Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Hysteresis in viscoelastic flow instability of confined cylinders

Manish Kumar and Arezoo M. Ardekani

  • Department of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA

Phys. Rev. Fluids 7, 093302 – Published 29 September, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.093302

Abstract

Viscoelastic flow through porous media is relevant in many industrial and biological applications including enhanced oil recovery and biofluids' transport inside the body, where the presence of large polymeric stresses in the porous media leads to viscoelastic instability. In the present study, we numerically investigate viscoelastic instability-induced flow states in the channels consisting of (i) a single cylinder and (ii) two streamwise located cylinders. We unravel the presence of a hysteresis for pulsatile viscoelastic flows. For both geometries, the quantitative value of flow asymmetry around the cylinder resulting from the viscoelastic instability forms a closed hysteresis loop. We investigate the effects of fluid rheological properties and periodic inlet flow rates on the hysteresis loop.

Physics Subject Headings (PhySH)

Article Text

References (64)

  1. M. Kumar, J. S. Guasto, and A. M. Ardekani, Transport of complex and active fluids in porous media, J. Rheol. 66, 375 (2022).
  2. L. Hall-Stoodley, J. W. Costerton, and P. Stoodley, Bacterial biofilms: from the Natural environment to infectious diseases, Nat. Rev. Microbiol. 2, 95 (2004).
  3. K. S. Sorbie, Polymer-Improved Oil Recovery (Springer Science & Business Media, New York 2013).
  4. D. J. Smith, E. A. Gaffney, and J. R. Blake, Modelling mucociliary clearance, Respir. Physiol. Neurobiol. 163, 178 (2008).
  5. P. Stoodley, I. Dodds, D. De Beer, H. L. Scott, and J. D. Boyle, Flowing biofilms as a transport mechanism for biomass through porous media under laminar and turbulent conditions in a laboratory reactor system, Biofouling 21, 161 (2005).
  6. D. Roote, Technology status report: In situ flushing, Ground Water Remediation Technology Analysis Center (1998), http://www.gwrtac.org.
  7. S. Aramideh, P. P. Vlachos, and A. M. Ardekani, Pore-scale statistics of flow and transport through porous media, Phys. Rev. E 98, 013104 (2018).
  8. C. A. Browne, A. Shih, and S. S. Datta, Pore-scale flow characterization of polymer solutions in microfluidic porous media, Small 16, 1903944 (2019).
  9. D. Kawale, G. Bouwman, S. Sachdev, P. L. Zitha, M. T. Kreutzer, W. R. Rossen, and P. E. Boukany, Polymer conformation during flow in porous media, Soft Matter 13, 8745 (2017).
  10. P. Pakdel and G. H. McKinley, Elastic Instability and Curved Streamlines, Phys. Rev. Lett. 77, 2459 (1996).
  11. G. H. McKinley, P. Pakdel, and A. Öztekin, Rheological and geometric scaling of purely elastic flow instabilities, J. Non-Newton. Fluid Mech. 67, 19 (1996).
  12. K. Weissenberg, A continuum theory of rhelogicalphenomena, Nature 159, 310 (1947).
  13. P. E. Arratia, C. C. Thomas, J. Diorio, and J. P. Gollub, Elasticinstabilities of Polymer Solutions in Cross-Channel Flow, Phys. Rev. Lett. 96, 144502 (2006).
  14. R. J. Poole, M. A. Alves, and P. J. Oliveira, Purely Elastic Flow Asymmetries, Phys. Rev. Lett. 99, 164503 (2007).
  15. A. Groisman and V. Steinberg, Elastic turbulence in a polymer solution flow, Nature (Lond.) 405, 53 (2000).
  16. D. M. Walkama, N. Waisbord, and J. S. Guasto, Disorder Suppresses Chaos in Viscoelastic Flows, Phys. Rev. Lett. 124, 164501 (2020).
  17. A. Groisman and V. Steinberg, Efficient mixing at low reynolds numbers using polymer additives, Nature (Lond.) 410, 905 (2001).
  18. C. A. Browne and S. S. Datta, Elastic turbulence generates anomalous flowresistance in porous media, Sci. Adv. 7, 1 (2021).
