Surface effects on spinodal decomposition in binary mixtures: The case with long-ranged surface fields

Abstract

We present detailed numerical results for phase-separation kinetics of critical binary mixtures in the vicinity of a surface that exerts a long-ranged attractive force on one of the components of the mixture. We consider surface potentials of the form $V\left(Z\right)\mathrm{}\sim Z^{-n}$, where $Z$ is the distance from the surface and $n=1,2,3\mathrm{}$. In particular, we investigate the interplay of the surface wetting layer with the dynamics of domain growth. We find that the wetting layer at the surface exhibits power-law growth with an exponent that depends on $n$, in contrast to the case with a short-ranged surface potential, where the growth is presumably logarithmic. From correlation functions, we identify characteristic length scales in directions parallel and perpendicular to the surface. We observe a regime of accelerated growth in the parallel direction and critically examine some possible explanations for this.