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

Asger Mortensen, Fridolin Okkels, Henrik Bruus

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    Abstract

    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
    Volume71
    Issue number5
    Pages (from-to)057301
    ISSN2470-0045
    DOIs
    Publication statusPublished - 2005

    Bibliographical note

    Copyright 2005 American Physical Society

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