Does the Chapman--Enskog expansion for sheared granular gases converge?

Details Does the Chapman--Enskog expansion for sheared granular gases converge? Does the Chapman--Enskog expansion for sheared granular gases converge?

2007-11-20

arxiv.org/abs/0711.3115v2

Phys. Rev. Lett. 100, 078003 (2008)

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 1 table, 2 figures; v2: minor changes,Fig. 2 redone

Scientific paper

10.1103/PhysRevLett.100.078003

The fundamental question addressed in this paper is whether the partial Chapman--Enskog expansion $P_{xy}=-\sum_{k=0}^\infty \eta_k ({\partial u_x}/{\partial y})^{2k+1}$ of the shear stress converges or not for a gas of inelastic hard spheres. By using a simple kinetic model it is shown that, in contrast to the elastic case, the above series does converge, the radius of convergence increasing with inelasticity. It is argued that this paradoxical conclusion is not an artifact of the kinetic model and can be understood in terms of the time evolution of the scaled shear rate in the uniform shear flow.

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