Wenzel wetting

A fully penetrated rough-surface wetting model with $\cos {\theta }^{\ast }=r\cos \theta$, where $r$ is actual wetted solid area divided by projected area. Roughness amplifies the planar surface tendency: it lowers contact angle when $\theta <90^{\circ }$.

The area ratio $r=A_{\mathrm{actual}}/A_{\mathrm{projected}}\ge 1$, not the projected fraction covered by particles. A hemispherical array of footprint coverage $\varphi$ on an exposed flat substrate has $r=1+\varphi$.