Droplet spreading and pinning on heterogeneous substrates

The contact angle of a fluid droplet on an heterogeneous surface is analyzed using the statistical dynamics of the spreading contact line. The statistical properties of the final droplet radius and contact angle are obtained through applications of depinning transitions of contact lines with nonlocal elasticity and features of pinning-depinning dynamics. Such properties not only depend on disorder strength and surface details, but also on the droplet volume and disorder correlation length. Deviations from Wenzel or Cassie-Baxter behavior are particularly apparent in the case of small droplet volumes and small contact angles.