The effect of heat transfer in an evaporatiing liquid layer on the droplets levitating above it

Studies concerning droplet interactions with liquid surfaces are important for a variety of applications, including spray cooling, aerosol drug distribution, and other particle transport problems. In this study, we consider a slowly condensing droplet levitating near the surface of an evaporating layer and develop a mathematical model to describe diffusion and heat transfer in the system. The method of separation of variables in bipolar coordinates is used to obtain the series expansions for temperature distribution in the air, droplet, and the liquid layer, as well as the vapor concentration. This framework, combined with the coupled boundary conditions at the interface, allows us to determine temperature profile and condensation rate at the surface of the droplet and the temperature profile on the surface of the liquid layer. From these findings, we can analyze the effect of the liquid layer on the droplet. On the layer surface under the droplet, there is a reduction in the rate of evaporation, possibly due to the constricting geometry of the problem. The temperature gradient along the layer surface leads to previously neglected Marangoni stresses. Their influence of the fluid flow is discussed.