论文标题
表面张力的液窗帘的悖论预测
Paradoxical predictions of liquid curtains with surface tension
论文作者
论文摘要
本文研究了二维液体窗帘，与水平和压力张力的影响一定角度弹出。流动的流量是无剪切和粘度，可以忽略不计。 Froude数量很大，因此窗帘的曲率半径超过其厚度。韦伯的数字接近统一，因此惯性和表面张力的力几乎完全平衡。在这些假设下得出了渐近方程，并探索了其稳定的解决方案。结果表明，对于给定的一对弹出速度/角度，存在无限的解决方案，每种解决方案都代表稳定的窗帘，上面有固定的毛细管波。这些解决方案描述了各种各样的行为：除了向下拱起外，窗帘还可以向下曲折，自我切割，甚至上升，直到用液体的动能的初始供应被用完为止。最后类型的解决方案对应于向上和向下弯曲的窗帘之间的分离 - 在这两种情况下，自我隔离（这种解决方案仅在第一个相交之前才有意义，此后液体只是溅出）。最后，提出了有关如何通过实验测试向上弯曲窗帘的存在的建议。
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.
