Numerical Study of Water Droplet Evaporation on a Superhydrophobic Surface

A comprehensive numerical model is developed to predict evaporation of a water droplet from an unheated superhydrophobic substrate. Analytical models that only consider vapor diffusion in the gas domain, and assume the system to be isothermal, over-predict the evaporation rates by similar to 25% compared to experiments conducted on such surfaces. The current model solves for conjugate heat and mass transfer in the solid substrate, liquid droplet, and surrounding gas. Evaporative cooling of the interface is accounted for, and vapor concentration is coupled to local temperature at the interface. Buoyancy-driven convective flows in the droplet and vapor domains are also simulated. A droplet evaporating in a constant-contact-angle mode with an initial volume of 3 ill and contact angle of 160 deg is considered at an ambient temperature of 21 degrees C and 29% relative humidity, to match conditions of related experiments. The interface cooling effect suppresses the evaporation rate significantly; however, natural convection in the gas and liquid domains has a negligible impact on the evaporation rate. The local evaporation flux along the droplet interface predicted by the model is compared to that predicted by an analytical diffusion-based model. The numerically calculated total evaporation rate agrees with experimental results to within 2%. The large deviations between past analytical models and the experimental data on superhydrophobic surfaces are reconciled.