Ng Chiu-On
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong.
Phys Rev E. 2016 Dec;94(6-1):063115. doi: 10.1103/PhysRevE.94.063115. Epub 2016 Dec 28.
This paper aims to look into how system rotation may modify the role played by boundary slip in controlling flow through a rotating channel bounded by stick-slip walls. A semianalytical model is developed for pressure-driven flow in a slit channel that rotates about an axis perpendicular to its walls, which are superhydrophobic surfaces patterned with periodic alternating no-shear and no-slip stripes. The cases where the flow is driven by a pressure gradient parallel or normal to the stripes are considered. The effects of the no-shear area fraction on the velocities and effective slip lengths for the primary and secondary flows are investigated as functions of the rotation rate and the channel height. It is mathematically proved that the secondary flow rate is exactly the same in the two cases, irrespective of whether the primary flow is parallel or normal to the wall stripes. For any rotation speed, there is an optimal value of the no-shear area fraction at which the primary flow rate is maximum. This is a consequence of two competing effects: the no-shear part of the wall may serve to reduce the wall resistance, thereby enhancing the flow especially at low rotation, but it also weakens the formation of the near-wall Ekman layer, which is responsible for pumping the flow especially at high rotation. Wall slip in a rotating environment is to affect flow in the Ekman layer, but not flow in the geostrophic core.
本文旨在研究系统旋转如何改变边界滑移在控制通过由粘滑壁界定的旋转通道的流动中所起的作用。针对在垂直于其壁面的轴上旋转的狭缝通道中的压力驱动流动，开发了一个半解析模型，该壁面为具有周期性交替无剪切和无滑移条纹的超疏水表面。考虑了流动由平行或垂直于条纹的压力梯度驱动的情况。研究了无剪切面积分数对一次和二次流动的速度和有效滑移长度的影响，这些影响是旋转速率和通道高度的函数。从数学上证明，在这两种情况下二次流率完全相同，而不管一次流是平行还是垂直于壁条纹。对于任何旋转速度，都存在一个无剪切面积分数的最佳值，此时一次流率最大。这是两种相互竞争的效应的结果：壁面的无剪切部分可能有助于降低壁面阻力，从而增强流动，尤其是在低旋转时，但它也会削弱近壁埃克曼层的形成，而近壁埃克曼层负责在高旋转时抽吸流动。旋转环境中的壁面滑移会影响埃克曼层中的流动，但不会影响地转核心中的流动。
