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An Equilibrium Lattice Model of Wetting on Rough Substrates

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Abstract

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies Δτ(r)=τ AW(r)−τ BW(r) of the two phases behaves like Δτ(r)∼rΔτ(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos θ(r)≈r cos θ(1), which relates the contact angle θ of a sessile droplet to the roughness of the substrate

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Authors and Affiliations

  1. Microsoft Research, Redmond, Washington, 98052

    C. Borgs

  2. Faculté des Sciences, Université de Mons-Hainaut, 7000-, Mons, Belgium

    J. DeConinck

  3. Center for Theoretical Study, Charles University, Prague, Czech Republic

    R. Kotecky´

Authors
  1. C. Borgs
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  2. J. DeConinck
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  3. R. Kotecky´
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Correspondence to R. Kotecky´.

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Borgs, C., DeConinck, J. & Kotecky´, R. An Equilibrium Lattice Model of Wetting on Rough Substrates. Journal of Statistical Physics 94, 299–320 (1999). https://doi.org/10.1023/A:1004531917428

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  • DOI: https://doi.org/10.1023/A:1004531917428

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