Range of validity of drop shape techniques for surface tension measurement

Drop shape techniques are widely used for surface tension measurement. As the shape becomes close to spherical, the performance of drop shape techniques deteriorates. A quantitative criterion called shape parameter was previously introduced to quantify the meaning of "well-deformed" drops and "close to spherical" drops. In this paper, a modified definition of the shape parameter that does not depend on the radius of curvature at the drop apex is proposed. Such definition is applicable to different constellations of pendant and sessile drops/bubbles. Dimensional analysis is used to describe similarity in constrained sessile drop shapes and to express the problem using appropriate dimensionless groups. The proposed shape parameter is found to depend only on two dimensionless groups: the dimensionless volume (drop volume normalized by the cube of the holder radius) and the Bond number (using the drop holder's radius as the length scale). 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.