We study in this work steady laminar flows in a low density granular gas modelled as a system of identical smooth hard spheres that collide inelastically. The system is excited by shear and temperature sources at the boundaries, which consist of two infinite parallel walls. Thus, the geometry of the system is the same that yields the planar Fourier and Couette flows in standard gases. We show that it is possible to describe the steady granular flows in this system, even at large inelasticities, by means of a (nonNewtonian) hydrodynamic approach. All five types of Couette-Fourier granular flows are systematically described, identifying the different types of hydrodynamic profiles. Excellent agreement is found between our classification of flows and simulation results. Also, we obtain the corresponding non-linear transport coefficients by following three independent and complementary methods: (1) an analytical solution obtained from Grad's 13-moment method applied to the inelastic Boltzmann equation, (2) a numerical solution of the inelastic Boltzmann equation obtained by means of the direct simulation Monte Carlo method and (3) event-driven molecular dynamics simulations. We find that, while Grad's theory does not describe quantitatively well all transport coefficients, the three procedures yield the same general classification of planar Couette-Fourier flows for the granular gas.
IntroductionThere have been in the recent years a large number of studies on the dynamics of granular gases, where 'granular gas' is a term used to refer to a low density system of many mesoscopic particles that collide inelastically in pairs. Due to inelasticity in the collisions, the granular gas particles tend to collapse to a rest state, unless there is some kind of energy input. In particular, Goldhirsch & Zanetti (1993) showed that clustering instabilities spontaneously appear in a freely evolving granular gas. Nevertheless, most situations of practical interest involve an energy input to compensate for the energy loss and sustain, in some cases, the 'gas' condition of the granular system. This type of problem has been extensively studied, giving rise to a subfield of granular dynamics: 'rapid granular flows ' (Jenkins & Savage 1983;Wang, Jackson & Sundaresan 1996;Goldhirsch 2003;Aranson & Tsimring 2006). Furthermore, it has been shown that rapid granular flows can attain steady states, some of which, under appropriate circumstances and for simple geometries, can give rise to laminar flows, in the same way as a regular gas does (see, for instance, the work by Tij, Tahiri, Montanero, Garzó, Santos & Dufty † Email address for correspondence: fvega@unex.es