonvolatile droplet and an infinite planar surface of an evaporating or condensing liquid is studied theoretically with allowance for effects that are linear with respect to the Knudsen number. The motion of the droplet in the direction normal to the planar liquid surface is considered at low Reynolds numbers and gradients of a gaseous medium temperature and the concentration of the substance evaporating or condensing on the planar liquid surface given at an infinitely large distance from the droplet. The presence of a temperature gradient in the liquid is taken into account in the analysis. The problem is solved in a bispherical coordinate system. The velocity of the steady motion of a castor oil droplet is numerically estimated near the planar surface of evaporating water.