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

Abstract

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.

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

References in corpus (5)

• Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
• Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
• Inherent Rheology of a Granular Fluid in Uniform Shear Flow
• Dynamics of a hard sphere granular impurity
• Aging to non-Newtonian hydrodynamics in a granular gas