Shape of a large drop on a rough hydrophobic surface

Abstract

Large drops on solid surfaces tend to flatten due to gravitational effect. Their shapes can be predicted by solving the Young-Laplace equation when their apparent contact angles are precisely given. However, for large drops sitting on rough surfaces, the apparent contact angles are often unavailable a priori and hard to define. Here we develop a model to predict the shape of a given volume of large drop placed on a rough hydrophobic surface using an overlapping geometry of double spheroids and the free energy minimization principle. The drop shape depends on the wetting state, thus our model can be used not only to predict the shape of a drop but also to infer the wetting state of a large drop through the comparison of theory and experiment. The experimental measurements of the shape of large water drops on various micropillar arrays agree well with the model predictions. Our theoretical model is particularly useful in predicting and controlling shapes of large drops on surfaces artificially patterned in microscopic scales, which are frequently used in microfluidics and lab-on-a-chip technology.