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Research Papers: Fundamental Issues and Canonical Flows

A General Model for Predicting Low Reynolds Number Flow Pressure Drop in Non-Uniform Microchannels of Non-Circular Cross Section in Continuum and Slip-Flow Regimes

[+] Author and Article Information
M. Akbari

e-mail: dr.mohsen.akbari@gmail.com

A. Tamayol

Biomedical Engineering Department,
McGill University,
Montreal, QC, H3A 1A4, Canada;
Center for Biomedical Engineering,
Department of Medicine,
Brigham and Women's Hospital,
Harvard Medical School,
Cambridge, MA 02139;
Harvard-MIT Division of Health
Sciences and Technology,
Massachusetts Institute of Technology,
Cambridge, MA 02139

M. Bahrami

Laboratory for Alternative Energy
Conversion (LAEC),
Mechatronic System Engineering
School of Engineering Science,
Simon Fraser University,
Surrey, BC, V3T 0A3, Canada

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 24, 2012; final manuscript received February 14, 2013; published online May 17, 2013. Assoc. Editor: Z. C. Zheng.

J. Fluids Eng 135(7), 071205 (May 17, 2013) (7 pages) Paper No: FE-12-1211; doi: 10.1115/1.4023785 History: Received April 24, 2012; Revised February 14, 2013

A general model that predicts single-phase creeping flow pressure drop in microchannels of a noncircular cross section under slip and no-slip regimes is proposed. The model accounts for gradual variations in the cross section and relates the pressure drop to geometrical parameters of the cross section, i.e., area, perimeter, and polar moment of inertia. The accuracy of the proposed model is assessed by comparing the results against experimental and numerical data collected from various studies in the literature for a wide variety of cross-sectional shapes. The suggested model can be used for the design and optimization of microsystems that contain networks of microchannels with noncircular cross sections resulting from different fabrication techniques.

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Figures

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Fig. 1

Schematic of (a) a straight, and (b) a variable cross section microchannel of arbitrary cross section

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Fig. 2

Comparison of the proposed model for the no-slip condition and the available data for the (a) rectangular [15,38,38-40], (b) trapezoidal [26], and (c) circular sector [26], and circular segment [26] microchannels

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Fig. 3

Comparison of the proposed model for the slip condition and the available data in the literature for the (a) circular (Kim et al. [41]), (b) rectangular (Morini [9]), (c) trapezoidal (Araki et al. [42]), and (d) double-trapezoidal (Morini [9]) cross section microchannels

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Fig. 5

Comparison of the proposed unified model and experimental data of Akbari et al. [25] for the stream-wise periodic geometry with rectangular cross section. Each data point is averaged over the considered range of Reynolds numbers 2–15. The flow resistance is normalized with a reference straight channel. The geometrical parameters in this plot are the deviation parameter defined as ξ = δ/a0 and the average aspect ratio defined as ε0 = h/a0, where h is the channel height, a0 is the average width of the channel, and δ is the maximum deviation of the channel width from its average.

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Fig. 4

Schematic of the studied channel with the stream-wise periodic wall with a linear wall profile. The channel cross section is rectangular with constant channel depth.

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