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Research Papers: Fundamental Issues and Canonical Flows

Slip-Flow Pressure Drop in Microchannels of General Cross Section

[+] Author and Article Information
M. Bahrami1

Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, BC, V3T 0A3, Canadambahrami@sfu.ca

A. Tamayol

Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, BC, V3T 0A3, Canadaata42@sfu.ca

P. Taheri

Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, Stn. CSC, Victoria, BC, V8W 3P6, Canada

1

Corresponding author.

J. Fluids Eng 131(3), 031201 (Feb 05, 2009) (8 pages) doi:10.1115/1.3059699 History: Received April 09, 2008; Revised October 02, 2008; Published February 05, 2009

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami (2006, “Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section  ,” ASME J. Fluids Eng., 128, pp. 1036–1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flow in arbitrary cross section microchannel

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Figure 2

Comparison of the model with experimental data of Kim (4) for circular channels

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Figure 3

Comparison of the model with numerical results of Morini (19) for rectangular channels

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Figure 4

Comparison of the model with experimental data of Araki (18) for trapezoidal channels (α=54.74 deg)

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Figure 5

Comparison of the model with numerical data of Morini (19) for double-trapezoidal conduits

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