Coalescence characteristics of bulk nanobubbles in water: A molecular dynamics study coupled with theoretical analysis

The coalescence of two nanobubbles (NBs) in water is a process of great importance to many industrial applications. In this work, we study the coalescence of two equal-sized nitrogen NBs in water using molecular dynamics (MD) simulations and continuum-based theoretical analysis. We vary the NB diameter from 30 to 50 nm and study the coalescence characteristics including the expansion speed of the capillary bridge between two coalescing NBs, the dynamic regime of NB coalescence, the diameter of fully merged NBs, and the temperature variation of NBs during the coalescence process. For all cases, we show the MD simulation results can be well understood by the theoretical models developed in this work. Due to the large Laplace pressure in the model NBs, the diameter ratio of fully merged NBs to their daughter NBs is root 2, which explains the recent experimental result showing that the size of NBs in water is distributed discretely with a uniform increment factor of root 2 [Ma et al., J. Phys. Chem. R 124. 5067 (2020)]. The expansion of gas inside the coalescing NBs and the heat transfer between the gas NB and surrounding liquid leads to fluctuations of gas temperature during coalescence. From the theoretical analysis, we find the coalescence dynamics of NBs is in the crossover regime where neither viscous stress nor inertial stress in the surrounding liquid dominates even when the viscous stress is more than ten times higher than inertial stress. In the range of Ohnesorge number from 0.33 to 0.82, we show the scaling exponent for the capillary bridge radius vs time at late times of NB coalescence is around 0.75 +/- 0.05, which is considerably higher than 0.5 in the viscous-dominated regime.