A driven two-dimensional granular gas with Coulomb friction

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...

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Published inPhysics 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
LanguageEnglish
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
Online AccessGet full text
ISSN1070-6631
1089-7666
1527-2435
1089-7666
DOI10.1063/1.2049277

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Abstract 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.
AbstractList 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.
Author Luding, Stefan
Zippelius, Annette
Cafiero, Raffaele
Herbst, Olaf
Herrmann, Hans Jürgen
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  surname: Herbst
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  givenname: Raffaele
  surname: Cafiero
  fullname: Cafiero, Raffaele
  organization: P.M.M.H., Ecole Supèrieure de Physique et de Chimie Industrielles (ESPCI), 10, rue Vauquelin-75251 Paris cedex 05, France
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  givenname: Annette
  surname: Zippelius
  fullname: Zippelius, Annette
  organization: Institut für Theoretische Physik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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  givenname: Hans Jürgen
  surname: Herrmann
  fullname: Herrmann, Hans Jürgen
  organization: P.M.M.H., Ecole Supèrieure de Physique et de Chimie Industrielles (ESPCI), 10, rue Vauquelin-75251 Paris cedex 05, France and Institute for Computer Physics, Pfaffenwaldring 27, 70569 Stuttgart, Germany
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  givenname: Stefan
  surname: Luding
  fullname: Luding, Stefan
  organization: Institute for Computer Physics, Pfaffenwaldring 27, 70569 Stuttgart, Germany and Particle Technology, DelftChemTech, TU Delft, Julianalaan 136, 2628 BL Delft, The Netherlands
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Issue 10
Keywords Modelling
Equations of state
Kinetic theory
Inelastic collision
Friction
Hard-sphere model
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Snippet 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...
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SubjectTerms Exact sciences and technology
Kinetic and transport theory of gases
Physics
Physics of gases
Physics of gases, plasmas and electric discharges
Title A driven two-dimensional granular gas with Coulomb friction
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