Stability of critical bubble in stretched fluid of square-gradient density-functional model with triple-parabolic free energy

TL;DR

This study investigates the stability of critical bubbles in stretched fluids using a square-gradient density-functional model with triple-parabolic free energy, revealing that the bubble remains stable up to the spinodal point with only one unstable mode.

Contribution

It applies a Schrödinger equation approach to analyze bubble stability in a specific density-functional model, showing the critical bubble's stability characteristics near the spinodal.

Findings

Only one negative eigenvalue indicating a single unstable mode.

The negative eigenvalue persists up to the spinodal point.

Critical bubbles are not fractal or ramified near the spinodal.

Abstract

The square-gradient density-functional model with triple-parabolic free energy, that was used previously to study the homogeneous bubble nucleation [J. Chem. Phys. 129, 104508 (2008)], is used to study the stability of the critical bubble nucleated within the bulk under-saturated stretched fluid. The stability of the bubble is studied by solving the Schr\"odinger equation for the fluctuation. The negative eigenvalue corresponds to the unstable growing mode of the fluctuation. Our results show that there is only one negative eigenvalue whose eigenfunction represents the fluctuation that corresponds to the isotropically growing or shrinking nucleus. In particular, this negative eigenvalue survives up to the spinodal point. Therefore the critical bubble is not fractal or ramified near the spinodal.