Droplet levitation over non-isothermal surface of evaporating liquid layer

Abstract We develop a mathematical model of heat and mass transfer in a configuration which involves a spherical droplet levitating near a flat liquid layer heated from below. Analytical solutions for vapor concentration in air and the temperature distributions both inside the droplet and in moist air around it are coupled to the numerical solution for heat transfer in the liquid layer. In the limit of weak evaporation, the liquid layer surface is cooled locally due to the presence of the droplet, while the effect is reversed for strong evaporation. The latter case is also characterized by higher temperature near the bottom of the droplet and stronger temperature gradients in the droplet itself, an unexpected conclusion given the high liquid-to-air thermal conductivity ratio. The observations are explained in terms of interplay between geometric and thermal effects of the presence of the droplet. A simple analytical criterion is formulated to determine the condition when the droplet presence has no effect on the layer temperature; remarkably, the condition does not depend on the distance between the droplet and the layer surface. The calculation of the evaporation rate leads to determination of the flow around the droplet, treated in the Stokes flow approximation, as well as the levitation height.