Modified Wenzel and Cassie Equations for Wetting on Rough Surfaces

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 is reduced 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.