Stability of similarity solutions of viscous thread pinch-off

Michael C Dallaston*, Chengxi Zhao, James E Sprittles, Jens Eggers

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
31 Downloads (Pure)


In this paper we compute the linear stability of similarity solutions of the breakup of viscous liquid threads, in which the viscosity and inertia of the liquid are in balance with the surface tension. The stability of the similarity solution is determined using numerical continuation to find the dominant eigenvalue of the correction problem. Stability of the first two solutions identified in Brenner et al.
[1] are considered. We find that the primary similarity solution, which is that seen in experiments and simulations, is linearly stable with a complex nontrivial eigenvalue, which could explain the phenomenon of break-up producing sequences of small satellite droplets of decreasing radius near a main pinch-off point. The second solution is seen to be linearly unstable. These linear stability
results compare favorably to numerical simulations for the stable similarity solution, while a profile starting near the unstable similarity solution is shown to very rapidly leave the linear regime.
Original languageEnglish
Article number104004
Number of pages15
JournalPhysical Review Fluids
Issue number10
Publication statusPublished - 8 Oct 2021

Bibliographical note

Funding Information:
C.Z. and J.E.S. acknowledge financial support from EPSRC Grant Nos. EP/N016602/1, EP/P020887/1, EP/S029966/1, and EP/P031684/1.

Publisher Copyright:
© 2021 American Physical Society.


  • Continuum mechanics
  • Drop breakup
  • Instability of free-surface flows
  • Liquid bridges


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