Retention Forces for Drops on Microstructured Superhydrophobic Surfaces

Accurate models of retention forces between drops and superhydrophobic (SH) surfaces are required to predict drop dynamics on the surface. This retention force is, in turn, useful in modeling heat transfer rates for dropwise condensation on a SH surface. Drop contact angle distribution and base area on SH surfaces are essential factors for predicting retention forces. The present work measures the contact angle distribution and base area shapes of various drop sizes over a wide range of solid fraction for inclined microstructured SH surfaces at the point of drop departure. Base area shape was found to be well approximated using two ellipses with different aspect ratios, and the contact angle distribution was found to be best fit by a sigmoid function. At an incline near the roll-off angle, drop base area for surfaces with solid fraction close to 1 and close to 0 were found to be nearly circular, whereas the base area of drops on surfaces with an intermediate solid fraction deviated from circular behavior. In this work, maximum advancing and minimum receding contact angles were found as a function of solid fraction and used to calculate retention forces. Contact angle distribution and base area shapes are then used to calculate retention forces between drops and SH surfaces. These calculations are compared with the component of measured drop weight acting parallel to the plane on a tilted surface for validation. Previous retention force studies that investigate base area shape and contact angle distribution for smooth surfaces are not applicable for microstructured SH surfaces. The work shows that using a sigmoid contact angle distribution and modified base area shape yields retention forces that are on average 50% better than previously reported methods. Retention forces for smooth and SH surfaces calculated in this study were used to suggest retention force factor values for varying solid fraction surfaces.