Sessile drop evaporation in a gap -- crossover between diffusion-limited and phase transition-limited regime

TL;DR

This paper develops a mesoscopic gradient dynamics model to study the evaporation of sessile drops in narrow gaps, capturing the transition between diffusion-limited and phase transition-limited regimes, and compares it with simulations and experiments.

Contribution

It introduces an efficient mesoscopic thin-film model that describes evaporation regimes and incorporates full curvature effects, bridging microscopic details and macroscopic behavior.

Findings

The model accurately captures the crossover between evaporation regimes.

Comparison with numerical simulations validates the model.

Experimental data supports the theoretical predictions.

Abstract

We consider the time evolution of a sessile drop of volatile partially wetting liquid on a rigid solid substrate. Thereby, the drop evaporates under strong confinement, namely, it sits on one of the two parallel plates that form a narrow gap. First, we develop an efficient mesoscopic thin-film description in gradient dynamics form. It couples the diffusive dynamics of the vertically averaged vapour density in the narrow gap to an evolution equation for the profile of the volatile drop. The underlying free energy functional incorporates wetting, interface and bulk energies of the liquid and gas entropy. The model allows us to investigate the transition between diffusion-limited and phase transition-limited evaporation for shallow droplets. Its gradient dynamics character also allows for a full-curvature formulation. Second, we compare results obtained with the mesoscopic model to corresponding direct numerical simulations solving the Stokes equation for the drop coupled to the diffusion equation for the vapour as well as to selected experiments. In passing, we discuss the influence of contact line pinning.