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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Lauga, E., Stroock, A. D., and Stone, H. A., 2004, “Three-Dimensional Flows in Slowly Varying Planar Geometries,” Phys. Fluids, 16, p. 3051. [CrossRef]
Juncker, D., Schmid, H., Drechsler, U., Wolf, H., Wolf, M., Michel, B., de Rooij, N., and Delamarche, E., 2002, “Autonomous Microfluidic Capillary System,” Anal. Chem., 74(24), pp. 6139–6144. [CrossRef] [PubMed]
Gunda, N. S. K., Joseph, J., Tamayol, A., Akbari, M., and Mitra, S. K., 2013, “Measurement of Pressure Drop and Flow Resistance in Microchannels With Integrated Micropillars,” Microfluid. Nanofluid.14(3-4), pp. 711–721. [CrossRef]
Fatanat-Didar, T., and Tabrizian, M., 2012, “Generating Multiplex Gradients of Biomolecules for Controlling Cellular Adhesion in Parallel Microfluidic Channels,” Lab Chip, 12, pp. 4363–4371. [CrossRef] [PubMed]
Kim, S. M., Sommer, G. J., Burns, M. A., and Hasselbrink, E. F., 2006, “Low-Power Concentration and Separation Using Temperature Gradient Focusing via Joule Heating,” Anal. Chem., 78(23), pp. 8028–8035. [CrossRef] [PubMed]
Akbari, M., Bahrami, M., and Sinton, D., 2012, “Optothermal Sample Preconcentration and Manipulation With Temperature Gradient Focusing,” Microfluid. Nanofluid., 12(1), pp. 221–228. [CrossRef]
Khademhosseini, A., Langer, R., Borenstein, J., and Vacanti, J. P., 2006, “Microscale Technologies for Tissue Engineering and Biology,” Proc. Natl. Acad. Sci. U.S.A., 103(8), pp. 2480–2487. [CrossRef] [PubMed]
Tamayol, A., Akbari, M., Annabi, N., Paul, A., Khademhosseini, A., and Juncker, D., 2012, “Fiber-Based Tissue Engineering: Progress, Challenges, and Opportunities,” Biotechnol. Adv. (in press). [CrossRef]
Morini, G. L., 2004, “Laminar-to-Turbulent Flow Transition in Microchannels,” Nanoscale Microscale Thermophys. Eng., 8(1), pp. 15–30. [CrossRef]
McDonald, J. C., Duffy, D. C., Anderson, J. R., Chiu, D. T., Wu, H., Schueller, O. J. A., and Whitesides, G. M., 2000, “Fabrication of Microfluidic Systems in Poly (Dimethylsiloxane),” Electrophoresis, 21(1), pp. 27–40. [CrossRef] [PubMed]
Oliveira, M. S. N., Alves, M. A., Pinho, F. T., and McKinley, G. H., 2007, “Viscous Flow Through Microfabricated Hyperbolic Contractions,” Exp. Fluids, 43(2), pp. 437–451. [CrossRef]
Akbari, M., Sinton, D., and Bahrami, M., 2011, “Geometrical Effects on the Temperature Distribution in a Half-Space Due to a Moving Heat Source,” ASME J. Heat Transfer, 133, p. 064502. [CrossRef]
Sparrow, E. M., and Prata, A. T., 1983, “Numerical Solutions for Laminar Flow and Heat Transfer in a Periodically Converging-Diverging Tube, With Experimental Confirmation,” Numer. Heat Transfer, Part A, 6(4), pp. 441–461.
Hemmat, M., and Borhan, A., 1995, “Creeping Flow Through Sinusoidally Constricted Capillaries,” Phys. Fluids, 7(9), pp. 2111–2121. [CrossRef]
Liu, D., and Garimella, S. V., 2004, “Investigation of Liquid Flow in Microchannels,” J. Thermophys. Heat Transfer, 18(1), pp. 65–72. [CrossRef]
Akbari, M., Sinton, D., and Bahrami, M., 2010, “Laminar Fully Developed Flow in Periodically Converging–Diverging Microtubes,” Heat Transfer Eng., 31(8), pp. 628–634. [CrossRef]
Akbari, M., Sinton, D., and Bahrami, M., 2011, “Viscous Flow in Variable Cross-Section Microchannels of Arbitrary Shapes,” Int. J. Heat Mass Transfer, 54(17), pp. 3970–3978. [CrossRef]
Tamayol, A., and Bahrami, M., 2010, “Laminar Flow in Microchannels With Noncircular Cross Section,” ASME J. Fluids Eng., 132(11), p. 111201. [CrossRef]
Kim, C., Lee, K., Kim, J. H., Shin, K. S., Lee, K. J., Kim, T. S., and Kang, J. Y., 2008, “A Serial Dilution Microfluidic Device Using a Ladder Network Generating Logarithmic or Linear Concentrations,” Lab Chip, 8(3), pp. 473–479. [CrossRef] [PubMed]
Muzychka, Y., and Yovanovich, M., 2009, “Pressure Drop in Laminar Developing Flow in Noncircular Ducts: A Scaling and Modeling Approach,” ASME J. Fluids Eng., 131(11), p. 111105. [CrossRef]
Muzychka, Y. S., and Yovanovich, M. M., 2002, “Laminar Flow Friction and Heat Transfer in Non-Circular Ducts and Channels—Part I: Hydrodynamic Problem,” Proceedings of Compact Heat Exchangers: A Festschrift on the 60th Birthday of Ramesh K. Shah, pp. 123–130.
