Diffusive growth of successive bubbles in confinement

• Published in: Journal of fluid mechanics 2020-01, Vol.882, Article A6
• Main Authors: Moreno Soto, Álvaro, Lohse, Detlef, van der Meer, Devaraj
• Format: Article
• Language: English
• Subjects: Bubbles; Concentration gradient; Confinement; Convection; Crossovers; Depletion; Dissolved gases; Experiments; Free convection; Gases; Hydrophobic surfaces; Mass transfer; Renewal; Supersaturation
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2019.806

We analyse how a succession of single bubbles extracts dissolved gas from a liquid solution while they grow and detach in a confinement induced by the presence of lateral walls. Like bubbles growing on a liquid-immersed unconfined surface, these bubbles absorb the dissolved gas in the liquid around them and hence deplete their surroundings. The supersaturation level, $\unicode[STIX]{x1D701}$ , stands out as the main parameter which determines the diffusive bubble dynamics, both in the confined and unconfined scenarios. For slightly supersaturated solutions, the bubble evolution is rather similar for the two cases. We observe nonetheless mildly higher concentration gradients within confinement due to the lack of gas renewal. This causes a slightly enhancement of density-driven convection as compared to the unconfined case, which results in a higher mass transfer rate towards the bubble and a somewhat faster long-term gas depletion. For larger supersaturations, the onset of natural convection is inhibited by the presence of the confinement. Confinement promotes the gas mixing within the cavity as well. These two effects combined result in a slower depletion in the confined case as compared to the unconfined one. The two opposite behaviours for small and large supersaturation suggest that there must be a transition in between the two scenarios. The cross-over has been estimated to occur at $\unicode[STIX]{x1D701}\approx 0.17$ . We propose a modified depletion model which accounts for the confined configuration and its effect on the effective area through which gas diffuses into the bubble. The model can accurately describe the experimental results and sheds more light on the origin of the depletion effect due to the successive bubble growth.