Hostname: page-component-7dd5485656-frp75 Total loading time: 0 Render date: 2025-10-31T13:30:36.476Z Has data issue: false hasContentIssue false
  • English
  • Français

Deformation of a flexible polymer in a random flow with long correlation time

Published online by Cambridge University Press:  07 February 2011

STEFANO MUSACCHIO  and
DARIO VINCENZI
STEFANO MUSACCHIO
Affiliation:
CNRS UMR 6621, Laboratoire J.-A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice, France
DARIO VINCENZI*
Affiliation:
CNRS UMR 6621, Laboratoire J.-A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice, France
*
†Email address for correspondence: dario.vincenzi@unice.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects induced by long temporal correlations of the velocity gradients on the dynamics of a flexible polymer are investigated by means of theoretical and numerical analysis of the Hookean and finitely extensible nonlinear elastic (FENE) dumbbell models in a random renewing flow. For Hookean dumbbells, we show that long temporal correlations strongly suppress the Weissenberg-number dependence of the power-law tail characterising the probability density function (PDF) of the elongation. For the FENE model, the PDF becomes bimodal, and the coil–stretch transition occurs through the simultaneous drop and rise of the two peaks associated with the coiled and stretched configurations, respectively.

JFM classification

Non-Newtonian Flows: Polymers

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 670 , 10 March 2011 , pp. 326 - 336
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Bagheri, F., Mitra, D., Perlekar, P. & Brandt, L. 2010 Statistics of polymer extensions in turbulent channel flow. arXiv:1011.3766v1 [physics.flu-dyn]Google Scholar
Balkovsky, E., Fouxon, A. & Lebedev, V. 2000 Turbulent dynamics of polymer solutions. Phys. Rev. Lett. 84, 4765–4768.CrossRefGoogle ScholarPubMed
Bird, R. B., Hassager, O., Armstrong, R. C. & Curtiss, C. F. 1977 Dynamics of Polymeric Liquids, vol. II. Wiley.Google Scholar
Boffetta, G., Celani, A. & Musacchio, S. 2003 Two-dimensional turbulence of dilute polymer solutions. Phys. Rev. Lett. 91, 034501.CrossRefGoogle ScholarPubMed
Celani, A., Musacchio, S. & Vincenzi, D. 2005 Polymer transport in random flow. J. Stat. Phys. 118, 531–554.CrossRefGoogle Scholar
Chertkov, M. 2000 Polymer stretching by turbulence. Phys. Rev. Lett. 84, 4761–4764.CrossRefGoogle ScholarPubMed
Chertkov, M., Falkovich, G., Kolokolov, I. & Lebedev, V. 1996 Theory of random advection in two dimensions. Intl J. Mod. Phys. B 10, 2273–2309.CrossRefGoogle Scholar
Childress, S. & Gilbert, A. D. 1995 Stretch, Twist, Fold: The Fast Dynamo. Springer.Google Scholar
Crisanti, A., Paladin, G. & Vulpiani, A. 1993 Products of Random Matrices in Statistical Physics. Springer.CrossRefGoogle Scholar
Davoudi, J. & Schumacher, J. 2006 Stretching of polymers around the Kolmogorov scale in a turbulent shear flow. Phys. Fluids 18, 025103.CrossRefGoogle Scholar
Eckhardt, B., Kronjäger, J. & Schumacher, J. 2002 Stretching of polymers in a turbulent environment. Comput. Phys. Commun. 147, 538–543.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence: The Legacy of A.N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
de Gennes, P. G. 1974 Coil–stretch transition of dilute flexible polymer under ultra-high velocity gradients. J. Chem. Phys. 60, 5030–5042.CrossRefGoogle Scholar
Gerashchenko, S., Chevallard, C. & Steinberg, V. 2005 Single polymer dynamics: coil–stretch transition in a random flow. Europhys. Lett. 71, 221–227CrossRefGoogle Scholar
Gilbert, A. D. & Bayly, B. G. 1992 Magnetic field intermittency and fast dynamo action in random helical flows. J. Fluid Mech. 241, 199–214.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2001 Stretching of polymers in a random three-dimensional flow. Phys. Rev. Lett. 86, 934–937.CrossRefGoogle Scholar
Honeycutt, R. L. 1992 Stochastic Runge–Kutta algorithms. Part I. White noise. Phys. Rev. A 45, 600–603.CrossRefGoogle Scholar
Larson, R. G. 2005 The rheology of dilute solutions of flexible polymers: progress and problems. J. Rheol. 49, 1–70.CrossRefGoogle Scholar
Liu, Y. & Steinberg, V. 2010 Stretching of polymer in a random flow: effect of a shear rate. Europhys. Lett. 90, 44005.CrossRefGoogle Scholar
Lumley, J. L. 1972 On the solution of equations describing small scale deformation. Symp. Math. 9, 315–334.Google Scholar
Lumley, J. L. 1973 Drag reduction in turbulent flow by polymer additives. J. Polym. Sci.: Macromol. Rev. 7, 263–290.Google Scholar
Martins Afonso, M. & Vincenzi, D. 2005 Nonlinear elastic polymers in random flow. J. Fluid Mech. 540, 99–108.CrossRefGoogle Scholar
Öttinger, H. C. 1996 Stochastic Processes in Polymeric Fluids. Springer.CrossRefGoogle Scholar
Perkins, T. T., Smith, D. E. & Chu, S. 1997 Single polymer dynamics in an elongational flow. Science 276, 2016–2021.CrossRefGoogle Scholar
Shaqfeh, E. S. G. 2005 The dynamics of a single-molecule DNA in flow. J. Non-Newtonian Fluid Mech. 130, 1–28.CrossRefGoogle Scholar
Thiffeault, J. L. 2003 Finite extension of polymers in turbulent flow. Phys. Lett. A 308, 445–450.CrossRefGoogle Scholar
Watanabe, T. & Gotoh, T. 2010 Coil–stretch transition in an ensemble of polymers in isotropic turbulence. Phys. Rev. E 81, 066301.Google Scholar
Zel'dovich, Ya. B., Ruzmaikin, A. A., Molchanov, S. A. & Sokoloff, D. D. 1984 Kinematic dynamo problem in a linear velocity field. J. Fluid Mech. 144, 1–11.CrossRefGoogle Scholar