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

  • KEN KAMRIN (a1), MARTIN Z. BAZANT (a2) and HOWARD A. STONE (a3)
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.

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Email address for correspondence: kkamrin@seas.harvard.edu
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

E. J. Hinch 1991 Perturbation Methods. Cambridge University Press.

S. Torquato 2002 Random Heterogeneous Materials. Springer.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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