Three-dimensional flows in slowly-varying planar geometries

TL;DR

This paper analyzes laminar flow in slowly varying planar microchannels, revealing conditions under which perpendicular flow components arise, and proposes the design of passive planar mixers based on streamwise dimension variations.

Contribution

It demonstrates that perpendicular flow components occur unless the channel has constant curvature and width, enabling the design of passive planar mixers using in-plane dimension variations.

Findings

Perpendicular flow component exists unless channel has constant curvature and width.

Passive planar mixers can be designed with streamwise in-plane dimension variations.

Numerical simulations confirm flow behavior in sinusoidally varying channels.

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.