Direct numerical simulations of non-coalescing floating bubbles: geometry and self-organisation

Interfacial interactions between gas bubbles and the free surface are a hallmark of flows involving aqueous foams. In practice, bubble foams commonly arise from processes such as breaking waves at the ocean–atmosphere interface, plunging liquid jets and the effervescence of carbonated liquids. Once generated, bubbles within foam layers remain afloat at the free surface for finite durations before finally bursting into a fine spray of droplets. While the birth and bursting of bubble foams have received considerable attention, the understanding of floating bubbles is limited mainly to a single bubble. To build on this, in this article, we undertake numerical simulations of two or more floating bubbles in various canonical settings to examine their geometry and self-organising nature, with implications for real-world phenomena such as ocean spray production. Under lateral confinement, floating bubbles are prone to form vertically stacked layers. To this end, we analyse the geometry of coaxial pairs of floating bubbles and link geometrical differences between single and coaxial bubbles to various aspects of the ensuing bursting stage. Furthermore, we extend the existing theory of isolated floating bubbles to obtain unified analytical expressions for the shape parameters of single and coaxial bubbles of small sizes. Next, we investigate a pair of side-by-side floating bubbles, which serves as a minimal configuration to understand the formation of bubble rafts through self-organisation. We discover that Bond numbers in the range $10\leqslant \textit{Bo}\leqslant 50$ are more favourable for raft formation due to pronounced capillary attraction. The time required for two floating bubbles to assemble through capillary attraction grows exponentially with their initial separation. We also develop a linear model to capture the evolution of bubble spacing during capillary migration at low Bond numbers. Lastly, we extend the two-bubble configuration and showcase the emergent dynamics of a swarm of floating bubbles in mono- and bilayer configurations.