- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Invited
  • Perspective
  • Access by Xinjiang University

Perspectives on viscoelastic flow instabilities and elastic turbulence

Sujit S. Datta*

Arezoo M. Ardekani

Paulo E. Arratia

Antony N. Beris

Irmgard Bischofberger and Gareth H. McKinley

Jens G. Eggers

J. Esteban López-Aguilar

Suzanne M. Fielding

Anna Frishman

Michael D. Graham

Jeffrey S. Guasto

Simon J. Haward and Amy Q. Shen

Sarah Hormozi

Alexander Morozov

Robert J. Poole

V. Shankar

Eric S. G. Shaqfeh

Holger Stark

Victor Steinberg

Ganesh Subramanian

Howard A. Stone†

  • Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA

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

  • Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

  • Center for Research in Soft Matter and Polymers, Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, USA

  • Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, United Kingdom

  • Facultad de Química, Departamento de Ingeniería Química, Universidad Nacional Autónoma de México (UNAM), Ciudad Universitaria, Coyoacán, Ciudad de México 04510, Mexico

  • Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom

  • Department of Physics, Technion Israel Institute of Technology, 32000 Haifa, Israel

  • Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706, USA

  • Department of Mechanical Engineering, Tufts University, Medford, Massachusetts 02155, USA

  • Okinawa Institute of Science and Technology, Onna-son, Okinawa 904-0495, Japan

  • Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA

  • SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom

  • School of Engineering, University of Liverpool, Liverpool, L69 3GH, United Kingdom

  • Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India

  • Department of Chemical Engineering and Department of Mechanical Engineering, Stanford University, Stanford, California 94305, USA

  • Institute of Theoretical Physics, Technische Universität Berlin, Berlin 10587, Germany

  • Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel and The Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel

  • Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India

  • Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA

  • *ssdatta@princeton.edu
  • †hastone@princeton.edu
PDF

Phys. Rev. Fluids 7, 080701 – Published 29 August, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.080701

Abstract

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with many of the hallmarks of turbulence—even though the effective Reynolds numbers may be O(1) or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (511)

