Reexamination of Hagen-Poiseuille flow: shape dependence of the hydraulic resistance in microchannels.
We consider pressure-driven, steady-state Poiseuille flow in straight channels with various cross-sectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C= P2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness of surface-related phenomena central to lab-on-a-chip applications. This measure also provides a simple way to evaluate the hydraulic resistance for the various shapes.
Mortensen
Niels Asger
NA
MIC, Department of Micro and Nanotechnology, Bldg. 345 east, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
Okkels
Fridolin
F
Bruus
Henrik
H