Size-dependent coalescence of nanobubbles in pure water

Previously, we experimentally demonstrated that similar-sized bulk nanobubbles (NBs) preferentially coalesce when the NB size is ∼100 nm. To explain this peculiar NB coalescence phenomenon, we performed a nanoparticle trajectory analysis to determine the size distribution profile and time-dependent concentration of the bulk NBs generated by pressurizing a porous alumina thin film with ordered straight nanoholes. Furthermore, we propose a physical model based on the hypothesis that the repulsive energy increases when two NBs establish contact, and that coalescence occurs when the kinetic energy of the NBs overcomes the repulsive energy. We simulated the observed NB-size distribution by using the proposed model. The simulation results explained the observed NB-size distribution and lifetime of the NBs. They further indicated that NB coalescence was suppressed for small NBs with diameters of approximately 100 nm or less, resulting in their long lifetimes.