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. (C) 2013 Elsevier B.V. All rights reserved.