is the asperity rise angle and u03b8 a 0 is the experimentally measured true advancing contact angle of the liquid on the asperity material the height z of asperities 24 must be at least equal to and is preferably greater than critical asperity height z c although in fig1 d 3 the asperity rise angle u03c9 is 90 degrees other asperity geometries are possible for example u03c9 may be an acute angle as depicted in fig9 or an obtuse angle as depicted in fig1 generally it is preferred that u03c9 be between 80 and 130 degrees it will also be appreciated that a wide variety of asperity shapes and arrangements are possible within the scope of the present invention for example asperities may be polyhedral cylindrical as depicted in fig1 12 cylindroid or any other suitable three dimensional shape in addition various strategies may be utilized to maximize contact line density of the asperities as depicted in fig1 and 15 the asperities 24 may be formed with a base portion 38 and a head portion 40 the larger perimeter of head portion 40 at top edge 30 increases the contact line density of the surface also features such as recesses 42 may be formed in the asperities 24 as depicted in fig1 to increase the perimeter at top edge 30 thereby increasing contact line density the asperities may also be cavities formed in the substrate the asperities may be arranged in a rectangular array as discussed above in a polygonal array such as the hexagonal array depicted in fig4.