Three-dimensional flows in slowly-varying planar geometries

Abstract

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.

Cited by in corpus (10)

• Tensorial hydrodynamic slip
• Flow rate--pressure drop relation for deformable shallow microfluidic channels
• Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: applications to Coanda effect in cardiology
• Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits
• Secondary flows of viscoelastic fluids in serpentine microchannels
• The motion of a deforming capsule through a corner
• Reduced models of unidirectional flows in compliant rectangular ducts at finite Reynolds number
• Giant enhancement of hydrodynamically enforced entropic trapping in thin channels
• Slow flow in channels with porous walls
• Simplified models for unsteady three-dimensional flows in slowly varying microchannels