Journal of Fluid Mechanics


Effective slip boundary conditions for arbitrary one-dimensional surfaces

Evgeny S. Asmolova1a2a3 c1 and Olga I. Vinogradovaa1a4a5

a1 A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31 Leninsky Prospect, 119991 Moscow, Russia

a2 Central Aero-Hydrodynamic Institute, 140180 Zhukovsky, Moscow region, Russia

a3 Institute of Mechanics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia

a4 Department of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia

a5 DWI, RWTH Aachen, Forckenbeckstr. 50, 52056 Aachen, Germany


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.

(Received March 03 2012)

(Reviewed April 21 2012)

(Accepted May 14 2012)

(Online publication June 07 2012)

Key Words:

  • low-Reynolds-number flows;
  • microfluidics;
  • effective slip


c1 Email address for correspondence:

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