Continuous wetting is studied on substrates with self-similar roughness (either fractal or self-affine). Surface tension forces control the asymptotic divergence of film thickness for fractal substrates, and for sufficiently rough self-affine substrates. Exponents are obtained by scaling arguments for complete wetting, and by replica methods for critical wetting. Recent experiments of nitrogen adsorbed on flash-deposited silver are reanalysed. They suggest that the substrate roughness is self-affine with a roughness exponent ζ S ≃ 0.37.
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Kardar et al. (1990) studied this question.
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