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.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Gad-el-Hak , M., 1997, The MEMS Handbook, CRC Press, Boca Raton, FL.
Schaaf, S. A. , and Chambre, P. L. , 1961, Flow of Rarefied Gases, Princeton University Press, Princeton, NJ.
White, F. M. , 1974, Viscous Fluid Flow, McGraw-Hill, New York.
Tritton, D. J. , 1998, Physical Fluid Dynamics, Oxford University Press, New York.
Maxwell, J. C. , 1879, “ On Stresses in Rarefied Gases Arising From Inequalities of Temperature,” Philos. Trans. R. Soc., 170, pp. 231–256. [CrossRef]
Gad-el-Hak, M. , 1999, “ The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture,” ASME J. Fluids Eng., 121(1), pp. 5–33. [CrossRef]
Colin, S. , 2005, “ Rarefaction and Compressibility Effects on Steady and Transient Gas Flows in Microchannels,” Microfluid. Nanofluid., 1(3), pp. 268–279. [CrossRef]
Barber, R. W. , and Emerson, D. R. , 2006, “ Challenges in Modeling Gas-Phase Flow in Microchannels: From Slip to Transition,” Heat Transfer Eng., 27(4), pp. 3–12. [CrossRef]
Cercignani, C. , Lampis, M. , and Lozenzani, S. , 2004, “ Variational Approach to Gas Flows in Microchannels,” Phys. Fluids, 16(9), pp. 3426–3437. [CrossRef]
Xue, H. , Ji, H. M. , and Shu, C. , 2001, “ Analysis of Micro-Couette Flow Using the Burnett Equations,” Int. J. Heat Mass Transfer, 44(21), pp. 4139–4146. [CrossRef]
Cao, B. Y. , Chen, M. , and Guo, Z. Y. , 2004, “ Rarefied Gas Flow in Rough Microchannels by Molecular Dynamics Simulation,” Chin. Phys. Lett., 21(9), pp. 1777–1779. [CrossRef]
Stevanovic, N. D. , 2007, “ A New Analytical Solution of Microchannel Gas Flow,” J. Micromech. Microeng., 17(8), pp. 1695–1702. [CrossRef]
Harley, J. C. , Huang, Y. , and Bau, H. , 1995, “ Gas Flow in Microchannels,” J. Fluid Mech., 284, pp. 257–274. [CrossRef]
Arkilic, E. B. , Schmidt, M. A. , and Breuer, K. S. , 1994, “ Gaseous Flow in Microchannels,” Application of Microfabrication to Fluid Mechanics, Vol. FED-197, ASME, New York, pp. 57–66.
Arkilic, E. B. , Schmidt, M. A. , and Breuer, K. S. , 1997, “ Gaseous Slip Flow in Long Microchannels,” J. Microelectromech. Syst., 6(2), pp. 167–178. [CrossRef]
Zohar, Y. , Lee, S. Y. K. , Lee, W. Y. , Jiang, L. , and Tong, P. , 2002, “ Subsonic Gas Flow in a Straight and Uniform Microchannel,” J. Fluid Mech., 472, pp. 125–151. [CrossRef]
Shih, J. C. , Ho, C. M. , Liu, J. , and Tai, Y. C. , 1996, Monatomic and Polyatomic Gas Flow Through Uniform Microchannels, Vol. DSC-59, ASME, New York, pp. 197–203.
Takuto, A. , Soo, K. M. , Hiroshi, I. , and Kenjiro, S. , 2000, “ An Experimental Investigation of Gas Flow Characteristics in Microchannels,” International Heat Transfer and Transport Phenomena in Microscale Conference, Banf, AB, Canada, Oct. 15–20, pp. 155–161.
Turner, E. S. , Fagri, L. M. , and Gregory, O. G. , 2004, “ Experimental Investigation of Gas Flow in Microchannels,” ASME J. Heat Transfer, 126(5), pp. 753–763. [CrossRef]
Hsieh, S. S. , Tsai, H. H. , Lin, C. Y. , Huang, C. F. , and Chein, C. M. , 2004, “ Gas Flow in a Long Microchannel,” Int. J. Heat Mass Transfer, 47(17–18), pp. 3877–3887. [CrossRef]
Zahid, W. A. , Yin, Y. , and Zhu, K. Q. , 2007, “ Couette-Poiseuille Flow of a Gas in Long Microchannels,” Microfluid. Nanofluid., 3(1), pp. 55–64. [CrossRef]
Sreekanth, A. K. , 1969, “ Slip Flow Through Long Circular Tubes,” Proceedings of the 6th International Symposium on Rarefied Gas Dynamics, Academic Press, New York, pp. 667–680.
Maurer, J. , Tabeling, P. , Joseph, P. , and Williame, H. , 2003, “ Second-Order Slip Laws in Microchannels for Helium and Nitrogen,” Phys. Fluids, 15(9), pp. 2613–2621. [CrossRef]
Dongari, N. , Agrawal, A. , and Agrawal, A. , 2007, “ Analytical Solution of Gaseous Slip Flow in Long Microchannels,” Int. J. Heat Mass Transfer, 50(17–18), pp. 3411–3421. [CrossRef]
