Analysis of Stokes flow in microchannels with superhydrophobic surfaces containing a periodic array of micro-grooves |
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Authors: | C J Teo B C Khoo |
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Affiliation: | (1) Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore, 117576, Singapore |
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Abstract: | 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. |
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