On Laminar Flow in Microfabricated Channels with Partial Semi-Circular Profiles

William J. Federspiel, Isabella Valenti

Medical Devices Laboratory, McGowan Institute for Regenerative Medicine, University of Pittsburgh.
Medical Devices Laboratory, McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, USA.

DOI: 10.4236/ojapps.2012.21003                

Abstract

Soft and hard micromachining techniques used to develop microfluidic devices can yield microchannels of many different cross-sectional profiles. For semi-circular microchannels, these techniques often produce only partialsemicircular (PSC) cross-sections. This study investigated fully developed laminar flow in PSC microchannels as a function of a circularity index, κ, defined as the ratio of the radiuses along the curved and flat surfaces of the PSC profile. A correction factor, K, to the Hagen-Poiseuille relation was determined and was well-fitted by the power-law relationship K=5.299/κ^2.56. Actual correction factors were compared to estimates based on several hydraulic models for flow in microchannels of arbitrary cross-section, as well as the half-ellipsoid cross-section. The level of wall shear stress, when normalized by the pressure drop per unit length, increased approximately linearly with increase in the circularity index, κ.

Keywords

Hagen-Poiseuille Flow; Poiseuille Flow; Flow Resistance; Wall Shear Stress

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	G. M. Whitesides and S. K. Sia, “Microfluidic Devices Fabricated in Poly(Dimethylsiloxane) for Biological Studies,” Electropheresis, Vol. 24, No. 21, 2003, pp. 3563-3576. doi:10.1002/elps.200305584
[2]	B. Ziaie, A. Baldi, M. Lei, Y. Gu and R. A. Siegel, “Hard and Soft Micromachining for BioMEMS: Review of Techniques and Examples of Applications in Microfluidics and Drug Delivery,” Advanced Drug Delivery Reviews, Vol. 56, No. 2, 2004, pp. 145-172. doi:10.1016/jaddr.2003.09.001
[3]	J. T. Borenstein, H. Terai, K. R. King, E. J. Weinberg, M. R. Kaazempur-Mofrad and J. P. Vacanti, “Microfabrication Technology for Vascularized Tissue Engineering,” Biomedical Microdevices, Vol. 4, No. 3, 2002, pp. 167- 175. doi:10.1023/A:1016040212127
[4]	M. Shin, M. K. Matsuda, O, Ishii, H. Terai, M. Kaazempur-Mofrad, J. Borenstein, M. Detmar and J. P. Vacanti, “Endothelialized Networks with a Vascular Geometry in Microfabricated Poly(Dimethyl Siloxane),” Biomedical Microdevices, Vol. 6, No. 4, 2004, pp. 269-278.
[5]	M. D. S. Frame, G. B. Chapman, Y. Makino and I. H. Sarelius, “Shear Stress Gradient over Endothelial Cells in a Curved Microchannel System,” Biorheology, Vol. 35, No. 4, 1998, pp. 245-261. doi:10.1016/S0006-355X(99)80009-2
[6]	O. L. Li, Y. L. Tong, Z. G. Chen, C. Liu, S. Zhao and J. Y. Mo, “A Glass/PDMS Hybrid Microfluidic Chip Embedded with Integrated Electrodes for Contactless Conductivity Detection,” Chromatographia, Vol. 68, No. 11, 2008, pp. 1039-1044. doi:10.1365/s10337-008-0808-y
[7]	C. H. Lin and G. B. Lee, “Micromachined Flow Cytometers with Embedded Etched Optic Fibers for Optical Detection,” Journal of Micromechanics and Microengineering, Vol. 13, No. 3, 2003, pp. 447-453. doi:10.1088/0960-1317/13/3/315
[8]	A. Homsy, S. Koster, J. C. T. Eijkel, A. Van den Berg, F. Lucklum, E. Verpoorte and N. F. de Rooij, “A High Current Density DC Magnetohydrodynamic (MHD) Micropump,” Lap on a Chip, Vol. 5, No. 4, 2005, pp. 466-471. doi:10.1039/b417892k
[9]	B. A. Peeni, D. B. Conkey, J. P. Barber, R. T. Kelly, M. L. Lee, A. T. Woolley and A. R. Hawkins, “Planar Thin Film Device for Capillary Electrophoresis,” Lap on a Chip, Vol. 5, No. 2, 2005, pp. 501-505. doi:10.1039/b500870k
[10]	K. Burgess, H. H. Hu, W. Wagner and W. J. Federspiel, “Towards Microfabricated Biohybrid Artificial Lung Modules for Chronic Respiratory Support,” Biomedical Microdevices, Vol. 11, No. 1, 2009, pp. 117-127. doi:10.1159/000331400
[11]	E. Oosterbroek, “Modeling, Design and Realization of Microfluidics Components,” Ph.D. Thesis, University of Twente, Enschede, 1999.
[12]	N. A. Mortensen, F. Okkels and H. Bruus, “Reexamination of Hagen-Poiseuille Flow: Shape Dependence of the Hydraulic Resistance in Microchannels,” Physical Review E, Vol. 71, No. 5, 2005, Article ID: 057301. doi:10.1103/PhysRevE.71.057301
[13]	M. Bahrami, M. Yovanovich and R. J. Culham, “A Novel Solution for Pressure Drop in Singly Connected Microchannels of Arbitrary Cross-Section,” International Jour- nal of Heat and Mass Transfer, Vol. 50, No. 13-14, 2007, pp. 2492-2502. doi:10.1016/j.ijheatmasstransfer.2006.12.019