Recently, the authors considered a thin steady developed viscous free-surface flow passing the sharp trailing edge of a horizontally aligned flat plate under surface tension and the weak action of gravity, acting vertically, in the asymptotic slender-layer limit (J. Fluid Mech., vol. 850, 2018, pp. 924–953). We revisit the capillarity-driven short-scale viscous–inviscid interaction, on account of the inherent upstream influence, immediately downstream of the edge and scrutinise flow detachment on all smaller scales. We adhere to the assumption of a Froude number so large that choking at the plate edge is insignificant but envisage the variation of the relevant Weber number of $O(1)$ . The main focus, tackled essentially analytically, is the continuation of the structure of the flow towards scales much smaller than the interactive ones and where it no longer can be treated as slender. As a remarkable phenomenon, this analysis predicts harmonic capillary ripples of Rayleigh type, prevalent on the free surface upstream of the trailing edge. They exhibit an increase of both the wavelength and amplitude as the characteristic Weber number decreases. Finally, the theory clarifies the actual detachment process, within a rational description of flow separation. At this stage, the wetting properties of the fluid and the microscopically wedge-shaped edge, viewed as infinitely thin on the larger scales, come into play. As this geometry typically models the exit of a spout, the predicted wetting of the wedge is related to what in the literature is referred to as the teapot effect.

中文翻译：

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通过平滑和楔形后缘的显影液膜：小规模分析和大雷诺数下的“茶壶效应”

最近，作者考虑了在表面张力和垂直作用下的弱重力作用下，在渐近细长层极限内，薄的稳定发展的粘性自由表面流通过水平对齐平板的尖锐后缘。J.流体机械。, 卷。850，2018，第 924-953 页）。我们重新审视毛细作用驱动的短尺度粘性-非粘性相互作用，考虑到固有的上游影响，紧邻边缘的下游，并在所有较小尺度上仔细检查流动分离。我们坚持一个如此大的弗劳德数的假设，以至于在板边缘窒息是微不足道的，但设想了相关韦伯数的变化 $O(1)$ . 主要关注点，基本上是分析解决的，是流动结构的延续，其尺度比交互式尺度小得多，并且不再可以被视为纤细的。作为一个显着的现象，该分析预测了瑞利型谐波毛细波纹，在后缘上游的自由表面上普遍存在。随着特征韦伯数的减少，它们表现出波长和幅度的增加。最后，该理论在对流动分离的合理描述中阐明了实际的分离过程。在这个阶段，流体的润湿特性和微观楔形边缘（在更大的尺度上被视为无限薄）开始发挥作用。由于这种几何形状通常模拟喷口的出口，