Effect of liquid-vapor interface area on the evaporation rate of small sessile droplets

This study is focused on the role of liquid-vapor interface area in the evaporation of small sessile droplets. The evaporation processes of small sessile droplets with different geometric parameters are numerically investigated with the quasi-steady diffusion model. The numerical results show that droplets with the same surface area are approximately equal in the evaporation rate despite the great differences in contact angles and base radii. It is attributed to the fact that the gradient distributions of vapor concentration surrounding droplets with the same surface area tend to be consistent as the distance from droplet surface increases. Based on the numerical results, a new simple expression with no fitting parameter is developed to calculate the evaporation rate of sessile droplets, and it is found that the evaporation rate is proportional to the square root of liquid-vapor interface area. The proposed expression is in good agreement with the expression of Picknett and Bexon and also validated by the experimental data in open literature. Finally, the evaporation cooling effect of small droplets on an isothermal substrate at room temperature is incorporated into the expression using the average temperature of liquid-vapor interface.