论文标题
发达的液体膜通过了尾边:小雷诺数的小规模分析和“茶壶效应”
Developed liquid film passing a trailing edge: small-scale analysis and the `teapot effect' at large Reynolds numbers
论文作者
论文摘要
最近,作者认为,在表面张力下的水平对齐平板的尖锐尾随边缘和重力的较弱的作用在渐近细长层限制下垂直起作用(J. FluidMech。850,第924----953,2018)。由于固有的上游影响,在边缘的下游,并在所有较小的尺度上仔细检查了流动偏离,因此我们重新审视了毛细管驱动的短尺寸粘性 - 视觉相互作用。我们遵守了如此之大的假设,以至于在板边缘处窒息是微不足道的,但是设想相关的o(1)相关的韦伯数的变化。基本上是在分析上解决的主要焦点的方面是,流向尺度的结构的延续要比交互式小得多,而不再将其视为细长。作为一种非凡的现象,该分析预测了雷利型的谐波毛细管波纹,在后缘的自由表面上盛行。随着特征Weber数量的降低,它们表现出波长和振幅的增加。最后,该理论阐明了实际的分离过程,这在流动分离的理性理论中是前所未有的。在此阶段,流体的润湿特性和显微镜楔形边缘在较大尺度上无限薄,从而发挥了作用。由于这种几何形状通常模拟了喷口的退出,因此楔形的预测润湿与文献中所谓的所谓茶壶效应有关。
Recently, the authors considered a thin steady developed viscous liquid wall jet 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. 850, pp. 924--953, 2018). 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 aspect in the main focus, tackled essentially analytically, is the continuation of the structure of the flow towards scales much smaller then 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, unprecedented in the rational theories 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 so-called teapot effect.