Thin filaments in Hele-Shaw cells

Nitay Ben-Shachar; Michael C. Dallaston; Scott W. McCue

doi:10.1007/978-3-032-16202-1_29

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arXiv · 2507.13507

Thin filaments in Hele-Shaw cells

Nitay Ben-Shachar·Michael C. Dallaston·Scott W. McCue

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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.

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Nitay Ben-Shachar, Michael C. Dallaston, Scott W. McCue. 2025-07-17. Thin filaments in Hele-Shaw cells. https://doi.org/10.1007/978-3-032-16202-1_29

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