We analyze the dynamics of liquid filling in a thin, slightly inflated rectangular channel driven by capillary forces. We show that although the amount of liquid m in the channel increases in time following the classical Lucas-Washburn law, m ∝ t^1/2, the prefactor is very sensitive to the deformation of the channel because the filling takes place by the growth of two parts, the bulk part (where the cross section is completely filled by the liquid), and the finger part (where the cross section is partially filled). We calculate the time dependence of m accounting for the coupling between the two parts and show that the prefactor for the filling can be reduced significantly by a slight deformation of the rectangular channel, e.g., the prefactor is reduced 50% for a strain of 0.1%. This offers an explanation for the large deviation on the value of the prefactor reported previously.

中文翻译：

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角通道中的润湿动力学

我们分析了由毛细管力驱动的薄而略微膨胀的矩形通道中的液体填充动力学。我们表明，尽管通道中的液体量m遵循经典的 Lucas-Washburn 定律随时间增加，m ∝ t ^1/2，但前因子对通道的变形非常敏感，因为填充是通过两部分，主体部分（横截面完全被液体填充）和手指部分（横截面部分填充）。我们计算m的时间依赖性考虑到两部分之间的耦合，并表明矩形通道的轻微变形可以显着降低填充的前因数，例如，对于 0.1% 的应变，前因数减少 50%。这解释了先前报告的前置因子值的大偏差。