  19. S. J. Haward, G. H. Mckinley, and A. Q. Shen, Elastic instabilities in planar elongational flow of monodisperse polymer solutions, Sci. Rep. 6, 33029 (2016).
  20. L. E. Rodd, T. P. Scott, D. V. Boger, J. J. Cooper-White, and G. H. McKinley, The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries, J. Non-Newton. Fluid Mech. 129, 1 (2005).
  21. A. Lanzaro and X.-F. Yuan, Effects of contraction ratio on non-linear dynamics of semi-dilute, highly polydisperse paam solutions in microfluidics, J. Non-Newton. Fluid Mech. 166, 1064 (2011).
  22. G. Batchelor, The stress generated in a non-dilute suspension of elongated particles by pure straining motion, J. Fluid Mech. 46, 813 (1971).
  23. D. V. Boger, Viscoelastic flows through contractions, Annu. Rev. Fluid Mech. 19, 157 (1987).
  24. A. Mongruel and M. Cloitre, Extensional flow of semidilute suspensions of rod-like particles through an orifice, Phys. Fluids 7, 2546 (1995).
  25. A. Mongruel and M. Cloitre, Axisymmetric orifice flow for measuring the elongational viscosity of semi-rigid polymer solutions, J. Non-Newton. Fluid Mech. 110, 27 (2003).
  26. S. Kenney, K. Poper, G. Chapagain, and G. F. Christopher, Large deborah number flows around confined microfluidic cylinders, Rheol. Acta 52, 485 (2013).
  27. X. Shi, S. Kenney, G. Chapagain, and G. F. Christopher, Mechanisms of onset for moderate mach number instabilities of viscoelastic flows around confined cylinders, Rheol. Acta 54, 805 (2015).
  28. B. Qin, P. F. Salipante, S. D. Hudson, and P. E. Arratia, Upstream vortex and elastic wave in the viscoelastic flow around a confined cylinder, J. Fluid Mech. 864, R2 (2019).
  29. S. J. Haward, C. C. Hopkins, and A. Q. Shen, Asymmetric flow of polymer solutions around microfluidic cylinders: Interaction between shear-thinning and viscoelasticity, J. Non-Newton. Fluid Mech. 278, 104250 (2020).
  30. S. Varchanis, C. C. Hopkins, A. Q. Shen, J. Tsamopoulos, and S. J. Haward, Asymmetric flows of complex fluids past confined cylinders: A comprehensive numerical study with experimental validation, Phys. Fluids 32, 053103 (2020).
  31. J. A. Deiber and W. R. Schowalter, Modeling the flow of viscoelastic fluids through porous media, AIChE J. 27, 912 (1981).
  32. M. J. Blunt, Multiphase Flow in Permeable Media: A Pore-scale Perspective (Cambridge University Press, Cambridge, London, 2017).
  33. X. Shi and G. F. Christopher, Growth of viscoelastic instabilities around linear cylinder arrays, Phys. Fluids 28, 124102 (2016).
  34. C. A. Browne, A. Shih, and S. S. Datta, Bistability in the unstable flow of polymer solutions through pore constriction arrays, J. Fluid Mech. 890, A2 (2020).
  35. A. Varshney and V. Steinberg, Elastic wake instabilities in a creeping flow between two obstacles, Phys. Rev. Fluids 2, 051301(R) (2017).
  36. M. Kumar and A. M. Ardekani, Elastic instabilities between two cylinders confined in a channel, Phys. Fluids 33, 074107 (2021).
  37. M. Kumar and A. M. Ardekani, Viscoelastic instability in an asymmetric geometry, Eur. Phys. J. Spec. Top. (2022), doi: 10.1140/epjs/s11734-022-00657-9.
  38. M. Kumar, S. Aramideh, C. A. Browne, S. S. Datta, and A. M. Ardekani, Numerical investigation of multistability in the unstable flow of a polymer solution through porous media, Phys. Rev. Fluids 6, 033304 (2021).
  39. D. Kawale, E. Marques, P. L. Zitha, M. T. Kreutzer, W. R. Rossen, and P. E. Boukany, Elastic instabilities during the flow of hydrolyzed polyacrylamide solution in porous media: Effect of pore-shape and salt, Soft Matter 13, 765 (2017).
  40. S. J. Haward, C. C. Hopkins, and A. Q. Shen, Stagnation points control chaotic fluctuations in viscoelastic porous media flow, Proc. Natl. Acad. Sci. USA 118, e2111651118 (2021).
