Asymptotic theory of intermediate-layer rupture

Determine the asymptotic structure of the thinning profile and the associated scaling laws for the minimum thickness of the intermediate liquid layer during rupture, and establish whether existing rupture theories for lubrication-type free-surface flows can be adapted to the three-layer cylindrical geometry.

Background

The paper identifies a rupture mechanism that is specific to the three-layer configuration: the intermediate liquid layer can locally collapse while the air core and the neighboring liquid layers remain finite. Numerical simulations indicate strongly localized thinning as the intermediate layer approaches extinction, but they do not resolve the local singularity structure or its scaling behavior.

The authors explicitly leave open the determination of the thinning profile’s asymptotic form, the scaling laws governing the minimum intermediate-layer thickness, and the applicability of existing lubrication-based rupture theories to this coupled three-interface cylindrical geometry.

References

Determining the asymptotic structure of the thinning profile, the associated scaling laws for the minimum middle-layer thickness, and the extent to which existing rupture theories for lubrication-type free-surface flows can be adapted to this three-layer geometry remain open problems.

— Stability and nonlinear dynamics of three-layer viscous films inside a vertical cylindrical tube  (2608.19417 - Halpern et al., 19 Aug 2026) in Section 6, Conclusion

Our attempts to optically image this potential trapped bubble were not successful, so we have not directly verified the hypothetical mechanism in Fig.~\ref{fig:meniscus}C.

— Droplet coalescence in fluids obeying Darcy's law  (2608.21192 - Wang et al., 21 Aug 2026) in Section V, paragraph discussing Fig. 5C