Analysis of evaporating droplets using ellipsoidal cap geometry

The evaporation of small droplets of volatile liquids from solid surfaces d epends on whether the initial contact angle is larger or less than 90 degre es. In the latter case, for much of me evaporation time the contact radius remains constant and the contact angle decreases. At equilibrium, the small er the drop, the more it is possible to neglect gravity and the more the pr ofile is expected to conform to a spherical cap shape. Recently published w ork suggests that a singular flow progressively develops within the drop du ring evaporation. This flow might create a pressure gradient and so result in more flattening of the profile as the drop size reduces, in contradictio n to expectations based on equilibrium ideas. In either case, it is importa nt to develop methods to quantify confidence in a deduction of elliptical d eviations from optically recorded droplet profiles. This paper discusses su ch methods and illustrates the difficulties that can arise when the drop si ze changes, but the absolute resolution of the system is fixed. In particul ar, the difference between local variables, such as contact angle, cap heig ht, and contact diameter, which depend on the precise location of the suppo rting surface, and global variables such as radii of curvature and eccentri city, is emphasized. The applicability of the ideas developed is not limite d to evaporation experiments, but is also relevant to experiments on contac t angle variation with drop volume.