The Importance of Reference Frame for Pressure at the Liquid-Vapour Interface

TL;DR

This paper clarifies the non-uniqueness of the liquid-vapour interface pressure tensor by analyzing the impact of reference frame choice, introducing a moving interface frame that resolves longstanding debates.

Contribution

It introduces a general mathematical framework for the pressure tensor at interfaces using a moving reference frame, clarifying non-uniqueness issues and extending validity beyond equilibrium.

Findings

Normal pressure balance is maintained by surface fluxes.

An additional curvature term is needed for volume-averaged pressure.

Using a moving reference frame clarifies pressure tensor non-uniqueness.

Abstract

The local pressure tensor is non-unique, a fact which has generated confusion and debate in the seventy years since the seminal work by Irving Kirkwood. This non-uniqueness is normally attributed to the interaction path between molecules, especially in the interfacial-science community. In this work we reframe this discussion of non-uniqueness in terms of the location, or reference frame, used to measure the pressure. By using a general mathematical description of the liquid-vapour interface, we obtain a reference frame that moves with the interface through time, providing a new insight into the pressure. We compare this instantaneous moving reference frame with the fixed Eulerian one. Through this process, we show the requirement that normal pressure balance at the moving surface is satisfied by surface fluxes, however an additional corrective term based on surface curvature is required for the average pressure in a volume. We make the case that a focus on the path of integration is the cause of much of the confusion in the literature. Using an explicit reference frame with a more general derivation of pressure clarifies some of the issues of uniqueness in the pressure tensor and provides a pressure tensor which is defined at any instant in time and valid away from thermodynamic equilibrium.