Zigzag and spiral path of a rising bubble

Settled in 2023 by Miguel Herrada, Jens Eggers (University of Seville / University of Bristol).

That rising bubbles deviate from a straight path once they exceed a critical size has been observed and modeled since at least the mid-20th century, with the instability long attributed loosely to wake dynamics analogous to vortex shedding behind rigid spheres. In 2023, Miguel Herrada and Jens Eggers used high-precision numerical simulation (a 'numerical mapping' technique) to show the true mechanism is a Hopf bifurcation driven by the coupling between the surrounding flow and the bubble's own deformable shape, correctly predicting the critical radius (about 0.926 mm) to within 2% of experiment, superseding the older wake-instability picture.

A bubble's wobbly rise, watched idly in any glass of soda, turns out to hide a precise mathematical bifurcation.

Explanations that circulated

• The long-standing assumption that instability of the bubble's turbulent wake (vortex shedding, as in the classic Kármán-vortex-street picture for rigid spheres) is what triggers zigzag/spiral motion; Herrada & Eggers's 2023 numerical study instead identified the interplay between the flow and the bubble's own shape deformation as the true trigger, matching the measured critical bubble size to within 2%.

References

• Path instability of an air bubble rising in water, M. A. Herrada, J. Eggers, Proceedings of the National Academy of Sciences, 2023