In this paper we re-examine the flow produced by the normal impact of a laminar liquid jet onto an infinite plane when the flow is dominated by surface tension. Over the range of parameters we consider, which are typical of water from a tap over a kitchen sink, it is observed experimentally that after impact the liquid spreads radially over the plane away from the point of impact in a thin film. It is also observed that, at a finite radius, there is an abrupt increase in thickness of the film which has been identified as a hydraulic jump. Once the jump is formed this radius remains constant in time and, further, is independent of the orientation of the surface showing that gravity is unimportant (Bhagat et al., J. Fluid Mech., vol. 851, 2018, R5). We show that the application of conservation of momentum in the film, subject only to viscosity and surface tension and ignoring gravity completely, predicts a singularity in the curvature of the liquid film and consequently a jump in the depth of the film at a finite radius. This location is almost identical to the radius of the jump predicted by conservation of energy and agrees with experimental observations. We also provide the correct boundary condition to be applied at an interface, where there is a change in interfacial area as a result of the fluid flow, that accounts for the energy change associated with fluid molecules’ exchange between the interface and the bulk.

中文翻译：

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圆毛细管跳跃

在本文中，我们重新研究了当流动受表面张力支配时层流液体射流法向撞击无限平面所产生的流动。在我们考虑的参数范围内，这是典型的厨房水槽上水龙头的水，通过实验观察到，在撞击后，液体在远离撞击点的平面上呈放射状扩散成薄膜。还观察到，在有限半径处，薄膜厚度突然增加，这已被确定为水跃。一旦形成跳跃，该半径在时间上保持不变，并且与表面方向无关，表明重力不重要（Bhagat 等人，J. Fluid Mech.，第 851 卷，2018 年，R5）。我们证明了动量守恒在电影中的应用，仅受粘度和表面张力影响而完全忽略重力，预测液膜曲率的奇点，因此在有限半径处膜的深度发生跳跃。这个位置几乎与能量守恒预测的跳跃半径相同，并与实验观察一致。我们还提供了在界面上应用的正确边界条件，其中由于流体流动而导致界面面积发生变化，这解释了与界面和主体之间的流体分子交换相关的能量变化。这个位置几乎与能量守恒预测的跳跃半径相同，并与实验观察一致。我们还提供了适用于界面的正确边界条件，其中界面面积因流体流动而发生变化，这解释了与界面和主体之间的流体分子交换相关的能量变化。这个位置几乎与能量守恒预测的跳跃半径相同，并与实验观察一致。我们还提供了适用于界面的正确边界条件，其中界面面积因流体流动而发生变化，这解释了与界面和主体之间的流体分子交换相关的能量变化。