# The Fourier state of a dilute granular gas described by the inelastic Boltzmann equation

@article{JavierBrey2009TheFS, title={The Fourier state of a dilute granular gas described by the inelastic Boltzmann equation}, author={J. Javier Brey and Nagi Khalil and M. J. Ruiz-Montero}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2009}, volume={2009}, pages={P08019} }

The existence of two stationary solutions of the nonlinear Boltzmann equation for inelastic hard spheres or disks is investigated. They are restricted neither to weak dissipation nor to small gradients. The one-particle distribution functions are assumed to have a scaling property, namely that all the position dependence occurs through the density and the temperature. At the macroscopic level, the state corresponding to both is characterized by uniform pressure, no mass flow, and a linear…

## 5 Citations

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Abstract We study in this work steady laminar flows in a low-density granular gas modelled as a system of identical smooth hard spheres that collide inelastically. The system is excited by shear and…

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A steady state of granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position-dependent force or by…

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This chapter addresses the study of non-Newtonian transport properties of several steady laminar flows in granular gases. As a first step, it analyzes the well-known simple or uniform shear flow…

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Thermal segregation of intruders in the Fourier state of a granular gas.

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A low density binary mixture of granular gases is considered within the Boltzmann kinetic theory and this solution has a macroscopic hydrodynamic representation with a constant temperature gradient and is referred to as the Fourier state.

## References

SHOWING 1-10 OF 51 REFERENCES

Fourier state of a fluidized granular gas

- Physics
- 2001

It is shown that the Boltzmann equation for smooth inelastic hard disks or spheres admits a solution describing a steady state characterized by uniform pressure and linear temperature profile. Such a…

Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations

- PhysicsJournal of Fluid Mechanics
- 1995

Collisional motion of a granular material composed of rough inelastic spheres is analysed on the basis of the kinetic Boltzmann–Enskog equation. The Chapman–Enskog method for gas kinetic theory is…

The granular phase diagram

- Physics
- 1997

The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions.…

Hydrodynamics for granular flow at low density

- Physics
- 1998

The hydrodynamic equations for a gas of hard spheres with dissipative dynamics are derived from the Boltzmann equation. The heat and momentum fluxes are calculated to Navier-Stokes order and the…

Self-diffusion in freely evolving granular gases

- Physics
- 2000

A self-diffusion equation for a freely evolving gas of inelastic hard disks or spheres is derived starting from the Boltzmann–Lorentz equation, by means of a Chapman–Enskog expansion in the density…

Validity of the Boltzmann equation to describe low-density granular systems.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

The Boltzmann equation accurately predicts the low-density limit of the system, as well as the relevant role played by the parallelization of the velocities as time proceeds and the dependence of this effect on the density.

Dissipative dynamics for hard spheres

- Physics, Mathematics
- 1997

The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated…

Boundary conditions and normal state for a vibrated granular fluid

- EngineeringPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

The steady state of a fluidized granular system confined between a vibrating wall and a reflecting one and the relevant role it is expected to play in the description of vibrated granular systems is discussed.

Granular Gas Dynamics

- Physics, Engineering
- 2010

Part I: Kinetic Theory.- Asymptotic Solutions of the Nonlinear Boltzmann Equation for Dissipative Systems.- The Homogeneous Cooling State Revisited.- The Inelastic Maxwell Model.- Cooling Granular…

RAPID GRANULAR FLOWS

- Geology
- 2003

▪ Abstract The recent avalanche of research activity in the field of granular matter has yielded much progress. The use of state-of-the-art (and other) computational and experimental methods has led…