Nucleation of spherical shell-like interfaces by second gradient theory: numerical simulations

TL;DR

This paper uses numerical simulations within second gradient theory to derive explicit relationships for surface properties of spherical interfaces, predicting minimal nucleation radii and advancing the understanding of phase interfaces.

Contribution

It introduces a numerical approach to derive explicit surface relationships in second gradient fluids, including minimal nucleation radii for spherical interfaces.

Findings

Derived relationships between surface tension, thickness, and radius.

Predicted minimal nucleation radii for various equations of state.

Validated the 2D-shell-like continuum model for phase interfaces.

Abstract

The theory of second gradient fluids (which are able to exert shear stresses also in equilibrium conditions) allows us: (i) to describe both the thermodynamical and the mechanical behavior of systems in which an interface is present; (ii) to express the surface tension and the radius of microscopic bubbles in terms of a functional of the chemical potential; (iii) to predict the existence of a (minimal) nucleation radius for bubbles. Moreover, the above theory supplies a 3D-continuum model which is endowed with sufficient structure to allow the construction of a 2D-shell-like continuum representing a consistent approximate 2D-model for the interface between phases. In this paper we use numerical simulations in the framework of second gradient theory to obtain explicit relationships for the surface quantities typical of 2D-models. In particular, for some of the most general two-parameter equations of state, it is possible to obtain the curves describing the relationship between the surface tension, the thickness, the surface mass density and the radius of the spherical interfaces between fluid phases of the same substance. These results allow us to predict the (minimal) nucleation radii for this class of equations of state.