By exploiting the reciprocal theorem of Stokes flow, we find an explicit expression for the first order slip length correction, for small protrusion angles, and for transverse shear over a periodic array of curved menisci. The result is the transverse flow analogue of the longitudinal flow result of Sbragaglia and Prosperetti [“A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces,” Phys. Fluids 19, 043603 (2007)]. For small protrusion angles, it also generalizes the dilute-limit result of Davis and Lauga [“Geometric transition in friction for flow over a bubble mattress,” Phys. Fluids 21, 011701 (2009)] to arbitrary no-shear fractions. While the leading order slip lengths for transverse and longitudinal flow over flat no-shear slots are well-known to differ by a factor of 2, the first order slip length corrections for weakly protruding menisci in each flow are found to be identical.

中文翻译：

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弱弯曲半月板周期性阵列上横向剪切流的滑移长度

通过利用斯托克斯流的倒数定理，我们找到了用于一阶滑移长度校正、小突出角和弯曲弯月面周期性阵列上的横向剪切的明确表达式。结果是横向流动模拟 Sbragaglia 和 Prosperetti 的纵向流动结果[“关于具有超疏水表面的微通道流动的有效滑动特性的说明，”Phys. 流体 19, 043603 (2007)]。对于小的突出角度，它还概括了 Davis 和 Lauga 的稀释极限结果 [“泡沫床垫上流动的摩擦几何过渡”，Phys. Fluids 21, 011701 (2009)] 到任意无剪切分数。虽然众所周知，平坦无剪切槽上横向和纵向流动的前级滑移长度相差 2 倍，