An image analysis procedure for measuring the surface tension of pendant micro-drops

Abstract

A method based on an image analysis procedure was developed to calculate the shape and surface tension of pendant droplets hanging down in air from the tip of a syringe. In contrast to most existing methods, a numerical solution of the Young-Laplace equation of capillarity for the calculation of the drop contour is not required. Apart from local gravity and densities of liquid and fluid phases, the only input information needed to determine the surface tension is given by the maximum equatorial radius of the drop and its degree of deformation defined by a shape factor. Specifically it is not necessary to determine the radius of curvature at the apex of the experimental drop profile, the drop height, or the contact angles. When the drops are formed from the tip of a capillary tube, the software obtains direct digitization of the drop image, performs edge detection, and reconstructs the three-dimensional drop from its digitized profile to accurately determine its volume. Surface tension measurements have been performed for distilled water drops suspended in air to test the reliability and accuracy of the method. The results show that reliable values of the surface tension can be obtained for drops larger than about 2--3 μl, with relative errors less than 0.08--0.29 mN m^{-1}, depending on the size of the holder.