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Inertial effects on the generation of co-laminar flows

Published online by Cambridge University Press:  12 February 2015

William A. Braff ,
Martin Z. Bazant  and
Cullen R. Buie
William A. Braff
Affiliation:
Giner Inc., Newton, MA 02466, USA Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Martin Z. Bazant
Affiliation:
Departments of Chemical Engineering and Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Cullen R. Buie*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

The assumption of low Reynolds number flow, or Stokes flow, is often applied to the understanding of a broad range of microfluidic devices, including micro-reactors, biomedical devices, and membraneless electrochemical cells. However, recent studies have shown that various inertial effects can play a significant role, even in microfluidic systems. In this work, two- and three-dimensional secondary flows are identified in a generic rectangular flow channel design consisting of a secondary channel feeding fluid into a main channel. We identify a scaling argument which is able to predict the occurrence of these secondary flows as a function of system parameters. The impact of these behaviours on the assumption of fully developed colaminar flow is investigated. This work considers a representative geometry, and identifies a set of conditions where inertial effects can play a key role in a microfluidic device.

JFM classification

Reacting Flows: Laminar reacting flows Micro-/Nano-fluid dynamics: Microfluidics Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , pp. 85 - 94
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Copyright
© 2015 Cambridge University Press 

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References

Berger, S. A., Talbot, L. & Yao, L. S. 1983 Flow in curved pipes. Annu. Rev. Fluid Mech. 15, 461–512.CrossRefGoogle Scholar
Braff, W. A., Bazant, M. Z. & Buie, C. R. 2013a Membrane-less hydrogen bromine flow battery. Nat. Commun. 4, 2346.CrossRefGoogle ScholarPubMed
Braff, W. A., Buie, C. R. & Bazant, M. Z. 2013b Boundary layer analysis of membraneless electrochemical cells. J. Electrochem. Soc. 160 (11), A2056–A2063.CrossRefGoogle Scholar
Braff, W. A., Buie, C. R. & Bazant, M. Z. 2013c Numerical and analytic modeling of a membraneless hydrogen bromine laminar flow battery. ECS Trans. 53 (7), 51–62.CrossRefGoogle Scholar
Chiu, D. T. 2006 Cellular manipulations in microvortices. Anal. Bioanal. Chem. 387 (1), 17–20.CrossRefGoogle Scholar
Dean, W. R. 1927 Note on the motion of fluid in a curved pipe. Phil. Mag. 4 (20), 208–223.CrossRefGoogle Scholar
Di Carlo, D. 2009 Inertial microfluidics. Lab on a Chip 9 (21), 3038–3046.CrossRefGoogle ScholarPubMed
Eyal, S. & Quake, S. R. 2002 Velocity-independent microfluidic flow cytometry. Electrophoresis 23, 2653–2657.3.0.CO;2-H>CrossRefGoogle ScholarPubMed
Gambin, Y., Vandelinder, V., Ferreon, A. C. M., Lemke, E. A., Groisman, A. & Deniz, A. A. 2011 Visualizing a one-way protein encounter complex by ultrafast single-molecule mixing. Nat. Meth. 8 (3), 239–241.CrossRefGoogle ScholarPubMed
Guglielmini, L., Rusconi, R, Lecuyer, S & Stone, H. A. 2010 Three-dimensional features in low-Reynolds-number confined corner flows. J. Fluid Mech. 668, 33–57.CrossRefGoogle Scholar