  1. G. V. Vinogradov and A. Y. Malkin, Rheology of Polymers (Springer-Verlag, Berlin, 1980).
  2. P. E. Rouse, A theory of the linear viscoelastic properties of dilute solutions of coiling polymers, J. Chem. Phys. 21, 1272 (1953).
  3. B. H. Zimm, Dynamics of polymer molecules in dilute solution: Viscoelasticity, flow birefringence and dielectric loss, J. Chem. Phys. 24, 269 (1956).
  4. P. G. de Gennes, Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients, J. Chem. Phys. 60, 5030 (1974).
  5. E. J. Hinch, Mechanical models of dilute polymer solutions in strong flows, Phys. Fluids 20, S22 (1977).
  6. P. Pakdel and G. H. McKinley, Elastic Instability and Curved Streamlines, Phys. Rev. Lett. 77, 2459 (1996).
  7. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, 2nd ed. (John Wiley & Sons, New York, 1987), Vol. 1.
  8. R. G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, New York, 1999).
  9. G. I. Taylor, VIII. Stability of a viscous liquid contained between two rotating cylinders, Philos. Trans. R. Soc. London A 223, 289 (1923).
  10. D. V. Boger, A highly elastic constant-viscosity fluid, J. Non-Newtonian Fluid Mech. 3, 87 (1977/78).
  11. D. F. James, Boger fluids, Annu. Rev. Fluid Mech. 41, 129 (2009).
  12. G. Prilutski, R. K. Gupta, T. Sridhar, and M. E. Ryan, Model viscoelastic liquids, J. Non-Newtonian Fluid Mech. 12, 233 (1983).
  13. S. L. Anna, G. H. McKinley, D. A. Nguyen, T. Sridhar, S. J. Muller, J. Huang, and D. F. James, An inter-laboratory comparison of measurements from filament-stretching rheometers using common test fluids, J. Rheol. 45, 83 (2001).
  14. J. M. Rallison and E. J. Hinch, Do we understand the physics in the constitutive equation? J. Non-Newtonian Fluid Mech. 29, 37 (1988).
  15. H. Giesekus, A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility, J. Non-Newtonian Fluid Mech. 11, 69 (1982).
  16. L. M. Quinzani, G. H. McKinley, R. A. Brown, and R. C. Armstrong, Modeling the rheology of polyisobutylene solutions, J. Rheol. 34, 705 (1990).
  17. R. G. Larson and P. S. Desai, Modeling the rheology of polymer melts and solutions, Annu. Rev. Fluid Mech. 47, 47 (2015).
  18. P. Saramito, A new elastoviscoplastic model based on the Herschel-Bulkley viscoplastic model, J. Non-Newtonian Fluid Mech. 158, 154 (2009).
  19. C. J. Dimitriou and G. H. McKinley, A canonical framework for modeling elasto-viscoplasticity in complex fluids, J. Non-Newtonian Fluid Mech. 265, 116 (2019).
  20. E. S. G. Shaqfeh and B. Khomami, The Oldroyd-B fluid in elastic instabilities, turbulence and particle suspensions, J. Non-Newtonian Fluid Mech. 298, 104672 (2021).
  21. J. M. Dealy, Weissenberg and Deborah numbers—Their definition and use, Rheol. Bull. 79, 14 (2010).
  22. E. S. G. Shaqfeh, Purely elastic instabilities in viscometric flows, Annu. Rev. Fluid Mech. 28, 129 (1996).
  23. S. J. Muller, R. G. Larson, and E. S. G. Shaqfeh, A purely elastic transition in Taylor-Couette flow, Rheol. Acta 28, 499 (1989).
  24. R. G. Larson, E. S. G. Shaqfeh, and S. J. Muller, A purely elastic instability in Taylor-Couette flow, J. Fluid Mech. 218, 573 (1990).
  25. E. S. G. Shaqfeh, S. J. Muller, and R. G. Larson, The effects of gap width and dilute solution properties on the viscoelastic Taylor-Couette instability, J. Fluid Mech. 235, 285 (1992).
  26. L. Pan, A. Morozov, C. Wagner, and P. E. Arratia, Nonlinear Elastic Instability in Channel Flows at Low Reynolds Numbers, Phys. Rev. Lett. 110, 174502 (2013).
  27. M. D. Graham, Effect of axial flow on viscoelastic Taylor-Couette instability, J. Fluid Mech. 360, 341 (1998).
  28. K. Arora and R. Sureshkumar, A viscoelastic flow instability near the solid body rotation limit, J. Non-Newtonian Fluid Mech. 132, 36 (2005).
  29. J. J. Magda and R. G. Larson, A transition occurring in ideal elastic liquids during shear flow, J. Non-Newtonian Fluid Mech. 30, 1 (1988).
  30. G. H. McKinley, J. A. Byars, R. A. Brown, and R. C. Armstrong, Observations on the elastic instability in cone-and-plate and parallel-plate flows of a polyisobutylene Boger fluid, J. Non-Newtonian Fluid Mech. 40, 201 (1991).
  31. G. H. McKinley, A. Oztekin, J. A. Byars, and R. A. Brown, Self-similar spiral instabilities in elastic flows between a cone and a plate, J. Fluid Mech. 285, 123 (1995).
  32. J. A. Byars, A. Oztekin, R. A. Brown, and G. H. McKinley, Spiral instabilities in the flow of highly elastic fluids between rotating parallel disks, J. Fluid Mech. 271, 173 (1994).
  33. H. Yamaguchi, J. Fujiyoshi, and H. Matsui, Spherical Couette flow of a viscoelastic fluid Part I: Experimental study of the inner sphere rotation, J. Non-Newtonian Fluid Mech. 69, 29 (1997).
  34. H. Yamaguchi and H. Matsui, Spherical Couette flow of a viscoelastic fluid Part II: Numerical study for the inner sphere rotation, J. Non-Newtonian Fluid Mech. 69, 47 (1997).
  35. H. Yamaguchi and B. Nishiguchi, Spherical Couette flow of a viscoelastic fluid—Part III: A study of outer sphere rotation, J. Non-Newtonian Fluid Mech. 84, 45 (1999).
  36. J. R. Stokes, L. J. W. Graham, N. J. Lawson, and D. V. Boger, Swirling flow of viscoelastic fluids. Part 1. Interaction between inertia and elasticity, J. Fluid Mech. 429, 67 (2001).
  37. J. R. Stokes, L. J. W. Graham, N. J. Lawson, and D. V. Boger, Swirling flow of viscoelastic fluids. Part 2. Elastic effects, J. Fluid Mech. 429, 117 (2001).
  38. P. Pakdel and G. H. McKinley, Cavity flows of elastic liquids: Purely elastic instabilities, Phys. Fluids 10, 1058 (1998).
  39. A. M. Grillet and E. S. G. Shaqfeh, Viscoelastic instabilities in recirculation flows of Boger fluids, J. Non-Newtonian Fluid Mech. 64, 141 (1996).
  40. A. M. Grillet, E. S. G. Shaqfeh, and B. Khomami, Observations of the viscoelastic instabilities in lid driven cavity flow, J. Non-Newtonian Fluid Mech. 94, 15 (2000).
  41. J.-H. Kim, A. Oztekin, and S. Neti, Instabilities in viscoelastic flow past a square cavity, J. Non-Newtonian Fluid Mech. 90, 261 (2000).
  42. Y. L. Joo and E. S. G. Shaqfeh, Viscoelastic Poiseuille flow through a curved channel: A new elastic instability, Phys. Fluids A 3, 1691 (1991).
  43. Y. L. Joo and E. S. G. Shaqfeh, A purely elastic instability in Dean and Taylor-Dean flow, Phys. Fluids A 4, 524 (1992).
  44. Y. L. Joo and E. S. G. Shaqfeh, The effects of inertia on the viscoelastic Dean and Taylor-Couette flow instabilities with application to coating flows, Phys. Fluids A 4, 2415 (1992).
  45. Y. L. Joo and E. S. G. Shaqfeh, Observations of purely elastic instabilities in the Taylor-Dean flow of a Boger fluid, J. Fluid Mech. 262, 27 (1994).
  46. J. A. Pathak, D. Ross, and K. B. Migler, Elastic flow instability, curved streamlines, and mixing in microfluidic flows, Phys. Fluids 16, 4028 (2004).
  47. K. Arora, R. Sureshkumar, and B. Khomami, Experimental investigation of purely elastic instabilities in periodic flows, J. Non-Newtonian Fluid Mech. 108, 209 (2002).
  48. A. Groisman and V. Steinberg, Elastic turbulence in a polymer solution flow, Nature (London) 405, 53 (2000).
  49. T. Burghelea, E. Segre, I. Bar-Joseph, A. Groisman, and V. Steinberg, Chaotic flow and efficient mixing in a microchannel with a polymer solution, Phys. Rev. E 69, 066305 (2004).
  50. J. Zilz, R. J. Poole, M. A. Alves, D. Bartolo, B. Levache, and A. Lindner, Geometric scaling of a purely elastic flow instability in serpentine channels, J. Fluid Mech. 712, 203 (2012).
  51. J. Soulages, M. S. N. Oliveira, P. C. Sousa, M. A. Alves, and G. H. McKinley, Investigating the stability of viscoelastic stagnation flows in T-shaped microchannels, J. Non-Newtonian Fluid Mech. 163, 9 (2009).
  52. P. E. Arratia, C. C. Thomas, J. Diorio, and J. P. Gollub, Elastic Instabilities of Polymer Solutions in Cross-Channel Flow, Phys. Rev. Lett. 96, 144502 (2006).
  53. R. J. Poole, M. A. Alves, and P. J. Oliveira, Purely Elastic Flow Asymmetries, Phys. Rev. Lett. 99, 164503 (2007).
  54. L. Xi and M. D. Graham, A mechanism for oscillatory instability in viscoelastic cross-slot flow, J. Fluid Mech. 622, 145 (2009).
  55. S. J. Haward and G. H. McKinley, Instabilities in stagnation point flows of polymer solutions, Phys. Fluids 25, 083104 (2013).
  56. 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).
  57. F. A. Cruz and M. A. Alves, Characterization of superimposed instabilities in the planar extensional flow of viscoelastic fluids, Phys. Rev. Fluids 3, 113301 (2018).
  58. B. Thomases and M. Shelley, Transition to Mixing and Oscillations in a Stokesian Viscoelastic Flow, Phys. Rev. Lett. 103, 094501 (2009).
  59. A. M. Afonso, M. A. Alves, R. J. Poole et al., Viscoelastic flows in mixing-separating cells, J. Eng. Math. 71, 3 (2011).
  60. M. S. N. Oliveira, F. T. Pinho, R. J. Poole, P. J. Oliveira, and M. A. Alves, Purely elastic flow asymmetries in flow-focusing devices, J. Non-Newtonian Fluid Mech. 160, 31 (2009).
  61. I. M. Dris and E. S. G. Shaqfeh, On purely elastic instabilities in eccentric cylinder flows, J. Non-Newtonian Fluid Mech. 56, 349 (1995).
  62. G. H. McKinley, R. C. Armstrong, and R. A. Brown, The wake instability in viscoelastic flow past confined circular cylinders, Philos. Trans. R. Soc. London A 344, 265 (1993).
  63. A. M. Howe, A. Clarke, and D. Giernalczyk, Flow of concentrated viscoelastic polymer solutions in porous media: Effect of MW and concentration on elastic turbulence onset in various geometries, Soft Matter 11, 6419 (2015).
  64. S. De, J. van der Schaaf, N. G. Deen, J. A. M. Kuipers, E. A. J. F. Peters, and J. T. Padding, Lane change in flows through pillared microchannels, Phys. Fluids 29, 113102 (2017).
  65. 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).
  66. M. A. Alves and R. J. Poole, Divergent flow in contractions, J. Non-Newtonian Fluid Mech. 144, 140 (2007).
  67. J. V. Lawler, S. J. Muller, R. A. Brown, and R. C. Armstrong, Laser Doppler velocimetry measurements of velocity fields and transitions in viscoelastic fluids, J. Non-Newtonian Fluid Mech. 20, 51 (1986).
  68. J. P. Rothstein and G. H. McKinley, Extensional flow of a polystyrene Boger fluid through a 4:1:4 axisymmetric contraction-expansion, J. Non-Newtonian Fluid Mech. 86, 61 (1999).
  69. D. G. Hassell, J. Embery, T. C. B. McLeish, and M. R. Mackley, An experimental evaluation of the formation of an instability in monodisperse and polydisperse polystyrenes, J. Non-Newtonian Fluid Mech. 157, 1 (2009).
  70. E. M. Ekanem, S. Berg, S. De, A. Fadili, T. Bultreys, M. Rucker, J. Southwick, J. Crawshaw, and P. F. Luckham, Signature of elastic turbulence of viscoelastic fluid flow in a single pore throat, Phys. Rev. E 101, 042605 (2020).
  71. A. Groisman and S. R. Quake, A Microfluidic Rectifier: Anisotropic Flow Resistance at Low Reynolds Numbers, Phys. Rev. Lett. 92, 094501 (2004).
  72. P. C. Sousa, F. T. Pinho, M. S. N. Oliveira, and M. A. Alves, Efficient microfluidic rectifiers for viscoelastic fluid flow, J. Non-Newtonian Fluid Mech. 165, 652 (2010).
  73. R. J. Poole, Three-dimensional viscoelastic instabilities in microchannels, J. Fluid Mech. 870, 1 (2019).
  74. G. H. McKinley, P. Pakdel, and A. Oztekin, Rheological and geometric scaling of purely elastic flow instabilities, J. Non-Newtonian Fluid Mech. 67, 19 (1996).
  75. G. H. McKinley, Dimensionless groups for understanding free surface flows of complex fluids, Rheol. Bull. 6 (2005), Society of Rheology.
  76. D. W. Beard, M. H. Davies, and K. Walters, The stability of elastico-viscous flow between rotating cylinders Part 3. Overstability in viscous and Maxwell fluids, J. Fluid Mech. 24, 321 (1966).
  77. R. F. Ginn and M. M. Denn, Rotational stability in viscoelastic liquids: Theory, AIChE J. 15, 450 (1969).
