The effect of electrical double layers on evaporation of sessile droplets

• Published in: Journal of engineering mathematics Vol. 134; no. 1
• Main Authors: Barrett, James A., Ajaev, Vladimir S.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Conduction heating; Conductive heat transfer; Contact angle; Droplets; Electric contacts; Evaporation rate; Evaporative cooling; Liquid surfaces; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Substrates; Theoretical and Applied Mechanics; Apparent contact lines; Disjoining pressure; Evaporation
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-022-10227-6

We develop a lubrication-type model of an axisymmetric evaporating sessile liquid droplet in contact with pure vapor. The liquid is a symmetric electrolyte, a two-component expression for disjoining pressure accounts for both unbalanced London–van der Waals interactions and repulsion of electrical double layers formed near liquid–solid and liquid–vapor interfaces. The electric potential in the liquid is described using the Debye–Hückel approximation. We consider nonequilibirum effects during evaporation from the liquid surface and an increase of solute concentration as a result of solvent evaporation. Electrostatic effects lead to reduction of the evaporation rates at initial stages of evolution but the trend is reversed at the later stages, resulting in significantly lower lifetimes of evaporating droplets. The apparent contact angle, defined by the maximum interfacial slope, tends to be lower when the electrostatic effects are more significant. Evaporative cooling is also considered in the framework that accounts for heat conduction in the substrate and shown to increase the droplet lifetime.