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Effective slip boundary conditions for arbitrary periodic surfaces: the surface mobility tensor

Published online by Cambridge University Press:  16 July 2010

KEN KAMRIN ,
MARTIN Z. BAZANT  and
HOWARD A. STONE
KEN KAMRIN*
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 01238, USA
MARTIN Z. BAZANT
Affiliation:
Departments of Chemical Engineering and Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
HOWARD A. STONE
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: kkamrin@seas.harvard.edu
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Abstract

In a variety of applications, most notably microfluidics design, slip-based boundary conditions have been sought to characterize fluid flow over patterned surfaces. We focus on laminar shear flows over surfaces with periodic height fluctuations and/or fluctuating Navier scalar slip properties. We derive a general formula for the ‘effective slip’, which describes equivalent fluid motion at the mean surface as depicted by the linear velocity profile that arises far from it. We show that the slip and the applied stress are related linearly through a tensorial mobility matrix, and the method of domain perturbation is then used to derive an approximate formula for the mobility law directly in terms of surface properties. The specific accuracy of the approximation is detailed, and the mobility relation is then utilized to address several questions, such as the determination of optimal surface shapes and the effect of random surface fluctuations on fluid slip.

JFM classification

Mathematical Foundations: General fluid mechanics Low-Reynolds-number flows: Stokesian dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 409 - 437
Copyright
Copyright © Cambridge University Press 2010

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