  We study a stationary wetting problem on rough and inhomogeneous solid
surfaces. We derive a new formula for the apparent contact angle by asymptotic
two-scale homogenization method. The formula reduces to a modified Wenzel
equation for geometrically rough surfaces and a modified Cassie equation for
chemically inhomogeneous surfaces. Unlike the classical Wenzel and Cassie
equations, the modified equations correspond to local minimizers of the total
interface energy in the solid-liquid-air system, so that they are consistent
with experimental observations. The homogenization results are proved
rigorously by a variational method.