  78. M. Renardy, Y. Renardy, R. Sureshkumar, and A. Beris, Hopf-Hopf and steady-Hopf mode interactions in Taylor-Couette flow of an upper convected Maxwell liquid, J. Non-Newtonian Fluid Mech. 63, 1 (1996).
  79. D. D. Joseph, Hyperbolic phenomena in the flow of viscoelastic fluids, in Viscoelasticity and Rheology, edited by A. S. Lodge, M. Renardy, and J. A. Nohel (Academic Press, Orlando, 1985), pp. 235–321.
  80. V. Delvaux and M. J. Crochet, Numerical prediction of anomalous transport properties in viscoelastic flow, J. Non-Newtonian Fluid Mech. 37, 297 (1990).
  81. B. Qin, P. F. Salipante, S. D. Hudson, and P. Arratia, Upstream vortex and elastic wave in the viscoelastic flow around a confined cylinder, J. Fluid Mech. 864, R2-1 (2019).
  82. Y. Zhao, A. Q. Shen, and S. J. Haward, Flow of wormlike micellar solutions around confined microfluidic cylinders, Soft Matter 12, 8666 (2016).
  83. A. Varshney and V. Steinberg, Elastic Alfvén waves in elastic turbulence, Nat. Commun. 10, 652 (2019).
  84. P. P. Bhat et al., Formation of beads-on-a-string structures during break-up of viscoelastic filaments, Nat. Phys. 6, 625 (2010).
  85. C. Clasen et al., Dispensing of rheologically complex fluids: The map of misery, AIChE J. 58, 3242 (2012).
  86. U. A. Al-Mubaiyedh et al., Effect of viscous heating on the stability of viscoelastic Taylor-Couette flow, J. Fluid Mech. 462, 111 (2000).
  87. J. P. Rothstein and G. H. McKinley, Non-isothermal modification of purely elastic flow instabilities in torsional flows of polymeric fluids, Phys. Fluids 13, 382 (2001).
  88. M. M. Denn et al., Shear thickening in concentrated suspensions of smooth spheres in Newtonian suspending fluids, Soft Matter 14, 170 (2018).
  89. V. Sharma and G. H. McKinley, An intriguing empirical rule for computing the first normal stress difference from steady shear viscosity data for concentrated polymer solutions and melts, Rheol. Acta 51, 487 (2012).
  90. S. J. Haward and G. H. McKinley, Stagnation point flow of wormlike micellar solutions in a microfluidic cross-slot device: Effects of surfactant concentration and ionic environment, Phys. Rev. E 85, 031502 (2012).
  91. 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-Newtonian Fluid Mech. 278, 104250 (2020).
  92. W. Ostwald and R. Auerbach, Ueber die Viskosität kolloider Lösungen im Struktur-, Laminar- und Turbulenzgebiet, Kolloid Z. 38, 261 (1926).
  93. H. Giesekus, Nicht-Lineare Effekte beim Strömen viskoelasticher Flüssigkeiten Schlitz- and Lochdüsen (Nonlinear effects for viscoelastic liquids flowing through rectangular and circular ducts), Rheol. Acta 7, 127 (1968).
  94. J. R. A. Pearson, Instability in non-Newtonian flow, Annu. Rev. Fluid Mech. 8, 163 (1976).
  95. M. M. Denn, Extrusion instabilities and wall slip, Annu. Rev. Fluid Mech. 33, 265 (2001).
  96. V. Steinberg, Elastic turbulence: An experimental view on inertialess random flow, Annu. Rev. Fluid Mech. 53, 27 (2021).
  97. M. Avgousti and A. N. Beris, Non-axisymmetric modes in viscoelastic Taylor-Couette flow, J. Non-Newtonian Fluid Mech. 50, 225 (1993).
  98. R. Sureshkumar, A. N. Beris, and M. Avgousti, Non-axisymmetric subcritical bifurcation in viscoelastic Taylor-Couette flow, Proc. R. Soc. London A 447, 135 (1994).
  99. B. M. Baumert and S. J. Muller, Flow visualization of the elastic Taylor-Couette instability in Boger fluids, Rheol. Acta 34, 147 (1995).
  100. B. M. Baumert and S. J. Muller, Flow regimes in model viscoelastic fluids in a circular Couette system with independently rotating cylinders, Phys. Fluids 9, 566 (1997).
  101. B. M. Baumert and S. J. Muller, Axisymmetric and non-axisymmetric elastic and inertio-elastic instabilities in Taylor-Couette flow, J. Non-Newtonian Fluid Mech. 83, 33 (1999).
  102. A. Groisman and V. Steinberg, Couette-Taylor Flow in a Dilute Polymer Solution, Phys. Rev. Lett. 77, 1480 (1996).
  103. A. Groisman and V. Steinberg, Solitary Vortex Pairs in Viscoelastic Couette Flow, Phys. Rev. Lett. 78, 1460 (1997).
  104. A. Groisman and V. Steinberg, Mechanism of elastic instability in Couette flow of polymer solutions: Experiment, Phys. Fluids 10, 2451 (1998).
  105. U. A. Al-Mubaiyedh, R. Sureshkumar, and B. Khomami, Linear stability of viscoelastic Taylor-Couette flow: Influence of fluid rheology and energetics, J. Rheol. 44, 1121 (2000).
  106. J. M. White and S. J. Muller, Viscous Heating and the Stability of Newtonian and Viscoelastic Taylor-Couette Flows, Phys. Rev. Lett. 84, 5130 (2000).
  107. J. M. White and S. J. Muller, Experimental studies on the stability of Newtonian Taylor-Couette flow in the presence of viscous heating, J. Fluid Mech. 462, 133 (2002).
  108. J. M. White and S. J. Muller, Experimental studies on the effect of viscous heating on the hydrodynamic stability of viscoelastic Taylor-Couette flow, J. Rheol. 47, 1467 (2003).
  109. C. Schäfer, A. Morozov, and C. Wagner, Geometric scaling of elastic instabilities in the Taylor-Couette geometry: A theoretical, experimental and numerical study, J. Non-Newton. Fluid Mech. 259, 78 (2018).
  110. K. A. Kumar and M. D. Graham, Solitary Coherent Structures in Viscoelastic Shear Flow: Computation and Mechanism, Phys. Rev. Lett. 85, 4056 (2000).
  111. K. A. Kumar and M. D. Graham, Finite-amplitude solitary states in viscoelastic shear flow: Computation and mechanism, J. Fluid Mech. 443, 301 (2000).
  112. D. G. Thomas, R. Sureshkumar, and B. Khomami, Pattern Formation in Taylor-Couette Flow of Dilute Polymer Solutions: Dynamical Simulations and Mechanism, Phys. Rev. Lett. 97, 054501 (2006).
  113. N. Liu and B. Khomami, Elastically induced turbulence in Taylor-Couette flow: Direct numerical simulation and mechanistic insight, J. Fluid Mech. 737, R4 (2013).
  114. R. Ghanbari and B. Khomami, The onset of purely elastic and thermo-elastic instabilities in Taylor-Couette flow: Influence of gap ratio and fluid thermal sensitivity, J. Non-Newtonian Fluid Mech. 208–209, 108 (2014).
  115. J. Song, H. Teng, N. Liu, H. Ding, X.-Y. Lu, and B. Khomami, The correspondence between drag enhancement and vortical structures in turbulent Taylor-Couette flows with polymer additives: A study of curvature dependence, J. Fluid Mech. 881, 602 (2019).
  116. F. A. Cruz, R. J. Poole, A. M. Afonso, F. T. Pinho, P. J. Oliveira, and M. A. Alves, Influence of channel aspect ratio on the onset of purely-elastic flow instabilities in three-dimensional planar cross-slots, J. Non-Newtonian Fluid Mech. 227, 65 (2016).
  117. R. I. Tanner, Engineering Rheology, 2nd ed. (Oxford University Press, Oxford, 2000).
  118. J. G. Oldroyd, On the formulation of rheological equations of state, Proc. R. Soc. London A 200, 523 (1950).
  119. R. B. Bird, C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, 2nd ed. (John Wiley & Sons, New York, 1987), Vol. 2.
  120. M. W. Johnson and D. Segalman, A model for viscoelastic fluid behavior which allows non-affine deformation, J. Non-Newtonian Fluid Mech. 2, 255 (1977).
  121. R. J. Gordon and W. R. Schowalter, Anisotropic fluid theory: A different approach to the dumbbell theory of dilute polymer solutions, Trans. Soc. Rheol. 16, 79 (1972).
  122. N. Phan-Thien and R. I. Tanner, A new constitutive equation derived from network theory, J. Non-Newtonian Fluid Mech. 2, 353 (1977).
  123. A. I. Leonov and A. N. Prokunin, Nonlinear Phenomena in Flows of Viscoelastic Polymer Fluids (Chapman & Hall, London, 1994).
  124. C. Truesdell and W. Noll, The non-linear field theories of mechanics, in Handbuch der Physik, 3rd ed., edited by S. Flügge (Springer, Berlin, 2004), Vol. III/3.
  125. M. Grmela and P. J. Carreau, Conformation tensor rheological models, J. Non-Newtonian Fluid Mech. 23, 271 (1987).
  126. A. N. Beris and B. J. Edwards, Thermodynamics of Flowing Systems with Internal Microstructure (Oxford University Press, New York, 1994).
  127. A. Souvaliotis and A. N. Beris, An extended White-Metzner viscoelastic fluid model based on an internal structural parameter, J. Rheol. 36, 241 (1992).
  128. R. Sureshkumar, A. N. Beris, and R. A. Handler, Direct numerical simulation of polymer-induced drag reduction in turbulent channel flow, Phys. Fluids 9, 743 (1997).
  129. K. D. Housiadas and A. N. Beris, Direct numerical simulations of viscoelastic turbulent channel flows at high drag reduction, Korea-Australia Rheol. J. 17, 131 (2005).
  130. M. D. Graham and D. Floryan, Exact coherent states and the nonlinear dynamics of wall-bounded turbulent flows, Annu. Rev. Fluid Mech. 53, 227 (2021).
  131. L. Zhu and L. Xi, Nonasymptotic elastoinertial turbulence for asymptotic drag reduction, Phys. Rev. Fluids 6, 014601 (2021).
  132. R. Fattal and R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123, 281 (2004).
  133. R. Fattal and R. Kupferman, Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation, J. Non-Newtonian Fluid Mech. 126, 23 (2005).
  134. T. Vaithianathan and L. R. Collins, Numerical approach to simulating turbulent flow of a viscoelastic polymer solution, J. Comput. Phys. 187, 1 (2003).
  135. M. A. Hulsen, R. Fattal, and R. Kupferman, Flow of viscoelastic fluids past a cylinder at high Weissenberg number: Stabilized simulations using matrix logarithms, J. Non-Newtonian Fluid Mech. 127, 27 (2005).
  136. M. A. Alves, P. J. Oliveira, and F. T. Pinho, Numerical methods for viscoelastic fluid flows, Annu. Rev. Fluid Mech. 53, 509 (2021).
  137. B. A. Toms, Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers, in Proceedings of the International Rheological Congress (North-Holland, Amsterdam, 1949), Vol. 2, pp. 135–141.
  138. A. Seyer and A. B. Metzner, Turbulence phenomena in drag-reducing systems, AIChE J. 15, 426 (1969).
  139. J. L. Lumley, Drag reduction by additives, Annu. Rev. Fluid Mech. 1, 367 (1969).
  140. P. S. Virk, Drag reduction fundamentals, AIChE J. 21, 625 (1975).
  141. P. Garg, I. Chaudhary, M. Khalid, V. Shankar, and G. Subramanian, Viscoelastic Pipe Flow Is Linearly Unstable, Phys. Rev. Lett. 121, 024502 (2018).
  142. I. Chaudhary, P. Garg, G. Subramanian, and V. Shankar, Linear instability of viscoelastic pipe flow, J. Fluid Mech. 908, A11 (2021).
  143. J. Page, Y. Dubief, and R. R. Kerswell, Exact Traveling Wave Solutions in Viscoelastic Channel Flow, Phys. Rev. Lett. 125, 154501 (2020).
  144. Y. Dubief, J. Page, R. R. Kerswell, V. E. Terrapon, and V. Steinberg, A first coherent structure in elasto-inertial turbulence, Phys. Rev. Fluids 7, 073301 (2022).
  145. P. S. Doyle and E. S. G. Shaqfeh, Dynamic simulation of freely-draining, flexible bead-rod chains: Start-up of extensional and shear flow, J. Non-Newtonian Fluid Mech. 76, 43 (1998).
  146. R. Radhakrishnan and P. T. Underhill, Models of flexible polymers in good solvents: Relaxation and coil-stretch transition, Soft Matter 8, 6991 (2012).
  147. G. Lielens, R. Keunings, and V. Legat, The FENE-L and FENE-LS closure approximations to the kinetic theory of finitely extensible dumbbells, J. Non-Newtonian Fluid Mech. 87, 179 (1999).
  148. C. M Schroeder, Single polymer dynamics for molecular rheology, J. Rheol. 62, 371 (2018).
  149. M. H. N. Sefiddashti, B. J. Edwards, and B. Khomami, Elucidating the molecular rheology of entangled polymeric fluids via comparison of atomistic simulations and model predictions, Macromolecules 52, 8124 (2019).
  150. S. M. Fielding, Complex dynamics of shear banded flows, Soft Matter 3, 1262 (2007).
  151. N. Germann, L. P. Cook, and A. N. Beris, Nonequilibrium thermodynamic modeling of the structure and rheology of concentrated wormlike micellar solutions, J. Non-Newtonian Fluid Mech. 196, 51 (2013).
