Abstract
We consider the problem of wetting on a heterogeneous wall with mesoscopic defects: i.e., defects of order L ε, 0<ε<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.(10, 11) 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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De Coninck, J., Dobrovolny, C., Miracle-Solé, S. et al. Wetting of Heterogeneous Surfaces at the Mesoscopic Scale. Journal of Statistical Physics 114, 575–604 (2004). https://doi.org/10.1023/B:JOSS.0000012503.98210.67
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DOI: https://doi.org/10.1023/B:JOSS.0000012503.98210.67