Predicting shape and stability of air-water interface on superhydrophobic surfaces with randomly distributed, dissimilar posts

A mathematical framework developed to calculate the shape of the air-water interface and predict the stability of a microfabricated superhydrophobic surface with randomly distributed posts of dissimilar diameters and heights is presented. Using the Young-Laplace equation, a second-order partial differential equation is derived and solved numerically to obtain the shape of the interface, and to predict the critical hydrostatic pressure at which the superhydrophobicity vanishes in a submersed surface. Two examples are given for demonstration of the method's capabilities and accuracy. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3590268]