Three-dimensional flows in slowly-varying planar geometries

Details Three-dimensional flows in slowly-varying planar geometries Three-dimensional flows in slowly-varying planar geometries

2003-06-23

arxiv.org/abs/cond-mat/0306572v2

Phys. Fluids (2004) 16, 3051-3062

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

10.1063/1.1760105

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.

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