Hydrophobicity of surfaces with cavities: Making hydrophobic substrates from hydrophilic materials?

Rough surfaces made of hydrophobic materials are known to exhibit enhanced hydrophobicity. Similarly, rough surfaces made of hydrophilic materials show increased hydrophilic behavior. The energetics of these observations is well explained by either Wenzel's or Cassie-Baxter's formulas. Recent experimental results have shown that rough surfaces made of hydrophilic materials can exhibit hydrophobic behavior. The idea is to make a rough surface with cavities. The apparent contact angle of a drop on such surfaces is reported to agree with Cassie-Baxter's formula even when the substrate material is hydrophilic. Others have interpreted this to imply that air remains trapped in the cavities after a liquid drop is deposited on it, thus making it effectively hydrophobic. In this work, we consider the effective energy of such surfaces theoretically.