Wetting of Heterogeneous Surfaces at the Mesoscopic Scale
Résumé
We consider the problem of wetting on a heterogeneous wall with mesoscopic defects: i.e.\ defects of order $L^{\varepsilon}$, $0<\varepsilon<1$, where $L$ is some typical length--scale of the system. In this framework, we extend several former rigorous results which were shown for walls with microscopic defects \cite{DMR,DMR2}. Namely, using statistical techniques applied to a suitably defined semi-infinite Ising-model, we derive a generalization of Young's law for rough and heterogeneous surfaces, which is known as the generalized Cassie-Wenzel's equation. In the homogeneous case, we also show that for a particular geometry of the wall, the model can exhibit a surface phase transition between two regimes which are either governed by Wenzel's or by Cassie's law.
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