Critical wetting in power-law wedge geometries

TL;DR

This paper studies how fluids wet surfaces with power-law shaped geometries, revealing three regimes of critical wetting behavior with non-universal properties and anisotropic correlations.

Contribution

It introduces a theoretical framework for critical wetting in power-law wedge geometries, identifying three distinct regimes based on the shape parameter and analyzing their critical properties.

Findings

Identifies three regimes of wetting behavior depending on geometry parameters.

Shows non-universality and anisotropic correlations in unbinding behavior.

Discusses phase boundary shifts and universal behavior in linear wedge limit.

Abstract

We investigate critical wetting transitions for fluids adsorbed in wedge-like geometries where the substrate height varies as a power-law, $z(x,y) \sim |x| ^\gamma$, in one direction. As $\gamma$ 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 $0<\gamma< 1$ falls into one of {\it{three}} possible regimes depending on the values of $\gamma$, 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.