An integrated molecular–thermodynamic framework for analyzing nanobubbles in supersaturated liquids

Abstract

Nano-sized gas bubbles have attracted significant interest in electro-chemical applications due to their durability and longevity. Accurately predicting nanobubble formation and their size is critical for advancing technologies such as electrolysis and fuel cell systems. This study presents an integrated framework combining molecular dynamics (MD) simulations and thermodynamic modelling to determine nanobubble formation and size in a closed system under isothermal–isobaric condition. Assuming the nanobubble consists of a van der Waals (vdW) gas, the vdW constants are extracted from MD simulations of pure gas systems. A thermodynamic model is then developed for a closed system by combining the vdW equation with the assumption of chemical and mechanical equilibrium, which establishes a predictive relationship between nanobubble size and gas concentration. To validate the framework, MD simulations are performed for hydrogen in water under supersaturation, and the results are compared with thermodynamic model predictions. Comparisons are also made with experimental reports of nanobubbles. Our findings reveal that nanobubbles only form above a critical supersaturation threshold. The framework accurately predicts nanobubble radii in hydrogen–water systems, matching MD results while requiring minimal computational effort. When the pressure inside the nanobubble is approximated from the vdW equation of state, the Young–Laplace equation is shown to be valid even at sub-10 nm scales, with a negligible Tolman length. In contrast, the assumption of an ideal gas in thermodynamic modelling leads to considerable discrepancy with MD simulations. Overall, the proposed approach—bridging MD and thermodynamic modelling—paves the way toward a quantitative understanding of nanobubble formation and size in supersaturated liquids.