Spline-based Interface Modeling and Optimization (SIMO) for Surface Tension and Contact Angle Measurements

Surface tension and contact angle measurements are fundamental characterization techniques relevant to thermal and fluidic applications. Drop shape analysis techniques for the measurement of interfacial tension are powerful, versatile and flexible. Here we develop a Spline-based Interface Modeling and Optimization (SIMO) tool for estimating the surface tension and the contact angle from the profiles of sessile and pendant drops of various sizes. The employed strategy models the profile using a vector parametrized cubic spline which is then evolved to the eventual equilibrium shape using a novel thermodynamic free-energy minimization-based iterative algorithm. We perform experiments to show that in comparison, the typical fitting-based techniques are very sensitive to errors due to image acquisition, digitization and edge detection, and do not predict the correct surface tension and the contact angle values. We mimic these errors in theoretical drop profiles by applying the Gaussian noise and the smoothing filters. We then demonstrate that our optimization algorithm can even drive such inaccurate digitized profiles to the minimum energy equilibrium shape for the precise estimation of the surface tension and the contact angle values. We compare our scheme with software tools available in public domain to characterize the accuracy and the precision of SIMO.