The Cassie equation: how it is meant to be used.

A review of literature shows that the majority of papers cite a potentially incorrect form of the Cassie and Cassie-Baxter equations to interpret or predict contact angle data. We show that for surfaces wet with a composite interface, the commonly used form of the Cassie-Baxter equation, cosθ(c)=f(1)cosθ-(1-f), is only correct for the case of flat topped pillar geometry without any penetration of the liquid. In general, the original form of the Cassie-Baxter equation, cosθ(c)=f(1)cosθ(1)-f(2), with f(1)+f(2)≥1, should be used. The differences between the two equations are discussed and the errors involved in using the incorrect equation are estimated to be between ~3° and 13° for superhydrophobic surfaces. The discrepancies between the two equations are also discussed for the case of a liquid undergoing partial, but increasing, levels of penetration. Finally, a general equation is presented for the transition/stability criterion between the Cassie-Baxter and Wenzel modes of wetting.