Abstract
The advent of digital image analysis permits the use of several hundred data points defining the profile of a pendant drop in order to determine the surface tension from a fit to a solution to the Young–Laplace equation. This paper discusses several improvements to both the experimental apparatus for carrying out pendant drop measurements and to the methodology for analyzing the drop profiles in order to determine the surface tension. Several standard minimization algorithms were evaluated for fitting the theoretical and experimental drop profiles. These algorithms are very reliable, although there is a tradeoff between robustness and speed of computation. The most robust algorithm was found to converge irrespective of the “roughness” of the experimental drop profile or the accuracy of the initial estimates of the fitting parameters. Whereas the standard deviation of the surface-tension data provides a measure of the precision, the objective function is shown to be an indicator of systematic error in the data. Surface-tension measurements are reported for two standard liquids, methanol and toluene. A standard deviation of 0.016 dyn/cm is obtained for methanol using the full drop profile; this is significantly below the value of 0.036 dyn/cm obtained using the selected plane method, thus indicating that this improved pendant drop technique can give very precise measurements of surface tension.
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