An Equilibrium Lattice Model of Wetting on Rough Substrates |
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Authors: | Borgs C DeConinck J Kotecky´ R |
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Institution: | (1) Microsoft Research, Redmond, Washington, 98052;(2) Faculté des Sciences, Université de Mons-Hainaut, 7000- Mons, Belgium;(3) Center for Theoretical Study, Charles University, Prague, Czech Republic |
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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 ![Delta](/content/u6247265217035p7/xxlarge916.gif) (r)=
AW(r)–
BW(r) of the two phases behaves like ![Delta](/content/u6247265217035p7/xxlarge916.gif) (r) r![Delta](/content/u6247265217035p7/xxlarge916.gif) (1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r) r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate |
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Keywords: | wetting surface tension rough surfaces Wenzel's law semi-infinite systems Ising model cluster expansions |
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