Theoretical Analysis on the Stability of Single Bulk Nanobubble - Wang, Yao; Zhou, Limin; Hu, Jun; Zhang, Lijuan (Frontiers in Materials, 2022)
As predicted by classical macroscopic theory, the lifetime for nanoscale gas bubbles is extremely short, which causes conflict when detecting stable bulk nanobubbles experimentally in recent years. In fact, the stability of bulk nanobubbles depends on the surrounding liquid environment. Also, the dynamic process of gas in water involves the dissolution, diffusion, release, and transportation of gas as well as the properties of nanobubbles inside. Here, based on previous reports, we introduce the gas transport parameter ℓ in the classical diffusion equation by considering the gas diffusion near the bulk nanobubble at different locations in a container and consider the MacLeod-Sugden relationship between the surface tension and densities of liquid and gas for computing the lifetime of single bulk nanobubbles in an open system. The results show that the single nanobubble lifetime depends on the inner density and gas transport length. It could reach the order of 10–100 s for a single nanobubble with an initial radius of 200 nm, and provides a new idea to prolong the lifetime of the single bulk nanobubble. Meanwhile, compared with the continuous influence of the inner density on the gas diffusion flux near the nanobubble, the range of the gas transport near the nanobubble on the gas diffusion flux is limited, which is affected by the dissolution time of the nanobubble. Our findings would be helpful to explore the storage conditions of nanobubbles and the mechanism of mass transfer at the gas-liquid interface at the micro-scale.