Three-dimensional flows in slowly varying planar geometries

Eric Lauga, Abraham D. Stroock, Howard A. Stone

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


We consider laminar flow in channels constrained geometrically to remain between two parallel planes; this geometry is typical of microchannels obtained with a single step by current microfabrication techniques. For pressure-driven Stokes flow in this geometry and assuming that the channel dimensions change slowly in the streamwise direction, we show that the velocity component perpendicular to the constraint plane cannot be zero unless the channel has both constant curvature and constant cross-sectional width. This result implies that it is, in principle, possible to design "planar mixers," i.e., passive mixers for channels that are constrained to lie in a flat layer using only streamwise variations of their in-plane dimensions. Numerical results are presented for the case of a channel with sinusoidally varying width.

Original languageEnglish (US)
Pages (from-to)3051-3062
Number of pages12
JournalPhysics of Fluids
Issue number8
StatePublished - Aug 2004

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


Dive into the research topics of 'Three-dimensional flows in slowly varying planar geometries'. Together they form a unique fingerprint.

Cite this