Skip to main content Accessibility help
×
×
Home

Polymer turbulence with Reynolds and Riemann

  • Michael D. Graham (a1) (a2)

Abstract

Models of flowing complex fluids such as polymer solutions often use a conformation tensor that reflects the state of the fluid microstructure. In polymer solutions, this quantity measures the orientation and stretching of the molecules, and reflects the fact that the squared length of a polymer molecule must be positive. By exploiting results from differential geometry and continuum mechanics, Hameduddin et al. (J. Fluid Mech., vol. 842, 2018, pp. 395–427) introduce a new approach for analysing the conformation tensor that respects this positivity constraint. With this approach, they present computational results for turbulent flow of a polymer solution that exhibits turbulent drag reduction, showing that the new measures of polymer stretching afforded by their approach lend insights not available in traditional methods.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Polymer turbulence with Reynolds and Riemann
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Polymer turbulence with Reynolds and Riemann
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Polymer turbulence with Reynolds and Riemann
      Available formats
      ×

Copyright

Corresponding author

Email address for correspondence: mdgraham@wisc.edu

References

Hide All
Arratia, P. E., Thomas, C. C., Diorio, J. & Gollub, J. P. 2006 Elastic instabilities of polymer solutions in cross-channel flow. Phys. Rev. Lett. 96, 144502.
Barthes-Biesel, D. & Rallison, J. M. 1981 The time-dependent deformation of a capsule freely suspended in a linear shear-flow. J. Fluid Mech. 113, 251267.
Doering, C., Eckhardt, B. & Schumacher, J. 2006 Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers. J. Non-Newtonian Fluid Mech. 135 (2–3), 9296.
Graham, M. D. 2014 Drag reduction and the dynamics of turbulence in simple and complex fluids. Phys. Fluids 26, 101301.
Hameduddin, I., Meneveau, C., Zaki, T. A. & Gayme, D. F. 2018 Geometric decomposition of the conformation tensor in viscoelastic turbulence. J. Fluid Mech. 842, 395427.
Lang, S. 1999 Fundamentals of Differential Geometry. Springer.
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 132.
Moyers-Gonzalez, M., Owens, R. G. & Fang, J. 2008 A non-homogeneous constitutive model for human blood. Part 1. Model derivation and steady flow. J. Fluid Mech. 617, 327.
Pan, L., Morozov, A., Wagner, C. & Arratia, P. E. 2013 Nonlinear elastic instability in channel flows at low Reynolds numbers. Phys. Rev. Lett. 110 (17), 174502.
Samanta, D., Dubief, Y., Holzner, M., Schäfer, C., Morozov, A. N., Wagner, C. & Hof, B. 2013 Elasto-inertial turbulence. Proc. Natl Acad. Sci. USA 110 (26), 1055710562.
Shaqfeh, E. S. G. 1996 Purely elastic instabilities in viscometric flows. Annu. Rev. Fluid Mech. 28, 129185.
Wang, S.-N., Graham, M. D., Hahn, F. J. & Xi, L. 2014 Time-series and extended Karhunen–Loève analysis of turbulent drag reduction in polymer solutions. AIChE J. 60 (4), 14601475.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed