Water Droplet Evaporation in Air—Effects of Interfacial Thermal and Mass Diffusion Resistance

Evaporation of water droplets in air is a process highly relevant to a variety of environmental, industrial, and biomedical applications such as development of effective ventilation methods for indoor droplet control, superfine inkjet printing, spray cooling, delivery of medical aerosols to the lungs, and prevention of the airborne spreading of viruses. The size of water droplets in these applications is usually in microscale. In conventional hydrodynamic modeling of droplet evaporation, it is usually assumed that thermodynamic equilibrium exists at the water-air interface. However, such an assumption could result in considerable errors in predicting the evaporation rate of micro/nanoscale water droplets in air.

In this work, we use the combination of kinetic theory-based model and hydrodynamic model to study the effects of interfacial resistance on the evaporation behavior of water droplets in air. Our modeling results show that the Kapitza resistance R_K and mass diffusion resistance R_M at the droplet-air interface can be well predicted by the kinetic theory-based model. The interfacial thermal resistance and interfacial mass diffusion resistance predicted by the kinetic theory-based model are first validated by MD simulation results, and then incorporated into the hydrodynamic model to predict the influence of the water droplet size, air temperature, pressure and humidity on the water droplet evaporation rate and droplet temperature. To determine the significance of the interfacial effects on droplet evaporation, one needs to compare the equivalent length of thermal resistance L_K = R_Kk_g (where k_g is the air thermal conductivity) and mass diffusion resistance L_M = R_MD_AB (where D_AB is mass diffusivity of water vapor in air) at the droplet-air interface to the droplet size r_d. If L_K and L_M are not negligible compared to r_d, the conventional thermodynamic equilibrium assumption at the droplet surface is invalid.

The evaporation behavior of water droplets in air predicted by our kinetic-hydrodynamic model are corroborated by MD simulation results and the recent experimental data. Our modeling results show that, at normal temperature and pressure (i.e., 25^oC and 1 atm by NIST), the equivalent length of thermal resistance and mass diffusion resistance at water-air interface are both ~ 200 nm. This indicates that, at normal temperature and pressure, the effects of interfacial thermal and mass diffusion resistance on evaporation of water droplets in air cannot be ignored if the droplet diameter is less than 20 μm. The thermodynamic equilibrium assumption is only valid if the droplet diameter is greater than 20 μm. Once the droplet size is greater than 100 μm, the radiation heat transfer and convection effects must also be taken into account to give a more accurate prediction of droplet evaporation rate.