2019 journal article
A generalized variational approach for predicting contact angles of sessile nano-droplets on both flat and curved surfaces
JOURNAL OF MOLECULAR LIQUIDS, 281, 196–203.
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6. Clean Water and Sanitation
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7. Affordable and Clean Energy
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Source: Web Of Science
Added: May 6, 2019
Derivations of Young's equation have traditionally neglected the Laplace pressure and its influence on the curvature of sessile droplets under thermodynamic equilibrium. Omission of the Laplace pressure results in overestimating the line tension by several orders of magnitude and contributes to significant errors in predicting the contact angle for droplet volumes ranging from micro-liters to atto-liters. This paper addresses this issue and offers a correct inclusion of VdP as a virtual work term in the free energy variation at the liquid-vapor boundary for both flat and curved surfaces. While the Laplace pressure is constant at the liquid-vapor interface as a condition of equilibrium, the variation of the Laplace pressure is not zero, as it influences both the shape (spherical cap) and contact angle of sessile droplets. Inclusion of this term leads naturally to a definition of the line tension as a volume dependent term, and more importantly to a correct prediction in both sign and magnitude of the line tension value. The inclusion of VdP work predicts a cubic relationship between the cosine of the contact angle and droplet line radius. This new model extends existing theories on the behavior of nanosized droplets and its predictions exhibit quantitative agreement with experimental results for nonane, dodecane, fullerene, and glycerol trioleate over a range of 15 orders of magnitude in droplet volume. Finally, we also theorize the existence of two different equilibrium contact angles at lower droplet volumes. These two values diverge with the inverse line radius.