Taylor-Culick退缩和周围环境的影响
Taylor-Culick retractions and the influence of the surroundings
摘要：
当自由悬浮的液膜破裂时，它在表面张力的作用下自发地收缩。如果薄膜被空气包围，则已知回缩速度接近恒定的泰勒-库里克速度。然而，当被外部粘性介质包围时，该介质内的耗散决定了回缩速度的大小。在本工作中，我们研究了液体（水）膜在粘性油环境（\emph{two-phase}泰勒-库里克收缩），夹在空气和粘性油（\emph{three-phase}泰勒-库里克收缩）。在后一种情况下，观察到实验测量的回缩速度与水膜完全被油包围的构造相比对油相的粘度具有较弱的依赖性。数值模拟表明，这种较弱的依赖性来自于三相接触线附近的粘性耗散的局部化。回缩的速度仅取决于周围介质的粘度，而不取决于膜的粘度。从实验和数值模拟，我们揭示了前所未有的制度的韦伯数$We_f$的缩放膜（基于其回缩速度）或周围环境的毛细管数$Ca_s$与周围环境的Ohnesorge数$Oh_s$的关系（$Oh_s \gg 1$），即用于两相Taylor-Culick配置的$We_f \sim Oh_s^{-2}$和$Ca_s \sim Oh_s^{0}$，以及用于三相Taylor-Culick配置的$We_f \sim Oh_s^{-1}$和$Ca_s \sim Oh_s^{1/2}$。
英文摘要：
When a freely suspended liquid film ruptures, it retracts spontaneously under the action of surface tension. If the film is surrounded by air, the retraction velocity is known to approach the constant Taylor-Culick velocity. However, when surrounded by an external viscous medium, the dissipation within that medium dictates the magnitude of the retraction velocity. In the present work, we study the retraction of a liquid (water) film in a viscous oil ambient (\emph{two-phase} Taylor-Culick retractions), and that sandwiched between air and a viscous oil (\emph{three-phase} Taylor-Culick retractions). In the latter case, the experimentally-measured retraction velocity is observed to have a weaker dependence on the viscosity of the oil phase as compared to the configuration where the water film is surrounded completely by oil. Numerical simulations indicate that this weaker dependence arises from the localization of viscous dissipation near the three-phase contact line. The speed of retraction only depends on the viscosity of the surrounding medium and not on that of the film. From the experiments and the numerical simulations, we reveal unprecedented regimes for the scaling of the Weber number $We_f$ of the film (based on its retraction velocity) or the capillary number $Ca_s$ of the surroundings vs. the Ohnesorge number $Oh_s$ of the surroundings in the regime of large viscosity of the surroundings ($Oh_s \gg 1$), namely $We_f \sim Oh_s^{-2}$ and $Ca_s \sim Oh_s^{0}$ for the two-phase Taylor-Culick configuration, and $We_f \sim Oh_s^{-1}$ and $Ca_s \sim Oh_s^{1/2}$ for the three-phase Taylor-Culick configuration.
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