Wetting in 1+11+1 dimensions with two-scale roughness

• Cassie–Baxter, Wenzel and intermediate wetting states.
• Hydrophobicity with two-scale roughness.
• Exact computation of surface phase diagrams in 1+11+1 dimensions.

We show that a two-scale model in 1+11+1 dimensions enhances superhydrophobicity. The two scales may differ by a factor of order two or three, or by a large factor in a scaling limit. In both cases, we compute explicitly the macroscopic contact angles as function of the flat material contact angle and aspect ratios. In addition to the Cassie–Baxter states with air cushion below the droplet and to the Wenzel states, completely wet, there appear several mixed states with air trapped in corners.