A proof of the Gibbs-Thomson formula in the droplet formation regime

TL;DR

This paper provides a rigorous microscopic derivation of the Gibbs-Thomson formula for droplet formation, confirming how interface curvature affects pressure and density deviations in two-phase systems.

Contribution

It offers the first self-contained microscopic proof of the Gibbs-Thomson formula, supported by a rigorous case study in the 2D Ising lattice gas.

Findings

Validated the Gibbs-Thomson relation in a microscopic setting

Established the effect of interface curvature on pressure and density deviations

Provided a rigorous proof in the two-dimensional Ising lattice gas

Abstract

We study equilibrium droplets in two-phase systems at parameter values corresponding to phase coexistence. Specifically, we give a self-contained microscopic derivation of the Gibbs-Thomson formula for the deviation of the pressure and the density away from their equilibrium values which, according to the interpretation of the classical thermodynamics, appears due to the presence of a curved interface. The general--albeit heuristic--reasoning is corroborated by a rigorous proof in the case of the two-dimensional Ising lattice gas.