A non-iterative method to evaluate surface tension and contact angle simultaneously by a sessile drop in gravity using universal figures

Abstract

A non-iterative method is proposed to evaluate surface tension and contact angle simultaneously from a sessile drop observation in gravity using two universal figures. A theory of the sessile drop in gravity is used assuming an axisymmetric profile of the drop. Numerical calculation is carried out to prepare the two figures. The first one of the figures is a relation between the normalized curvature at the top of the drop and the geometry ratio of height to radius of a point on the drop surface. The second one of the figures is a relation between the normalized curvature and the normalized height of the point. The position and the tangential angle of the point on the drop surface are obtained from the sessile drop observation. Using the first figure, the normalized curvature can be determined from the position and the tangential angle of the point. Using the second figure, the normalized height of the point can be determined from the normalized curvature determined. Since the height and the normalized heights can be obtained from the measurement, the normalizing factor can be obtained. Because the factor is a function of the gravity and the surface tension of the liquid, we can evaluate the surface tension of the liquid from the point on the sessile drop surface. By taking average using several points, we can improve accuracy of the surface tension evaluated. Also, the first figure can be used to evaluate the contact angle from the position of the drop edge without measurement of angle. The present method is demonstrated using a pure water droplet on a water-repellent surface. It shows a successful evaluation of the surface tension and the contact angle, simultaneously from the droplet observation, without any iterative calculation.