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.

arXiv comment4 pages, 1 table, 2 figures; v2: minor changes,Fig. 2 redone

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Cited by in corpus (6)

• Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
• Role of roughness on the hydrodynamic homogeneous base state of inelastic spheres
• Hydrodynamic Correlation Functions of a Driven Granular Fluid in Steady State
• Non-Newtonian granular hydrodynamics. What do the inelastic simple shear flow and the elastic Fourier flow have in common?
• Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases
• Unsteady non-Newtonian hydrodynamics in granular gases