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Stability of similarity solutions of viscous thread pinch-off
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Dallaston, Michael C., Zhao, Chengxi, Sprittles, James E. and Eggers, Jens (2021) Stability of similarity solutions of viscous thread pinch-off. Physical Review Fluids, 6 (10). 104004. doi:10.1103/PhysRevFluids.6.104004 ISSN 2469-990X.
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WRAP-Stability-similarity-solutions-viscous-thread-pinch-off-2021.pdf - Accepted Version - Requires a PDF viewer. Download (659Kb) | Preview |
Official URL: https://doi.org/10.1103/PhysRevFluids.6.104004
Abstract
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 eigenvalues. Stability of the first two solutions (those with largest minimum radius) is considered. We find that the first similarity solution, which is the one 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.
Item Type: | Journal Article | |||||||||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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Library of Congress Subject Headings (LCSH): | Jets -- Fluid dynamics, Jets -- Fluid dynamics -- Mathematical models, Fluid dynamics -- Mathematics, Surface tension | |||||||||||||||
Journal or Publication Title: | Physical Review Fluids | |||||||||||||||
Publisher: | American Physical Society | |||||||||||||||
ISSN: | 2469-990X | |||||||||||||||
Official Date: | October 2021 | |||||||||||||||
Dates: |
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Volume: | 6 | |||||||||||||||
Number: | 10 | |||||||||||||||
Article Number: | 104004 | |||||||||||||||
DOI: | 10.1103/PhysRevFluids.6.104004 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
Copyright Holders: | © 2021 American Physical Society | |||||||||||||||
Date of first compliant deposit: | 24 September 2021 | |||||||||||||||
Date of first compliant Open Access: | 28 September 2021 | |||||||||||||||
RIOXX Funder/Project Grant: |
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