Validity of the equations for the contact angle on real surfaces

Abstract

The wetting property between liquid and solid is very important in many industries besides natural systems. The simplest method to determine the wetting property is just dropping a liquid drop on a solid surface and measuring a contact angle from the shape of the drop. Since the Young's equation has been used as a basic equation to relate a contact angle and interfacial tensions over 200 years, it is important to understand a derivation and limits of the Young's equation. We derived the Young's equation following energy minimization with simple mathematics. By expanding the derivation, the modified forms of the Cassie-Baxter equation and the Wenzel equation were also derived. From analyses of the derivations, it was deduced that a contact angle on an ideal surface is only related to the infinitesimal region in the vicinity of contact line, not internal area surrounded by the contact line. Although the Cassie-Baxter model and the Wenzel model were not rigorously built, they have been widely used for a superhydrophobic surface, because the apparent forms are similar to those of rigorously derived models when the contact line can easily move on the surface.