Rivulet flow over a flexible beam
Rivulet flow over a flexible beam
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柔性梁上的溪流
DOI：
10.1017/jfm.2016.258
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发表时间：
2016
影响因子：
3.7
通讯作者：
Howard A. Stone
中科院分区：
文献类型：
--
作者：
Peter Howell;Hyoungsoo Kim;Marinela Popova;Howard A. Stone
我们从理论和实验上研究了薄层液体如何沿柔性梁流动。流动模型采用润滑理论，衬底模型为弹性体，根据Euler-Bernoulli方程变形。在梁的一端提供恒定的液体流量，梁的一端水平夹紧，而梁的另一端自由。随着液膜的扩散，其重量会导致光束偏转增加，这反过来又会提高液体的扩散速度。这种反馈机制使前端位置${it\sigma}(T)$和前端的偏转角${\it\Phi}(T)$经历了许多不同的幂定律行为。在早期，液体像水平重力流一样扩散，以${it\sigma}(T)\propto t^{4/5}$和${\it\phi}(T)\proposto t^{13/5}$。在中间时刻，光束的偏转导致液层的快速加速，分别为t^4}和t^9}。最后，当光束下垂到几乎垂直时，液膜以${it\sigma}(T)\proporto t$和${\it\phi}(T)\sim{\rm\pi}/2$向下流动。我们证明了这些理论预测与实验结果很好地吻合。
We study theoretically and experimentally how a thin layer of liquid flows along a flexible beam. The flow is modelled using lubrication theory and the substrate is modelled as an elastica which deforms according to the Euler–Bernoulli equation. A constant flux of liquid is supplied at one end of the beam, which is clamped horizontally, while the other end of the beam is free. As the liquid film spreads, its weight causes the beam deflection to increase, which in turn enhances the spreading rate of the liquid. This feedback mechanism causes the front position ${\it\sigma}(t)$ and the deflection angle at the front ${\it\phi}(t)$ to go through a number of different power-law behaviours. For early times, the liquid spreads like a horizontal gravity current, with ${\it\sigma}(t)\propto t^{4/5}$ and ${\it\phi}(t)\propto t^{13/5}$ . For intermediate times, the deflection of the beam leads to rapid acceleration of the liquid layer, with ${\it\sigma}(t)\propto t^{4}$ and ${\it\phi}(t)\propto t^{9}$ . Finally, when the beam has sagged to become almost vertical, the liquid film flows downward with ${\it\sigma}(t)\propto t$ and ${\it\phi}(t)\sim {\rm\pi}/2$ . We demonstrate good agreement between these theoretical predictions and experimental results.