Determination of Interfacial Tension from the Profile of a Pendant Drop Using Computer-Aided Image Processing: 1. Theoretical

Abstract

A method of profile optimization for determining the surface and interfacial tension (IFT) of liquid–fluid systems from the profile of a pendant drop is described. A new, versatile routine for estimating the drop shape parameter is introduced. The factors that affect the available accuracy of the method have been analyzed using theoretical simulations. It was found that the tilt of the drop profiles may lead to large errors in the resultant IFT values if the tilt was not corrected before or during the optimization procedure. This effect could be reduced drastically if a profile were averaged between its two sides and the mean profile were used for optimization. The aspect ratio of a drop image (or profile) can be determined reliably by considering it one of the parameters to be optimized. The dependence of the error in the resultant IFT value on the error in the aspect ratio was found to be highly sensitive to drop shape. The available accuracy of IFT determination using this method depends strongly on the precision of the determination of the drop profiles. After error analysis using theoretical simulations a 95% confidence interval of ca. 0.05 and 0.12% was estimated for this method for the profiles determined with maximum statistical error of 3.5 and 7.0 μm, respectively.