  41. M. Kumar, J. S. Guasto, and A. M. Ardekani, Lagrangian stretching reveals stress topology in viscoelastic flows, arXiv:2206.11800.
  42. C. Gin and P. Daripa, Time-dependent injection strategies for multilayer Hele-Shaw and porous media flows, Phys. Rev. Fluids 6, 033901 (2021).
  43. Q. Yuan and J. Azaiez, Miscible displacements in porous media with time-dependent injection velocities, Transp. Porous Media 104, 57 (2014).
  44. C. Pankiewitz and E. Meiburg, Miscible porous media displacements in the quarter five-spot configuration. Part 3. Non-monotonic viscosity profiles, J. Fluid Mech. 388, 171 (1999).
  45. S. Aramideh, P. P. Vlachos, and A. M. Ardekani, Unstable displacement of non-aqueous phase liquids with surfactant and polymer, Transp. Porous Media 126, 455 (2019).
  46. A. B. Mann, S. Shaheen, K. Maqbool, and S. Poncet, Fractional Burgers fluid flow due to metachronal ciliary motion in an inclined tube, Front. Physiol. 10, 588 (2019).
  47. B. K. Huang and M. A. Choma, Microscale imaging of cilia-driven fluid flow, Cell. Molec. Life Sci. 72, 1095 (2015).
  48. R. Bird, R. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids: Fluid Mechanics, 2nd ed. (John Wiley & Sons Inc., New York, 1987), Vol. 1.
  49. R. B. Bird, C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids: Kinetic Theory, 2nd ed. (Wiley, New York, 1987), Vol. 2.
  50. R. B. Bird, P. J. Dotson, and N. L. Johnson, Polymer solution rheology based on a finitely extensible bead-spring chain model, J. Non-Newton. Fluid Mech. 7, 213 (1980).
  51. M. D. Chilcott and J. M. Rallison, Creeping flow of dilute polymer solutions past cylinders and spheres, J. Non-Newton. Fluid Mech. 29, 381 (1988).
  52. P. J. Oliveira, An exact solution for tube and slit flow of a FENE-P fluid, Acta Mech. 158, 157 (2002).
  53. J. G. Oldroyd, On the formulation of rheological equations of state, Proc. Roy. Soc. Lond. Ser. A, Math. Phys. Sci. 200, 523 (1950).
  54. D. Boger, A highly elastic constant-viscosity fluid, J. Non-Newton. Fluid Mech. 3, 87 (1977).
  55. K. Walters and M. F. Webster, The distinctive CFD challenges of computational rheology, Int. J. Numer. Methods Fluids 43, 577 (2003).
  56. R. Fattal and R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newton. Fluid Mech. 123, 281 (2004).
  57. R. Fattal and R. Kupferman, Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation, J. Non-Newton. Fluid Mech. 126, 23 (2005).
  58. H. Jasak, A. Jemcov, and Z. Tukovic, Openfoam: A c++ library for complexphysics simulations, in Proceedings of the International Workshop on Coupled Methods in Numerical Dynamics (IUC, Dubrovnik Croatia, 2007).
  59. F. Pimenta and M. A. Alves, Stabilization of an open-source finite-volume solver for viscoelastic fluid flows, J. Non-Newton. Fluid Mech. 239, 85 (2017).
  60. F. Habla, M. W. Tan, J. Haßlberger, and O. Hinrichsen, Numerical simulation of the viscoelastic flow in a three-dimensional lid-driven cavity using the log-conformation reformulation in OpenFOAM®, J. Non-Newton. Fluid Mech. 212, 47 (2014).
  61. J. M. Dealy, Weissenberg and deborah numbers-their definition and use, Rheol. Bull. 79, 14 (2010).
  62. G. H. McKinley, R. C. Armstrong, and R. A. Brown, The wake instability in viscoelastic flow past confined circular cylinders, Philos. Trans. Roy. Soc. Lond. Ser. A: Phys. Eng. Sci. 344, 265 (1993).
  63. S. J. Haward, N. Kitajima, K. Toda-Peters, T. Takahashi, and A. Q. Shen, Flow of wormlike micellar solutions around microfluidic cylinders with high aspect ratio and low blockage ratio, Soft Matter 15, 1927 (2019).
  64. T. L. Bergman, F. P. Incropera, D. P. DeWitt, and A. S. Lavine, Fundamentals of Heat and Mass Transfer (John Wiley & Sons, New York, 2011).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation