Generalized transport coefficients for inelastic Maxwell mixtures under shear flow
Vicente Garzó1, Emmanuel Trizac2
1Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
Summary
This study analyzes transport coefficients in granular mixtures under shear flow using the Boltzmann equation. Generalized coefficients are nonlinear functions of shear rate and dissipation, deviating significantly from equilibrium values.
Area of Science:
- Physics
- Statistical Mechanics
- Granular Materials
Background:
- Granular mixtures exhibit complex transport phenomena, especially under shear flow.
- Understanding these transport coefficients is crucial for modeling granular dynamics.
Purpose of the Study:
- To determine transport coefficients for mass, momentum, and heat fluxes in granular binary mixtures near simple shear flow.
- To develop a theoretical framework using the Boltzmann equation for inelastic Maxwell models.
Main Methods:
- Solving the Boltzmann equation via Chapman-Enskog-type expansion.
- Utilizing tensorial quantities to describe anisotropic transport processes.
- Analytically solving coupled equations for transport tensors as functions of shear rate and restitution coefficients.
Main Results:
- Generalized transport coefficients are nonlinear functions of shear rate and dissipation.
- Tensorial diffusion coefficients show significant deviations from vanishing shear rate values.
- Good agreement was found with Grad's moment method for inelastic hard spheres.
Conclusions:
- The derived generalized coefficients accurately describe transport in sheared granular mixtures.
- The study provides a robust theoretical framework for non-equilibrium granular systems.
- Applications include understanding thermal diffusion segregation in granular gases.
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