ABSTRACT
The nature of the evaporation of sessile drops of a volatile liquid resting on a solid surface depends on the initial contact angle [1, 2]. For an initial angle less than 90°, for much of the evaporation time the contact radius remains constant as the droplet mass reduces [1-4]. In contrast, for an initial contact angle of greater than 90°, it is the contact angle which remains approximately constant [5]. To explain
the observed dependence of the geometrical parameters, Birdi and Vu [2] modelled the evaporation process using a diffusion model and a spherical shape with a single radius of curvature, R. This model was later extended to include the effect of the two radii of curvature (spherical radius R and contact radius r) and was applied to both regimes of initial contact angle [3, 5] (also see ref. [4]). Whilst the model accounts well for the observed data, it has been criticized for its assumption of a spherical cap shape [6, 7]. A generalization of the model based on an elliptical cap model has been given by Erbil and Meric [6]. In this work, it was suggested from a re-analysis of previously published data, for a water-on-poly(methyl methacrylate) (PMMA) system, that such an elliptical shape was more appropriate. It was also concluded that the elliptical shape was more pronounced for the smallest drops. In studying the equilibrium contact angle, a convenient measure of the relative importance of gravity to capillary forces is given by the capillary length ĸ~ l = (yi.v/py)1'2, where Yiy is the liquid-vapor surface tension, p is the density of the liquid, and g is the acceleration due to gravity. In the data for water on PMMA, the capillary length was 2.8 mm and the range of contact radii for the droplets studied was 0.3-0.6 mm. It is therefore plausible that gravity would lead to a small flattening of the droplets, but the same considerations would also suggest that as the droplet volume reduced, gravity would become less important and the droplet would become more spherical in shape. Thus, more intriguing than the existence of a small correction to the spherical cap shape is the suggestion that a droplet may deviate towards an elliptical shape as the droplet evaporates. This would be contrary to initial expectations based on equilibrium ideas and the capillary length.
