School of Engineering and Materials Science, Queen Mary University of London, London, E1 4NS, United Kingdom.
Departamento de Física, Universidad de Santiago de Chile, Av. Ecuador, 3493, Estación Central, Santiago, Chile.
Sci Rep. 2019 Oct 29;9(1):15488. doi: 10.1038/s41598-019-51824-3.
We study the capillary retraction of a Newtonian semi-infinite liquid filament through analytical methods. We derive a long-time asymptotic-state expansion for the filament profile using a one-dimensional free-surface slender cylindrical flow model based on the three-dimensional axisymmetric Navier-Stokes equations. The analysis identifies three distinct length and time scale regions in the retraction domain: a steady filament section, a growing spherical blob, and an intermediate matching zone. We show that liquid filaments naturally develop travelling capillary waves along their surface and a neck behind the blob. We analytically prove that the wavelength of the capillary waves is approximately 3.63 times the filament's radius at the inviscid limit. Additionally, the waves' asymptotic wavelength, decay length, and the minimum neck size are analysed in terms of the Ohnesorge number. Finally, our findings are compared with previous results from the literature and numerical simulations in Basilisk obtaining a good agreement. This analysis provides a full picture of the recoiling process going beyond the classic result of the velocity of retraction found by Taylor and Culick.
我们通过分析方法研究了牛顿半无限液体细丝的毛细回缩。我们使用基于三维轴对称纳维-斯托克斯方程的一维自由表面细长圆柱流模型，为细丝轮廓推导了一个长时间渐近状态扩展。该分析确定了回缩域中的三个不同的长度和时间尺度区域：稳定的细丝部分、增长的球形团块和中间匹配区域。我们表明，液体细丝自然地在其表面和团块后面的颈部发展出移动的毛细波。我们从无粘性极限的角度分析证明，毛细波的波长约为细丝半径的 3.63 倍。此外，还根据奥内佐格数分析了波的渐近波长、衰减长度和最小颈部尺寸。最后，我们的研究结果与 Basilisk 中的文献和数值模拟结果进行了比较，得到了很好的一致性。该分析提供了回缩过程的全貌，超越了 Taylor 和 Culick 发现的回缩速度的经典结果。
