A Dimensionless Number for Evaluating the Influence of Heat Conduction in the Gas Phase on Liquid Evaporation

Heat conduction in the gas phase may influence liquid evaporation, yet a quantitative characterization of this effect still remains lacking. Here, through dimensionless analysis of the theoretical model for droplet evaporation, two limiting solutions were obtained for the droplet evaporation considering heat conduction in the gas phase. Based on these solutions, a dimensionless number, HCg, was introduced to evaluate the influence of heat conduction in the gas phase on liquid evaporation. Further analysis indicates that HCg is a function of the relative thermal conductivity of the surrounding air, the evaporative cooling number of the liquid, and the contact angle of the droplet. Analytical expressions for both HCg and the droplet evaporation rate were acquired by fitting the numerical simulations. These results show that the effect of gas-phase heat conduction can generally be neglected due to the typically small values of HCg but becomes significant in cases involving atmospheres with higher thermal conductivity, liquids with smaller evaporative cooling numbers, or droplets with larger contact angles. This work may provide a simple yet accurate criterion for estimating the effects of gas-phase heat conduction on liquid evaporation.