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Effective slip in pressure-driven flow past super-hydrophobic stripes

Published online by Cambridge University Press:  19 May 2010

A. V. BELYAEV  and
O. I. VINOGRADOVA
A. V. BELYAEV
Affiliation:
Departments of Physics and Chemistry, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31 Leninsky Prospect, 119991 Moscow, Russia
O. I. VINOGRADOVA*
Affiliation:
Departments of Physics and Chemistry, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31 Leninsky Prospect, 119991 Moscow, Russia ITMC and DWI, RWTH Aachen, Pauwelsstrasse 8, 52056 Aachen, Germany
*
†Email address for correspondence: [email protected]
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Abstract

A super-hydrophobic array of grooves containing trapped gas (stripes) has the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused on idealized cases of stick-perfect slip stripes. Here, we analyse the experimentally more relevant situation of a pressure-driven flow past striped slip-stick surfaces with arbitrary local slip at the gas sectors. We derive approximate formulas for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that are in a good agreement with the exact numerical solution for any surface slip fraction. By representing eigenvalues of the slip length tensor, we obtain the effective slip for any orientation of stripes with respect to the mean flow. Our results imply that flow past stripes is controlled by the ratio of the local slip length to texture size. In the case of a large (compared to the texture period) slip at the gas areas, surface anisotropy leads to a tensorial effective slip, by attaining the values predicted earlier for a perfect local slip. Both effective slip lengths and anisotropy of the flow decrease when local slip becomes of the order of texture period. In the case of a small slip, we predict simple surface-averaged isotropic flows (independent of orientation).

Type
Papers
Information
Journal of Fluid Mechanics , Volume 652 , 10 June 2010 , pp. 489 - 499
Copyright
Copyright © Cambridge University Press 2010

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