Effective slip boundary conditions for arbitrary one-dimensional surfaces

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 $b(y)$ , varying in only one direction. We derive gen...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 706; pp. 108 - 117
Main Authors Asmolov, Evgeny S., Vinogradova, Olga I.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 10.09.2012
Subjects
Boundary conditions
Eigenvalues
Fluid dynamics
Fluid mechanics
Laminar
Mathematical analysis
Reynolds number
Scalars
Slip
Tensors
effective slip
low-Reynolds-number flows
microfluidics
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Summary: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 $b(y)$ , 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, $2b(y)$ . 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.
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content type line 23
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2012.228