A Robust Polynomial Fitting Approach for Contact Angle Measurements

Polynomial fitting to drop profile offers an alternative to Well-established drop shape techniques for contact angle from sessile drops without a need for liquid physical properties. Here, we evaluate the accuracy of contact angles resulting from fitting polynomials Of various orders to drop profiles in a Cartesian coordinate :system, over a wide range of contact angles. We develop a differentiator mask; to automatically find a range of required number of pixels from a drop, profile over which a Stable contact angle obtained. The polynomial order results, in the longest stable regime and returns the standard error and the highest Correlation coefficient is selected to determine drop contact angles. We find,that; unlike previous reports, a single polynomial order cannot be used to accurately estimate a wide range of contact angles and that a larger order polynomial is needed for drops with larger contact angles. Our method returns contact angles with an accuracy of <0.4 degrees for solid-liquid systems with theta < similar to 60 degrees. This compares well with the axisymmetric drop shape analysis profile (ADSA-P) methodology results. Above about 60 degrees, we observe significant deviations from ADSA-P results, most likely because a polynomial cannot trace the profile of drops with close-to-vertical and vertical segments. To overcome this limitation, we implement a new polynomial fitting g scheme by transforming drop, profiles into polar coordinate system. T eliminates the well problem with high curvature drops and enables estimating contact angles in a wide range with a fourth-order polynomial. We show that this approach returns dynamic Contact angles with less than 0.7 degrees error as compared to ADSA-P, for the solid-liquid systems tested. This new approach is a powerful alternative to drop shape techniques for estimating contact angles of drops regardless of drop symmetry and without a need for liquid properties.