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Long-ranged correlations in sheared fluids.

James F Lutsko1, James W Dufty

  • 1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, CP 231, 1050 Brussels, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 22, 2002
PubMed
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Long-ranged correlations in shear flow fluids decay faster than predicted by simple theories. A new model shows crossover behavior in density autocorrelation functions, revealing a characteristic length scale dependent on sound damping and shear rate.

Area of Science:

  • Fluid dynamics
  • Statistical mechanics
  • Nonlinear dynamics

Background:

  • Uniform shear flow in fluids can exhibit long-ranged correlations.
  • Simple mode-coupling theories predict a specific decay rate for these correlations.
  • Understanding correlation decay is crucial for fluid behavior analysis.

Purpose of the Study:

  • Investigate long-ranged correlations in fluids under uniform shear flow.
  • Re-evaluate predictions of simple mode-coupling theory regarding correlation decay.
  • Determine the characteristic length scale of these correlations.

Main Methods:

  • Derived an exact relation between density autocorrelation and density-momentum correlation functions.
  • Employed analytic and numerical evaluations of a nonperturbative mode-coupling model.

Related Experiment Videos

  • Analyzed the asymptotic power-law decay of correlation functions.

    • Main Results:

    • The density autocorrelation function decays more rapidly than 1/r.
    • Confirmed a crossover from 1/r behavior at small distances to a stronger power-law decay.
    • Identified the characteristic length scale as approximately sqrt[sound damping/shear rate].

    Conclusions:

    • Simple mode-coupling theory predictions for correlation decay are challenged.
    • The fluid's correlation behavior exhibits a crossover, deviating from simple models.
    • The characteristic length scale provides insight into the fluid's response to shear.