Covariance for Conic and Wedge Complete Filling

TL;DR

This paper reveals a covariance relation in three-dimensional fluid wetting phenomena, linking properties in wedge and cone geometries, which enhances understanding of interfacial behavior near critical points.

Contribution

It extends the concept of covariance from two-dimensional systems to three-dimensional geometries, providing new analytical relations and critical exponent insights for wetting phenomena.

Findings

Covariance relation holds in 3D wedge and cone geometries.

Valid for both short-ranged and long-ranged forces.

Identifies critical exponents and amplitudes in confining geometries.

Abstract

Interfacial phenomena associated with fluid adsorption in two dimensional systems has recently been shown to exhibit hidden symmetries, or covariances, which precisely relate local adsorption properties in different confining geometries. We show that covariance also occurs in three dimensional systems and is likely to be verifiable experimentally and in Ising model simulations studies. Specifically, we study complete wetting in wedge (W) and cone (C) geometries as bulk coexistence is approached and show that the equilibrium mid-point heights satisfy $l_c (h,\alpha)=l_w(\frac{h}{2} ,\alpha),$ where $h$ measures the partial pressure and $\alpha$ is the tilt angle. This covariance is valid for both short-ranged and long-ranged intermolecular forces and identifies both leading and next-to-leading order critical exponents and amplitudes in the confining geometries. Connection with capillary condensation-like phenomena is also made.