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Effective slip boundary conditions for arbitrary one-dimensional surfaces

Published online by Cambridge University Press:  07 June 2012

Evgeny S. Asmolov  and
Olga I. Vinogradova
Evgeny S. Asmolov*
Affiliation:
A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31 Leninsky Prospect, 119991 Moscow, Russia Central Aero-Hydrodynamic Institute, 140180 Zhukovsky, Moscow region, Russia Institute of Mechanics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
Olga I. Vinogradova
Affiliation:
A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31 Leninsky Prospect, 119991 Moscow, Russia Department of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia DWI, RWTH Aachen, Forckenbeckstr. 50, 52056 Aachen, Germany
*
†Email address for correspondence: [email protected]
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Abstract

In many applications it is advantageous to construct effective slip boundary conditions, which could fully characterize flow over patterned surfaces. Here we focus on laminar shear flows over smooth anisotropic surfaces with arbitrary scalar slip , varying in only one direction. We derive general expressions for eigenvalues of the effective slip-length tensor, and show that the transverse component is equal to half of the longitudinal one, with a two times larger local slip, . A remarkable corollary of this relation is that the flow along any direction of the one-dimensional surface can be easily determined, once the longitudinal component of the effective slip tensor is found from the known spatially non-uniform scalar slip.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 706 , 10 September 2012 , pp. 108 - 117
Copyright
Copyright © Cambridge University Press 2012

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