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

    Cite this

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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.",
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    Reexamination of Hagen-Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels. / Mortensen, Asger; Okkels, Fridolin; Bruus, Henrik.

    In: Physical Review E, Vol. 71, No. 5, 2005, p. 057301.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Reexamination of Hagen-Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels

    AU - Mortensen, Asger

    AU - Okkels, Fridolin

    AU - Bruus, Henrik

    N1 - Copyright 2005 American Physical Society

    PY - 2005

    Y1 - 2005

    N2 - 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.

    AB - 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.

    U2 - 10.1103/PhysRevE.71.057301

    DO - 10.1103/PhysRevE.71.057301

    M3 - Journal article

    VL - 71

    SP - 057301

    JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

    JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

    SN - 2470-0045

    IS - 5

    ER -