Theory of Dilute Binary Granular Gas Mixtures

D. Serero; S. H. Noskowicz; I. Goldhirsch

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 6, Issue: 1, page 17-47
  • ISSN: 0973-5348

Abstract

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A computer-aided method for accurately carrying out the Chapman-Enskog expansion of the Boltzmann equation, including its inelastic variant, is presented and employed to derive a hydrodynamic description of a dilute binary mixture of smooth inelastic spheres. Constitutive relations, formally valid for all physical values of the coefficients of restitution, are calculated by carrying out the pertinent Chapman-Enskog expansion to sufficient high orders in the Sonine polynomials to ensure numerical convergence. The resulting hydrodynamic description is applied to the analysis of a vertically vibrated binary mixture of particles (under gravity) differing only in their respective coefficients of restitution. It is shown that even with this “minor”difference the mixture partly segregates, its steady state exhibiting a sandwich-like configuration.

How to cite

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Serero, D., Noskowicz, S. H., and Goldhirsch, I.. "Theory of Dilute Binary Granular Gas Mixtures." Mathematical Modelling of Natural Phenomena 6.1 (2010): 17-47. <http://eudml.org/doc/197699>.

@article{Serero2010,
abstract = { A computer-aided method for accurately carrying out the Chapman-Enskog expansion of the Boltzmann equation, including its inelastic variant, is presented and employed to derive a hydrodynamic description of a dilute binary mixture of smooth inelastic spheres. Constitutive relations, formally valid for all physical values of the coefficients of restitution, are calculated by carrying out the pertinent Chapman-Enskog expansion to sufficient high orders in the Sonine polynomials to ensure numerical convergence. The resulting hydrodynamic description is applied to the analysis of a vertically vibrated binary mixture of particles (under gravity) differing only in their respective coefficients of restitution. It is shown that even with this “minor”difference the mixture partly segregates, its steady state exhibiting a sandwich-like configuration.},
author = {Serero, D., Noskowicz, S. H., Goldhirsch, I.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {kinetic theory; granular gases; mixtures; segregation; Chapman-Enskog expansion; hydrodynamics},
language = {eng},
month = {6},
number = {1},
pages = {17-47},
publisher = {EDP Sciences},
title = {Theory of Dilute Binary Granular Gas Mixtures},
url = {http://eudml.org/doc/197699},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Serero, D.
AU - Noskowicz, S. H.
AU - Goldhirsch, I.
TI - Theory of Dilute Binary Granular Gas Mixtures
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/6//
PB - EDP Sciences
VL - 6
IS - 1
SP - 17
EP - 47
AB - A computer-aided method for accurately carrying out the Chapman-Enskog expansion of the Boltzmann equation, including its inelastic variant, is presented and employed to derive a hydrodynamic description of a dilute binary mixture of smooth inelastic spheres. Constitutive relations, formally valid for all physical values of the coefficients of restitution, are calculated by carrying out the pertinent Chapman-Enskog expansion to sufficient high orders in the Sonine polynomials to ensure numerical convergence. The resulting hydrodynamic description is applied to the analysis of a vertically vibrated binary mixture of particles (under gravity) differing only in their respective coefficients of restitution. It is shown that even with this “minor”difference the mixture partly segregates, its steady state exhibiting a sandwich-like configuration.
LA - eng
KW - kinetic theory; granular gases; mixtures; segregation; Chapman-Enskog expansion; hydrodynamics
UR - http://eudml.org/doc/197699
ER -

References

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