  152. V. G. Mavrantzas and A. N. Beris, A hierarchical model for surface effects on chain conformation and rheology of polymer solutions. I. General formulation, J. Chem. Phys. 110, 616; II. Application to a neutral surface, 110, 628 (1999).
  153. A. Groisman and V. Steinberg, Elastic turbulence in curvilinear flows of polymer solutions, New J. Phys. 6, 29 (2004).
  154. R. van Buel and H. Stark, Elastic turbulence in two-dimensional Taylor-Couette flows, Europhys. Lett. 124, 14001 (2018).
  155. A. Fouxon and V. Lebedev, Spectra of turbulence in dilute polymer solutions, Phys. Fluids 15, 2060 (2003).
  156. G. I. Taylor, The spectrum of turbulence, Proc. R. Soc. A 164, 476 (1938).
  157. P. C. Sousa, F. T. Pinho, and M. A. Alves, Purely-elastic flow instabilities and elastic turbulence in microfluidic cross-slot devices, Soft Matter 14, 1344 (2018).
  158. Y. Liu and V. Steinberg, Stretching of polymer in a random flow: Effect of a shear rate, Europhys. Lett. 90, 44005 (2010).
  159. R. Neelamegam, V. Shankar, and D. Das, Suppression of purely elastic instabilities in the torsional flow of viscoelastic fluid past a soft solid, Phys. Fluids 25, 124102 (2013).
  160. M. Davoodi, A. F. Domingues, and R. J. Poole, Control of a purely elastic symmetry-breaking flow instability in cross-slot geometries, J. Fluid Mech. 881, 1123 (2019).
  161. D. M. Walkama, N. Waisbord, and J. S. Guasto, Disorder Suppresses Chaos in Viscoelastic Flows, Phys. Rev. Lett. 124, 164501 (2020).
  162. R. van Buel and H. Stark, Active open-loop control of elastic turbulence, Sci. Rep. 10, 15704 (2020).
  163. V. A. Gorodtsov and A. I. Leonov, On a linear instability of a plane parallel Couette flow of viscoelastic fluid, J. Appl. Math. Mech. 31, 310 (1967).
  164. T. C. Ho and M. M. Denn, Stability of plane Poiseuille flow of a highly elastic liquid, J. Non-Newtonian Fluid Mech. 3, 179 (1977).
  165. K.-C. Lee and B. A. Finlayson, Stability of plane Poiseuille and Couette flow of a Maxwell fluid, J. Non-Newtonian Fluid Mech. 21, 65 (1986).
  166. M. Renardy and Y. Renardy, Linear stability of plane Couette flow of an upper convected Maxwell fluid, J. Non-Newtonian Fluid Mech. 22, 23 (1986).
  167. M. Renardy, A rigorous stability proof for plane Couette flow of an upper convected Maxwell fluid at zero Reynolds number, Euro. J. Mech. Fluids B 11, 511 (1992).
  168. R. G. Larson, Instabilities in viscoelastic flows, Rheol. Acta 31, 213 (1992).
  169. H. J. Wilson and J. M. Rallison, Instability of channel flow of a shear-thinning White-Metzner fluid, J. Non-Newtonian Fluid Mech. 87, 75 (1999).
  170. H. J. Wilson and V. Loridan, Linear instability of a highly shear-thinning fluid in channel flow, J. Non-Newtonian Fluid Mech. 223, 200 (2015).
  171. M. Khalid, V. Shankar, and G. Subramanian, Continuous Pathway between the Elasto-Inertial and Elastic Turbulent States in Viscoelastic Channel Flow, Phys. Rev. Lett. 127, 134502 (2021).
  172. G. Buza, J. Page, and R. R. Kerswell, Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers, J. Fluid Mech. 940, A11 (2022).
  173. P. J. Schmid, Nonmodal stability theory, Annu. Rev. Fluid Mech. 39, 129 (2007).
  174. S. Grossmann, The onset of shear flow turbulence, Rev. Mod. Phys. 72, 603 (2000).
  175. L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, Hydrodynamic stability without eigenvalues, Science 261, 578 (1993).
  176. P. J. Schmid and D. S. Henningson, Stability and Transition in Shear Flows, Applied Mathematical Sciences (Springer, New York, NY, 2000).
  177. M. R. Jovanovic and S. Kumar, Transient growth without inertia, Phys. Fluids 22, 023101 (2010).
  178. M. R. Jovanovic and S. Kumar, Nonmodal amplification of stochastic disturbances in strongly elastic channel flows, J. Non-Newtonian Fluid Mech. 166, 755 (2011).
  179. J. E. Page and T. Zaki, Streak evolution in viscoelastic Couette flow, J. Fluid Mech. 742, 520 (2014).
  180. J. E. Page and T. Zaki, The dynamics of spanwise vorticity perturbations in homogeneous viscoelastic shear flow, J. Fluid Mech. 777, 327 (2015).
  181. G. Hariharan, M. R. Jovanovic, and S. Kumar, Localized stress amplification in inertialess channel flows of viscoelastic fluids, J. Non-Newtonian Fluid Mech. 291, 104514 (2021).
  182. F. Waleffe, Transition in shear flows. Nonlinear normality versus non-normal linearity, Phys. Fluids 7, 3060 (1995).
  183. B. Eckhardt, T. Schneider, B. Hof, and J. Westerweel, Turbulence transition in pipe flow, Annu. Rev. Fluid Mech. 39, 447 (2007).
  184. B. Meulenbroek, C. Storm, V. Bertola, C. Wagner, D. Bonn, and W. van Saarloos, Intrinsic Route to Melt Fracture in Polymer Extrusion: A Weakly Nonlinear Subcritical Instability of Viscoelastic Poiseuille Flow, Phys. Rev. Lett. 90, 024502 (2003).
  185. V. Bertola, B. Meulenbroek, C. Wagner, C. Storm, A. Morozov, W. van Saarloos, and D. Bonn, Experimental Evidence for an Intrinsic Route to Polymer Melt Fracture Phenomena: A Nonlinear Instability of Viscoelastic Poiseuille Flow, Phys. Rev. Lett. 90, 114502 (2003).
  186. A. Morozov and W. van Saarloos, Subcritical Finite-Amplitude Solutions for Plane Couette Flow of Viscoelastic Fluids, Phys. Rev. Lett. 95, 024501 (2005).
  187. A. N. Morozov and W. van Saarloos, An introductory essay on subcritical instabilities and the transition to turbulence in viscoelastic parallel shear flows, Phys. Rep. 447, 112 (2007).
  188. L. S. Tuckerman, M. Chantry, and D. Barkley, Patterns in wall-bounded shear flows, Annu. Rev. Fluid Mech. 52, 343 (2020).
  189. M. Nagata, Three-dimensional finite-amplitude solutions in plane Couette flow: Bifurcation from infinity, J. Fluid Mech. 217, 519 (1990).
  190. F. Waleffe, On a self-sustaining process in shear flows, Phys. Fluids 9, 883 (1997).
  191. B. Hof, C. W. H. van Doorne, J. Westerweel, F. T. M. Nieuwstadt, H. Faisst, B. Eckhardt, H. Wedin, R. R. Kerswell, and F. Waleffe, Experimental observation of nonlinear traveling waves in turbulent pipe flow, Science 305, 1594 (2004).
  192. J. Hamilton, J. Kim, and F. Waleffe, Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech. 287, 317 (1995).
  193. D. J. C. Dennis and F. M. Sogaro, Distinct Organizational States of Fully Developed Turbulent Pipe Flow, Phys. Rev. Lett. 113, 234501 (2014).
  194. D. Bonn, F. Ingremeau, Y. Amarouchene, and H. Kellay, Large velocity fluctuations in small-Reynolds-number pipe flow of polymer solutions, Phys. Rev. E 84, 045301(R) (2011).
  195. B. Qin and P. E. Arratia, Characterizing elastic turbulence in channel flows at low Reynolds number, Phys. Rev. Fluids 2, 083302 (2017).
  196. B. Qin, P. F. Salipante, S. D. Hudson, and P. E. Arratia, Flow Resistance and Structures in Viscoelastic Channel Flows at Low Re, Phys. Rev. Lett. 123, 194501 (2019).
  197. 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).
  198. N. K. Jha and V. Steinberg, Coherent structures of elastic turbulence in straight channel with viscoelastic fluid flow, arXiv:2009.12258.
  199. N. K. Jha and V. Steinberg, Elastically driven Kelvin-Helmholtz-like instability in straight channel flow, Proc. Natl. Acad. Sci. USA 118, e2105211118 (2021).
  200. R. Shnapp and V. Steinberg, Nonmodal elastic instability and elastic waves in weakly perturbed channel flow Ron Shnapp and Victor Steinberg, Phys. Rev. Fluids 7, 063901 (2022).
  201. R. Shnapp and V. Steinberg, Splitting of localized disturbances in viscoelastic channel flow, J. Fluid Mech. 941, R3 (2022).
  202. R. Zheng, N. Phan-Thien, and R. I. Tanner, The flow past a sphere in a cylindrical tube: Effects of intertia, shear-thinning and elasticity, Rheol. Acta 30, 499 (1991).
  203. L. E. Becker, G. H. McKinley, H. Rasmussen, and O. Hassager, The unsteady motion of a sphere in a viscoelastic fluid, J. Rheol. 38, 377 (1994).
  204. M. J. Solomon and S. J. Muller, Flow past a sphere in polystyrene-based Boger fluids: The effect on the drag coefficient of finite extensibility, solvent quality and polymer molecular weight, J. Non-Newtonian Fluid Mech. 62, 81 (1996).
  205. G. H. McKinley, Steady and transient motion of spherical particles in viscoelastic liquids, in Transport Processes in Bubble, Drops, and Particles, edited by R. P. Chhabra and D. DeKee (Taylor & Francis, 2002), p. 338.
  206. A. Jayaraman and A. Belmonte, Oscillations of a solid sphere falling through a wormlike micellar fluid, Phys. Rev. E 67, 065301(R) (2003).
  207. S. Chen and J. P. Rothstein, Flow of a wormlike micelle solution past a falling sphere, J. Non-Newtonian Fluid Mech. 116, 205 (2004).
  208. K. D. Housiadas, G. C. Georgiou, and R. I. Tanner, A note on the unbounded creeping flow past a sphere for Newtonian fluids with pressure-dependent viscosity, Int. J. Eng. Sci. 86, 1 (2015).
  209. H. Mohammadigoushki and S. J. Muller, Sedimentation of a sphere in wormlike micellar fluids, J. Rheol. 60, 587 (2016).
  210. A. Anbari, H.-T. Chien, S. S. Datta, W. Deng, and D. A. Weitz, J. Fan. Microfluidic model porous media: Fabrication and applications, Small 14, 1703575 (2018).
  211. M. Müller, J. Vorwerk, and P. O. Brunn, Optical studies of local flow behaviour of a non-Newtonian fluid inside a porous medium, Rheol. Acta 37, 189 (1998).
  212. U. Eberhard, H. J. Seybold, E. Secchi, J. Jiménez-Martínez, P. A. Rühs, A. Ofner, J. S. Andrade, Jr., and M. Holzne, Mapping the local viscosity of non-Newtonian fluids flowing through disordered porous structures, Sci. Rep. 10, 11733 (2020).
  213. D. Kawale, E. Marques, P. L. J. 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).
  214. A. Varshney and V. Steinberg, Elastic wake instabilities in a creeping flow between two obstacles, Phys. Rev. Fluids 2, 051301(R) (2017).
  215. A. Varshney and V. Steinberg, Mixing layer instability and vorticity amplification in a creeping viscoelastic flow, Phys. Rev. Fluids 3, 103303 (2018).
  216. A. Varshney and V. Steinberg, Drag enhancement and drag reduction in viscoelastic flow, Phys. Rev. Fluids 3, 103302 (2018).
  217. A. A. Dey, Y. Modarres-Sadeghi, and J. P. Rothstein, Viscoelastic fluid-structure interactions between a flexible cylinder and wormlike micelle solution, Phys. Rev. Fluids 3, 063301 (2018).
  218. C. C. Hopkins, S. J. Haward, and A. Q. Shen, Purely elastic fluid-structure interactions in microfluidics: Implications for mucociliary flows, Small 16, 1903872 (2020).
  219. H. Rehage and H. Hoffmann, Rheological properties of viscoelastic surfactant systems, J. Phys. Chem. 92, 4712 (1988).
  220. H. Rehage and H. Hoffmann, Viscoelastic surfactant solutions-model system for rheological research, Mol. Phys. 74, 933 (1991).
  221. S. M. Fielding, Triggers and signatures of shear banding in steady and time-dependent flows, J. Rheol. 60, 821 (2016).
  222. 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).
  223. C. C. Hopkins, S. J. Haward, and A. Q. Shen, Tristability in Viscoelastic Flow Past Side-by-Side Microcylinders, Phys. Rev. Lett. 126, 054501 (2021).
  224. S. J. Haward, K. Toda-Peters, and A. Q. Shen, Steady viscoelastic flow around high-aspect-ratio, low-blockage-ratio microfluidic cylinders, J. Non-Newtonian Fluid Mech. 254, 23 (2018).
  225. 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).
  226. G. N. Rocha, R. J. Poole, M. A. Alves, and P. J. Oliveira, On extensibility effects in the cross-slot flow bifurcation, J. Non-Newtonian Fluid Mech. 156, 58 (2009).
  227. 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-Newtonian Fluid Mech. 166, 1064 (2011).
  228. 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-Newtonian Fluid Mech. 129, 1 (2005).
  229. 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).
