Simple improvements to classical bubble nucleation models

TL;DR

This paper refines classical bubble nucleation models by introducing a new prefactor accounting for thermal conduction, viscosity, and inertia, leading to significantly more accurate predictions aligned with recent simulations and experiments.

Contribution

It presents an improved nucleation rate formula with a novel prefactor and incorporates Tolman correction, enhancing the accuracy of bubble nucleation predictions.

Findings

The deviation from classical nucleation theory can be several orders of magnitude.

The Tolman length for argon bubbles is approximately 0.3 times the Lennard-Jones sigma.

The improved model aligns well with molecular dynamics simulations and laboratory data.

Abstract

We revisit classical nucleation theory (CNT) for the homogeneous bubble nucleation rate and improve the classical formula using a new prefactor in the nucleation rate. Most of the previous theoretical studies have used the constant prefactor determined by the bubble growth due to the evaporation process from the bubble surface. However, the growth of bubbles is also regulated by the thermal conduction, the viscosity, and the inertia of liquid motion. These effects can decrease the prefactor significantly, especially when the liquid pressure is much smaller than the equilibrium one. The deviation in the nucleation rate between the improved formula and the CNT can be as large as several orders of magnitude. Our improved, accurate prefactor and recent advances in molecular dynamics simulations and laboratory experiments for argon bubble nucleation enable us to precisely constrain the free energy barrier for bubble nucleation. Assuming the correction to the CNT free energy is of the functional form suggested by Tolman, the precise evaluations of the free energy barriers suggest the Tolman length is $\simeq 0.3 \sigma$ independently of the temperature for argon bubble nucleation, where $\sigma$ is the unit length of the Lenard-Jones potential. With this Tolman correction and our new prefactor one gets accurate bubble nucleation rate predictions in the parameter range probed by current experiments and molecular dynamics simulations.