Comparison of one-sided and diffusion-limited evaporation models for thin liquid droplets

Abstract

Evaporating sessile droplets are critical to many industrial applications and are also ubiquitous in nature. Two predominant evaporation models have emerged in the literature, one-sided and diffusion-limited, with differing assumptions on the evaporation process. Both models are used widely, and their predictions can differ greatly from each other, but the physical mechanisms responsible for these differences are not yet well understood. Here, we develop a lubrication-theory-based model of a thin evaporating sessile droplet, and compare predictions from both evaporation models to elucidate the origins of the differences in their predictions. For the one-sided model, we derive expressions for the droplet lifetime, show that in certain parameter regimes the total evaporation rate is proportional to the droplet surface area, and demonstrate that the contact line is always warmer than the bulk of the droplet. Furthermore, we show that differences in the structures of the evaporation models near the contact line lead to qualitatively different behaviour of the apparent contact angles and interface temperature profiles. The fundamental understanding gained from this work is expected to be helpful in determining which evaporation model is most appropriate for describing experimental observations.