  230. S. S. Datta, H. Chiang, T. S. Ramakrishnan, and D. A. Weitz, Spatial Fluctuations of Fluid Velocities in Flow through a Three-Dimensional Porous Medium, Phys. Rev. Lett. 111, 064501 (2013).
  231. C. A. Browne, A. A. Shih, and S. S. Datta. Pore-scale flow characterization of polymer solutions in microfluidic porous media, Small 16, 1903944 (2019).
  232. K. S. Sorbie, Polymer-Improved Oil Recovery (Springer Science & Business Media, 2013).
  233. D. S. Roote, Technology status report: In situ flushing, Ground Water Remediation Technology Analysis Center, http://www.gwrtac.org (1998).
  234. M. M. Smith, J. A. K. Silva, J. Munakata-Marr, and J. E. McCray, Compatibility of polymers and chemical oxidants for enhanced groundwater remediation, Environ. Sci. Technol. 42, 9296 (2008).
  235. P. Naik, P. Pandita, S. Aramideh, I. Bilionis, and A. M. Ardekani, Bayesian model calibration and optimization of surfactant-polymer flooding, Comput. Geosci. 23, 981 (2019).
  236. P. Naik, S. Aramideh, and A. M. Ardekani, History matching of surfactant-polymer flooding using polynomial chaos expansion, J. Pet. Sci. Eng. 173, 1438 (2019).
  237. S. Aramideh, R. Borgohain, P. K. Naik, C. T. Johnston, P. P. Vlachos, and A. M. Ardekani, Multi-objective history matching of surfactant-polymer flooding, Fuel 228, 418 (2018).
  238. S. S. Datta, J.-B. Dupin, and D. A. Weitz, Fluid breakup during simultaneous two-phase flow through a three-dimensional porous medium, Phys. Fluids 26, 062004 (2014).
  239. S. S. Datta, T. S. Ramakrishnan, and D. A. Weitz, Mobilization of a trapped non-wetting fluid from a three-dimensional porous medium, Phys. Fluids 26, 022002 (2014).
  240. 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).
  241. J. Mitchell, K. Lyons, A. M. Howe, and A. Clarke, Viscoelastic polymer flows and elastic turbulence in three-dimensional porous structures, Soft Matter 12, 460 (2016).
  242. A. Clarke, A. M. Howe, J. Mitchell, J. Staniland, and L. A. Hawkes, How viscoelastic-polymer flooding enhances displacement efficiency, SPE J. 21, 0675 (2016).
  243. S. Aramideh, P. P. Vlachos, and A. M. Ardekani, Nanoparticle dispersion in porous media in viscoelastic polymer solutions, J. Non-Newtonian Fluid Mech. 268, 75 (2019).
  244. S. Parsa, E. Santanach-Carreras, L. Xiao, and D. A. Weitz, Origin of anomalous polymer-induced fluid displacement in porous media, Phys. Rev. Fluids 5, 022001 (2020).
  245. S. Kenney, K. Poper, G. Chapagain, and G. F. Christopher, Large Deborah number flows around confined microfluidic cylinders, Rheol. Acta 52, 485 (2013).
  246. 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).
  247. X. Shi and G. F. Christopher, Growth of viscoelastic instabilities around linear cylinder arrays, Phys. Fluids 28, 124102 (2016).
  248. D. Kawale, E. Marques, P. L. J. 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).
  249. D. Kawale, G. Bouwman, S. Sachdev, P. L. J. Zitha, M. T. Kreutzer, W. R. Rossen, and P. E. Boukany, Polymer conformation during flow in porous media, Soft Matter 13, 8745 (2017).
  250. G. Astarita, Objective and generally applicable criteria for flow classification, J. Non-Newton. Fluid 6, 69 (1979).
  251. D. E. Smith, H. P. Babcock, and S. Chu, Single-polymer dynamics in steady shear flow, Science 283, 1724 (1999).
  252. G. G. Fuller and L. G. Leal, Flow birefringence of dilute polymer solutions in two-dimensional flows, Rheol. Acta 19, 580 (1980).
  253. N. Burshtein, S. T. Chan, K. Toda-Peters, A. Q. Shen, and S. J. Haward, 3D-printed glass microfluidics for fluid dynamics and rheology, Curr. Opin. Colloid Interface Sci. 43, 1 (2019).
  254. R. S. Maier, D. M. Kroll, R. S. Bernard, S. E. Howington, J. F. Peters, and H. T. Davis, Pore-scale simulation of dispersion, Phys. Fluids 12, 2065 (2000).
  255. S. De, S. P. Koesen, R. V. Maitri, M. Golombok, J. T. Padding, and J. F. M. van Santvoort, Flow of viscoelastic surfactants through porous media, AIChE J. 64, 773 (2018).
  256. E. Marafini, M. La Rocca, A. Fiori, I. Battiato, and P. Prestininzi, Suitability of 2D modelling to evaluate flow properties in 3D porous media, Transp. Porous Media 134, 315 (2020).
  257. R. Marshall and A. Metzner, Flow of viscoelastic fluids through porous media, Ind. Eng. Chem. Fundam. 6, 393 (1967).
  258. D. F. James and D. McLaren, The laminar flow of dilute polymer solutions through porous media, J. Fluid Mech. 70, 733 (1975).
  259. F. Durst, R. Haas, and B. Kaczmar, Flows of dilute hydrolyzed polyacrylamide solutions in porous media under various solvent conditions, J. Appl. Polym. Sci. 26, 3125 (1981).
  260. F. Durst and R. Haas, Dehnstromungen mit verdunnten Polymerlosungen: Ein theoretisches Modell und seine experimentelle Verifikations, Rheol. Acta 20, 179 (1981).
  261. N. Kauser, L. D. Santos, M. Delgado, A. Muller, and A. Saez, Flow of mixtures of poly(ethylene oxide) and hydrolyzed polyacrylamide solutions through porous media, J. Appl. Polym. Sci. 72, 783 (1999).
  262. C. A. Browne and S. S. Datta, Elastic turbulence generates anomalous flow resistance in porous media, Sci. Adv. 7, eabj2619 (2021).
  263. P. De Gennes, Molecular individualism, Science 276, 1999 (1997).
  264. S. De, J. A. M. Kuipers, E. A. J. F. Peters, and J. T. Padding, Viscoelastic flow simulations in random porous media, J. Non-Newtonian Fluid Mech. 248, 50 (2017).
  265. D. F. do Nascimento, J. R. Vimieiro Junior, S. Paciornik, and M. S. Carvalho, Pore scale visualization of drainage in 3D porous media by confocal microscopy, Sci. Rep. 9, 12333 (2019).
  266. T. Guo, A. M. Ardekani, and P. P. Vlachos, Microscale, scanning defocusing volumetric particle-tracking velocimetry, Exp. Fluids 60, 89 (2019).
  267. B. Qin, R. Ran, P. F. Salipante, S. D. Hudson, and P. E. Arratia, Three-dimensional structures and symmetry breaking in viscoelastic cross-channel flow, Soft Matter 16, 6969 (2020).
  268. S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, Real-time 3D imaging of Haines jumps in porous media flow, Proc. Natl. Acad. Sci. USA 110, 3755 (2013).
  269. T. Pak, I. B. Butler, S. Geiger, M. I. J. Van Dijke, and K. S. Sorbie, Droplet fragmentation: 3D imaging of a previously unidentified pore-scale process during multiphase flow in porous media, Proc. Natl. Acad. Sci. USA 112, 1947 (2015).
  270. O. Reynolds, An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and of the law of resistance in parallel channels, Philos. Trans. R. Soc. London A 174, 935 (1883).
  271. W. Pfenniger, Transition in the inlet length of tubes at high Reynolds numbers, in Boundary Layer and Flow Control, edited by G. V. Lachman (Pergamon, New York, 1961), pp. 970–980.
  272. A. Meseguer and L. N. Trefethen, Linearized pipe flow to Reynolds number 107, J. Comput. Phys. 186, 178 (2003).
  273. C. D. Andereck, S. S. Liu, and H. L. Swinney, Flow regimes in a circular Couette system with independently rotating cylinders, J. Fluid Mech. 164, 155 (1986).
  274. K. Avila, D. Moxey, A. De Lozar, D. Barkley, and B. Hof, The onset of turbulence in pipe flow, Science 333, 192 (2011).
  275. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981).
  276. F. Waleffe, Three-Dimensional Coherent States in Plane Shear Flows, Phys. Rev. Lett. 81, 4140 (1998).
  277. F. Waleffe, Exact coherent structures in channel flow, J. Fluid Mech. 435, 93 (2001).
  278. H. Wedin and R. R. Kerswell, Exact coherent structures in pipe flow: Travelling wave solutions, J. Fluid Mech. 508, 333 (2004).
  279. R. R. Kerswell, Recent progress in understanding the transition to turbulence in a pipe, Nonlinearity 18, R17 (2005).
  280. D. Barkley, Theoretical perspective on the route to turbulence in a pipe, J. Fluid Mech. 803, P1 (2016).
  281. N. B. Budanur, K. Y. Short, M. Farazmand, A. P. Willis, and P. Cvitanović, Relative periodic orbits form the backbone of turbulent pipe flow, J. Fluid Mech. 833, 274 (2017).
  282. B. A. Toms, in Proceedings of International Congress of Rheology (North-Holland, Amsterdam, 1949).
  283. B. A. Toms, On the early experiments on drag reduction by polymers, Phys. Fluids 20, S3 (1977).
  284. E. D. Burger, W. R. Munk, and H. A. Wahl, Flow increase in the trans Alaska pipeline through use of a polymeric drag-reducing additive, J. Petrol. Technol. 34, 377 (1982).
  285. J. K. Fink, Petroleum Engineer's Guide to Oil Field Chemicals and Fluids (Gulf Professional Publishing, 2012).
  286. G. E. King, Hydraulic fracturing 101: What every representative, environmentalist, regulator, reporter, investor, university researcher, neighbor and engineer should know about estimating frac risk and improving frac performance in unconventional gas and oil wells, in SPE Hydraulic Fracturing Technology Conference (Society of Petroleum Engineers, The Woodlands, TX, 2012).
  287. K. Kim, C.-F. Li, R. Sureshkumar, S. Balachandar, and R. J. Adrian, Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow, J. Fluid Mech. 584, 281 (2007).
  288. C. M. White and M. G. Mungal, Mechanics and prediction of turbulent drag reduction with polymer additives, Annu. Rev. Fluid Mech. 40, 235 (2008).
  289. P. A. Stone, F. Waleffe, and M. D. Graham, Toward a Structural Understanding of Turbulent Drag Reduction: Nonlinear Coherent States in Viscoelastic Shear Flows, Phys. Rev. Lett. 89, 208301 (2002).
  290. P. A. Stone, A. Roy, R. G. Larson, F. Waleffe, and M. D. Graham, Polymer drag reduction in exact coherent structures of plane shear flow, Phys. Fluids 16, 3470 (2004).
  291. W. Li and M. D. Graham, Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow, Phys. Fluids 19, 083101 (2007).
  292. W. Li, P. A. Stone, and M. D. Graham, Viscoelastic nonlinear traveling waves and drag reduction in plane Poiseuille flow, in Fluid Mechanics and Its Applications: Proceedings of the IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions Vol. 77 (2005), p. 285.
  293. W. Li, L. Xi, and M. D. Graham, Nonlinear travelling waves as a framework for understanding turbulent drag reduction, J. Fluid Mech. 565, 353 (2006).
  294. P. A. Stone and M. D. Graham, Polymer dynamics in a model of the turbulent buffer layer, Phys. Fluids 15, 1247 (2003).
  295. A. Roy, A. Morozov, W. van Saarloos, and R. G. Larson, Mechanism of Polymer Drag Reduction Using a Low-Diemensional Model, Phys. Rev. Lett. 97, 234501 (2006).
  296. D. Samanta, Y. Dubief, M. Holzner, C. Schäfer, A. N. Morozov, C. Wagner and B. Hof, Elasto-inertial turbulence, Proc. Nat. Acad. Sci. USA 110, 10557 (2013).
  297. J. M. Lopez, G. H. Choueiri, and B. Hof, Dynamics of viscoelastic pipe flow at low Reynolds numbers in the maximum drag reduction limit, J. Fluid Mech. 874, 699 (2019).
  298. V. E. Terrapon, Y. Dubief, and J. Soria, On the role of pressure in elasto-inertial turbulence, J. Turbul. 16, 26 (2014).
  299. A. Shekar, R. M. McMullen, S.-N. Wang, B. J. McKeon, and M. D. Graham, Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence, Phys. Rev. Lett. 122, 124503 (2019).
  300. G. H. Choueiri, J. M. Lopez, and B. Hof, Exceeding the Asymptotic Limit of Polymer Drag Reduction, Phys. Rev. Lett. 120, 124501 (2018).
  301. S. J. Haward, J. Page, T. A. Zaki, and A. Q. Shen, Inertioelastic Poiseuille flow over a wavy surface, Phys. Rev. Fluids 3, 091302(R) (2018).
  302. J. Page and T. A. Zaki, Viscoelastic shear flow over a wavy surface, J. Fluid Mech. 801, 392 (2016).
  303. S. J. Haward, J. Page, T. A. Zaki and A. Q. Shen, “Phase diagram” for viscoelastic Poiseuille flow over a wavy surface, Phys. Fluids 30, 113101 (2018).
  304. A. Shekar, R. M. McMullen, B. J. McKeon, and M. D. Graham, Self-sustained elastoinertial Tollmien–Schlichting waves, J. Fluid Mech. 897, A3 (2020).
