The pressure tensor across a liquid-vapour interface

TL;DR

This paper generalizes the theoretical framework for the pressure tensor at liquid-vapor interfaces, accounting for thermal fluctuations and capillary waves, and introduces expressions applicable to non-equilibrium, inhomogeneous systems.

Contribution

It extends Irving and Kirkwood's formalism to fluctuating, non-planar surfaces, providing a more precise molecular-level description of interfacial pressure.

Findings

Derived a new expression for the pressure tensor that accounts for thermal fluctuations.

Identified the exact location of surface tension across the molecular dividing surface.

Extended the formalism to systems far from equilibrium.

Abstract

Inhomogeneous fluids exhibit physical properties that are neither uniform nor isotropic. The pressure tensor is a case in point, key to the mechanical description of the interfacial region. Kirkwood and Buff, and later Irving and Kirkwood, obtained a formal treatment based on the analysis of the pressure across a planar surface [J.G. Kirkwood and F.P. Buff, J. Chem. Phys., 17(3), (1949), J.H. Irving and J.G. Kirkwood, J. Chem. Phys. 18, 817 (1950)]. We propose a generalisation of Irving and Kirkwood's argument to fluctuating, non-planar surfaces and obtain an expression for the pressure tensor that is not smeared by thermal fluctuations at the molecular scale and corresponding capillary waves [F.P. Buff, R.A. Lovett, and F.H. Stillinger, Jr., Phys. Rev. Lett. 15, 621 (1965)]. We observe the emergence of surface tension, defined as an excess tangential stress, acting exactly across the dividing surface at the sharpest molecular resolution. The new statistical mechanical expressions extend current treatments to fluctuating inhomogeneous systems far from equilibrium.