Effect of Hierarchical Architecture of Super-Hydrophobic Surface on the Condensed Drop's Final State

Abstract

The interface free energy of a local condensate from the growth and combination of numerous initial condensation nuclei was calculated during its shape changes from an early flat shape to a Wenzel or Cassie state on the super-hydrophobic surface (SHS). The final state of the condensed drop was determined according to whether the interface free energy continuously decreased or it had a minimum value. Our calculations indicate that condensation drops on a surface only with micro roughness display Wenzel state because the interface free energy curve of a condensed drop first decreases and then increases, existing a minimum value corresponding to Wenzel drop. On a surface with appropriate hierarchical roughness, however, the interface energy curve of a condensed drop will constantly decline until it reaches the Cassie state. Therefore, a condensed drop on a hierarchical roughness surface can spontaneously reach the Cassie state. In addition, the states and apparent contact angles of condensed drops on a SHS with different structural parameters were calculated and compared with experimental observations. Results show that the calculated condensed drop states agree well with the experimental results. It can be concluded that micro and nano hierarchical roughness is the key structural factor responsible for sustaining condensed drops in the Cassie state on a SHS.