3D wedge filling and 2D random-bond wetting

TL;DR

This paper investigates the critical and tricritical filling transitions of fluids in 3D wedges, providing analytic solutions and linking these phenomena to 2D wetting with random bond disorder.

Contribution

It introduces an effective interfacial model for 3D wedge filling and connects critical behaviors to 2D wetting with disorder, offering new analytical insights.

Findings

Analytic solutions for interfacial height distributions at criticality and tricriticality.

Identification of the relation between 3D wedge filling and 2D wetting with random bonds.

Demonstration of critical singularities linked to disorder effects in wetting.

Abstract

Fluids adsorbed in 3D wedges are shown to exhibit two types of continuous interfacial unbinding corresponding to critical and tricritical filling respectively. Analytic solution of an effective interfacial model based on the transfer-matrix formalism allows us to obtain the asymptotic probability distribution functions for the interfacial height when criticality and tricriticality are approached. Generalised random walk arguments show that, for systems with short-ranged forces, the critical singularities at these transitions are related to 2D complete and critical wetting with random bond disorder respectively.