Analysis of an Evaporating Sessile Droplet on a Non-Wetted Surface

TL;DR

This paper develops a unified model for evaporation flux of a sessile droplet on non-wetted surfaces, providing accurate expressions valid for a wide range of contact angles and analyzing the resulting internal flow.

Contribution

It introduces a new, simple expression for evaporation flux on non-wetted surfaces that avoids singularities and extends previous models.

Findings

Derived a unified evaporation flux expression valid for 90° < θ < 180°

Proposed an accurate evaporation rate expression without singularity at θ = 180°

Estimated internal flow velocity consistent with experimental observations

Abstract

We investigate evaporation of a sessile droplet on a non-wetted surface in the framework of diffusion-limited and quasi-steady evaporation. We extend previous models and numerically solve Laplace equation for the diffusion of liquid vapor in ambient. We propose a unified, simple and accurate expression of the evaporation mass flux valid for 90^o < theta < 180^o, where theta is the equilibrium contact angle. In addition, using the derived expression of the evaporation mass flux, we propose a simple and accurate expression of the evaporation mass rate for a non-wetted surface, which does not exhibit singularity at theta = 180^o. Finally, using the scaling analysis, the expression of the evaporation mass flux is utilized to estimate the direction and magnitude of the characteristic evaporation-driven flow velocity inside the droplet on a non-wetted surface. The predicted flow direction is found to be consistent with the previous measurements.