The investigation of equilibrium contact state of liquid droplet on determined rough surfaces

This paper studied the rigorous derivations of Young, Wenzel and Cassie-Baxter (CB) equations based on Gibbs free energy. Two theoretical surface models, i.e. flat-top pillars and sinusoidal surface, were established to predict the equilibrium contact state, contact angle and wetted area. The intrinsic hydrophilic surface (θy =70°) and hydrophobic surface (θy =110°) were discussed, respectively. The contact states were investigated according to the Gibbs free energy minimization theory. It can be noted that the lower Gibbs free energy, the lower contact angle. The local or border minima of Gibbs energy indicates the existence of metastable or stable contact state. The influences of pillar height and sinusoidal amplitude on Gibbs energy and contact angles were also investigated. The transition point between Wenzel and CB state could be obtained. Furthermore, the wetted area, as the indicator to measure roll-off angle, demonstrates that in all cases, the wetted area under CB state was much smaller than Wenzel state for both flat-top pillars and sinusoidal surface models.