Does air-bubble pinch-off in water reach a universal self-similar state?
In plain words
When an air bubble detaches underwater, its neck thins to zero width in a fraction of a millisecond. Theory predicts that the final collapse forgets how it started, but experiments show that small initial asymmetries persist to the end.
Precise statement
For an air bubble detaching from a nozzle in a low-viscosity liquid, the minimum neck radius $h_{\min} \sim \tau^{\alpha}$, with $\tau$ the time to pinch-off. Theory for an axisymmetric cavity predicts $\alpha \to 1/2$ with slowly varying logarithmic corrections (Eggers et al. 2007), while experiments show memory of initial asymmetry as neck vibrations (Keim et al. 2006). Does the collapse approach the universal axisymmetric solution as $\tau \to 0$ for generic small asymmetry, and what sets the final breakup mode?
What would settle it
Imaging and simulations resolving $h_{\mathrm{min}}$ below about $10^{-4}\ \mathrm{cm}$ with controlled initial asymmetry, compared with the asymmetric perturbation theory.
Status in the literature
The axisymmetric theory is established, but experiments do not reach it because azimuthal perturbations persist rather than decay.