Ewart, T. , Perrier, P. , Graur, I. A. , and Meolans, J. G. , 2007, “ Mass Flow Rate Measurements in a Microchannel, From Hydrodynamic to Near Free Molecular Regimes,” J. Fluid Mech., 584, pp. 337–356. [CrossRef]
Dust, F. , Sambasivam, R. , and Filimonov, D. , 2013, “ Ideal Gas Flow Though Microchannels: Revisited,” Int. J. Eng. Appl. Sci., 2(1), pp. 44–63. [CrossRef]
Azad, Q. Z. , Amir, A. Z. , and Metin, R. , 2012, “ A Detailed Comparison Between Navier-Stokes and DMSC Simulation of Multicomponent Gaseous Flow in Microchannels,” Int. J. Heat Mass Transfer, 55(17), pp. 4673–4681.
Deng, Z. , Chen, Y. , and Shao, C. , 2016, “ Gas Flow Through Rough Microchannels in the Transition Flow Regime,” Phys. Rev. E, 93(1), p. 013128. [CrossRef] [PubMed]
Ebert, W. A. , and Sparrow, E. M. , 1965, “ Slip Flow in Rectangular and Annular Ducts,” J. Basic Eng., 87(4), pp. 1018–1024. [CrossRef]
Morini, G. L. , and Spiga, M. , 1998, “ Slip Flow in Rectangular Microtubes,” Microscale Thermophys. Eng., 2(4), pp. 273–282. [CrossRef]
Aubert, C. , and Colin, S. , 2001, “ Higher Order Boundary Conditions for Gaseous Flow in Rectangular Microducts,” Microscale Thermophys. Eng., 5(1), pp. 41–54. [CrossRef]
Deissler, R. G. , 1964, “ An Analysis of Second-Order Slip Flow and Temperature-Jump Boundary Conditions for Rarefied Gases,” Int. J. Heat Mass Transfer, 7(6), pp. 681–694. [CrossRef]
Colin, S. , Lalonde, P. , and Caen, R. , 2004, “ Validation of a Second-Order Slip Flow Model in Rectangular Microchannels,” Heat Transfer Eng., 25(3), pp. 23–30. [CrossRef]
Chen, C. S. , Lee, S. M. , and Sheu, J. D. , 1998, “ Numerical Analysis of Gas Flow in Microchannels,” Numer. Heat Transfer Part A, 33(7), pp. 749–762. [CrossRef]
Pong, K. C. , Ho, C. , Liu, J. , and Tai, Y. , 1994, “ Non-Linear Pressure Distribution in Uniform Microchannels,” Application of Microfabrication to Fluid Mechanics, Vol. FED-197, ASME, New York, pp. 51–56.
Roy, S. , Raju, R. , Chuang, H. , Kruden, B. , and Meyyappan, M. , 2003, “ Modeling Gas Flow Through Microchannels and Nanopores,” J. Appl. Phys., 93(8), pp. 4870–4879. [CrossRef]
Morini, G. L. , Spiga, M. , and Tartarani, P. , 2004, “ The Rarefaction Effect on the Friction Factor of Gas Flow in Microchannels,” Superlattices Microstruct., 35(3–6), pp. 587–599. [CrossRef]
Cai, C. P. , and Boyd, I. D. , 2007, “ Compressible Gas Flow Inside a Two-Dimensional Uniform Microchannel,” J. Thermophys. Heat Transfer, 21(3), pp. 608–615. [CrossRef]
Jain, V. , and Lin, C. X. , 2006, “ Numerical Modeling of Three-Dimensional Compressible Gas Flow in Microchannels,” J. Micromech. Microeng., 16(2), pp. 292–302. [CrossRef]
Morini, G. L. , Yang, Y. , and Lorenzini, M. , 2011, “ A Critical Review of the Measurement Techniques for the Analysis of Gas Microflows Through Microchannels,” Exp. Therm. Fluid Sci., 35(6), pp. 849–865. [CrossRef]
Karniadakis, G. E. , and Beskok, A. , 2002, Microflows: Fundamentals and Simulation, Springer, Berlin.
Arkilic, E. B. , Schmidt, M. A. , and Breuer, K. S. , 2001, “ Mass Flow and Tangential Momentum Accommodation Coefficient in Silicon Micromachined Channels,” J. Fluid Mech., 437, pp. 29–43. [CrossRef]
Srinivasan, K. , Subbarao, P. M. V. , Kale, S. R. , and Chandra, S. , 2007, “ Fabrication and Interface Characterization of a Microchannel System Using a Simple Alignment Technique,” Sens. Lett., 5(3), pp. 584–591.


Grahic Jump Location
Fig. 1

Schematic of microchannel geometry

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

Experimental setup

Grahic Jump Location
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

Grahic Jump Location
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



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In