Droplet levitation over non-isothermal surface of evaporating liquid layer

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 a possibility of strong 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. The calculation of the evaporation rate leads to determination of the flow around the droplet, treated in the Stokes flow approximation, and thus the levitation height. The latter is reduced as a result of heat transfer effects in the liquid layer. We also discuss possible mechanisms of droplet self-organization into large ordered arrays.