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Turbulent dynamics of polymer solutions

Balkovsky1, Fouxon, Lebedev

  • 1Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel and School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA.

Physical Review Letters
|September 16, 2000
PubMed
Summary

In dilute polymer solutions, turbulent flow affects polymer extension. When the Lyapunov exponent is low, polymers maintain equilibrium size with a power tail. High exponents cause significant stretching, impacting molecular behavior.

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Area of Science:

  • Fluid dynamics
  • Polymer physics
  • Statistical mechanics

Background:

  • Dilute polymer solutions exhibit complex behavior in flow fields.
  • Understanding polymer conformation is crucial for fluid dynamics.
  • Previous studies (Lumley, 1972) explored polymer extensions in turbulence.

Purpose of the Study:

  • To investigate the probability density function (PDF) of polymer end-to-end extensions in turbulent flows.
  • To analyze the influence of the Lyapunov exponent (lambda) and molecular relaxation time (tau) on polymer behavior.
  • To determine the conditions under which polymers significantly affect turbulent flow.

Main Methods:

  • Theoretical analysis of polymer dynamics in turbulent flow.
  • Examination of the probability density function (PDF) for polymer end-to-end extensions (R).

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  • Comparison of the Lyapunov exponent (lambda) with the inverse molecular relaxation time (1/tau).

    • Main Results:

    • At lambda * tau < 1, the PDF shows a peak at equilibrium size (R0) and a power tail for large extensions (R >> R0).
    • In this regime (lambda * tau < 1), polymers have minimal influence on the turbulent flow.
    • At lambda * tau > 1, most polymers stretch to a size R(op) >> R0, potentially smaller than their maximal length due to back-reaction.

    Conclusions:

    • The study confirms and extends previous findings on polymer extensions in turbulence.
    • Polymer stretching behavior is critically dependent on the ratio of the Lyapunov exponent to the inverse relaxation time.
    • Significant polymer stretching occurs at high lambda * tau values, indicating potential back-reaction effects.