  305. A. Shekar, R. M. McMullen, B. J. McKeon, and M. D. Graham, Tollmien-Schlichting route to elastoinertial turbulence in channel flow, Phys. Rev. Fluids 6, 093301 (2021).
  306. A. Pereira, R. L. Thompson, and G. Mompean, Beyond the maximum drag reduction asymptote: The pseudo-laminar state, arXiv:1911.00439.
  307. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981).
  308. M. Zhang, Energy growth in subcritical viscoelastic pipe flows, J. Non-Newton. Fluid Mech. 294, 104581 (2021).
  309. M. Khalid, I. Chaudhary, P. Garg, V. Shankar, and G. Subramanian, The centre-mode instability of viscoelastic plane Poiseuille flow, J. Fluid Mech. 915, A43 (2021).
  310. G. H. Choueiri, J. M. Lopez, A. Varshney, S. Sankar, and B. Hof, Experimental observation of the origin and structure of elasto-inertial turbulence, Proc National Acad Sci 118, e2102350118 (2021).
  311. L. Xi and M. D. Graham, Dynamics on the Laminar-Turbulent Boundary and the Origin of the Maximum Drag Reduction Asymptote, Phys. Rev. Lett. 108, 028301 (2012).
  312. I. Chaudhary, P. Garg, V. Shankar, and G. Subramanian, Elasto-inertial wall mode instabilities in viscoelastic plane Poiseuille flow, J. Fluid Mech. 881, 119 (2019).
  313. S. Sid and V. E. Terrapon, and Y. Dubief, Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction, Phys. Rev. Fluids 3, 011301(R) (2018).
  314. A. Shekar, Structures and Mechanisms in Elastoinertial Turbulence. Ph.D. thesis, University of Wisconsin–Madison (2021).
  315. H. J. Wilson, M. Renardy, and Y. Renardy, Structure of the spectrum in zero Reynolds number shear flow of the UCM and Oldroyd-B liquids, J. Non-Newtonian Fluid Mech. 80, 251 (1999).
  316. M. Zhang, I. Lashgari, T. A. Zaki, and L. Brandt, Linear stability analysis of channel flow of viscoelastic Oldroyd-B and FENE-P fluids, J. Fluid Mech. 737, 249 (2013).
  317. F. Snijkers and D. Vlassopoulos, Cone-partitioned-plate geometry for the ARES rheometer with temperature control, J. Rheol. 55, 1167 (2011).
  318. E. A. Jensen and J. de C. Christiansen, Measurements of first and second normal stress differences in a polymer melt, J. Non-Newtonian Fluid Mech. 148, 41 (2008).
  319. C.-S. Lee, B. C. Tripp, and J. J. Magda, Does N1 or N2 control the onset of edge fracture? Rheol. Acta 31, 306 (1992).
  320. Y. W. Inn, K. F. Wissbrun, and M. M. Denn, Effect of edge fracture on constant torque rheometry of entangled polymer solutions, Macromolecules 38, 9385 (2005).
  321. C. Sui and G. B. McKenna, Instability of entangled polymers in cone and plate rheometry, Rheol. Acta 46, 877 (2007).
  322. T. Schweizer and M. Stöckli, Departure from linear velocity profile at the surface of polystyrene melts during shear in cone-plate geometry, J. Rheol. 52, 713 (2008).
  323. K. M. Mattes, R. Vogt, and C. Friedrich, Analysis of the edge fracture process in oscillation for polystyrene melts, Rheol. Acta 47, 929 (2008).
  324. S.-C. Dai, E. Bertevas, F. Qi, and R. I. Tanner, Viscometric functions for noncolloidal sphere suspensions with Newtonian matrices, J. Rheol. 57, 493 (2013).
  325. S. E. Mall-Gleissle, W. Gleissle, G. H. McKinley, and H. Buggisch, The normal stress behaviour of suspensions with viscoelastic matrix fluids, Rheol. Acta 41, 61 (2002).
  326. Th. Schweizer, Comparing cone-partitioned plate and cone-standard plate shear rheometry of a polystyrene melt, J. Rheol. 47, 1071 (2003).
  327. T. Schweizer, J. van Meerveld, and H. Christian Öttinger, Nonlinear shear rheology of polystyrene melt with narrow molecular weight distribution—Experiment and theory, J. Rheol. 48, 1345 (2004).
  328. J. Meissner, R. W. Garbella, and J. Hostettler, Measuring normal stress differences in polymer melt shear flow, J. Rheol. 33, 843 (1989).
  329. T. Schweizer and W. Schmidheiny, A cone-partitioned plate rheometer cell with three partitions (CPP3) to determine shear stress and both normal stress differences for small quantities of polymeric fluids, J. Rheol. 57, 841 (2013).
  330. S. Costanzo, G. Ianniruberto, G. Marrucci, and D. Vlassopoulos, Measuring and assessing first and second normal stress differences of polymeric fluids with a modular cone-partitioned plate geometry, Rheol. Acta 57, 363 (2018).
  331. R. I. Tanner and M. Keentok, Shear fracture in cone-plate rheometry, J. Rheol. 27, 47 (1983).
  332. M. Keentok and S.-C. Xue, Edge fracture in cone-plate and parallel plate flows, Rheol. Acta 38, 321 (1999).
  333. E. J. Hemingway, H. Kusumaatmaja, and S. M. Fielding, Edge Fracture in Complex Fluids, Phys. Rev. Lett. 119, 028006 (2017).
  334. E. J. Hemingway and S. M. Fielding, Edge fracture instability in sheared complex fluids: Onset criterion and possible mitigation strategy, J. Rheol. 63, 735 (2019).
  335. E. J. Hemingway and S. M. Fielding, Edge-Induced Shear Banding in Entangled Polymeric Fluids, Phys. Rev. Lett. 120, 138002 (2018).
  336. E. J. Hemingway and S. M. Fielding, Interplay of edge fracture and shear banding in complex fluids, J. Rheol. 64, 1147 (2020).
  337. J. L. Goveas and P. D. Olmsted, A minimal model for vorticity and gradient banding in complex fluids, Eur. Phys. J. E 6, 79 (2001).
  338. E. J. Hinch, O. J. Harris, and J. M. Rallison, The instability mechanism for two elastic liquids being co-extruded, J. Non-Newtonian Fluid Mech. 43, 311 (1992).
  339. H. J. Wilson and J. M. Rallison, Short wave instability of co-extruded elastic liquids with matched viscosities, J. Non-Newtonian Fluid Mech. 72, 237 (1997).
  340. P. Nghe, S. M. Fielding, P. Tabeling, and A. Ajdari, Interfacially Driven Instability in the Microchannel Flow of a Shear-Banding Fluid, Phys. Rev. Lett. 104, 248303 (2010).
  341. S. Skorski and P. D. Olmsted, Loss of solutions in shear banding fluids driven by second normal stress differences, J. Rheol. 55, 1219 (2011).
  342. Y. Li and G. B. McKenna, Startup shear of a highly entangled polystyrene solution deep into the nonlinear viscoelastic regime, Rheol. Acta 54, 771 (2015).
  343. Y. Li, M. Hu, G. B. McKenna, C. J. Dimitriou, G. H. McKinley, R. M. Mick, D. C. Venerus, and L. A. Archer, Flow field visualization of entangled polybutadiene solutions under nonlinear viscoelastic flow conditions, J. Rheol. 57, 1411 (2013).
  344. S.-Q. Wang, G. Liu, S. Cheng, P. E. Boukany, Y. Wang, and X. Li, Letter to the editor: Sufficiently entangled polymers do show shear strain localization at high enough Weissenberg numbers, J. Rheol. 58, 1059 (2014).
  345. Y. Li, M. Hu, G. B. McKenna, C. J. Dimitriou, G. H. McKinley, R. M. Mick, D. C. Venerus, and L. A. Archer, Response to: Sufficiently entangled polymers do show shear strain localization at high enough Weissenberg numbers, J. Rheol. 58, 1071 (2014).
  346. P. E. Boukany, S.-Q. Wang, S. Ravindranath, and L. J. Lee, Shear banding in entangled polymers in the micron scale gap: A confocal-rheoscopic study, Soft Matter 11, 8058 (2015).
  347. M. M. Denn and J. F. Morris, Rheology of non-Brownian suspensions, Annu. Rev. Chem. Biomol. Eng. 5, 203 (2014).
  348. G. H. McKinley and T. Sridhar, Filament-stretching rheometry of complex fluids, Annu. Rev. Fluid Mech. 34, 375 (2002).
  349. T. Sridhar, V. Tirtaatmadja, D. A. Nguyen, R. K. Gupta, Measurement of extensional viscosity of polymer solutions, J. Non-Newtonian Fluid Mech. 40, 271 (1991).
  350. H. Münstedt, Viscoelasticity of polystyrene melts in tensile creep experiments, Rheol. Acta 14, 1077 (1975).
  351. H. Münstedt and Z. Starý, Steady states in extensional flow of strain hardening polymer melts and the uncertainties of their determination, J. Rheol. 57, 1065 (2013).
  352. H. Münstedt, Rheological experiments at constant stress as efficient method to characterize polymeric materials, J. Rheol. 58, 565 (2014).
  353. N. J. Alvarez, J. Marín, Q. Huang, M. Michelsen, and O. Hassager, Creep Measurements Confirm Steady Flow after Stress Maximum in Extension of Branched Polymer Melts, Phys. Rev. Lett. 110, 168301 (2013).
  354. M. H. Wagner, H. Bastian, A. Bernnat, S. Kurzbeck, and C. K. Chai, Determination of elongational viscosity of polymer melts by RME and Rheotens experiments, Rheol. Acta 41, 316 (2002).
  355. P. Szabo, G. H. McKinley, and C. Clasen, Constant force extensional rheometry of polymer solutions, J. Non-Newtonian Fluid Mech. 169–170, 26 (2012).
  356. V. C. Barroso and J. M. Maia, Influence of long-chain branching on the rheological behavior of polyethylene in shear and extensional flow, Polym. Eng. Sci. 45, 984 (2005).
  357. G. Liu, H. Ma, H. Lee, H. Xu, S. Cheng, H. Sun, T. Chang, R. P. Quirk, and S.-Q. Wang, Long-chain branched polymers to prolong homogeneous stretching and to resist melt breakup, Polymer 54, 6608 (2013).
  358. T. I. Burghelea, Z. Starý, and H. Münstedt, On the viscosity overshoot during the uniaxial extension of a low density polyethylene, J. Non-Newtonian Fluid Mech. 166, 1198 (2011).
  359. A. Tripathi, K. C. Tam, and G. H. McKinley, Rheology and Dynamics of Associative Polymer Solutions in Shear and Extension: Theory and Experiments, Macromolecules 39, 1981 (2006).
  360. A. Bhardwaj, E. Miller, and J. P. Rothstein, Filament stretching and capillary breakup extensional rheometry measurements of viscoelastic wormlike micelle solutions, Journal of Rheology 51, 693 (2007).
  361. M. Arciniaga, C.-C. Kuo, and M. Dennin, Size dependent brittle to ductile transition in bubble rafts, Colloids Surf. A 382, 36 (2011).
  362. M. I. Smith, R. Besseling, M. E. Cates, and V. Bertola, Dilatancy in the flow and fracture of stretched colloidal suspensions, Nat. Commun. 1, 114 (2010).
  363. R. J. Andrade and J. M. Maia, A study on the flow, failure, and rupture mechanisms of low-density polyethylene in controlled-stress uniaxial extensional flow, J. Rheol. 55, 925 (2011).
  364. A. Ya. Malkin, A. Arinstein, and V. G. Kulichikhin, Polymer extension flows and instabilities, Prog. Polym. Sci. 39, 959 (2014).
  365. Y. Wang, P. Boukany, S.-Q. Wang, and X. Wang, Elastic Breakup in Uniaxial Extension of Entangled Polymer Melts, Phys. Rev. Lett. 99, 237801 (2007).
  366. S. M. Fielding, Criterion for Extensional Necking Instability in Polymeric Fluids, Phys. Rev. Lett. 107, 258301 (2011).
  367. D. M. Hoyle and S. M. Fielding, Age-Dependent Modes of Extensional Necking Instability in Soft Glassy Materials, Phys. Rev. Lett. 114, 158301 (2015).
  368. D. M. Hoyle and S. M. Fielding, Criteria for extensional necking in complex fluids: Strain-imposed protocols, J. Rheol. 60, 1347 (2016).
  369. D. M. Hoyle and S. M. Fielding, Criteria for extensional necking in complex fluids: Stress- and force-imposed protocols, J. Rheol. 60, 1377 (2016).
  370. D. M. Hoyle and S. M. Fielding, Necking after extensional filament stretching of complex fluids and soft solids, J. Non-Newtonian Fluid Mech. 247, 132 (2017).
  371. R. Larson, Constitutive Equations for Polymer Melts and Solutions (Butterworth Publishers, Stoneham, MA, 1988).
  372. A. E. Likhtman and R. S. Graham, Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie-poly equation, J. Non-Newtonian Fluid Mech. 114, 1 (2003).
  373. T. C. B. McLeish and R. G. Larson, Molecular constitutive equations for a class of branched polymers: The pom-pom polymer, J. Rheol. 42, 81 (1998).
  374. G. H. McKinley, Visco-elasto-capillary thinning and break-up of complex fluids, in Rheology Reviews (British Society of Rheology, Aberystwyth, 2005), pp. 1–49.
  375. A. V. Bazilevskii, S. I. Voronkov, V. M. Entov, and A. N. Rozhkov, Orientational effects in the decomposition of streams and strands of diluted polymer solutions, Sov. Phys. Dokl. 26, 333 (1981).
  376. J. Eggers, Nonlinear dynamics and breakup of free-surface flows, Rev. Mod. Phys. 69, 865 (1997).
