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

  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},
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
Steady base states for non-Newtonian granular hydrodynamics
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
Heat flux of a granular gas with homogeneous temperature
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
Non-Newtonian Steady States for Granular Gases
  • V. Garzó
  • Engineering
    Granular Gaseous Flows
  • 2019
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
Unsteady non-Newtonian hydrodynamics in granular gases.
The temporal evolution of a dilute granular gas is investigated by means of the direct simulation Monte Carlo method to solve the Boltzmann equation and the rheological functions obtained from simulation are well described by an approximate analytical solution of a model kinetic equation.
Thermal segregation of intruders in the Fourier state of a granular gas.
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.


Fourier state of a fluidized granular gas
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
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
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
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
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.
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
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
  • Brey, Ruiz-Montero, Moreno
  • Engineering
    Physical 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
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
▪ 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