Thin filaments in Hele-Shaw cells
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914465402847232 |
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| author | Ben-Shachar, Nitay Dallaston, Michael C. McCue, Scott W. |
| author_facet | Ben-Shachar, Nitay Dallaston, Michael C. McCue, Scott W. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thin filaments in Hele-Shaw cells Ben-Shachar, Nitay Dallaston, Michael C. McCue, Scott W. Fluid Dynamics 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. |
| title | Thin filaments in Hele-Shaw cells |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2507.13507 |