Generalized Young's equation for rough and heterogeneous substrates: A microscopic proof

We derive by microscopic techniques applied to a 3d lattice gas model, a generalization of Young's equation for rough and chemically heterogeneous substrates, which combines both Cassie's and Wenzel's laws. We also show that, already in the homogeneous case, the model can exhibit, for particular geometries and appropriated values of the parameters, two regimes governed either by the Wenzel's law or by the Cassie's law.