Critical wetting in power - law wedge geometries

We investigate critical wetting transitions for fluids adsorbed in wedge-like geometries where the substrate height varies as a power-law, z(x, y) ∼ |x| γ , in one direction. As γ is increased from 0 to 1 the substrate shape is smoothly changed from a planar-wall to a linear wedge. The continuous wetting and filling transitions pertinent to these limiting geometries are known to have distinct phase boundaries and critical singularities. We predict that the intermediate critical wetting behaviour occurring for 0 < γ < 1 falls into one of three possible regimes depending on the values of γ, p and q. The unbinding behaviour is characterised by a high degree of non-universality, strongly anisotropic correlations and enhanced interfacial roughness. The shift in phase boundary and emergence of universal critical behaviour in the linear wedge limit is discussed in detail. There is growing interest from theorists and experimentalists in fluid adsorption on micro-patterned and sculpted solid Surface decoration and structure can substantially alter the character of fluid adsorption and lead to novel examples of interfacial phase transitions and enhanced fluctuation related effects. There is also strong evidence that there are fundamental connections between geometry-induced and fluctuation-induced interfacial phenomena at wedge filling transitions [11] and also between wedge filling and unzipping transitions for doubled-stranded DNA [16]. The purpose of the present article is to focus on interfacial adsorption in generalised 3D wedge shaped geometries, which are translationally invariant in one direction (along the y axis, say), but whose height above some reference plane varies as a power law z(x, y) ∼ |x| γ , for large distances in the x direction. We refer to this particular class of surface geometry as the gamma-wall which may be viewed as an example of † To whom correspondence should be addressed ([email protected])