论文标题
毛细管在带有拐角的管子中升起
Capillary rising in a tube with corners
论文作者
论文摘要
我们研究了带有角落的毛细管中液体上升的动力学。在拐角管中，与圆形管不同，流体用两个部分（整个横截面都被流体占据的散装部分）以及横截面部分仅部分填充的散装部分。使用OnSager原理，我们得出了两个部分的耦合时间进化方程。我们表明（a）在上升的早期阶段，动力学由散装部分和流体高度$ h_0（t）$所支配，其行为与圆管中相同的行为，（b）在后期，散装部分停止上升，但手指部分在缩放法律的缩放定律$ h_1（t）（t）（t）（t）（t）（t）\ sim \ sim \ sim t^^^$ 3^$ 3^^^^^^$ sim n and naking laws nible升高。我们还表明，由于这两个部分之间的耦合，平衡的体积高度小于Jurin的高度，该高度忽略了手指部分的效果。
We study the dynamics of a fluid rising in a capillary tube with corners. In the cornered tube, unlike the circular tube, fluid rises with two parts, the bulk part where the entire cross-section is occupied by the fluid, and the finger part where the cross-section is only partially filled. Using Onsager principle, we derive coupled time-evolution equations for the two parts. We show that (a) at the early stage of rising, the dynamics is dominated by the bulk part and the fluid height $h_0(t)$ shows the same behavior as that in the circular tube, and (b) at the late stage, the bulk part stops rising, but the finger part keeps rising following the scaling law of $h_1(t) \sim t^{1/3}$. We also show that due to the coupling between the two parts, the equilibrium bulk height is smaller than the Jurin's height which ignores the effect of the finger part.
