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Nonlinear shear viscosity and long time tails.

R Zwanzig1

  • 1Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742.

Proceedings of the National Academy of Sciences of the United States of America
|June 1, 1981
PubMed
Summary

This study reveals a theoretical link between nonlinear shear viscosity and fluid dynamics. It connects the long-time behavior of stress correlations to a rheological model incorporating fluid rotation.

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Area of Science:

  • Fluid dynamics
  • Rheology
  • Theoretical physics

Background:

  • Understanding fluid behavior under shear is crucial in various scientific and engineering fields.
  • Existing models often simplify the complex dynamics of rotating fluids in shear flow.
  • The long-time tail of correlation functions provides insights into the memory effects in fluids.

Purpose of the Study:

  • To establish a theoretical connection between nonlinear shear viscosity and the equilibrium stress-stress correlation function.
  • To explore the implications of fluid angular rotation in steady uniform shear flow.
  • To validate the Goddard-Miller rheological equation of state.

Main Methods:

  • Theoretical analysis of fluid dynamics.
  • Derivation of rheological equations of state.
  • Investigation of stress-stress correlation functions.

Main Results:

  • A direct theoretical link was established between nonlinear shear viscosity and the long-time tail of the stress-stress correlation function.
  • The Goddard-Miller rheological equation of state was shown to incorporate the angular rotation of fluids.
  • This connection is a consequence of accounting for fluid rotation in steady uniform shear.

Conclusions:

  • The Goddard-Miller model provides a framework for understanding the relationship between macroscopic rheological properties and microscopic correlation functions.
  • Accounting for fluid angular rotation is essential for accurate theoretical descriptions of non-Newtonian fluids.
  • This work offers a new perspective on the theoretical underpinnings of fluid viscoelasticity.

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