A modelling approach to explore the optimum bubble size for micro-nanobubble aeration

Bubble aeration has been widely applied in water/wastewater treatment, however its low gas utilization rate results in high energy consumption. Application of micro-nanobubbles (MNB) has emerged as a process with the potential to significantly increase gas utilisation due to their high relative surface area and high gas-liquid mass transfer efficiency. In this study, we demonstrate through calibrated models that MNB of an optimum bubble size can shrink and burst at or below the water surface enabling (1) all encapsulated gas to thoroughly dissolve in water, and (2) the bursting of nanobubbles to potentially generate free radicals. Through the understanding of MNB dimensional characteristics and bubble behaviour in water, a dynamic model that integrated force balance (i.e. buoyancy force, gravity, drag force, Basset force and virtual mass force), and mass transfer was developed to describe the rising velocity and radius variation of MNB along its upward trajectory. Unlike for conventional millimetre-sized bubbles, intensive gas dissolution of MNBs led to radius reduction for small bubbles, while a large initial radius triggers bubble swelling. The initial water depth was also crucial, where greater depth could drive the potential for bubble shrinkage so that they were more liable to contract. For example, the optimum bubble size of air (42-194 μm) and oxygen (127-470 μm) MNB that could achieve complete gas transfer (100% gas utilisation) for a range of specific water depths (0.5-10 m) were calculated. The modelling results for microbubbles (10-530 μm) were well validated by the experimental data (R2>0.85). However, the validation of the modelling results for nanobubble (<1 μm) aeration requires further study due to a lack of available empirical data. In this study, the proposed model and analysis provided new insights into understanding bubble dynamics in water and offered fundamental guidance for practitioners looking to upgrade bubble aeration system.