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Tensorial hydrodynamic slip

Published online by Cambridge University Press:  01 October 2008

MARTIN Z. BAZANT  and
OLGA I. VINOGRADOVA
MARTIN Z. BAZANT
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA CNRS UMR Gulliver 7083 and PMMH 7636, École Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, F-75005 Paris, France
OLGA I. VINOGRADOVA
Affiliation:
A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31 Leninsky Prospect, 119991 Moscow, Russia CNRS UMR Gulliver 7083 and PMMH 7636, École Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, F-75005 Paris, France
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Abstract

We describe a tensorial generalization of the Navier slip boundary condition and illustrate its use in solving for flows around anisotropic textured surfaces. Tensorial slip can be derived from molecular or microstructural theories or simply postulated as a constitutive relation, subject to certain general constraints on the interfacial mobility. The power of the tensor formalism is to capture complicated effects of surface anisotropy, while preserving a simple fluid domain. This is demonstrated by exact solutions for laminar shear flow and pressure-driven flow between parallel plates of arbitrary and different textures. From such solutions, the effects of rotating a texture follow from simple matrix algebra. Our results may be useful for extracting local slip tensors from global measurements, such as the permeability of a textured channel or the force required to move a patterned surface, in experiments or simulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 613 , 25 October 2008 , pp. 125 - 134
Copyright
Copyright © Cambridge University Press 2008

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