Thin filaments in Hele-Shaw cells

[2507.13507] Thin filaments in Hele-Shaw cells Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Physics > Fluid Dynamics arXiv:2507.13507 (physics) [Submitted on 17 Jul 2025] Title: Thin filaments in Hele-Shaw cells Authors: Nitay Ben-Shachar , Michael C. Dallaston , Scott W. McCue View a PDF of the paper titled Thin filaments in Hele-Shaw cells, by Nitay Ben-Shachar and 2 other authors View PDF HTML (experimental) Abstract: Using a recently derived filament model, the stability of fluid filaments in Hele-Shaw cells, driven by a constant pressure gradient, is studied. It is found that thin circular filaments grow if their initial radius exceeds a dimensionless critical radius. Further, linear stability of the axisymmetric solution reveals that all modes are stable for twice this critical radius, with modes becoming unstable for larger radii. A translating circular solution is found for asymptotically large radius, termed a `pinned circle'. These are thought to describe the observed non-linear growth of filament into circular-like solutions. The solutions exhibit a finite-time blow up in the pinned circle radius, attributed to the circle shedding mass as it grows. This report presents the results of a project undertaken by the first author at the Matrix Workshop Instabilities in Porous Media, April 3-23, 2024, under the supervision of the other authors. Comments: 17 pages, 9 figures Subjects: Fluid Dynamics (physics.flu-dyn) Cite as: arXiv:2507.13507 [physics.flu-dyn] (or arXiv:2507.13507v1 [physics.flu-dyn] for this version) https://doi.org/10.48550/arXiv.2507.13507 Focus to learn more arXiv-issued DOI via DataCite Journal reference: 2024 MATRIX Annals, Part I Related DOI : https://doi.org/10.1007/978-3-032-16202-1_29 Focus to learn more DOI(s) linking to related resources Submission history From: Michael Dallaston [ view email ] [v1] Thu, 17 Jul 2025 19:26:31 UTC (2,988 KB) Full-text links: Access Paper: View a PDF of the paper titled Thin filaments in Hele-Shaw cells, by Nitay Ben-Shachar and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: physics.flu-dyn < prev | next > new | recent | 2025-07 Change to browse by: physics References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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