2025/07/17 by Ben-Shachar, Nitay, Dallaston, Michael C., McCue, Scott W.
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2507.13507
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.