Impurity in a granular gas under nonlinear Couette flow

We study in this work the transport properties of an impurity immersed in a granular gas under stationary nonlinear Couette flow. The starting point is a kinetic model for low-density granular mixtures recently proposed by the authors [Vega Reyes F et al. 2007 Phys. Rev. E 75 061306]. Two routes have been considered. First, a hydrodynamic or normal solution is found by exploiting a formal mapping between the kinetic equations for the gas particles and for the impurity. We show that the transport properties of the impurity are characterized by the ratio between the temperatures of the impurity and gas particles and by five generalized transport coefficients: three related to the momentum flux (a nonlinear shear viscosity and two normal stress differences) and two related to the heat flux (a nonlinear thermal conductivity and a cross coefficient measuring a component of the heat flux orthogonal to the thermal gradient). Second, by means of a Monte Carlo simulation method we numerically solve the kinetic equations and show that our hydrodynamic solution is valid in the bulk of the fluid when realistic boundary conditions are used. Furthermore, the hydrodynamic solution applies to arbitrarily (inside the continuum regime) large values of the shear rate, of the inelasticity, and of the rest of parameters of the system. Preliminary simulation results of the true Boltzmann description show the reliability of the nonlinear hydrodynamic solution of the kinetic model. This shows again the validity of a hydrodynamic description for granular flows, even under extreme conditions, beyond the Navier-Stokes domain.Comment: 23 pages, 11 figures; v2: Preliminary DSMC results from the Boltzmann equation included, Fig. 11 is ne

Thermal diffusion segregation of an impurity in a driven granular fluid

We study segregation of an impurity in a driven granular fluid under two types of \emph{steady} states. In the first state, the granular gas is driven by a stochastic volume force field with a Fourier-type profile while in the second state, the granular gas is sheared in such a way that inelastic cooling is balanced by viscous heating. We compare theoretical results derived from a solution of the (inelastic) Boltzmann equation at Navier-Stokes (NS) order with those obtained from the Direct Monte Carlo simulation (DSMC) method and molecular dynamics (MD) simulations. Good agreement is found between theory and simulation, which provides strong evidence of the reliability of NS granular hydrodynamics for these steady states (including the dynamics of the impurity), even at high inelasticities. In addition, preliminary results for thermal diffusion in granular fluids at moderate densitis are also presented. As for dilute gases \cite{VGK14}, excellent agreement is also found in this more general case.Comment: 6 pages; 4 figures; contributed paper at the 29th International Symposium on Rarefied Gas Dynamics (Xi'an, China, July 13-18th, 2012); 29th International Symposium on Rarefied Gas Dynamics 201

Steady base states for non-Newtonian granular hydrodynamics

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 (non-Newtonian) 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 gasComment: 33 pages, 11 figures; v2: improved version accepted for publication in J. Fluid Mec