The shape of heavy droplets on superhydrophobic surfaces

Abstract

An analytical model is developed to describe the shape of heavy droplets on solid surfaces with arbitrary wetting properties (corresponding to the contact angles ranging from 0 to 180°). This model, based on a surface of revolution by rotating two elliptic arcs, reduces to the ellipsoid model for a hydrophilic case. Experimental measurements are also conducted to verify the model. It shows that the mean curvature distribution of the developed model agrees well with that of real droplets on hydrophobic surfaces, even on superhydrophobic surfaces. For water droplets with a volume up to 1000 μL on superhydrophobic surfaces having a 162° contact angle, the errors of the predicted heights, maximum radius, and wetting radius using this model are less than 1.7%, which suggests the capability of this model in studying the wettability of heavy droplets. This model provides an accurate theoretical basis for designing and controlling the spread, transport, condensation, and evaporation of heavy droplets on superhydrophobic surfaces.