Modeling Micro- and Nano-Bubble Stability and Treatment Mechanisms in Batch Reactors

Micro and nano bubbles have increased water treatment efficiency in laboratory and field experiments due to the elevated pressure inside small bubbles and their large specific surface area, which enhance mass transfer into surrounding water. Existing theoretical studies are limited to size dynamics and stability of (mostly) single bubbles or transport of stable bubbles through porous media. We present a theoretical modeling approach combining bubble generation, stability, and treatment reaction mechanisms in batch reactors. We consider bubble dynamics as quasi-steady compared to other reaction time-scales involved. For a single treatment gas, we demonstrate two regimes (stable bubbles or not) in agreement with previous work. The critical transition point into the stable bubble regime is defined in terms of a minimum treatment substance concentration and minimum stable bubble radius. The results are discussed through hypothetical examples and further validated using existing ozone nanobubble batch experiment data for butylated hydroxytoluene (BHT) remediation.