Self-Similar Draining near a Vertical Edge
Self-Similar Draining near a Vertical Edge
复制标题
垂直边缘附近的自相似排水
DOI：
10.1103/physrevlett.125.064502
复制
发表时间：
2020
影响因子：
8.6
通讯作者：
Stone, Howard A.
中科院分区：
文献类型：
--
作者：
Xue, Nan;Stone, Howard A.
当液体薄膜在垂直板上流失时，薄膜在垂直边缘附近变得不均匀。在这里，我们实验报道了这种薄膜的三维（3D）自相似形状。基于众所周知的远离边缘的排水膜的二维自相似解，我们确定了一种新的三维自相似标度，将具有三个自变量的膜厚度偏微分方程转化为常微分方程。用干涉测量法测量了薄膜厚度随位置和时间的变化，结果与理论预测非常吻合。
When a liquid film drains on a vertical plate, the film becomes nonuniform near the vertical edge. Here we experimentally report the three-dimensional (3D) self-similar shape of this film. Based on the well-known 2D self-similar solution of a draining film far from the edge, we identify a new 3D self-similar scaling, which converts the partial differential equation for the film thickness with three independent variables into an ordinary differential equation. Interferometry is performed to measure the film thickness as a function of position and time, and the results are in excellent agreement with the theoretical predictions.