粗糙毛细管中的塞子：运动对塞子长度的增强依赖性
Plugs in rough capillary tubes: enhanced dependence of motion on plug length
摘要：
本文讨论了可忽略粘度的塞子在充满载液的粗糙毛细管中的蠕动运动。这扩展了Bretherton的研究工作的无限长气泡运动在圆柱形或光滑管小毛细数Ca。我们首先推导出光滑管情形下，塞子速度对有限长度的渐近依赖性。这种对长度的依赖性是指数小的，衰减长度远小于管半径R。讨论了管壁方位粗糙度对塞速的影响。管的粗糙度导致不平衡的毛细管压力和载流流体通量的方位平面。这个通量控制着塞子形状的松弛，使其达到无限长的极限。对于长波长粗糙度，我们发现上述衰减长度在粗糙管中要长得多，在某些情况下甚至变得与管半径R相当。这意味着插塞速度对插塞长度的依赖性大大增强。这一机制可以解释实验中观察到的追赶效应。
英文摘要：
We discuss the creeping motion of plugs of negligible viscosity in rough capillary tubes filled with carrier fluids. This extends Bretherton's research work on the infinite-length bubble motion in a cylindrical or smooth tube for small capillary numbers Ca. We first derive the asymptotic dependence of the plug speed on the finite length in the smooth tube case. This dependence on length is exponentially small, with a decay length much shorter than the tube radius R. Then we discuss the effect of azimuthal roughness of the tube on the plug speed. The tube roughness leads to an unbalanced capillary pressure and a carrier fluid flux in the azimuthal plane. This flux controls the relaxation of the plug shape to its infinite-length limit. For long-wavelength roughness, we find that the above decay length is much longer in the rough tube, and even becomes comparable to the tube radius R in some cases. This implies a much-enhanced dependence of the plug speed on the plug length. This mechanism may explain the catch-up effect seen experimentally.
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