Back
 OJAppS  Vol.2 No.1 , March 2012
On Laminar Flow in Microfabricated Channels with Partial Semi-Circular Profiles
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/κ2.56. 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.
Cite this paper: nullW. Federspiel and I. Valenti, "On Laminar Flow in Microfabricated Channels with Partial Semi-Circular Profiles," Open Journal of Applied Sciences, Vol. 2 No. 1, 2012, pp. 28-34. doi: 10.4236/ojapps.2012.21003.
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

 
 
Top