Size dependence of the surface tension of a free surface of an isotropic fluid

TL;DR

This paper investigates how the surface tension of an isotropic fluid's free surface varies with size, using the Gibbs-Tolman-Koenig-Buff equation, and provides a continuous model that aligns well with experimental and molecular data.

Contribution

It introduces a continuous model for size-dependent surface tension that avoids discontinuities at zero curvature, validated with experimental data for water droplets.

Findings

Surface tension varies with droplet size and curvature.

The model's Tolman length agrees with molecular dynamics and experimental data.

A continuous function for surface tension across different curvatures is achieved.

Abstract

We report on the size dependence of the surface tension of a free surface of an isotropic fluid. The size dependence of the surface tension is evaluated based on the Gibbs-Tolman-Koenig-Buff equation for positive and negative values of curvatures and the Tolman lengths. For all combinations of positive and negative signs of curvature and the Tolman length, we succeed to have a continuous function, avoiding the existing discontinuity at zero curvature (flat interfaces). As an example, a water droplet in the thermodynamical equilibrium with the vapor is analyzed in detail. The size dependence of the surface tension and the Tolman length are evaluated with the use of experimental data of the International Association for the Properties of Water and Steam. The evaluated Tolman length of our approach is in good agreement with molecular dynamics and experimental data