Nucleation and growth dynamics of nanobubbles on smooth and rough surfaces

<sec>The interfacial nanobubbles (INBs) have been confirmed to exist, and have significant potential for applications in fields such as mineral flotation, aquaculture, and wastewater treatment. However, the microscopic nucleation process of INBs is still poorly understood. This study investigates the nucleation process and growth dynamics of INBs on smooth and rough surfaces under different levels of gas supersaturation. Molecular dynamics (MD) simulations using GROMACS software package are conducted to observe the microscopic nucleation process and the temporal evolution of the geometric characteristics of the INBs. Additionally, a growth dynamics model for INBs is derived based on the Epstein-Plesset gas diffusion theory, and the predictions from the model are compared with the MD simulation data.</sec><sec>The results indicate that on smooth homogeneous surfaces, the curvature radius and width of INBs increase progressively with time after nucleation. This growth process is well captured by the theoretical model, indicating that the gas diffusion theory provides an accurate description of INB growth dynamics. In addition, the contact angle (measured on the gas side) during INB growth is not constant but increases initially before stabilizing. This phenomenon is caused by reducing solid-gas interfacial tension due to higher Laplace pressure, thus leading the contact angle to increase as the INB radius grows. Furthermore, on smooth homogeneous surfaces, INBs are observed to nucleate at 81, 17, 6, and 1.3 ns under gas supersaturation levels of 100, 120, 150, and 200, respectively. This demonstrates that higher gas supersaturation significantly shortens the nucleation time. Additionally, as gas supersaturation increases, the growth rate of INBs after nucleation will also accelerate. However, at a gas supersaturation level of 50, no nucleation occurrs during the simulation period of 200 ns. Theoretical analysis reveals that the INBs can only nucleate and grow when the radius of gas aggregates exceeds the critical nucleation radius (<inline-formula><tex-math id="M1">\begin{document}$ {R}_{{\mathrm{critical}}} = {\sigma }/({\zeta {P}_{0}}) $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$ \sigma $\end{document}</tex-math></inline-formula> is the liquid-gas interfacial tension, <inline-formula><tex-math id="M3">\begin{document}$ \zeta $\end{document}</tex-math></inline-formula> is the gas supersaturation level, and <inline-formula><tex-math id="M4">\begin{document}$ {P}_{0} $\end{document}</tex-math></inline-formula> is the ambient pressure). As gas supersaturation decreases, <inline-formula><tex-math id="M5">\begin{document}$ {R}_{{\mathrm{c}}{\mathrm{r}}{\mathrm{i}}{\mathrm{t}}{\mathrm{i}}{\mathrm{c}}{\mathrm{a}}{\mathrm{l}}} $\end{document}</tex-math></inline-formula> increases, thus significantly increasing the difficulty of nucleation.</sec><sec>On rough surfaces, pits with widths of 1, 2, 4, and 10 nm are introduced. At a gas supersaturation of 50, where no INB nucleation occurrs on the smooth surfaces, gas nuclei rapidly form within the pits. However, only gas nuclei in pits with widths larger than 2 nm can grow into INBs. This is because in the growth process the pinning effect at the pit edges causes the curvature radius of the gas nucleus to initially decrease and then increase. Only when the minimum curvature radius exceeds the critical nucleation radius, can gas nuclei develop into INBs.</sec><sec>The findings of this study provide more in-depth insights into the nucleation mechanism of INBs, and practical guidance for controlling their generation, and they also deliver theoretical support for relevant applications such as mineral flotation and other industrial processes.</sec>