Analysis of Stokes flow in microchannels with superhydrophobic surfaces containing a periodic array of micro-grooves
Analysis of Stokes flow in microchannels with superhydrophobic surfaces containing a periodic array of micro-grooves
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DOI：
10.1007/s10404-008-0387-0
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发表时间：
2009-09
影响因子：
2.8
通讯作者：
C. Teo;B. Khoo
中科院分区：
文献类型：
--
作者：
C. Teo;B. Khoo
超疏水表面已被证明能够降低微米和纳米流体应用中的流体阻力。本文的目的是给出采用具有交替微槽和肋条的超疏水表面的微通道中Stokes流动的解析解。给出了微槽平行和垂直于流动方向对齐的两种情况下的结果。还分析了在一个或两个沟道壁上图案化沟槽的影响。用无量纲有效滑移长度来量化流体阻力的减小，发现有效滑移长度随着无剪切分数和由通道半高归一化的每个凹槽-肋条组合的周期程度而单调增加。导出了归一化有效滑移长度与归一化槽肋周期的大、小极限值的渐近关系。对在一个或两个通道壁上形成图案的横向和纵向沟槽进行了详细的比较，以评估它们在提高有效滑移长度方面的有效性。对小的极限值和大的极限值，以及无剪切分数和归一化槽肋周期的有限值进行了比较。将归一化有效滑移长度对应于横向和纵向沟槽的结果进一步应用于采用超疏水表面的微通道中的Stokes流动的模拟，该表面包含与外加压力梯度方向成一定角度倾斜的周期性微槽阵列。给出了平行于外加压力梯度方向的归一化有效滑移长度和垂直于外加压力梯度方向的归一化横向流量。
Superhydrophobic surfaces have been demonstrated to be capable of reducing fluid resistance in micro- and nanofluidic applications. The objective of this paper is to present analytical solutions for the Stokes flow through microchannels employing superhydrophobic surfaces with alternating micro-grooves and ribs. Results are presented for both cases where the micro-grooves are aligned parallel and perpendicular to the flow direction. The effects of patterning the grooves on one or both channel walls are also analyzed. The reduction in fluid resistance has been quantified in terms of a dimensionless effective slip length, which is found to increase monotonically with the shear-free fraction and the periodic extent of each groove–rib combination normalized by the channel half-height. Asymptotic relationships have been derived for the normalized effective slip length corresponding to large and small limiting values of the shear-free fraction and the normalized groove–rib period. A detailed comparison has been made between transverse and longitudinal grooves, patterned on one or both channel walls, to assess their effectiveness in terms of enhancing the effective slip length. These comparisons have been carried out for small and large limiting values, as well as finite values of the shear-free fraction and normalized groove–rib period. Results for the normalized effective slip length corresponding to transverse and longitudinal grooves are further applied to model the Stokes flow through microchannels employing superhydrophobic surfaces containing a periodic array of micro-grooves inclined at an angle to the direction of the applied pressure gradient. Results are presented for the normalized effective slip lengths parallel to the direction of the applied pressure gradient and the normalized cross flow rate perpendicular to the direction of the applied pressure gradient.