A driven two-dimensional granular gas with Coulomb friction

• Published in: Physics of fluids (1994) Vol. 17; no. 10; pp. 107102 - 107102-16
• Main Authors: Herbst, Olaf, Cafiero, Raffaele, Zippelius, Annette, Herrmann, Hans Jürgen, Luding, Stefan
• Format: Journal Article
• Language: English
• Published: Melville, NY American Institute of Physics 01.10.2005
• Subjects: Exact sciences and technology; Kinetic and transport theory of gases; Physics; Physics of gases; Physics of gases, plasmas and electric discharges; Modelling; Equations of state; Kinetic theory; Inelastic collision; Friction; Hard-sphere model
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.2049277

We study a homogeneously driven granular gas of inelastic hard particles with rough surfaces subject to Coulomb friction. The stationary state as well as the full dynamic evolution of the translational and rotational granular temperatures are investigated as a function of the three parameters of the friction model. Four levels of approximation to the (velocity-dependent) tangential restitution are introduced and used to calculate translational and rotational temperatures in a mean field theory. When comparing these theoretical results to numerical simulations of a randomly driven monolayer of particles subject to Coulomb friction, we find that already the simplest model leads to qualitative agreement, but only the full Coulomb friction model is able to reproduce/predict the simulation results quantitatively for all magnitudes of friction. In addition, the theory predicts two relaxation times for the decay to the stationary state. One of them corresponds to the equilibration between the translational and rotational degrees of freedom. The other one, which is slower in most cases, is the inverse of the common relaxation rate of translational and rotational temperatures.