标题： 薄丝在Hele-Shaw细胞中 显示英文标题

标题： Thin filaments in Hele-Shaw cells

摘要： 使用一个最近推导出的纤维模型，研究了在恒定压力梯度驱动下的Hele-Shaw细胞中流体纤维的稳定性。发现如果初始半径超过无量纲临界半径，细小的圆形纤维会生长。此外，轴对称解的线性稳定性表明，当半径为该临界半径的两倍时，所有模式都是稳定的，而当半径更大时，模式变得不稳定。发现了一个渐近大半径的移动圆形解，称为“固定圆”。这些解被认为可以描述观察到的纤维非线性生长为类似圆形的解。这些解在固定圆半径上表现出有限时间爆破，这是由于圆在生长过程中失去质量所致。本报告介绍了第一作者在2024年4月3日至23日举行的Matrix Workshop多孔介质不稳定性项目中的研究成果，在其他作者的监督下完成。 显示英文摘要

摘要： 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.