具有表面张力的液幕的实验预测
Paradoxical predictions of liquid curtains with surface tension
摘要：
本文研究了受重力和表面张力影响的与水平面成一定角度喷射的二维液幕。流动是，到主导阶，无剪切和粘度，可以忽略不计。弗劳德数很大，所以窗帘的曲率半径超过了它的厚度。韦伯数接近于1，因此惯性力和表面张力几乎完全平衡。在这些假设下，导出了一个渐近方程，并探讨了其稳态解。结果表明，对于一对给定的喷射速度/角度，存在无限多的解决方案，每一个代表一个稳定的窗帘与一个固定的毛细波叠加在it. These解决方案描述了丰富的各种行为：除了向下弯曲，窗帘可以之字形向下，自相交，甚至上升，直到最初供应的液体的动能用完。最后一种解决方案对应于向上和向下弯曲的窗帘之间的分界线-在这两种情况下，自相交（这种解决方案只有在第一次相交之前才有意义，之后液体只是飞溅下来）。最后，建议如何向上弯曲的窗帘的存在，可以通过实验来测试。
英文摘要：
This paper examines two-dimensional liquid curtains ejected at an angle to the horizontal and affected by gravity and surface tension. The flow is, to leading order, shearless and viscosity, negligible. The Froude number is large, so that the radius of the curtain's curvature exceeds its thickness. The Weber number is close to unity, so that the forces of inertia and surface tension are almost perfectly balanced. An asymptotic equation is derived under these assumptions, and its steady solutions are explored. It is shown that, for a given pair of ejection velocity/angle, infinitely many solutions exist, each representing a steady curtain with a stationary capillary wave superposed on it. These solutions describe a rich variety of behaviours: in addition to arching downwards, curtains can zigzag downwards, self-intersect, and even rise until the initial supply of the liquid's kinetic energy is used up. The last type of solutions corresponds to a separatrix between upward- and downward-bending curtains -- in both cases, self-intersecting (such solutions are meaningful only until the first intersection, after which the liquid just splashes down). Finally, suggestions are made as to how the existence of upward-bending curtains can be tested experimentally.
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