Observations of Singularity Formation during the Capillary Collapse and Bubble Pinch-off of a Soap Film Bridge
Observations of Singularity Formation during the Capillary Collapse and Bubble Pinch-off of a Soap Film Bridge
复制标题
皂膜桥毛细管塌陷和气泡夹断过程中奇点形成的观察
DOI：
10.1006/jcis.2001.7717
复制
发表时间：
2001
影响因子：
9.9
通讯作者：
P. Steen
中科院分区：
文献类型：
--
作者：
N. Robinson;P. Steen
摘要本文报道了由毛细驱动的肥皂膜桥的坍塌和由此引起的气泡夹断的观察结果。根据最近的一个数学表面模型，表面张力仅受流体惯性的抵抗，在固体支撑之间的中间平面上开始有一个颈，并分裂成跨越中间平面的两个镜像对称的颈，这些颈“翻转”（界面变得多值），之后随着夹断显示出两个主曲率的有限时间膨胀，自相似性发展。奇异曲率意味着一个无界的压力和发散的轴向和径向速度。因此，可以预期，模型在接近掐断的长度尺度上破裂，此时被忽略的物理在实验中变得重要。本文考察了该模型在何处以及如何失效。从200毫米到0.2毫米的长度尺度（时间尺度从1.0秒到10−4秒）上的观测表明，该模型定量地预测了小于毫米尺度的行为，低于毫米尺度会出现偏差。这些偏差归因于肥皂膜的有限厚度，其惯性在接近10米/秒的运动中可以相当大。
Abstract Observations of capillary-driven collapse of a soap film bridge and consequent bubble pinch-off are reported. According to a recent mathematical surface model, in which the surface tension force is resisted only by the fluid inertia, a neck starts on the midplane between the solid supports and splits into two mirror-symmetric necks that straddle the midplane, and these necks “turn over” (the interface becomes multivalued), after which self-similarity develops as the pinch-off exhibits finite time blow-up of both principal curvatures. Singular curvatures imply an unbounded pressure and diverging axial and radial velocities. It is therefore anticipated that the model breaks down at a length scale near pinch-off where neglected physics becomes important in the experiment. This paper examines where and how the model breaks down. Observations on length scales from 200 mm down to 0.2 mm (time scales from 1.0 s down to 10−4 s) show that the model quantitatively predicts behavior down to the millimeter scale below which deviations occur. These deviations are attributed to the finite thickness of the soap film whose inertia can be considerable in motions approaching 10 m/s.