Predicting nucleation pressure under rapid depressurization: Bridging positive and negative pressure regions

A thermodynamic model is developed to predict the onset of nucleate boiling (ONB) under rapid depressurization, addressing key challenges stemming from the fact that nucleation can take place across both positive and negative pressure regions, in tensioned liquids. By introducing a normalized Jakob number and demonstrating its relation to a normalized depressurization rate (Ja_r=F(Σ_r)), the model establishes an analytical framework capable of predicting nucleation onset across a broad range of thermodynamic states (0.4<T_r≤0.98,10⁻⁹≤Σ_r≤1). The model addresses two open questions: the determination of the critical depressurization rate necessary to reach spinodal conditions, and the prediction of nucleation pressure for a given fluid and set of initial conditions. We further highlight the increase role of surface tension at high superheating levels and derive temperature-dependent Tolman length correlation for H₂O, CO₂, R22 and H₂. Additionally, a new semi-empirical correlation for the heterogeneity factor is developed, extending its applicability across a wide range. The model is validated against expansion tube experiments with CO₂ and R22, and further applied to hydrogen, where lack of experimental results was identified. This work seeks to bridge the gap between classical nucleation theory and dynamic depressurization processes, providing a novel, predictive tool for nucleation onset under extreme conditions. The model's analytical framework enables seamless integration into both in-house and commercial computational fluids dynamics (CFD) software, bypassing the need for complex micro-scale simulations and dramatically lowering computational expenses while maintaining predictive precision.