Three-dimensional wedge filling in ordered and disordered systems

TL;DR

This paper explores the effects of fluctuations on interfacial filling transitions in 3D wedge geometries, revealing covariance relations, the impact of disorder, and the role of interfacial fluctuations through theoretical and numerical analyses.

Contribution

It extends fluctuation-induced wedge covariance relations from 2D to 3D systems and analyzes the effects of disorder and interfacial fluctuations on filling critical behavior.

Findings

Classical wedge covariance applies to shallow wedges in 3D.

Pseudo-one-dimensional fluctuations alter mean-field critical exponents.

Universal critical exponents are predicted for random-bond disorder.

Abstract

We investigate interfacial structural and fluctuation effects occurring at continuous filling transitions in 3D wedge geometries. We show that fluctuation-induced wedge covariance relations that have been reported recently for 2D filling and wetting have mean-field or classical analogues that apply to higher-dimensional systems. Classical wedge covariance emerges from analysis of filling in shallow wedges based on a simple interfacial Hamiltonian model and is supported by detailed numerical investigations of filling within a more microscopic Landau-like density functional theory. For sufficiently short-ranged forces mean-field predictions for the filling critical exponents and covariance are destroyed by pseudo-one-dimensional interfacial fluctuations. In this filling fluctuation regime we argue that the critical exponents describing the divergence of lengthscales are related to values of the interfacial wandering exponent $\zeta(d)$ defined for planar interfaces in (bulk) two-dimensional ($d=2$) and three-dimensional ($d=3$) systems, recovering the known results for pure (thermal disorder) systems and predicting universal critical exponents for the case of random-bond disorder. Finally we revisit the transfer matrix theory of three-dimensional filling based on an effective interfacial Hamiltonian model and discuss the interplay between breather, tilt and torsional interfacial fluctuations.