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

Ken Kamrin, Martin Z. Bazant, Howard A. Stone

Research output: Contribution to journalArticlepeer-review

111 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)409-437
Number of pages29
JournalJournal of Fluid Mechanics
StatePublished - Sep 2010

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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


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