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Effective slip boundary conditions for arbitrary one-dimensional surfaces
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- Journal:
- Journal of Fluid Mechanics / Volume 706 / 10 September 2012
- Published online by Cambridge University Press:
- 07 June 2012, pp. 108-117
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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.
, 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.EFFECTIVE SLIP LENGTH OF NANOSCALE MIXED-SLIP SURFACES
- Part of
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- Journal:
- The ANZIAM Journal / Volume 50 / Issue 3 / January 2009
- Published online by Cambridge University Press:
- 03 November 2009, pp. 381-394
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