arXiv subjects

Vicente Garzo

Publications and source records attributed to Vicente Garzo.

27 records · Page 2Linked to original sources

arXiv2005

Instabilities in a free granular fluid described by the Enskog equation

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability as functions of the wave vector, the dissipation, and the density. In contrast to previous studies, this description is based on the results derived from the Enskog equation for inelastic hard spheres [V. Garzó and J. W. Dufty, Phys. Rev. E {\bf 59}, 5895 (1999)], which takes into account the dependence of the transport coefficients on dissipation. As expected, linear stability shows two transversal (shear) modes and a longitudinal (``heat'') mode to be unstable with respect to long enough wavelength excitations. Comparison with previous results (which neglect the influence of dissipation on transport) shows quantitative discrepancies for strong dissipation.

cond-mat.stat-mech↗

arXiv2004

Hydrodynamics for inelastic Maxwell mixtures: Some applications

Hydrodynamic equations for a binary mixture of inelastic Maxwell models described by the Boltzmann equation are derived. The Navier-Stokes transport coefficients are {\em exactly} obtained by solving the Boltzmann equation from the Chapman-Enskog method for states close to the (local) homogeneous cooling state (HCS). The knowledge of the transport coefficients allows one to analyze two different problems. First, we solve the linearized hydrodynamic equations around the homogeneous (cooling) state and identify the conditions for stability as functions of the wave vector, the dissipation, and the parameters of the mixture. As happens for monocomponent systems, the analysis shows that the HCS is unstable to long enough wavelength perturbation. As a second problem, we explore the validity of Onsager's reciprocal relations of a granular binary mixture. As expected, since a granular system is not time reversal invariant, Onsager's reciprocal relations do not apply for inelastic collisions. The results show that the absence of the Gibbs state (non-Maxwellian behavior of the velocity distribution functions describing the HCS), the collisional cooling, and the occurrence of different kinetic temperatures for both species (breakdown of energy equipartition) are responsible for a violation of Onsager's relations

cond-mat.stat-mech↗

arXiv2004

Transport coefficients for inelastic Maxwell mixtures

The Boltzmann equation for inelastic Maxwell models is used to determine the Navier-Stokes transport coefficients of a granular binary mixture in $d$ dimensions. The Chapman-Enskog method is applied to solve the Boltzmann equation for states near the (local) homogeneous cooling state. The mass, heat, and momentum fluxes are obtained to first order in the spatial gradients of the hydrodynamic fields, and the corresponding transport coefficients are identified. There are seven relevant transport coefficients: the mutual diffusion, the pressure diffusion, the thermal diffusion, the shear viscosity, the Dufour coefficient, the pressure energy coefficient, and the thermal conductivity. All these coefficients are {\em exactly} obtained in terms of the coefficients of restitution and the ratios of mass, concentration, and particle sizes. The results are compared with known transport coefficients of inelastic hard spheres obtained analytically in the leading Sonine approximation and by means of Monte Carlo simulations. The comparison shows a reasonably good agreement between both interaction models for not too strong dissipation, especially in the case of the transport coefficients associated with the mass flux.

cond-mat.stat-mech↗

arXiv2004

On the Einstein relation in a heated granular gas

Recent computer simulation results [Barrat {\em et al.}, Physica A 334 (2004) 513] for granular mixtures subject to stochastic driving have shown the validity of the Einstein relation $ε\equiv D/(T_0λ)=1$ between the diffusion $D$ and mobility $λ$ coefficients when the temperature of the gas $T$ is replaced by the temperature of the impurity $T_0$ in the usual Einstein relation. This problem is analyzed in this paper by solving analytically the Boltzmann-Lorentz equation from the Chapman-Enskog method. The gas is heated by the action of an external driving force (thermostat) which does work to compensate for the collisional loss of energy. Two types of thermostats are considered: (a) a deterministic force proportional to the particle velocity (Gaussian thermostat), and (b) a white noise external force (stochastic thermostat). The diffusion and mobility coefficients are given in terms of the solutions of two linear integral equations, which are approximately solved up to the second order in a Sonine polynomial expansion. The results show that the violation of the Einstein relation ($ε\neq 1$) is only due to the non-Maxwellian behavior of the impurity velocity distribution function (absence of the Gibbs state). At a quantitative level, the kinetic theory results also show that the deviation of $ε$ from 1 is more significant in the case of the Gaussian thermostat than in the case of the stochastic one, in which case the deviation of the Einstein relation is in general smaller than 1%. This conclusion agrees quite well with the results found in computer simulations.

