Lifetime of evaporating two-dimensional sessile droplets

Area of Science:

• Fluid dynamics
• Thermodynamics
• Mass transfer

Background:

• Diffusion-limited evaporation of sessile droplets is typically modeled using quasisteady approximations.
• Two-dimensional models face challenges with logarithmic concentration growth at large distances, conflicting with equilibrium requirements.

Purpose of the Study:

• To develop a self-consistent model for evaporating sessile droplets that overcomes limitations of quasisteady approximations.
• To accurately predict droplet lifetime by resolving vapor concentration evolution in two dimensions.

Main Methods:

• Utilized matched asymptotic expansions to decompose the vapor domain into near-field (quasisteady) and far-field (unsteady) regions.
• Applied asymptotic matching to ensure a self-consistent description across different scales.
• Avoided artificial remote boundaries that introduce nonphysical parameter dependencies.

Main Results:

• The model provides a self-consistent description of time-evolving evaporation.
• Droplet lifetime is determined as a universal function of a single physical parameter.
• Successfully resolved the incompatibility of quasisteady models with large-distance behavior.

Conclusions:

• Matched asymptotic expansions offer a robust solution for diffusion-limited evaporation analysis.
• The derived universal function simplifies the prediction of droplet lifetime.
• This approach provides a more accurate and physically grounded understanding of sessile droplet evaporation.