Local heat flux and energy loss in a 2D vibrated granular gas

Abstract

We performed event-driven simulations of a two-dimensional granular gas between two vibrating walls and directly measured the local heat flux and energy dissipation rate in the stationary state. Describing the local heat flux as a function of the coordinate x in the direction perpendicular to the driving walls, we use a generalization of Fourier's law, q_x(x) = kappa d_x T(x) + mu d_x rho(x), to relate the local heat flux to the local gradients of the temperature and density. This ansatz accounts for the fact that density gradients also generate heat flux, not only temperature gradients. The transport coefficients kappa and mu are assumed to be independent of x, and we check the validity of this assumption in the simulations. Both kappa and mu are determined for different system parameters, in particular, for a wide range of coefficients of restitution. We also compare our numerical results to existing hydrodynamic theories. Agreement is found for kappa for very small inelasticities only. Beyond this region, kappa and mu exhibit a striking non-monotonic behavior.

arXiv comment8 pages, 5 figures

References in corpus (5)

• Collision statistics of driven granular materials
• Transport Coefficients for Granular Media from Molecular Dynamics Simulations
• Two-dimensional Granular Gas of Inelastic Spheres with Multiplicative Driving
• Local Equation of State and Velocity Distributions of a Driven Granular Gas
• Hydrodynamics of driven granular gases

Cited by in corpus (6)

• On the role of the Knudsen layer in rapid granular flows
• Hydrodynamic Correlation Functions of a Driven Granular Fluid in Steady State
• Granular Gas: Vibrating Walls, Two-Peak Distribution and Hydrodynamics
• Meso-scale modeling: beyond local equilibrium assumption for multiphase flow
• Model for Density Waves in Gravity-Driven Granular Flow in Narrow Pipes
• Fluctuations in granular gases