Showing papers by "Vicente Garzó published in 2010"

Non-Newtonian Granular Hydrodynamics. What Do the Inelastic Simple Shear Flow and the Elastic Fourier Flow Have in Common?

Abstract: We describe a special class of steady Couette flows in dilute granular gases admitting a non-Newtonian hydrodynamic description for strong dissipation. The class occurs when viscous heating exactly balances inelastic cooling, resulting in a uniform heat flux. It includes the Fourier flow of ordinary gases and the simple or uniform shear flow (USF) of granular gases as special cases. The rheological functions have the same values as in the USF and generalized thermal conductivity coefficients can be identified. These points are confirmed by molecular dynamics simulations, Monte Carlo simulations of the Boltzmann equation, and analytical results from Grad's 13-moment method.

Thermal diffusion segregation in granular binary mixtures described by the Enskog equation

Abstract: Diffusion induced by a thermal gradient in a granular binary mixture is analyzed in the context of the (inelastic) Enskog equation. Although the Enskog equation neglects velocity correlations among particles which are about to collide, it retains spatial correlations arising from volume exclusion effects and thus it is expected to apply to moderate densities. In the steady state with gradients only along a given direction, a segregation criterion is obtained from the thermal diffusion factor $\Lambda$ measuring the amount of segregation parallel to the thermal gradient. As expected, the sign of the factor $\Lambda$ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the mixture (masses, sizes, concentration, solid volume fraction, and coefficients of restitution). The form of the phase diagrams for the BNE/RBNE transition is illustrated in detail for several systems, with special emphasis on the significant role played by the inelasticity of collisions. In particular, an effect already found in dilute gases (segregation in a binary mixture of identical masses and sizes {\em but} different coefficients of restitution) is extended to dense systems. A comparison with recent computer simulation results shows a good qualitative agreement at the level of the thermal diffusion factor. The present analysis generalizes to arbitrary concentration previous theoretical results derived in the tracer limit case.

Energy Production Rates in Fluid Mixtures of Inelastic Rough Hard Spheres

Abstract: The aim of this work is to explore the combined effect of polydispersity and roughness on the partial energy production rates and on the total cooling rate of a granular fluid mixture. We consider a mixture of inelastic rough hard spheres of different number densities, masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution. Starting from the first equation of the BBGKY hierarchy, the collisional energy production rates associated with the translational and rotational temperatures (T tr i and T rot i ) are expressed in terms of two-body average values. Next, those average values are estimated by assuming a velocity distribution function based on maximum-entropy arguments, allowing us to express the energy production rates and the total cooling rate in terms of the partial temperatures and the parameters of the mixture. Finally, the results are applied to the homogeneous cooling state of a binary mixture and the influence of inelasticity and roughness on the temperature ratios T tr 1 /T rot 1 , T tr 2 /T tr 1 ,a ndT rot 2 /T rot 1 is analyzed.

Rheological properties for inelastic Maxwell mixtures under shear flow

Abstract: The Boltzmann equation for inelastic Maxwell models is considered to determine the rheological properties in a granular binary mixture in the simple shear flow state. The transport coefficients (shear viscosity and viscometric functions) are exactly evaluated in terms of the coefficients of restitution, the (reduced) shear rate and the parameters of the mixture (particle masses, diameters and concentration). The results show that in general, for a given value of the coefficients of restitution, the above transport properties decrease with increasing shear rate.

Hydrodynamics of inelastic Maxwell models

Abstract: An overview of recent results pertaining to the hydrodynamic description (both Newtonian and non-Newtonian) of granular gases described by the Boltzmann equation for inelastic Maxwell models is presented. The use of this mathematical model allows us to get exact results for different problems. First, the Navier--Stokes constitutive equations with explicit expressions for the corresponding transport coefficients are derived by applying the Chapman--Enskog method to inelastic gases. Second, the non-Newtonian rheological properties in the uniform shear flow (USF) are obtained in the steady state as well as in the transient unsteady regime. Next, an exact solution for a special class of Couette flows characterized by a uniform heat flux is worked out. This solution shares the same rheological properties as the USF and, additionally, two generalized transport coefficients associated with the heat flux vector can be identified. Finally, the problem of small spatial perturbations of the USF is analyzed with a Chapman--Enskog-like method and generalized (tensorial) transport coefficients are obtained.

Enskog Theory for Polydisperse Granular Mixtures. III. Comparison of dense and dilute transport coefficients and equations of state for a binary mixture

Abstract: The objective of this study is to assess the impact of a dense-phase treatment on the hydrodynamic description of granular, binary mixtures relative to a previous dilute-phase treatment. Two theories were considered for this purpose. The first, proposed by Garzo and Dufty (GD) [Phys. Fluids {\bf 14}, 146 (2002)], is based on the Boltzmann equation which does not incorporate finite-volume effects, thereby limiting its use to dilute flows. The second, proposed by Garzo, Hrenya and Dufty (GHD) [Phys. Rev. E {\bf 76}, 31303 and 031304 (2007)], is derived from the Enskog equation which does account for finite-volume effects; accordingly this theory can be applied to moderately dense systems as well. To demonstrate the significance of the dense-phase treatment relative to its dilute counterpart, the ratio of dense (GHD) to dilute (GD) predictions of all relevant transport coefficients and equations of state are plotted over a range of physical parameters (volume fraction, coefficients of restitution, material density ratio, diameter ratio, and mixture composition). These plots reveal the deviation between the two treatments, which can become quite large ($>$100%) even at moderate values of the physical parameters. Such information will be useful when choosing which theory is most applicable to a given situation, since the dilute theory offers relative simplicity and the dense theory offers improved accuracy. It is also important to note that several corrections to original GHD expressions are presented here in the form of a complete, self-contained set of relevant equations.

Segregation by thermal diffusion in granular shear flows

Abstract: Segregation by thermal diffusion of an intruder immersed in a sheared granular gas is analyzed from the (inelastic) Boltzmann equation. Segregation is induced by the presence of a temperature gradient orthogonal to the shear flow plane and parallel to gravity. We show that, like in analogous systems without shear, the segregation criterion yields a transition between upwards segregation and downwards segregation. The form of the phase diagrams is illustrated in detail showing that they depend sensitively on the value of gravity relative to the thermal gradient. Two specific situations are considered: (i) absence of gravity and (ii) homogeneous temperature. We find that both mechanisms (upwards and downwards segregation) are stronger and more clearly separated when compared with segregation criteria in systems without shear.