You know those underwater bubble rings? Math just proved that 'fat' ones are actually physically impossible to make.
March 26, 2026
Original Paper
Non-Existence of thick bubble rings at low Weber numbers
arXiv · 2603.24217
The Takeaway
While we can blow chunky rings of smoke in the air, surface tension in liquids works against the formation of thick underwater rings. This research shows that the physics of water forces bubble rings to stay thin or collapse, explaining why you never see 'fat' air rings in a swimming pool.
From the abstract
We examine the existence of thick bubble rings within the framework of the free-boundary capillary Euler equations, focusing on the regime of low Weber numbers. Although spheroidal bubbles are known to approach a spherical shape in this limit, the possibility of thick bubble rings persisting at low Weber numbers has remained uncertain. In contrast to the ordinary Euler equations, which admit thick vortex ring solutions, our analysis reveals that the free-boundary capillary Euler equations do not