Does the Chapman-Enskog expansion for viscous granular flows converge?

Details Does the Chapman-Enskog expansion for viscous granular flows converge? Does the Chapman-Enskog expansion for viscous granular flows converge?

2008-04-16

arxiv.org/abs/0804.2563v1

The XVth International Congress on Rheology, A. Co, G. Leal, R. Colby, and A. J. Giacomin, eds. (AIP Conference Proceedings, v

Physics

Condensed Matter

Soft Condensed Matter

3 pages, 1 figure; submitted for publication in the Proceedings of the XVth International Congress on Rheology (August 3-8, 20

Scientific paper

10.1063/1.2964892

This paper deals with the convergence/divergence issue of the Chapman-Enskog series expansion of the shear and normal stresses for a granular gas of inelastic hard spheres. From the exact solution of a simple kinetic model in the uniform shear and longitudinal flows, it is shown that (except in the elastic limit) both series converge and their respective radii of convergence increase with inelasticity. This paradoxical result can be understood in terms of the time evolution of the Knudsen number and the existence of a nonequilibrium steady state.

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