Bahrami, M., Yovanovich, M. M., and Culham, J. R., 2006, “Pressure Drop of Fully-Developed, Laminar Flow in Microchannels of Arbitrary Cross-Section,” ASME J. Fluids Eng., 128, pp. 1036–1044. [CrossRef]
Bahrami, M., Tamayol, A., and Taheri, P., 2009, “Slip-Flow Pressure Drop in Microchannels of General Cross Section,” ASME J. Fluids Eng., 131, p. 031201. [CrossRef]
Tamayol, A., and Hooman, K., 2011, “Slip-Flow in Microchannels of Non-Circular Cross Sections,” ASME J. Fluids Eng., 133, p. 091202. [CrossRef]
Akbari, M., Bahrami, M., and Sinton, D., 2011, “Viscous Flow in Arbitrary Cross-Section Microchannels of Arbitrary Shape,” Int. J. Heat Mass Transfer, 54, pp. 3970–3978. [CrossRef]
Shah, R. K., London, A. L., and White, F. M., 1980, “Laminar Flow Forced Convection in Ducts,” ASME J. Fluids Eng., 102, pp. 256–258. [CrossRef]
White, F. M., 1991, Viscous Fluid Flow, McGraw-Hill New York.
Muzychka, Y. S., and Yovanovich, M. M., 2001, “Thermal Resistance Models for Non-Circular Moving Heat Sources on a Half Space,” ASME J. Heat Transfer, 123(4), pp. 624–632. [CrossRef]
Taheri, P., Torrilhon, M., and Struchtrup, H., 2009, “Couette and Poiseuille Microflows: Analytical Solutions for Regularized 13-Moment Equations,” Phys. Fluids, 21, p. 017102. [CrossRef]
Roy, S., Raju, R., Chuang, H. F., Cruden, B. A., and Meyyappan, M., 2003, “Modeling Gas Flow Through Microchannels and Nanopores,” J. Appl. Phys., 93, pp. 4870–4879. [CrossRef]
Renksizbulut, M., Niazmand, H., and Tercan, G., 2006, “Slip-Flow and Heat Transfer in Rectangular Microchannels With Constant Wall Temperature,” Int. J. Therm. Sci., 45(9), pp. 870–881. [CrossRef]
Karniadakis, G., Beşkök, A., and Aluru, N. R., 2005, Microflows and Nanoflows: Fundamentals and Simulations, Springer Verlag, Berlin.
Manton, M. J., 1971, “Low Reynolds Number Flow in Slowly Varying Axisymmetric Tubes,” J. Fluid Mech., 49(03), pp. 451–459. [CrossRef]
Chow, J. C. F., and Soda, K., 1972, “Laminar Flow in Tubes With Constriction,” Phys. Fluids, 15, p. 1700. [CrossRef]
Van Dyke, M., 1987, “Slow Variations in Continuum Mechanics,” Adv. Appl. Mech., 25, pp. 1–45. [CrossRef]
Wild, R., Pedley, T. J., and Riley, D. S., 1977, “Viscous Flow in Collapsible Tubes of Slowly Varying Elliptical Cross-Section,” J. Fluid Mech., 81(02), pp. 273–294. [CrossRef]
Wu, H. Y., and Cheng, P., 2003, “Friction Factors in Smooth Trapezoidal Silicon Microchannels With Different Aspect Ratios,” Int. J. Heat Mass Transfer, 46(14), p. 2519. [CrossRef]
Stanley, R. S., Ameel, T. A., and Barron, R. F., 1997, “Two-Phase Flow in Microchannels,” DTIC Document.
Papautsky, I., Ameel, T., and Frazier, A. B., “A Review of Laminar Single-Phase Flow in Microchannels,” Proceedings of the International Mechanical Engineers Congress Expos (IMECE), pp. 3067–3075.
Akbari, M., Sinton, D., and Bahrami, M., 2009, “Pressure Drop in Rectangular Microchannels as Compared With Theory Based on Arbitrary Cross Section,” ASME J. Fluids Eng., 131, p. 041202. [CrossRef]
Kim, M. S., Araki, T., Inaoka, K., and Suzuki, K., 2000, “Gas Flow Characteristics in Microtubes,” JSME Int. J. Ser. B, 43(4), pp. 634–639. [CrossRef]
Araki, T., Kim, M. S., Iwai, H., and Suzuki, K., 2002, “An Experimental Investigation of Gaseous Flow Characteristics in Microchannels,” Nanoscale Microscale Thermophys. Eng., 6(2), pp. 117–130. [CrossRef]


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
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.




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