When a column of water drains from a vertical tube, it often leaves behind a trailing film that forms intricate, axisymmetric liquid structures. Using high-speed imaging and first-principles modeling, we investigate the formation and breakup of these fluted films and demonstrate that their diverse morphologies arise from the evolving balance of inertia, surface tension, gravity, and viscous forces. By analyzing the characteristic timescales for film emergence, retraction, and rupture, we classify the observed behaviors into distinct regimes and predict the transitions between them. Our theoretical framework captures the transient velocity and thickness of the film at the tube exit and yields regime boundaries that closely match experimental observations. These results not only explain a deceptively simple fluid dynamic system but also provide insight into film stability, merging, and rupture processes relevant to falling film evaporators, coating flows, and capillary-inertial instabilities across soft matter and multiphase systems. Published by the American Physical Society 2025

中文翻译：

---

落水柱后面的瞬态凹槽薄膜

当水柱从垂直管中排出时，通常会留下一层拖曳膜，形成复杂的轴对称液体结构。使用高速成像和第一性原理建模，我们研究了这些凹槽薄膜的形成和破裂，并证明它们的不同形态源于惯性、表面张力、重力和粘性力的不断发展的平衡。通过分析电影出现、收缩和破裂的特征时间尺度，我们将观察到的行为分为不同的状态并预测它们之间的过渡。我们的理论框架捕获了管出口处薄膜的瞬态速度和厚度，并产生了与实验观察结果非常匹配的状态边界。这些结果不仅解释了一个看似简单的流体动力学系统，而且还提供了对与软物质和多相系统中下落薄膜蒸发器、涂层流动和毛细管惯性不稳定性相关的薄膜稳定性、合并和破裂过程的见解。 美国物理学会 2025 年出版