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Revisiting the Taylor-Culick approximation. II. Retraction of a viscous sheet
Physical Review Fluids ( IF 2.7 ) Pub Date : 2020-09-18 , DOI: 10.1103/physrevfluids.5.093603
Hiranya Deka , Jean-Lou Pierson

We study the retraction of a viscous liquid sheet of finite length with negligible effect of the ambient medium. Using the long-wavelength model we derive the scaling laws and similarity solution for the interface profile of the retracting sheet. Far from the tip, the similarity solution for the interface profiles converges to an asymptotic value of 1/4. Direct numerical simulations are performed to compare the theoretical results with the simulations. When the inertia is negligible, the interface profiles remain flat during the retraction process which is in agreement with the self-similar solution. Using this similarity solution we derive the expression for the temporal variation of the tip speed for finite liquid sheets. We demonstrate that unlike an infinite sheet where the sheet retracts with a steady speed (known as Taylor-Culick speed), the tip speed decreases as a function of time for a finite liquid sheet. This is true when the viscous effects are larger than or of the same order with the inertia effects. Otherwise, the sheet retracts with the formation of a bulbous tip whose speed reaches a value closer to the Taylor-Culick speed.

中文翻译:

再谈泰勒-库利克逼近。二。缩回粘性薄片

我们研究了有限长度的粘性液体片材的回缩,而环境介质的影响可忽略不计。使用长波长模型,我们得出缩回片的界面轮廓的缩放定律和相似性解决方案。远离尖端,接口轮廓的相似性解决方案收敛到1/4的渐近值。进行直接数值模拟以将理论结果与模拟进行比较。当惯性可忽略不计时,界面轮廓在缩回过程中保持平坦,这与自相似解一致。使用这种相似性解决方案,我们可以得出有限液膜的叶尖速度随时间变化的表达式。我们证明了,与无限张纸不同,后者以稳定的速度(称为泰勒-克里克速度)缩回,对于有限的液体片材,尖端速度随时间而降低。当粘性作用大于或等于惯性作用时,这是正确的。否则,纸张会缩回并形成球根状尖端,球状尖端的速度达到接近泰勒-克里克速度的值。
更新日期:2020-09-20
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