  377. J. Li and M. A. Fontelos, Drop dynamics on the beads-on-string structure of viscoelastic jets: A numerical study, Phys. Fluids 15, 922 (2003).
  378. C. Wagner, Y. Amarouchene, D. Bonn, and J. Eggers, Droplet Detachment and Satellite Bead Formation in Visco-Elastic Fluids, Phys. Rev. Lett. 95, 164504 (2005).
  379. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Volume I: Fluid Mechanics; Volume II: Kinetic Theory (Wiley, New York, 1987).
  380. A. V. Bazilevskii, V. M. Entov, and A. N. Rozhkov, Liquid filament microrheometer and some of its applications, in Proceedings of the Third European Rheology Conference, edited by D. R. Oliver (Elsevier Applied Science, New York, 1990), p. 41.
  381. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).
  382. V. M. Entov and E. J. Hinch, Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquids, J. Non-Newtonian Fluid Mech. 72, 31 (1997).
  383. S. L. Anna and G. H. McKinley, Elasto-capillary thinning and breakup of model elastic liquids, J. Rheol. 45, 115 (2001).
  384. C. Clasen, J. P. Plog, W. M. Kulicke, M. Owens, C. Macisko, L. E. Seriven, V. Verani, and G. H. McKinley, How dilute are dilute solutions in extensional flows? J. Rheol. 50, 849 (2006).
  385. A. Deblais, K. P. Velikov, and D. Bonn, Pearling Instabilities of a Viscoelastic Thread, Phys. Rev. Lett. 120, 194501 (2018).
  386. A. Deblais, M. A. Herrada, J. Eggers, and D. Bonn, Self-similarity in the breakup of very dilute viscoelastic solutions, J. Fluid Mech. 904, R2 (2020).
  387. C. Clasen, J. Eggers, M. A. Fontelos, J. Li, and G. H. McKinley, The beads-on-string structure of viscoelastic jets, J. Fluid Mech. 556, 283 (2006).
  388. J. Eggers, M. A. Herrada, and J. H. Snoeijer, Self-similar breakup of polymeric threads as described by the Oldroyd-B model, J. Fluid Mech. 887, A19 (2020).
  389. J. Dinic and V. Sharma, Macromolecular relaxation, strain, and extensibility determine elastocapillary thinning and extensional viscosity of polymer solutions, Proc. Natl. Acad. Sci. USA 116, 8766 (2019).
  390. J. Dinic and V. Sharma, Flexibility, extensibility, and ratio of Kuhn length to packing length govern the pinching dynamics, coil-stretch transition, and rheology of polymer solutions, Macromolecules 53, 4821 (2020).
  391. M. Renardy, Similarity solutions for jet break-up for various models of viscoelastic fluids, J. Non-Newtonian Fluid Mech. 104, 65 (2002).
  392. M. A. Fontelos and J. Li, On the evolution and rupture of filaments in Giesekus and FENE models, J. Non-Newtonian Fluid Mech. 118, 1 (2004).
  393. J. Eggers and E. Villermaux, Physics of liquid jets, Rep. Prog. Phys. 71, 036601 (2008).
  394. M. S. N. Oliveira and G. H. McKinley, Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of high extensible flexible polymers, Phys. Fluids 17, 071704 (2005).
  395. H.-C. Chang, E. A. Demekhin, and E. Kalaidin, Iterated stretching of viscoelastic jets, Phys. Fluids 11, 1717 (1999).
  396. R. Sattler, C. Wagner, and J. Eggers, Blistering Pattern and Formation of Nanofibers in Capillary Thinning of Polymer Solutions, Phys. Rev. Lett. 100, 164502 (2008).
  397. R. Sattler, S. Gier, J. Eggers, and C. Wagner, The final stages of capillary break-up of polymer solutions, Phys. Fluids 24, 023101 (2012).
  398. J. Eggers, Instability of a polymeric thread, Phys. Fluids 26, 033106 (2014).
  399. E. Helfand and G. H. Fredrickson, Large Fluctuations in Polymer Solutions under Shear, Phys. Rev. Lett. 62, 2468 (1989).
  400. M. Cromer, M. C. Villet, G. H. Fredrickson, and L. G. Leal, Shear banding in polymer solutions, Phys. Fluids 25, 051703 (2013).
  401. A. N. Beris and V. G. Mavrantzas, On the compatibility between various macroscopic formalisms for the concentration and flow of dilute polymer solutions, J. Rheol. 38, 1235 (1994).
  402. S. Ya. Frenkel', V. G. Baranov, N. G. Belanikevich, and Yu. N. Panov, Orientation mechanism of solid phase formation in polymer solutions subjected to a longitudinal hydrodynamic field, Polym. Sci. USSR 6, 2124 (1964).
  403. A. V. Semakov, V. G. Kulichikhin, A. K. Tereshin, S. V. Antonov, and A. Ya. Malkin, On the nature of phase separation of polymer solutions at high extension rates, J. Polym. Sci. B 53, 559 (2015).
  404. N. J. Balmforth, I. A. Frigaard, and G. Ovarlez, Yielding to stress: Recent developments in viscoplastic fluid mechanics, Annu. Rev. Fluid Mech. 46, 121 (2014).
  405. G. Ovarlez and S. Hormozi, Lectures on Visco-Plastic Fluid Mechanics, edited by G. Ovarlez and S. Hormozi, CISM International Centre for Mechanical Sciences (Springer, Cham, 2019).
  406. Y. Holenberg, O. M. Lavrenteva, U. Shavit, and A. Nir, Particle tracking velocimetry and particle image velocimetry study of the slow motion of rough and smooth solid spheres in a yield-stress fluid, Phys. Rev. E 86, 066301 (2012).
  407. F. Ahonguio, L. Jossic, and A. Magnin, Influence of surface properties on the flow of a yield stress fluid around spheres, J. Non-Newtonian Fluid Mech. 206, 57 (2014).
  408. M. Firouznia, B. Metzger, G. Ovarlez, and S. Hormozi, The interaction of two spherical particles in simple-shear flows of yield stress fluids, J. Non-Newtonian Fluid Mech. 255, 19 (2018).
  409. D. Fraggedakis, Y. Dimakopoulos, and J. Tsamopoulos, Yielding the yield-stress analysis: A study focused on the effects of elasticity on the settling of a single spherical particle in simple yield-stress fluids, Soft Matter 12, 5378 (2016).
  410. M. Sarabian, M. Rosti, L. Brandt, and S. Hormozi, Numerical simulations of a sphere settling in simple shear flows of yield stress fluids, J. Fluid Mech. 896, A17-1 (2020).
  411. C. J. Dimitriou, R. H. Ewoldt and G. H. McKinley, Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress), J. Rheol. 57, 27 (2013).
  412. C. J. Dimitriou and G. H. McKinley, A comprehensive constitutive law for waxy crude oil: A thixotropic yield stress fluid, Soft Matter 10, 6619 (2014).
  413. C. Nouar et al., Modal and non-modal linear stability of the plane Bingham-Poiseuille flow, J. Fluid Mech. 577, 211 (2007).
  414. C. Metivier, C. Nouar, and J. P. Brancher, Linear stability involving the Bingham model when the yield stress approaches zero, Phys. Fluids 17, 104106 (2005).
  415. S. Hormozi and I. A. Frigaard, Nonlinear stability of a visco-plastically lubricated viscoelastic fluid flow, J. Non-Newtonian Fluid Mech. 169-170, 61 (2012).
  416. C. Metivier, C. Nouar and J. P. Brancher, Weakly nonlinear dynamics of thermoconvective instability involving viscoplastic fluids, J. Fluid Mech. 660, 316 (2010).
  417. M. A. Moyers-Gonzalez et al., Transient effects in oilfield cementing flows: Qualitative behaviour, Eur. J. Appl. Math. 18, 477 (2007).
  418. C. Nouar and I. A. Frigaard, Nonlinear stability of Poiseuille flow of a Bingham fluid: Theoretical results and comparison with phenomenological criteria, J. Non-Newtonian Fluid Mech. 100, 127 (2001).
  419. J. P. Rothstein and H. Mohammadigoushki, Complex flows of viscoelastic wormlike micelle solutions, J. Non-Newtonian Fluid Mech. 285, 104382 (2020).
  420. C. A. Dreiss, Wormlike micelles: Where do we stand? Recent developments, linear rheology and scattering techniques, Soft Matter 3, 956 (2007).
  421. J. Yang, Viscoelastic wormlike micelles and their applications, Curr. Opin. Colloid Interface Sci. 7, 276 (2002).
  422. P. D. Olmsted, Perspectives on shear banding in complex fluids, Rheol. Acta 47, 283 (2008).
  423. M.-A. Fardin and S. Lerouge, Flows of living polymer fluids, Soft Matter 10, 8789 (2014).
  424. N. Kumar, S. Majumdar, A. Sood, R. Govindarajan, S. Ramaswamy, and A. K. Sood, Oscillatory settling in wormlike-micelle solutions: Bursts and a long time scale, Soft Matter 8, 4310 (2012).
  425. M. Kostrzewa, A. Delgado, and A. Wierschem, Particle settling in micellar solutions of varying concentration and salt content, Acta Mech. 227, 677 (2016).
  426. S. Wu and H. Mohammadigoushki, Sphere sedimentation in wormlike micelles: Effect of micellar relaxation spectrum and gradients in micellar extensions, J. Rheol. 62, 1061 (2018).
  427. H. Mohammadigoushki and S. J. Muller, Creeping flow of a wormlike micelle solution past a falling sphere: Role of boundary conditions, J. Non-Newtonian Fluid Mech. 257, 44 (2018).
  428. Y. Zhang and S. J. Muller, Unsteady sedimentation of a sphere in wormlike micellar fluids, Phys. Rev. Fluids 3, 043301 (2018).
  429. Z. Wang, S. Wang, L. Xu, Y. Dou, and X. Su, Extremely slow settling behavior of particles in dilute wormlike micellar fluid with broad spectrum of relaxation times, J. Disp. Sci. Tech. 41, 639 (2020).
  430. C. Sasmal, Unsteady motion past a sphere translating steadily in wormlike micellar solutions: A numerical analysis, J. Fluid Mech. 912, A52 (2021).
  431. P. A. Vasquez, G. H. McKinley, and L. P. Cook, A network scission model for wormlike micellar solutions I. Model formulation and viscometric flow predictions, J. Non-Newtonian Fluid Mech. 144, 122 (2007).
  432. C. J. Pipe, N. J. Kim, P. A. Vasquez, L. P. Cook, and G. H. McKinley, Wormlike micellar solutions: II. Comparison between experimental data and scission model predictions, J. Rheol. 54, 881 (2010).
  433. L. Zhou, G. H. McKinley, and L. P. Cook, Wormlike micellar solutions: III. VCM model predictions in steady and transient shearing flows, J. Non-Newtonian Fluid Mech. 211, 70 (2014).
  434. J. E. López-Aguilar, M. F. Webster, H. R. Tamaddon-Jahromi, and O. Manero, Predictions for circular contraction-expansion flows with viscoelastoplastic & thixotropic fluids, J. Non-Newtonian Fluid Mech. 261, 188 (2018).
  435. J. Gladden and A. Belmonte, Motion of a Viscoelastic Micellar Fluid Around a Cylinder: Flow and Fracture, Phys. Rev. Lett. 98, 224501 (2007).
  436. G. R. Moss and J. P. Rothstein, Flow of wormlike micelle solutions past a confined circular cylinder, J. Non-Newtonian Fluid Mech. 165, 1505 (2010).
  437. M. B. Khan and C. Sasmal, Effect of chain scission on flow characteristics of wormlike micellar solutions past a confined microfluidic cylinder: A numerical, Soft Matter 16, 5261 (2020).
  438. T. Hashimoto, K. Kido, S. Kaki, T. Yamamoto, and N. Mori, Effects of surfactant and salt concentrations on capillary flow and its entry flow for wormlike micelle solutions, Rheol. Acta 45, 841 (2006).
  439. V. Lutz-Bueno, J. Kohlbrecher, and P. Fischer, Micellar solutions in contraction slit-flow: Alignment mapped by SANS, J. Non-Newtonian Fluid Mech. 215, 8 (2015).
  440. P. F. Salipante, S. E. Meek, and S. D. Hudson, Flow fluctuations in wormlike micelle fluids, Soft Matter 14, 9020 (2018).
  441. R. M. Matos, M. A. Alves, and F. T. Pinho, Instabilities in micro-contraction flows of semi-dilute CTAB and CPyCl solutions: Rheology and flow instabilities, Exp. Fluids 60, 145 (2019).
  442. C. Sasmal, Flow of wormlike micellar solutions through a long micropore with step expansion and contraction, Phys. Fluids 32, 013103 (2020).
  443. J. E. López-Aguilar, M. F. Webster, H. R. Tamaddon-Jahromi, and O. Manero, A new constitutive model for worm-like micellar systems—Numerical simulation of confined contraction-expansion flows, J. Non-Newtonian Fluid Mech. 204, 7 (2014).
  444. J. E. López-Aguilar, M. F. Webster, H. R. Tamaddon-Jahromi, and O. Manero, High-Weissenberg predictions for micellar fluids in contraction-expansion flows, J. Non-Newtonian Fluid Mech. 222, 190 (2015).
  445. J. E. López-Aguilar, M. F. Webster, H. R. Tamaddon-Jahromi, and O. Manero, Numerical modelling of thixotropic and viscoelastoplastic materials in complex flows, Rheol. Acta 54, 307 (2015).
  446. S. Tabatabaei, J. E. López-Aguilar, H. R. Tamaddon-Jahromi, M. F. Webster, and R. Williams, Modified Bautista-Manero (MBM) modelling for hyperbolic contraction-expansion flows, Rheol. Acta 54, 869 (2015).
