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Shear viscosity for a heated granular binary mixture at low density.

José María Montanero1, Vicente Garzó

  • 1Departamento de Electrónica e Ingeniería Electromecánica, Universidad de Extremadura, E-06071 Badajoz, Spain. jmm@unex.es

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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This study analyzes shear viscosity in heated granular binary mixtures using Boltzmann kinetic theory. Results from Chapman-Enskog and direct simulation Monte Carlo methods show excellent agreement, validating the theoretical approach for granular flow.

Area of Science:

  • Physics
  • Granular Materials Science
  • Statistical Mechanics

Background:

  • Granular mixtures exhibit complex behavior due to inelastic collisions and external driving forces.
  • Understanding transport properties like shear viscosity is crucial for modeling granular flows.
  • Previous work analyzed free cooling granular systems, motivating further investigation into heated systems.

Purpose of the Study:

  • To analyze the shear viscosity of a heated granular binary mixture of smooth hard spheres.
  • To investigate the validity of Boltzmann kinetic theory for such systems.
  • To compare theoretical predictions with numerical simulations.

Main Methods:

  • Utilized Boltzmann kinetic theory solved via the Chapman-Enskog method.
  • Employed a Sonine polynomial approximation for practical evaluation of transport coefficients.

Related Experiment Videos

  • Performed numerical simulations using the direct simulation Monte Carlo (DSMC) method.
  • Applied a Gaussian thermostat to control inelastic cooling in the simulations.

    • Main Results:

    • Determined mass, heat, and momentum fluxes and identified corresponding transport coefficients.
    • Obtained shear viscosity using the Chapman-Enskog method up to first order in spatial gradients.
    • Demonstrated excellent agreement between Chapman-Enskog results and DSMC simulations.
    • Validated the theoretical framework across various restitution coefficients and mixture parameters.

    Conclusions:

    • The Boltzmann kinetic theory, particularly the Chapman-Enskog method, accurately predicts shear viscosity in heated granular binary mixtures.
    • The Gaussian thermostat effectively compensates for collisional cooling, enabling stable heated states.
    • The study provides a robust theoretical and computational framework for analyzing transport phenomena in driven granular systems.