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Polymer stress tensor in turbulent shear flows.

Victor S L'vov1, Anna Pomyalov, Itamar Procaccia

  • 1Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
Summary

Polymers in turbulent shear flows exhibit a universal stress tensor structure at high Deborah numbers (De >> 1). This structure explains drag reduction and involves hydroelastic waves converting kinetic energy to polymer potential energy.

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Area of Science:

  • Fluid Dynamics
  • Polymer Physics
  • Turbulence

Background:

  • Understanding polymer behavior in turbulent flows is crucial for applications like drag reduction.
  • The elastic stress tensor, linked to polymer conformation, is key to describing these interactions.

Purpose of the Study:

  • To investigate the universal structure of the polymer stress tensor in turbulent shear flows.
  • To analyze polymer behavior across different turbulence complexities: isotropic, anisotropic, and wall-bounded.

Main Methods:

  • Analytical investigation of the polymer conformation tensor.
  • Examination of the elastic stress tensor in various turbulent flow regimes.
  • Analysis in the limit of large Deborah numbers (De >> 1).

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Main Results:

  • A universal structure for the polymer stress tensor was found for De >> 1.
  • Suppression of the coil-stretch transition and formation of hydroelastic waves were observed.
  • An effective polymer viscosity was derived, proportional to the cross-stream stress component.

Conclusions:

  • The universal structure governs polymer stress in diverse turbulent flows.
  • Hydroelastic waves play a role in energy exchange but not the stress tensor's universal structure.
  • Results clarify polymer-induced drag reduction mechanisms in wall-bounded turbulence.