Numerical models for the evaluation of the contact angle from axisymmetric drop profiles: A statistical comparison

Axisymmetric drop shape analysis (ADSA) is a well-established methodology for estimating the contact angle value and the surface tension of liquids starting from sessile drops images. It consists of an iterative procedure in which a best fit between a theoretical axisymmetric Laplacian curve and an experimental drop profile is performed. When only an evaluation of the geometric contact angle value is needed, a similar numerical approach can be adopted by using simpler algebraic models in place of a Laplace profile, thus allowing more straightforward implementations and shorter computation times. In this work the relative merits of the different methodologies are compared. Beside the standard ADSA procedure, four different mathematical models are examined, namely the circular and elliptical models, the first-order perturbative solution of the Laplace equation, and a cubic spline model. Their relative statistical performances are tested on both calculated and experimental drop profiles. For simulated drops, the actual capability of the models to predict the correct contact angle is also investigated