cond-mat.stat-mech↗

arXiv2003

Shear viscosity for a moderately dense granular binary mixture

The shear viscosity for a moderately dense granular binary mixture of smooth hard spheres undergoing uniform shear flow is determined. The basis for the analysis is the Enskog kinetic equation, solved first analytically by the Chapman-Enskog method up to first order in the shear rate for unforced systems as well as for systems driven by a Gaussian thermostat. As in the elastic case, practical evaluation requires a Sonine polynomial approximation. In the leading order, we determine the shear viscosity in terms of the control parameters of the problem: solid fraction, composition, mass ratio, size ratio and restitution coefficients. Both kinetic and collisional transfer contributions to the shear viscosity are considered. To probe the accuracy of the Chapman-Enskog results, the Enskog equation is then numerically solved for systems driven by a Gaussian thermostat by means of an extension to dense gases of the well-known Direct Simulation Monte Carlo (DSMC) method for dilute gases. The comparison between theory and simulation shows in general an excellent agreement over a wide region of the parameter space.

cond-mat.stat-mech↗

arXiv2002

Nonlinear transport in inelastic Maxwell mixtures under simple shear flow

The Boltzmann equation for inelastic Maxwell models is used to analyze nonlinear transport in a granular binary mixture in the steady simple shear flow. Two different transport processes are studied. First, the rheological properties (shear and normal stresses) are obtained by solving exactly the velocity moment equations. Second, the diffusion tensor of impurities immersed in a sheared inelastic Maxwell gas is explicitly determined from a perturbation solution through first order in the concentration gradient. The corresponding reference state of this expansion corresponds to the solution derived in the (pure) shear flow problem. All these transport coefficients are given in terms of the restitution coefficients and the parameters of the mixture (ratios of masses, concentration, and sizes). The results are compared with those obtained analytically for inelastic hard spheres in the first Sonine approximation and by means of Monte Carlo simulations. The comparison between the results obtained for both interaction models shows a good agreement over a wide range values of the parameter space.

cond-mat.stat-mech↗

arXiv2002

Kinetic Temperatures for a Granular Mixture

An isolated mixture of smooth, inelastic hard spheres supports a homogeneous cooling state with different kinetic temperatures for each species. This phenomenon is explored here by molecular dynamics simulation of a two component fluid, with comparison to predictions of the Enskog kinetic theory. The ratio of kinetic temperatures is studied for two values of the restitution coefficient, $α=0.95$ and 0.80, as a function of mass ratio, size ratio, composition, and density. Good agreement between theory and simulation is found for the lower densities and higher restitution coefficient; significant disagreement is observed otherwise. The phenomenon of different temperatures is also discussed for driven systems, as occurs in recent experiments. Differences between the freely cooling state and driven steady states are illustrated.

cond-mat.stat-mech↗

arXiv2002

Tracer diffusion in granular shear flows

Tracer diffusion in a granular gas in simple shear flow is analyzed. The analysis is made from a perturbation solution of the Boltzmann kinetic equation through first order in the gradient of the mole fraction of tracer particles. The reference state (zeroth-order approximation) corresponds to a Sonine solution of the Boltzmann equation, which holds for arbitrary values of the restitution coefficients. Due to the anisotropy induced in the system by the shear flow, the mass flux defines a diffusion tensor $D_{ij}$ instead of a scalar diffusion coefficient. The elements of this tensor are given in terms of the restitution coefficients and mass and size ratios. The dependence of the diffusion tensor on the parameters of the problem is illustrated in the three-dimensional case. The results show that the influence of dissipation on the elements $D_{ij}$ is in general quite important, even for moderate values of the restitution coefficients. In the case of self-diffusion (mechanically equivalent particles), the trends observed in recent molecular dynamics simulations are similar to those obtained here from the Boltzmann kinetic theory.

cond-mat.stat-mech↗

arXiv2002

Energy nonequipartition in a sheared granular mixture

The kinetic granular temperatures of a binary granular mixture in simple shear flow are determined from the Boltzmann kinetic theory by using a Sonine polynomial expansion. The results show that the temperature ratio is clearly different from unity (as may be expected since the system is out of equilibrium) and strongly depends on the restitution coefficients as well as on the parameters of the mixture. The approximate analytical calculations are compared with those obtained from Monte Carlo simulations of the Boltzmann equation showing an excellent agreement over the range of parameters investigated. Finally, the influence of the temperature differences on the rheological properties is also discussed.

cond-mat.stat-mech↗