Ismagilov, R. F., Stroock, A. D., Kenis, P. J. A., Whitesides, G. & Stone, H. A. 2000 Experimental and theoretical scaling laws for transverse diffusive broadening in two-phase laminar flows in microchannels. Appl. Phys. Lett. 76 (17), 2376–2378.CrossRefGoogle Scholar
Jayashree, R. S., Gancs, L., Choban, E. R., Primak, A., Natarajan, D., Markoski, L. J. & Kenis, P. J. A. 2005 Air-breathing laminar flow-based microfluidic fuel cell. J. Am. Chem. Soc. 127 (48), 16758–16759.CrossRefGoogle ScholarPubMed
Jayashree, R. S., Yoon, S. K., Brushett, F. R., Lopez-Montesinos, P. O., Natarajan, D., Markoski, L. J. & Kenis, P. J. A. 2010 On the performance of membraneless laminar flow-based fuel cells. J. Power Sources 195 (11), 3569–3578.CrossRefGoogle Scholar
Kenis, P. J. A., Ismagilov, R. F. & Whitesides, G. M. 1999 Microfabrication inside capillaries using multiphase laminar flow patterning. Science 285 (5424), 83–85.CrossRefGoogle ScholarPubMed
Kundu, P. K., Cohen, I. M. & Dowling, D. R. 2012 Fluid Mechanics, 5th edn. Academic.Google Scholar
Lauga, E., Stroock, A. D. & Stone, H. A. 2004 Three-dimensional flows in slowly varying planar geometries. Phys. Fluids 16 (8), 3051–3062.CrossRefGoogle Scholar
Mao, X., Nawaz, A. A., Lin, S.-C. S., Lapsley, M. I., Zhao, Y., McCoy, J. P., El-Deiry, W. S. & Huang, T. J. 2012 An integrated, multiparametric flow cytometry chip using ‘microfluidic drifting’ based three-dimensional hydrodynamic focusing. Biomicrofluidics 6 (2), 24113–241139.CrossRefGoogle ScholarPubMed
Nasir, M., Mott, D. R., Kennedy, M. J., Golden, J. P. & Ligler, F. S. 2011 Parameters affecting the shape of a hydrodynamically focused stream. Microfluid. Nanofluid. 11 (2), 119–128.CrossRefGoogle Scholar
Norouzi, M. & Biglari, N. 2013 An analytical solution for Dean flow in curved ducts with rectangular cross section. Phys. Fluids 25 (5), 053602.CrossRefGoogle Scholar
Rusconi, R., Lecuyer, S., Guglielmini, L. & Stone, H. A. 2010 Laminar flow around corners triggers the formation of biofilm streamers. J. R. Soc. Interface 7 (50), 1293–1299.CrossRefGoogle ScholarPubMed
Salloum, K. S. & Posner, J. D. 2010 Counter flow membraneless microfluidic fuel cell. J. Power Sources 195 (19), 6941–6944.CrossRefGoogle Scholar
Shankar, P. N. 2000 On Stokes flow in a semi-infinite wedge. J. Fluid Mech. 422, 69–90.CrossRefGoogle Scholar
Sprague, I. B. & Dutta, P. 2012 Depth averaged analytic solution for a laminar flow fuel cell with electric double layer effects. SIAM J. Appl. Maths 72 (4), 1149–1168.CrossRefGoogle Scholar
Sudarsan, A. P. & Ugaz, V. M. 2006 Multivortex micromixing. Proc. Natl Acad. Sci. USA 103 (19), 7228–7233.CrossRefGoogle ScholarPubMed
Thorson, M. R., Brushett, F. R., Timberg, C. J. & Kenis, P. J. A. 2012 Design rules for electrode arrangement in an air-breathing alkaline direct methanol laminar flow fuel cell. J. Power Sources 218 (C), 28–33.CrossRefGoogle Scholar
Van Hirtum, A., Grandchamp, X. & Cisonni, J. 2012 Reynolds number dependence of near field vortex motion downstream from an asymmetrical nozzle. Mech. Res. Commun. 44, 47–50.CrossRefGoogle Scholar
Zhang, J., Li, M., Li, W. H. & Alici, G. 2013 Inertial focusing in a straight channel with asymmetrical expansion–contraction cavity arrays using two secondary flows. J. Micromech. Microengng 23 (8), 085023.CrossRefGoogle Scholar