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Divergent streamlines and free vortices in Newtonian fluid flows in microfluidic flow-focusing devices

Published online by Cambridge University Press:  28 September 2012

M. S. N. Oliveira ,
F. T. Pinho  and
M. A. Alves
M. S. N. Oliveira*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK Faculdade de Engenharia, Universidade do Porto, Centro de Estudos de Fenómenos de Transporte, Rua Dr Roberto Frias, 4200-465 Porto, Portugal
F. T. Pinho
Affiliation:
Faculdade de Engenharia, Universidade do Porto, Centro de Estudos de Fenómenos de Transporte, Rua Dr Roberto Frias, 4200-465 Porto, Portugal
M. A. Alves
Affiliation:
Faculdade de Engenharia, Universidade do Porto, Centro de Estudos de Fenómenos de Transporte, Rua Dr Roberto Frias, 4200-465 Porto, Portugal
*
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The appearance of divergent streamlines and subsequent formation of free vortices in Newtonian fluid flows through microfluidic flow-focusing geometries is discussed in this work. The micro-geometries are shaped like a cross-slot but comprise three entrances and one exit. The divergent flow and subsequent symmetric vortical structures arising near the centreline of the main inlet channel are promoted even under creeping flow conditions, and are observed experimentally and predicted numerically above a critical value of the ratio of inlet velocities (VR). As VR is further increased these free vortices continue to grow until a maximum size is reached due to geometrical constraints. The numerical calculations are in good agreement with the experimental observations and we probe numerically the effects of the geometric parameters and of inertia on the flow patterns. In particular, we observe that the appearance of the central recirculations depends non-monotonically on the relative width of the entrance branches and we show that inertia enhances the appearance of the free vortices. On the contrary, the presence of the walls in three-dimensional geometries has a stabilizing effect for low Reynolds numbers, delaying the onset of these secondary flows to higher VR. The linearity of the governing equations for creeping flow of Newtonian fluids was invoked to determine the flow field for any VR as a linear combination of the results of three other independent solutions in the same geometry.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 711 , 25 November 2012 , pp. 171 - 191
Copyright
Copyright © Cambridge University Press 2012

