The evaporation of water droplets placed on heated hydrophilic, hydrophobic, and superhydrophobic sub- strates is numerically investigated. Simplified analytical models for droplet evaporation only include va- por diffusion transport in the surrounding gas domain and assume an isothermal droplet interface at the substrate temperature. The comprehensive model developed in this study accounts for all of the per- tinent transport mechanisms. The interface is cooled via absorption of latent heat during evaporation, and the saturated vapor concentration is coupled to local temperature at the droplet interface. Conjugate heat and mass transfer are solved throughout the system using temperature-dependent physical prop- erties. Buoyancy-driven convective flows (induced by both species concentration and temperature gradi- ents) in the droplet and gas domains are also simulated. The evaporation rates predicted as a function of the substrate wettability (contact angle from 10 °to 160 °) and substrate temperature (40 °C to 65.4 °C) are validated against experiments from the literature. The modeling approach yields quantitative insights into the influence of these transport mechanisms on the evaporation characteristics. As substrate tem- perature is increased, the buoyancy-induced convection significantly increases the evaporation rate by up to ~60% on the hottest substrate compared to the diffusion-based model, by enhancing vapor transport in the gas domain. Simultaneously, the liquid-gas interface is increasingly cooled by evaporation, lead- ing to a large temperature drop across the droplet height, ~18 °C for a 3 μL droplet evaporating on the superhydrophobic substrate at 60 °C. This significantly alters the distribution of the vapor fraction and evaporation flux along the interface and suppresses the evaporation rate (by ~53%). When both factors are considered together, the net effect (namely, enhancement or suppression) on the evaporation rate is dependent on the competition between the buoyancy-induced convection and evaporative cooling. On hydrophilic substrates, the evaporative cooling effect is weak because the flat droplet shape results in a relatively small temperature difference between the interface and the heated substrate; upward gas-phase natural convection is dominant and enhances evaporation. On the hydrophobic substrate, these respective suppression and enhancement effects counterbalance each other. On the superhydrophobic substrate, the effect of evaporative cooling is further amplified by the large thermal resistance between the substrate and interface, dominating the transport process and entirely suppressing the influence of upward natural convection in the gas phase.
droplet evaporation, convection, evaporative cooling, heated substrates, superhydrophobic
Date of this Version
Z. Pan, J. A. Weibel, and S.V. Garimella, “Transport Mechanisms during Water Droplet Evaporation on Heated Substrates,” International Journal of Heat and Mass Transfer, Vol 152, 119524, 2020.