Volume evolution of small sessile droplets evaporating in stick-slip mode

This work is aimed at developing a simple and efficient predictive model and revealing the volume evolution behavior of small sessile droplets evaporating in stick-slip (SS) mode, covering a wide range of initial (θ_{0}) and receding (θ_{rec}) contact angles (0^{∘}<θ_{rec}≤θ_{0}<180^{∘}). For this purpose, simple closed-form expressions for the evolutions of the contact angle and contact radius of droplets evaporating in SS mode are first developed, and are then validated with the experimental data in the literature. With the proposed expressions, the volume evolutions of evaporating droplets with different θ_{0} and θ_{rec} are predicted and analyzed. The results show that on a hydrophilic surface (θ_{0}≤90^{∘}), the volume evolution of droplets in SS mode always occurs in a way between the constant contact radius (CCR) and constant contact angle (CCA) modes (i.e., two extreme modes); however, on a hydrophobic surface (θ_{0}>90^{∘}), as θ_{rec} increases from 0 to θ_{0}, the volume evolution of droplets in SS mode first departs from the CCR mode, then approaches the SS mode with θ_{rec}=90^{∘}, and finally returns to the CCA mode. More interestingly, the initially identical droplets evaporating on hydrophobic surfaces with different receding contact angles (θ_{rec}=90^{∘}±Δθ) can even have approximately the same volume evolution behavior. It is also found that the widely accepted 2/3 law is applicable only for volume evolution of droplets in SS mode with large initial contact angle or small contact angle hysteresis, with the predicted deviation less than 1.5% for θ_{0}≥150^{∘} or θ_{0}≥50^{∘} when θ_{0}-θ_{rec}≤15^{∘}. Finally, a physical interpretation for the volume evolution behaviors of droplets in SS mode is proposed.