Predicting shape and stability of air-water interface on superhydrophobic surfaces comprised of pores with arbitrary shapes and depths

An integro-differential equation for the three dimensional shape of air-water interface on superhydrophobic surfaces comprised of pores with arbitrary shapes and depths is developed and used to predict the static critical pressure under which such surfaces depart from the non-wetting state. Our equation balances the capillary forces with the pressure of the air entrapped in the pores and that of the water over the interface. Stability of shallow and deep circular, elliptical, and polygonal pores is compared with one another and a general conclusion is drawn for designing pore shapes for superhydrophobic surfaces with maximum stability. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3673619]