Wetting transitions on rough substrates: General considerations

General properties of wetting transitions for droplets on rough substrates are analyzed theoretically. The energy barrier to be surpassed for wetting transitions is much lower than the heat of evaporation of the droplet; this makes wetting transitions possible. It is shown that the energy curve of the transition state, i.e., the dependence of the interfacial part of the Gibbs free energy on the apparent contact angle in this state, as well as the energy barriers, can be expressed through the contact angles in the initial and final states without going into the geometric details of the given substrate relief. On this basis, the reason for the irreversibility of the Cassie-Wenzel transitions is elucidated: the energy barrier of the reverse transition is shown to be much higher. The scheme is also applicable to the substrates with disordered reliefs. Time-scaling arguments are important for understanding wetting transitions.