Roughness of the contact line on random self-affine rough surfaces

Abstract

We investigate the roughness properties of the three-phase contact line on random self-affine rough surfaces by means of numerical simulations in the framework of the full capillary model. In contrast to the theoretically predicted universal exponents ${\ensuremath{\zeta}}_{s}=1/2$ for short and ${\ensuremath{\zeta}}_{l}=1/3$ for long length scales determined within the assumption for weak heterogeneity, a broad range of roughness exponents have been reported in numerous experimental studies. We show that both scaling exponents depend on the surface properties as well as on the equilibrium contact angle, and that their values lie within the intervals ${\ensuremath{\zeta}}_{s}\ensuremath{\in}[0.75,0.9]$ and ${\ensuremath{\zeta}}_{l}\ensuremath{\in}[0,0.65]$. Our results explain the origin of the experimentally obtained roughness exponents and show that the assumption of randomly distributed isolated defects is insufficient when wetting on real surfaces is considered.