General equation of wettability: A tool to calculate the contact angle for a rough surface

This work introduces a mathematical tool, namely general equation of wettability, which simplifies the determination of the contact angle for rough surfaces. A free energy minimization method is applied to an intermediate wetting state with partial liquid penetration into roughness valleys in addition to the well-known states of Wenzel and Cassie wetting. A wetting parameter is coined, which stands out as a fingerprint of a particular wetting state of a surface topology. Substitution of the appropriate wetting parameter returns the Cassie and Wenzel equations, while an implicit solution is presented for the intermediate state, which is consistent with energy minimization.