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Nonlinear viscosity and velocity distribution function in a simple longitudinal flow

Santos1

  • 1Departamento de Fisica, Universidad de Extremadura, E-06071 Badajoz, Spain.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|December 2, 2000
PubMed
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This study analyzes compressible flow using kinetic models, revealing that gas expansion or condensation depends on the deformation rate. Non-Newtonian viscosity and velocity distribution tails impact fluid behavior.

Area of Science:

  • Fluid Dynamics
  • Statistical Mechanics
  • Non-equilibrium Thermodynamics

Background:

  • Compressible flow phenomena are crucial in various scientific and engineering applications.
  • Understanding non-Newtonian fluid behavior is essential for accurate modeling.
  • Kinetic theory provides a microscopic approach to macroscopic fluid properties.

Purpose of the Study:

  • To analyze a specific compressible flow velocity field using kinetic models.
  • To investigate the influence of the longitudinal deformation rate on gas expansion and condensation.
  • To characterize the non-Newtonian behavior and velocity distribution functions.

Main Methods:

  • Analysis of the Boltzmann equation and the Bhatnagar-Gross-Krook (BGK) kinetic model.
  • Investigation of a compressible flow with velocity field u(x)(x, t)=ax/(1+at).

Related Experiment Videos

  • Application of Chapman-Enskog expansion to analyze dimensionless nonlinear viscosity.

    • Main Results:

    • The sign of the longitudinal deformation rate (a) determines expansion (a>0) or condensation (a<0).
    • Temperature decreases with time during expansion and increases during condensation.
    • A dimensionless nonlinear viscosity eta(*) depends on the dimensionless rate a(*), with asymptotic Chapman-Enskog expansion.
    • The velocity distribution function exhibits an algebraic high-velocity tail, causing moment divergence.

    Conclusions:

    • The study provides insights into the non-Newtonian behavior of gases under compressible flow conditions.
    • The divergence of velocity moments is linked to the high-velocity tail of the distribution function.
    • The findings are relevant for understanding complex fluid dynamics from a kinetic perspective.