Optimisation of calculation methods for determination of surface tensions by drop profile analysis tensiometry

The standard technique for measuring surface or interfacial tension by drop profile analysis requires two main steps: (i) acquisition of drop/bubble images and determination of the profile coordinates via edge detection techniques; (ii) fitting of the theoretical drop/bubble profile to the experimental coordinates using the interfacial tension γ as adjustable parameter. As to edge detection technique, usually the position of the maximum grey level gradient is assumed to be the drop edge. In order to increase the accuracy of edge detection the procedure of fitting a normal distribution function to the experimental grey level gradients yields accurate results when the drop edge is located into the distribution centre. Conventional algorithms use the arc length along the drop profile as independent variable and fit in a vertical, horizontal or normal direction to the experimental shape coordinates, requiring that the coordinates have to be interpolated between experimental points. For small drops having an almost spherical shape, this technique leads to rather large errors. To avoid this interpolation problem a transformation of the Gauss–Laplace equation into polar coordinates can provide higher accuracy. For this, the angle of rotation is used as independent variable and the origin of the coordinate system is located exactly between the drop apex and the capillary tip at which the drop or bubble is formed.