Accuracy of surface tension measurement from drop shapes: The role of image analysis

Abstract

Axisymmetric Drop Shape Analysis (ADSA) has been extensively used for surface tension measurement. In essence, ADSA works by matching a theoretical profile of the drop to the extracted experimental profile, taking surface tension as an adjustable parameter. Of the three main building blocks of ADSA, i.e. edge detection, the numerical integration of the Laplace equation for generating theoretical curves and the optimization procedure, only edge detection (that extracts the drop profile line from the drop image) needs extensive study. For the purpose of this article, the numerical integration of the Laplace equation for generating theoretical curves and the optimization procedure will only require a minor effort. It is the aim of this paper to investigate how far the surface tension accuracy of drop shape techniques can be pushed by fine tuning and optimizing edge detection strategies for a given drop image. Two different aspects of edge detection are pursued here: sub-pixel resolution and pixel resolution. The effect of two sub-pixel resolution strategies, i.e. spline and sigmoid, on the accuracy of surface tension measurement is investigated. It is found that the number of pixel points in the fitting procedure of the sub-pixel resolution techniques is crucial, and its value should be determined based on the contrast of the image, i.e. the gray level difference between the drop and the background. On the pixel resolution side, two suitable and reliable edge detectors, i.e. Canny and SUSAN, are explored, and the effect of user-specified parameters of the edge detector on the accuracy of surface tension measurement is scrutinized. Based on the contrast of the image, an optimum value of the user-specified parameter of the edge detector, SUSAN, is suggested. Overall, an accuracy of 0.01mJ/m2 is achievable for the surface tension determination by careful fine tuning of edge detection algorithms.