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

Asger Mortensen; Fridolin Okkels; Henrik Bruus

doi:10.1103/PhysRevE.71.057301

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 language	English
Journal	Physical Review E
Volume	71
Issue number	5
Pages (from-to)	057301
ISSN	2470-0045
DOIs	https://doi.org/10.1103/PhysRevE.71.057301
Publication status	Published - 2005

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title = "Reexamination of Hagen-Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels",

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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AU - Mortensen, Asger

AU - Okkels, Fridolin

AU - Bruus, Henrik

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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

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

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

SN - 2470-0045

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