  447. J. E. López-Aguilar, M. F. Webster, H. R. Tamaddon-Jahromi, and O. Manero, Convoluted models and high-Weissenberg predictions for micellar thixotropic fluids in contraction-expansion flows, J. Non-Newtonian Fluid Mech. 232, 55 (2016).
  448. J. E. López-Aguilar, M. F. Webster, H. R. Tamaddon-Jahromi, and O. Manero, A comparative numerical study of time-dependent structured fluids in complex flows, Rheol. Acta 55, 197 (2016).
  449. J. A. Pathak and S. D. Hudson, Rheo-optics of equilibrium polymer solutions: Wormlike micelles in elongational flow in a microfluidic cross-slot, Macromolecules 39, 8782 (2006).
  450. N. Dubash, P. Cheung, and A. Q. Shen, Elastic instabilities in a microfluidic cross-slot flow of wormlike micellar solutions, Soft Matter 8, 5847 (2012).
  451. A. Kalb, L. A. Villasmil-Urdaneta, and M. Cromer, Role of chain scission in cross-slot flow of wormlike micellar solutions, Phys. Rev. Fluids 2, 071301(R) (2017).
  452. A. Kalb, L. A. Villasmil-Urdaneta, and M. Cromer, Elastic instability and secondary flow in cross-slot flow of wormlike micellar solutions, J. Non-Newtonian Fluid Mech. 262, 79 (2018).
  453. J. P. Rothstein, Transient extensional rheology of wormlike micelle solutions,, J. Rheol. 47, 1227 (2003).
  454. E. Miller, C. Clasen, and J. P. Rothstein, The effect of step-stretch parameters on capillary breakup extensional rheology (CaBER) measurements, Rheol. Acta 48, 625 (2009).
  455. B. Yesilata, C. Clasen, and G. H. McKinley, Nonlinear shear and extensional flow dynamics of wormlike surfactant solutions, J. Non-Newtonian Fluid Mech. 133, 73 (2006).
  456. N. J. Kim, C. J. Pipe, K. H. Ahn, S. J. Lee, and G. H. McKinley, Capillary breakup extensional rheometry of a wormlike micellar solution, Korea-Australia Rheol. J. 22, 31 (2010).
  457. D. Sachsenheimer, C. Oelschlaeger, S. Müller, J. Küstner, S. Bindgen, and N. Willenbacher, Elongational deformation of wormlike micellar solutions, J. Rheol. 58, 2017 (2017).
  458. R. Omidvar, A. Dalili, A. Mir, and H. Mohammadigoushki, Exploring sensitivity of the extensional flow to wormlike micellar structure, J. Non-Newtonian Fluid Mech. 252, 48 (2018).
  459. R. Omidvar, S. Wu, and H. Mohammadigoushki, Detecting wormlike micellar microstructure using extensional rheology, J. Rheol. 63, 33 (2019).
  460. M. Cromer, L. P. Cook, and G. H. McKinley, Extensional flow of wormlike micellar solutions, Chem. Eng. Sci. 64, 4588 (2009).
  461. A. A. Dey, Y. Modarres-Sadeghi, and J. P. Rothstein, Viscoelastic flow-induced oscillations of a cantilevered beam in the crossflow of a wormlike micelle solution, J. Non-Newtonian Fluid Mech. 286, 104433 (2020).
  462. S. Lerouge and J. F. Berret, Shear-induced transitions and instabilities in surfactant wormlike micelles, in K. Dusek, J. F. Joanny (eds.) Adv. Polym. Sci.: Polym. Charact. 230, 1 (2009).
  463. S. Lerouge, M. Argentina, and J. P. Decruppe, Interface Instability in Shear-Banding Flow, Phys. Rev. Lett. 96, 088301 (2006).
  464. S. Lerouge, M. A. Fardin, M. Argentina, G. Grégoire, and O. Cardoso, Interface dynamics in shear-banding flow of giant micelles, Soft Matter 4, 1808 (2008).
  465. M. A. Fardin, B. Lasne, O. Cardoso, G. Grégoire, M. Argentina, J. P. Decruppe, and S. Lerouge, Taylor-Like Vortices in Shear-Banding Flow of Giant Micelles, Phys. Rev. Lett. 103, 028302 (2009).
  466. M. A. Fardin, D. Lopez, J. Croso, G. Grégoire, O. Cardoso, G. H. McKinley, and S. Lerouge, Elastic Turbulence in Shear Banding Wormlike Micelles, Phys. Rev. Lett. 104, 178303 (2010).
  467. S. Fielding, Viscoelastic Taylor-Couette Instability of Shear Banded Flow, Phys. Rev. Lett. 104, 198303 (2010).
  468. A. Nicolas and A. Morozov, Nonaxisymmetric Instability of Shear-Banded Taylor-Couette Flow, Phys. Rev. Lett. 108, 088302 (2012).
  469. M. A. Fardin, T. J. Ober, C. Gay, G. Grégoire, G. H. McKinley, and S. Lerouge, Criterion for purely elastic Taylor-Couette instability in the flows of shear-banding fluids, Europhys. Lett. 96, 44004 (2011).
  470. M. A. Fardin, T. J. Ober, V. Grenard, T. Divoux, S. Manneville, G. H. McKinley, and S. Lerouge, Interplay between elastic instabilities and shear-banding: Three categories of Taylor-Couette flows and beyond, Soft Matter 8, 10072 (2012).
  471. M. A. Fardin, C. Perge, N. Taberlet, and S. Manneville, Flow-induced structures versus flow instabilities, Phys. Rev. E 89, 011001(R) (2014).
  472. C. Perge, M. A. Fardin, and S. Manneville, Inertio-elastic instability of non shear-banding wormlike micelles, Soft Matter 10, 1450 (2013).
  473. M. A. Fardin, L. Casanellas, B. Saint-Michel, S. Manneville, and S. Lerouge, Shear-banding in wormlike micelles: Beware of elastic instabilities, J. Rheol. 60, 917 (2016).
  474. M. S. Turner and M. E. Cates, Flow-induced phase transitions in rod-like micelles, J. Phys.: Condens. Matter 4, 3719 (1992).
  475. S. Dutta and M. D. Graham, Mechanistic constitutive model for wormlike micelle solutions with flow-induced structure formation, J. Non-Newtonian Fluid Mech. 251, 97 (2018).
  476. R. J. Hommel and M. D. Graham, Constitutive modeling of dilute wormlike micelle solutions: Shear-induced structure and transient dynamics, J. Non-Newtonian Fluid Mech. 295, 104606 (2021).
  477. J. E. López-Aguilar, M. F. Webster, H. R. Tamaddon-Jahromi, and O. Manero, On shear-banding and wormlike micellar system response under complex flow, Ann. Trans. Nord. Soc. Rheol. 25, 197 (2017).
  478. F. Bautista, J. H. Pérez-López, J. P. García, J. E. Puig, and O. Manero, Stability analysis of shear banding flow with the BMP model, J. Non-Newton. Fluid Mech. 144, 160 (2007).
  479. J. P. García-Sandoval, O. Manero, F. Bautista, and J. E. Puig, Inhomogeneous flows and shear banding formation in micellar solutions: Predictions of the BMP model, J. Non-Newton. Fluid Mech. 179–180, 43 (2012).
  480. S. Hooshyar and N. Germann, Shear banding of semidilute polymer solutions in pressure-driven channel flow, J. Non-Newton. Fluid Mech. 242, 1 (2017).
  481. S. Hooshyar and N. Germann, Shear banding in 4:1 planar contraction, Polymers 11, 417 (2019).
  482. P. D. Olmsted, O. Radulescu, and C. Y. F. Lu, Johnson-Segalman model with a diffusion term in a cylindrical Couette flow, J. Rheol. 44, 257 (2000).
  483. A. K. Gurnon and N. J. Wagner, Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles, J. Rheol. 56, 333 (2012).
  484. N. Germann, A. K. Gurnon, L. Zhou, L. P. Cook, A. N. Beris, and N. J. Wagner, Validation of constitutive modeling of shear banding, threadlike wormlike micellar fluids, J. Rheol. 60, 983 (2016).
  485. R. Radhakrishnan, T. Divoux, S. Manneville, and S. M. Fielding, Understanding rheological hysteresis in soft glassy materials, Soft Matter 13, 1834 (2017).
  486. R. Radhakrishnan and S. M. Fielding, Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of soft glassy materials, J. Rheol. 62, 559 (2018)\.
  487. M. F. Webster, H. R. Tamaddon-Jahromi, J. E. López-Aguilar, and D. M. Binding, Enhanced pressure drop, planar contraction flows and continuous-spectrum models, J. Non-Newtonian Fluid Mech. 273, 104184 (2019).
  488. M. T. Arigo and G. H. McKinley, An experimental investigation of negative wakes behind spheres settling in a shear-thinning viscoelastic fluid, Rheol. Acta 37, 307 (1998).
  489. A. N. Beris, B. J. Edwards et al., Thermodynamics of Flowing Systems: With Internal Microstructure, no. 36 (Oxford University Press, Oxford, 1994).
  490. P. Oswald and P. Pieranski, Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments (CRC Press, Boca Raton, FL, 2005).
  491. P. Mather, D. Pearson, and R. Larson, Flow patterns and disclination-density measurements in sheared nematic liquid crystals II: Tumbling 8CB, Liq. Cryst. 20, 539 (1996).
  492. R. Larson and D. Mead, Development of orientation and texture during shearing of liquid-crystalline polymers, Liq. Cryst. 12, 751 (1992).
  493. G. Duclos, R. Adkins, D. Banerjee, M. S. Peterson, M. Varghese, I. Kolvin, A. Baskaran, R. A. Pelcovits, T. R. Powers, A. Baskaran et al., Topological structure and dynamics of three-dimensional active nematics, Science 367, 1120 (2020).
  494. P. J. Collings, J. N. Goldstein, E. J. Hamilton, B. R. Mercado, K. J. Nieser, and M. H. Regan, The nature of the assembly process in chromonic liquid crystals, Liq. Cryst. Rev. 3, 1 (2015).
  495. S. Zhou, A. Sokolov, O. D. Lavrentovich, and I. S. Aranson, Living liquid crystals, Proc. Natl. Acad. Sci. USA 111, 1265 (2014).
  496. C. Peng, T. Turiv, Y. Guo, Q.-H. Wei, and O. D. Lavrentovich, Command of active matter by topological defects and patterns, Science 354, 882 (2016).
  497. S. Zhou, Y. A. Nastishin, M. Omelchenko, L. Tortora, V. Nazarenko, O. Boiko, T. Ostapenko, T. Hu, C. Almasan, S. Sprunt et al., Elasticity of Lyotropic Chromonic Liquid Crystals Probed by Director Reorientation in a Magnetic Field, Phys. Rev. Lett. 109, 037801 (2012).
  498. L. Tortora and O. D. Lavrentovich, Chiral symmetry breaking by spatial confinement in tactoidal droplets of lyotropic chromonic liquid crystals, Proc. Natl. Acad. Sci. USA 108, 5163 (2011).
  499. G. Park, S. Copar, A. Suh, M. Yang, U. Tkalec, and D. K. Yoon, Periodic arrays of chiral domains generated from the self-assembly of micropatterned achiral lyotropic chromonic liquid crystal, ACS Cent. Sci. 6, 1964 (2020).
  500. H. Baza, T. Turiv, B.-X. Li, R. Li, B. M. Yavitt, M. Fukuto, and O. D. Lavrentovich, Shear-induced polydomain structures of nematic lyotropic chromonic liquid crystal disodium cromoglycate, Soft Matter 16, 8565 (2020).
  501. Q. Zhang, B. Ge, R. Zhang, Z. Yaqoob, P. T. C. So, and I. Bischofberger, Structures and topological defects in pressure-driven lyotropic chromonic liquid crystals, Proc. Natl. Acad. Sci. USA 118, e2108361118 (2021).
  502. E. Balkovsky, A. Fouxon, and V. Lebedev, Turbulence of polymer solutions, Phys. Rev. E 64, 056301 (2001).
  503. E. Afik and V. Steinberg, On the role of initial velocities in pair dispersion in a microfluidic chaotic flow, Nat. Commun. 8, 468 (2017).
  504. V. Kumar, A. Varshney, D. Li, and V. Steinberg, Relaminarization of elastic turbulence, Phys. Rev. Fluids 7, L081301 (2022).
  505. A. Groisman and V. Steinberg, Efficient mixing at low Reynolds numbers using polymer additives, Nature (London) 410, 905 (2001).
  506. T. Burghelea, E. Segre, and V. Steinberg, Mixing by Polymers: Experimental Test of Decay Regime of Mixing, Phys. Rev. Lett. 92, 164501 (2004).
  507. B. Traore, C. Castelain, and T. Burghelea, Efficient heat transfer in a regime of elastic turbulence, J. Non-Newtonian Fluid Mech. 223, 62 (2015).
  508. W. M. Abed, R. D. Whalley, D. J. Dennis, and R. J. Poole, Experimental investigation of the impact of elastic turbulence on heat transfer in a serpentine channel, J. Non-Newtonian Fluid Mech. 231, 68 (2016).
  509. D. Y. Li, H. Zhang, J. P. Cheng, X. B. Li, F. C. Li, S. Qian, and S. W. Joo, Numerical simulation of heat transfer enhancement by elastic turbulence in a curvy channel, Microfluid. Nanofluid. 21, 25 (2017).
  510. H. Yang, G. Yao, and D. Wen, Experimental investigation on convective heat transfer of Shear-thinning fluids by elastic turbulence in a serpentine channel, Exp. Therm. Fluid Sci. 112, 109997 (2020).
  511. R. J. Poole, B. Budhiraja, A. R. Cain, and P. A. Scott, Emulsification using elastic turbulence, J. Non-Newtonian Fluid Mech. 177-178, 15 (2012).

Outline

Information

Phys. Rev. Fluids 7, 080701– Published 29 August, 2022
  • Received 1 August 2021
  • Accepted 21 March 2022
Article part of CHORUS
Crossmark - Check for updates button

©2022 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation