Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media

Abstract

In this study, two microfluidic devices are proposed as simplified 1-D microfluidic analogues of a porous medium. The objectives are twofold: firstly to assess the usefulness of the microchannels to mimic the porous medium in a controlled and simplified manner, and secondly to obtain a better insight about the flow characteristics of viscoelastic fluids flowing through a packed bed. For these purposes, flow visualizations and pressure drop measurements are conducted with Newtonian and viscoelastic fluids. The 1-D microfluidic analogues of porous medium consisted of microchannels with a sequence of contractions/expansions disposed in symmetric and asymmetric arrangements. The real porous medium is in reality, a complex combination of the two arrangements of particles simulated with the microchannels, which can be considered as limiting ideal configurations. The results show that both configurations are able to mimic well the pressure drop variation with flow rate for Newtonian fluids. However, due to the intrinsic differences in the deformation rate profiles associated with each microgeometry, the symmetric configuration is more suitable for studying the flow of viscoelastic fluids at low De values, while the asymmetric configuration provides better results at high De values. In this way, both microgeometries seem to be complementary and could be interesting tools to obtain a better insight about the flow of viscoelastic fluids through a porous medium. Such model systems could be very interesting to use in polymer-flood processes for enhanced oil recovery, for instance, as a tool for selecting the most suitable viscoelastic fluid to be used in a specific formation. The selection of the fluid properties of a detergent for cleaning oil contaminated soil, sand, and in general, any porous material, is another possible application.

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References

  1. Alves MA, Poole RJ (2007) Divergent flow in contractions. J Non-Newton Fluid Mech 144:140–148

    Article  MATH  Google Scholar 

  2. Balhoff MT, Thompson KE (2004) Modeling the steady flow of yield-stress fluids in packed beds. AIChE J 50(12):3034–3048

    Article  Google Scholar 

  3. Blunt MJ (2001) Flow in porous media - pore-network models and multiphase flow. Curr Opin Colloid Interface Sci 6:197–207

    Article  Google Scholar 

  4. Campo-Deaño L, Clasen C (2010) The slow retraction method (SRM) for the determination of ultra-short relaxation times in capillary breakup extensional rheometry experiments. J Non-Newton Fluid Mech 165:1688–1699

    Article  Google Scholar 

  5. Chhabra RP, Comiti J, Machac I (2001) Flow of non-Newtononian fluids in fixed and fluidised beds. Chem Eng Sci 56:1–27

    Article  Google Scholar 

  6. Christopher RH, Middleman S (1965) Power-law flow through a packed tube. Ind Eng Chem Fundam 4(4):422–426

    Article  Google Scholar 

  7. Darcy H (1856) Les fountains publiques de la Ville de Dijon: exposition et application des principes à suivre et des formules à employer dans les questions de distribution d’eau. Victor Dalmont, Paris

    Google Scholar 

  8. Devasenathipathy S, Santiago JG, Wereley ST, Meinhart CD, Takehara K (2003) Particle imaging techniques for microfabricated fluidic systems. Exp Fluids 34:504514

    Google Scholar 

  9. Duda JL, Hong SA, Klaus EE (1983) Flow of polymer solutions in porous media: Inadequacy of the capillary model. Ind Eng Chem Fundam 22:299–305

    Article  Google Scholar 

  10. Einstein A (1906) Eine neue Bestimmung der Moleküldimensionen. Annalen der Physik 19:298–306

    Google Scholar 

  11. Entov VM, Hinch EJ (1997) Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J Colloid Interface Sci 72(1):31–51

    Article  Google Scholar 

  12. Gaitonde NY, Middleman S (1966) Flow of viscoelastic fluids through porous media. Ind Eng Chem Fundam 6(1):145–147

    Article  Google Scholar 

  13. Groisman A, Enzelberger M, Quake SR (2003) Microfluidic Memory and Control Devices. Science 300:955–958

    Article  Google Scholar 

  14. Holdich R (2002) Fundamentals of particle technology. Midland Information Technology and Publishing, Loughborough

    Google Scholar 

  15. Larson RG, Shaqfeh ESG, Muller SJ (1990) A purely elastic instability in Taylor-Couette flow. J Non-Newton Fluid Mech 218:573–600

    MATH  MathSciNet  Google Scholar 

  16. Liu Y, Wu SP (2009) Numerical simulations of non-Newtonian viscoelastic flows through porous media, in: Flow in porous media—from phenomena to engineering and beyond, Orient ACAD Forum, Marrickville, Australia, pp 187–193

  17. López X (2004) Pore-Scale modelling of non-Newtonian flow. PhD thesis. Imperial College London

  18. Macosko CW (1994) Rheology: principles, measurements, and applications. Wiley-VCH, Inc, New York

  19. Marshall RJ, Metzner AB (1967) Flow of viscoelastic fluids through porous media. Ind Eng Chem Fundam 6(3):393–400

    Article  Google Scholar 

  20. Martins A, Laranjeira PE, Braga CH, Mata TM (2009) Progress in Porous Media Research. Chapter 5: Modeling of transport phenomena in porous media using networks models. Nova Science Publishers, Inc, New York

  21. McDonald JC, Dufy DC, Anderson JR, Chiu DT, Wu H, Whitesides GM (2000) Fabrication of microfluidic systems in poly(dimethylsiloxane). Electrophoresis 21:27–40

    Article  Google Scholar 

  22. McKinley GH, Pakdel P, Oztekin A (1996) Rheological and geometric scaling of purely elastic flow instabilities. J Non-Newton Fluid Mech 67:19–47

    Article  Google Scholar 

  23. Meinhart CD, Wereley ST, Gray MHB (2000) Volume illumination for two-dimensional particle image velocimetry. Meas Sci Technol 11:809–814

    Article  Google Scholar 

  24. Metzner AB, Metzner AP (1970) Stress levels in rapid extensional flows of polymeric fluids. Rheol Acta 9(2):174–181

    Article  Google Scholar 

  25. Moffatt HK (1964) Viscous and resistive eddies near sharp corners. J Fluid Mech 18(1):l–18

    Article  Google Scholar 

  26. Oliveira MSN, Alves MA, Pinho FT, McKinley GH (2007) Viscous flow through microfabricated hyperbolic contractions. Exp Fluids 43:437–451

    Article  Google Scholar 

  27. Oliveira MSN, Rodd LE, McKinley GH, Alves MA (2008) Simulations of extensional flow in microrheometric devices. Microfluid Nanofluid 5:809–826

    Article  Google Scholar 

  28. Pakdel P, McKinley GH (1996) Elastic instability and curved streamlines. Phys Rev Lett 77:2459–462

    Article  Google Scholar 

  29. Pakdel P, McKinley GH (1998) Cavity flows of elastic liquids: purely elastic instabilities. Phys Fluids 10(5):1058–1070

    Article  Google Scholar 

  30. Pearson JRA, Tardy PMJ (2002) Models for flow of non-Newtonian and complex fluids through porous media. J Non-Newton Fluid Mech 102(2):447–473

    Article  MATH  Google Scholar 

  31. Petrie CJS (2006a) Extensional viscosity: a critical discussion. J Non-Newton Fluid Mech 137:15–23

    Article  MATH  Google Scholar 

  32. Petrie CJS (2006b) One hundred years of extensional flow. J Non-Newton Fluid Mech 137:1–14

    Article  MATH  Google Scholar 

  33. Rhodes M (2008) Introduction to particle technology. 2nd edn. John Wiley & Sons, Ltd, England

    Google Scholar 

  34. Rodd LE, Cooper-White JJ, Boger DV, McKinley GH (2007) The role of elasticity number in the entry flow of dilute polymer solutions in micro-fabricated contraction geometries. J Non-Newton Fluid Mech 143:170–191

    Article  Google Scholar 

  35. Rodd LE, Scott TP, Boger DV, Cooper-White JJ, McKinley GH (2005) The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries. J Non-Newton Fluid Mech 129:1–22

    Article  Google Scholar 

  36. Santiago JG, Wereley ST, Meinhart C, Beebe DJ, Adrian RJ (1998) A particle image velocimetry system for microfluidics. Exp Fluids 25:316–319

    Article  Google Scholar 

  37. Savins JG (1969) Non-Newtonian flow through porous media. Ind Eng Chem 61(10):18–47

    Article  Google Scholar 

  38. Scott TP (2004) Contraction/Expansion flow of dilute elastic solutions in Microchannels. Master’s thesis. Massachusetts Institute of Technology

  39. Sdougos HP, Bussolari SR, Dewey CF (1984) Secondary flow and turbulence in a cone-and-plate device. J Fluid Mech 138:379–404

    Article  Google Scholar 

  40. Sinton D (2004) Microscale flow visualization. Microfluid Nanofluid 1(1):2–21

    Article  Google Scholar 

  41. Sochi T (2007) Pore-Scale modeling of non-Newtonian flow in porous media. PhD thesis. Imperial College London

  42. Sochi T (2009) Pore-scale modeling of viscoelastic flow in porous media using a Bautista-Manero fluid. Int J Heat Fluid Flow 30:1202–1217

    Article  Google Scholar 

  43. Sochi T (2010) Flow of non-Newtonian fluids in porous media. J Polymer Sci Part B Polymer Phys 48:2437–2467

    Article  Google Scholar 

  44. Sorbie KS, Clifford PJ, Jones ERW (1989) The rheology of pseudo-plastic fluids in porous media using network modeling. J Colloid Interface Sci 130(2):508–534

    Article  Google Scholar 

  45. Soulages J, Oliveira MSN, Sousa PC, Alves MA, McKinley GH (2009) Investigating the stability of viscoelastic stagnation flows in T-shaped microchannels. J Non-Newton Fluid Mech 163:9–24

    Article  Google Scholar 

  46. Sousa PC, Pinho FT, Oliveira MSN, Alves MA (2010) Efficient microfluidic rectifiers for viscoelastic fluid flow. J Non-Newton Fluid Mech 165:652–671

    Article  Google Scholar 

  47. Stone HA, Stroock AD, Ajdari A (2004) Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu Rev Fluid Mech 36:381411

    Article  Google Scholar 

  48. Taylor KC, Nasr-El-Din HA (1998) Water-soluble hydrophobically associating polymers for improved oil recovery: a literature review. J Petroleum Sci Eng 19:265–280

    Article  Google Scholar 

  49. Whitesides GM (2006) The origins and future of microfluidics. Nature 42:368–370

    Article  Google Scholar 

  50. Wissler EH (1971) Viscoelastic effects in the flow of non-Newtonian fluids through a porous medium. Ind Eng Chem Fundam 10(3):411–417

    Article  Google Scholar 

Download references

Acknowledgments

Authors acknowledge financial support from Fundação para a Ciência e a Tecnologia (FCT), COMPETE and FEDER through projects PTDC/EQU-FTT/71800/2006, REEQ/262/EME/2005 and PTDC/EME-MFE/99109/2008. SEM images were taken at CEMUP, which is grateful for the financial support to FCT through projects REEQ/1062/CTM/2005 and REDE/1512/RME/2005. The technical support of L.C. Matos is also acknowledged. F.J. Galindo-Rosales would like to acknowledge FCT for financial support (SFRH/BPD/69663/2010). M.A. Alves acknowledges the Chemical Engineering Department of FEUP for conceding a sabbatical leave.

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Correspondence to F. J. Galindo-Rosales.

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Galindo-Rosales, F.J., Campo-Deaño, L., Pinho, F.T. et al. Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media. Microfluid Nanofluid 12, 485–498 (2012). https://doi.org/10.1007/s10404-011-0890-6

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Keywords

  • Microfluidics
  • Porous media
  • Rheology
  • Contraction-expansion
  • Viscoelastic fluids