Reexamination of Hagen-Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels

Publication: Research - peer-reviewJournal article – Annual report year: 2005

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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= P-2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor a. We find that a 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.
Original languageEnglish
JournalPhysical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Publication date2005
Volume71
Issue5
Pages057301
ISSN1539-3755
DOIs
StatePublished

Bibliographical note

Copyright 2005 American Physical Society

CitationsWeb of Science® Times Cited: 55
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