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Research Papers: Fundamental Issues and Canonical Flows

Experimental and Numerical Studies on Gas Flow Through Silicon Microchannels

[+] Author and Article Information
K. Srinivasan

Department of Mechanical Engineering,
Indian Institute of Technology Delhi,
New Delhi 110016, India;
Research and Development Centre,
BMS College of Engineering,
Bangalore 560019, India
e-mails: srinivasank@bmsce.ac.in; ksrini23@gmail.com

P. M. V. Subbarao

Department of Mechanical Engineering,
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mail: pmvs@mech.iitd.ac.in

S. R. Kale

Department of Mechanical Engineering,
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mail: srk@mech.iitd.ac.in

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 2, 2016; final manuscript received February 26, 2017; published online June 5, 2017. Assoc. Editor: Moran Wang.

J. Fluids Eng 139(8), 081205 (Jun 05, 2017) (12 pages) Paper No: FE-16-1717; doi: 10.1115/1.4036249 History: Received November 02, 2016; Revised February 26, 2017

The present work investigates the extension of Navier–Stokes equations from slip-to-transition regimes with higher-order slip boundary condition. To achieve this, a slip model based on the second-order slip boundary condition was derived and a special procedure was developed to simulate slip models using FLUENT®. The boundary profile for both top and bottom walls was solved for each pressure ratio by the customized user-defined function and then passed to the FLUENT® solver. The flow characteristics in microchannels of various aspect ratios (a = H/W = 0.002, 0.01, and 0.1) by generating accurate and high-resolution experimental data along with the computational validation was studied. For that, microchannel system was fabricated in silicon wafers with controlled surface structure and each system has several identical microchannels of same dimensions in parallel and the processed wafer was bonded with a plane wafer. The increased flow rate reduced uncertainty substantially. The experiments were performed up to maximum outlet Knudsen number of 1.01 with nitrogen and the second-order slip coefficients were found to be C1 = 1.119–1.288 (TMAC = 0.944–0.874) and C2 = 0.34.

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Figures

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Fig. 1

Schematic of microchannel geometry

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Fig. 2

Relative magnitudes of the three terms of Eq. (20)

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Fig. 3

Comparison of (a) centerline u-velocity along x-axis with the numerical solutions of Ref. [31], (b) velocity profile taken along the channel length with Ref. [31], and (c) mass flow rates with Refs. [15], [31], and [33] for slip and no-slip conditions at Kno = 0.155 for a helium gas

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Fig. 4

Comparison of mass flow rate with pressure ratio for channel aspect ratio of 0.01 at (a) Kno = 0.3 of nitrogen and (b) Kno = 0.47 of helium

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Fig. 5

Microchannel sketch with inlet and outlet plenum: (a) before bonding and (b) after bonding (not to scale)

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Fig. 6

Experimental setup

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Fig. 7(a)

Comparison of experimental and numerical values of mass flow rates at Kno = 0.652, a = 0.01, and pout = 1.1 × 104 Pa, (b) centerline pressure distribution along x-axis for nitrogen at Kno = 0.652, (c) velocity profile taken at three places along the channel length for nitrogen at Kno = 0.652, and (d) v-velocity in the y-direction at three different sections along the length of the microchannel

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Fig. 8

Comparison of experimental and numerical values of mass flow rates at (a) Kno = 0.772, a = 0.01, and pout = 9.3 × 103  Pa, (b) Kno = 0.896, a = 0.01, and pout = 8.01 × 103  Pa, (c) Kno = 1.012, a = 0.01, and pout = 7.1 × 103  Pa, and (d) the variation of TMAC with respect to change in outlet Kn numbers

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