Empirical Formulae in Correlating Droplet Shape and Contact Angle

Abstract

In contact angle measurements, direct identification of the contact angles from images taken from a goniometer suffers from errors caused by optical scatterings. Contact angles can be more accurately identified by the height and width of the droplet. Spherical dome is a simple model used to correlate the contact angles to the droplet shape; however, it features intrinsic errors caused by gravity-induced shape deformation. This paper demonstrates a simple method of obtaining an empirical formula, determined from experiments, to correct the gravity-induced error in the spherical dome model for contact angle calculations. A series of contact angles, heights, and surface contact widths are simultaneously collected for a large amount of samples, and the contact angles are also calculated using the spherical dome model. The experimental data are compared with those obtained from the spherical dome model to acquire an empirical formula for contact angles. Compared with the spherical dome model, the empirical formula can reduce the average errors of the contact angle from –16.3 % to 0.18 %. Furthermore, the same method can be used to correct the gravity errors in the spherical dome for the volume (calculated by height and width), height (calculated by contact angle and volume), and width (calculated by contact angle and volume), and the spherical dome errors can be reduced from –20.9 %, 24.6 %, and –4.8 % to 2 %, –0.13 %, and –0.6 %, respectively. Our method is generic and applicable for all kinds of solvent and substrates, and the derived empirical formulae can be directly used for water droplets on any substrate.