Homogeneous states in driven granular mixtures: Enskog kinetic theory versus molecular dynamics simulations

Abstract

The homogeneous state of a binary mixture of smooth inelastic hard disks or spheres is analyzed. The mixture is driven by a thermostat composed by two terms: a stochastic force and a drag force proportional to the particle velocity. The combined action of both forces attempts to model the interaction of the mixture with a bath or surrounding fluid. The problem is studied by means of two independent and complementary routes. First, the Enskog kinetic equation with a Fokker-Planck term describing interactions of particles with thermostat is derived. The ratio of kinetic temperatures $T_1/T_2$ and the fourth-degree velocity moments ${\lambda }_1$ and ${\lambda }_2$ (which measure non-Gaussian properties of ${\phi }_i$) are explicitly determined as a function of the mass ratio, size ratio, composition, density and coefficients of restitution. Secondly, to assess the reliability of the theoretical results, molecular dynamics simulations of a binary granular mixture of spheres are performed for two values of the coefficient of restitution ($\alpha =0.9$ and 0.8) and three different solid volume fractions ($\varphi =0.00785$, 0.1 and 0.2). Comparison between kinetic theory and computer simulations for the temperature ratio shows excellent agreement, even for moderate densities and strong dissipation. In the case of the cumulants ${\lambda }_1$ and ${\lambda }_2$, good agreement is found for the lower densities although significant discrepancies between theory and simulation are observed with increasing density.

11 pages, 5 figures, to be published in J. Chem. Phys

References in corpus (12)

• Stationary state volume fluctuations in a granular medium
• Approach to jamming in an air-fluidized granular bed
• Universal reference state in a driven homogeneous granular gas
• The second and third Sonine coefficients of a freely cooling granular gas revisited
• Long Range Correlation in Granular Shear Flow II: Theoretical Implications
• Instabilities in moderately dense granular binary mixtures
• Theory of thermostatted inhomogeneous granular fluids: a self-consistent density functional description
• Transport coefficients for driven granular mixtures at low-density
• The homogeneous steady state of a confined granular gas
• Modified Sonine approximation for granular binary mixtures
• Aging to non-Newtonian hydrodynamics in a granular gas
• Long-range interactions in randomly driven granular fluids

Cited by in corpus (14)

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• Enskog kinetic theory for multicomponent granular suspensions
• Kinetic theory of granular particles immersed in a molecular gas
• Time-dependent homogeneous states of binary granular suspensions
• Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture
• Granular rotor as a probe for a non-equilibrium bath
• Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation
• Heat flux of driven granular mixtures at low density. Stability analysis of the homogeneous steady state
• Tracer diffusion coefficients in a moderately dense granular suspension. Stability analysis and thermal diffusion segregation
• Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient
• Enskog kinetic theory of binary granular suspensions: heat flux and stability analysis of the homogeneous steady state
• Mobility and diffusion of intruders in granular suspensions. Einstein relation
• Kinetic theory of polydisperse granular mixtures: influence of the partial temperatures on transport properties. A review
• Kinetic glass transition in granular gases and non-linear molecular fluids