A Letters Journal Exploring

The evolution to the steady state of a granular gas subject to simple shear flow is analyzed by means of computer simulations. It is found that, regardless of its initial preparation, the system reaches (after a transient period lasting a few collisions per particle) a non-Newtonian (unsteady) hydrodynamic regime, even at strong dissipation and for states where the time scale associated with inelastic cooling is shorter than the one associated with the irreversible fluxes. Comparison with a simplified rheological model shows a good agreement. Copyright c © EPLA, 2007 Introduction. – A granular gas is a large collection of (mesoscopic or macroscopic) particles which collide inelastically and are usually kept in a state of continuous agitation. Apart from their interest in industrial and technological applications, granular gases are important at a fundamental level as physical systems intrinsically out of equilibrium and thus exhibiting a wide spectrum of complex behavior [1–6]. Although the number of grains in a fluidized granular system is of course much smaller than the number of atoms or molecules in a conventional gas, it is large enough as to make nonequilibrium statisticalmechanical concepts and tools applicable. In particular, a kinetic theory approach (based on the Boltzmann and Enskog equations suitably modified to account for inelastic collisions) has proven to be very useful [6]. However, because of the energy dissipation upon collisions and the associated lack of detailed balance and Gibbs equilibrium state, one is not allowed to take for granted any phenomenology that applies to normal gases, unless much caution is exercised. Quoting Kadanoff, “one might even say that the study of granular materials gives one a chance to reinvent statistical mechanics in a new context” [1]. Hydrodynamics is one of the key features of standard fluids. As is well known, the hydrodynamic description of a conventional fluid consists of closing the exact balance equations for the densities of the conserved quantities (mass, momentum and energy) with constitutive equations relating the momentum and heat fluxes to the conserved densities (usually referred to as hydrodynamic fields) and their gradients. If the hydrodynamic gradients are weak, the fluxes can be assumed to be linear in those gradients, what results in the Navier-Stokes (NS) hydrodynamic description. On the other hand, even if the gradients are strong, a (non-Newtonian) hydrodynamic regime beyond the NS one is still possible. The conventional scenario for the “aging to hydrodynamics” in a normal gas can be summarized as follows [7]. Given an arbitrary initial state, the evolution proceeds along two successive stages. First, during the so-called kinetic stage there is a fast relaxation (lasting a few collision times) to a “universal” (or “normal”’) velocity distribution f(r,v; t) that is a functional of the hydrodynamic fields (number density, flow velocity and temperature). Subsequently, the hydrodynamic stage is described through a slower evolution of the hydrodynamic fields as they approach equilibrium or an externally imposed nonequilibrium steady state. The first stage is sensitive to the initial preparation of the system, while in the hydrodynamic regime the system has practically “forgotten” the details of its initial state (except for an implicit dependence on the initial conditions through the hydrodynamic fields). If the hydrodynamic gradients are small enough when the hydrodynamic state is reached, the latter can be described by the NS terms in the Chapman-Enskog expansion [8]. However, a normal (or hydrodynamic) velocity distribution function is not restricted to the NS domain but can apply to the non-Newtonian regime as well [9]. The applicability of a hydrodynamic description to granular fluids is not self-evident at all [1]. In particular, the absence of energy conservation gives rise to a sink term