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References

1. Alves, M. A., Oliveira, P. J. & Pinho, F. T. 2003 A convergent and universally bounded interpolation scheme for the treatment of advection. J. Non-Newtonian Fluid Mech. 41, 47–75.Google Scholar
2. Alves, M. A. & Poole, R. J. 2007 Divergent flow in contractions. J. Non-Newtonian Fluid Mech. 144, 140–148.Google Scholar
3. Anna, S. L., Bontoux, N. & Stone, H. A. 2003 Formation of dispersions using ‘flow focusing’ in microchannels. Appl. Phys. Lett. 82, 364–366.Google Scholar
4. Anna, S. L. & Mayer, H. C. 2006 Microscale tipstreaming in a microfluidic flow. Phys. Fluids 18, 121512.Google Scholar
5. Arratia, P. E., Gollub, J. P. & Durian, D. J. 2008 Polymeric filament thinning and breakup in microchannels. Phys. Rev. E 77, 036309.CrossRefGoogle ScholarPubMed
6. Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, vol. 1: Fluid Dynamics. Wiley.Google Scholar
7. Boger, D. V. & Binnington, R. J. 1990 Circular entry flows of fluid M1. J. Non-Newtonian Fluid Mech. 35, 339–360.Google Scholar
8. Campo-Deaño, L., Galindo-Rosales, F. J., Pinho, F. T., Alves, M. A. & Oliveira, M. S. N. 2011 Flow of low viscosity Boger fluids through a microfluidic hyperbolic contraction. J. Non-Newtonian Fluid Mech. 166, 1286–1296.CrossRefGoogle Scholar
9. Chiang, T. P., Sheu, T. W. H. & Wang, S. K. 2000 Side wall effects on the structure of laminar flow over a plane-symmetric sudden expansion. Comp. Fluids 29, 467–492.Google Scholar
10. Dendukuri, D. & Doyle, P. S. 2009 The synthesis and assembly of polymeric microparticles using microfluidics. Adv. Mater. 21, 1–16.CrossRefGoogle Scholar
11. Escudier, M. 1988 Vortex breakdown: observations and explanations. Prog. Aerosp. Sci. 25, 189–229.Google Scholar
12. Evans, R. E. & Walters, K. 1989 Further remarks on the lip-vortex mechanism of vortex enhancement in planar-contraction flows. J. Non-Newtonian Fluid Mech. 32, 95–105.Google Scholar
13. Garstecki, P., Stone, H. A. & Whitesides, G. M. 2005 Mechanism for flowrate controlled breakup in confined geometries: a route to monodisperse emulsions. Phys. Rev. Lett. 94, 164501.Google Scholar
14. Hulsen, M. A. 1993 Numerical simulation of the divergent flow regime in a circular contraction flow of a viscoelastic fluid. Theor. Comput. Fluid Dyn. 5, 33–48.CrossRefGoogle Scholar
15. James, D. F., Chandler, G. M. & Armour, S. J. 1990 A converging channel rheometer for the measurement of extensional viscosity. J. Non-Newtonian Fluid Mech. 35, 421–443.Google Scholar
16. Jensen, K. 1998 Chemical kinetics: smaller, faster chemistry. Nature 393, 735–737.CrossRefGoogle Scholar
17. Knight, J. B., Vishwanath, A., Brody, J. P. & Austin, R. H. 1998 Hydrodynamic focusing on a silicon chip: mixing nanoliters in microseconds. Phys. Rev. Lett. 80, 3863–3866.Google Scholar
18. Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10, 221–246.CrossRefGoogle Scholar
19. Lucca-Negro, O. & O’Doherty, T. 2001 Vortex breakdown: a review. Prog. Energy Combust. Sci. 27, 431–481.CrossRefGoogle Scholar
20. Luo, W.-J. 2009 Effect of ionic concentration on electrokinetic instability in a cross-shaped microchannel. Microfluid. Nanofluid. 6, 189–202.CrossRefGoogle Scholar
21. McDonald, J. C., Dufy, D. C., Anderson, J. R., Chiu, D. T., Wu, H. & Whitesides, G. M. 2000 Fabrication of microfluidic systems in poly (dimethylsiloxane). Electrophoresis 21, 27–40.Google Scholar
22. Meinhart, C. D., Wereley, S. T. & Gray, M. H. B. 2000 Volume illumination for two-dimensional particle image velocimetry. Meas. Sci. Technol. 11, 809–814.Google Scholar
23. Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1–18.Google Scholar
24. Nie, Z., Seo, M., Xu, S., Lewis, P. C., Mok, M., Kumacheva, E., Whitesides, G. M., Garstecki, P. & Stone, H. A. 2008 Emulsification in a microfluidic flow-focusing device: effect of the viscosities of the liquids. Microfluid. Nanofluid. 5, 585–594.Google Scholar
25. Nisisako, T., Torii, T. & Higuchi, T. 2004 Novel microreactors for functional polymer beads. Chem. Engng J. 101, 23–29.CrossRefGoogle Scholar
26. Oliveira, P. J. 2003 Asymmetric flows of viscoelastic fluids in symmetric planar expansion geometries. J. Non-Newtonian Fluid Mech. 114, 33–63.Google Scholar
27. Oliveira, M. S. N., Alves, M. A., McKinley, G. H. & Pinho, F. T. 2007 Viscous flow through microfabricated hyperbolic contraction. Exp. Fluids 43, 437–451.Google Scholar
28. Oliveira, P. J. & Pinho, F. T. 1999 Numerical procedure for the computation of fluid flow with arbitrary stress–strain relationships. Numer. Heat Transfer B 35, 295–315.Google Scholar
29. Oliveira, P. J., Pinho, F. T. & Pinto, G. A. 1998 Numerical simulation of nonlinear elastic flows with a general collocated finite-volume method. J. Non-Newtonian Fluid Mech. 79, 1–43.Google Scholar
30. Oliveira, M. S. N., Pinho, F. T., Poole, R. J., Oliveira, P. J. & Alves, M. A. 2009 Purely elastic flow asymmetries in flow-focusing devices. J. Non-Newtonian Fluid Mech. 160, 31–39.Google Scholar
31. Oliveira, M. S. N., Rodd, L. E., McKinley, G. H. & Alves, M. A. 2008 Simulations of extensional flow in microrheometric devices. Microfluid. Nanofluid. 5, 809–826.CrossRefGoogle Scholar
32. Phan-Thien, N. & Tanner, R. I. 1977 A new constitutive equation derived from network theory. J. Non-Newtonian Fluid Mech. 2, 353–365.CrossRefGoogle Scholar
33. Rodd, L. E., Scott, T. P., Boger, D. V., Cooper-White, J. J. & McKinley, G. H. 2005 The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries. J. Non-Newtonian Fluid Mech. 129, 1–22.CrossRefGoogle Scholar
34. Soulages, J., Oliveira, M. S. N., Sousa, P. C., Alves, M. A. & McKinley, G. H. 2009 Investigating the stability of viscoelastic stagnation flows in T-shaped microchannels. J. Non-Newtonian Fluid Mech. 163, 9–24.Google Scholar
35. Sousa, P. C., Coelho, P. M., Oliveira, M. S. N. & Alves, M. A. 2011 Laminar flow in three-dimensional square–square expansions. J. Non-Newtonian Fluid Mech. 166, 1033–1048.Google Scholar
36. Townsend, P. & Walters, K. 1994 Expansion flows of non-Newtonian liquids. Chem. Engng Sci. 49, 749–763.Google Scholar
37. Tsai, C.-H., Chen, H.-T., Wang, Y.-N., Lin, C.-H. & Fu, L.-M. 2006 Capabilities and limitations of two-dimensional and three-dimensional numerical methods in modelling the fluid flow in sudden expansion microchannels. Microfluid. Nanofluid. 3, 13–18.CrossRefGoogle Scholar