Local pressure for confined systems

TL;DR

This paper derives a general expression for local pressure on confining walls in fluid systems, highlighting limitations of approximate models due to the non-local nature of particle interactions.

Contribution

It provides a new closed-form expression for local pressure in confined fluids and analyzes the limitations of existing approximate models.

Findings

The local pressure depends on the wall shape as a functional.

Approximate schemes are valid only for small wall curvatures.

Non-local interactions limit the applicability of surface tension concepts.

Abstract

We derive a general closed expression for the local pressure exerted onto the corrugated walls of a channel confining a fluid medium. When the fluid medium is at equilibrium the local pressure is a functional of the shape of the walls. It is shown that, due to the intrinsic non-local character of the interactions among the particles forming the fluid, the applicability of approximate schemes such as the concept of a surface of tension or morphometric thermodynamics is limited to wall curvatures small compared to the range of particle-particle interactions.