Radius and surface tension of microscopic bubbles by second gradient theory

TL;DR

This paper introduces a second gradient fluid theory to accurately describe the surface tension and radius of microscopic bubbles, extending classical models to better account for their unique behaviors.

Contribution

It develops a new theoretical framework based on second gradient fluids to model microscopic bubbles, generalizing classical results like Cahn-Hilliard and Tolman.

Findings

Derived new expressions for bubble surface tension and radius

Extended classical theories to microscopic scales

Provided a more accurate description of microscopic bubble behavior

Abstract

The classical theory of Laplace is not suitable for describing the behavior of microscopic bubbles. The theory of second gradient fluids (which are able to exert shear stresses in equilibrium conditions) allows us to obtain a new expression for surface tension and radius of these bubbles in terms of functionals of the chemical potential. This relationship allows us to generalize the results of Cahn-Hilliard and Tolman.