Journal of Fluid Mechanics

Papers

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

KEN KAMRINa1 c1, MARTIN Z. BAZANTa2 and HOWARD A. STONEa3

a1 School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 01238, USA

a2 Departments of Chemical Engineering and Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

a3 Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA

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.

(Received November 07 2009)

(Revised April 09 2010)

(Accepted April 10 2010)

(Online publication July 16 2010)

Key words:

  • general fluid mechanics;
  • micro-/nanofluid dynamics;
  • Stokesian dynamics

Correspondence:

c1 Email address for correspondence: kkamrin@seas.harvard.edu

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