Design and accuracy of pendant drop methods for surface tension measurement

Drop shape techniques are extensively used for surface tension measurement. The accuracy of surface tension measurements using a pendant drop setup depends mainly on the drop shape. As the pendant drop shape becomes close to spherical, the performance of drop shape techniques deteriorates. It is important to consider how to optimize the pendant drop design and how to quantify the accuracy of the surface tension measurements. In this paper, the design and accuracy of pendant drop methods is considered in detail. Dimensional analysis is used to describe similarity in pendant drop shapes and to express the problem using appropriate dimensionless groups. A quantitative criterion called shape parameter is then used to express quantitatively the difference in shape between a given experimental drop and a spherical shape. The shape parameter is found to depend only on two dimensionless groups: the dimensionless volume and the Bond number. A critical shape parameter (minimum value of the shape parameter that guarantees a specified accuracy) is shown to depend only on Bond number. A set of experiments were performed with pure liquids to illustrate the change of the critical shape parameter with the Bond number. Results show that high accuracy is indeed reachable independent of the algorithms used.