Singularities in a glass of champagne

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Speaker

Vatsal Sanjay (CoMPhy Lab)

When a bubble bursts at a liquid surface, like the ones in a glass of champagne, capillary waves travel along its cavity and can focus the flow into a thin, fast Worthington jet. Although surface tension initiates this motion, the singular dynamics near jet inception are governed solely by inertia. Using direct numerical simulations and reduced-order theory, we show how the conical cavity selects a family of self-similar solutions whose exponents depend on the cone angle. The dynamics near the singularity are self-similar but not universal. For the bursting bubble geometries that I will discuss in this talk, the self-similarity exponents lie close to the classical value, but the local Weber number diverges as the jet radius shrinks, revealing a purely inertial force balance. Viscosity helps select the cavity geometry through capillary-wave damping. For micron-sized water bubbles, the expected regularization from viscous stresses only happen at nanometric scales where the continuum description may no longer apply [1].

We then ask how other features could regularize this singularity. For example, how this singular focusing changes when the liquid can sustain elastic stresses or resist flow below a yield stress. We show that yield stress can completely arrest cavity collapse, leaving a residual crater and suppressing jet formation [2]. Elastic stresses can also alter jet growth and breakup, allowing a jet to form without ejecting droplets [3]. In elastoviscoplastic liquids, elastic stress relaxation modifies the effect of yield stress, and jet development depends non-monotonically on the relaxation time [4]. Droplet ejection can thus be suppressed before a jet forms, by arresting cavity collapse, or after it forms, by preventing pinch-off.

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Videos

Singularities in a glass of champagne

Video: Arup K. Das and Thomas Séon, Institut d’Alembert, Sorbonne Université. Ghabache et al., Scientific Reports 6, 25148 (2016). Original slide.

Bursting bubbles in a non-Newtonian medium

Mud pots in Yellowstone National Park. Watch on YouTube · Original slide.

References

[1] J. M. Gordillo, J. Rodríguez-Rodríguez, and V. Sanjay, “Self-similar Worthington jets,” arXiv:2607.08972, 2026. Preprint.

[2] V. Sanjay, D. Lohse, and M. Jalaal, “Bursting bubble in a viscoplastic medium,” J. Fluid Mech., vol. 922, A2, 2021. doi:10.1017/jfm.2021.489.

[3] A. K. Dixit, A. Oratis, K. Zinelis, D. Lohse, and V. Sanjay, “Viscoelastic Worthington jets and droplets produced by bursting bubbles,” J. Fluid Mech., vol. 1010, A2, 2025. doi:10.1017/jfm.2025.237.

[4] A. G. Balasubramanian, V. Sanjay, M. Jalaal, R. Vinuesa, and O. Tammisola, “Bursting bubble in an elastoviscoplastic medium,” J. Fluid Mech., vol. 1001, A9, 2024. doi:10.1017/jfm.2024.1073.