Showing papers by "Vicente Garzó published in 2006"

Transport coefficients for an inelastic gas around uniform shear flow: linear stability analysis.

Abstract: The inelastic Boltzmann equation for a granular gas is applied to spatially inhomogeneous states close to uniform shear flow. A normal solution is obtained via a Chapman-Enskog-like expansion around a local shear flow distribution. The heat and momentum fluxes are determined to first order in the deviations of the hydrodynamic field gradients from their values in the reference state. The corresponding transport coefficients are determined from a set of coupled linear integral equations which are approximately solved by using a kinetic model of the Boltzmann equation. The main new ingredient in this expansion is that the reference state f(0) (zeroth-order approximation) retains all the hydrodynamic orders in the shear rate. In addition, since the collisional cooling cannot be compensated locally for viscous heating, the distribution f(0) depends on time through its dependence on temperature. This means that in general, for a given degree of inelasticity, the complete nonlinear dependence of the transport coefficients on the shear rate requires analysis of the unsteady hydrodynamic behavior. To simplify the analysis, the steady-state conditions have been considered here in order to perform a linear stability analysis of the hydrodynamic equations with respect to the uniform shear flow state. Conditions for instabilities at long wavelengths are identified and discussed.

Segregation in granular binary mixtures: Thermal diffusion

Abstract: A solution of the inelastic Boltzmann equation that applies for strong dissipation and takes into account non-equipartition of energy is used to derive an explicit expression for the thermal diffusion factor. This parameter provides a criterion for segregation that involves all the parameters of the granular binary mixture (composition, masses, sizes, and coefficients of restitution). The present work is consistent with recent experimental results and extends previous results obtained in the intruder limit case.

Mass and heat fluxes for a binary granular mixture at low density

Abstract: The Navier–Stokes order hydrodynamic equations for a low-density granular mixture obtained previously from the Chapman–Enskog solution to the Boltzmann equation are considered further. The six transport coefficients associated with mass and heat flux in a binary mixture are given as functions of the mass ratio, size ratio, composition, and coefficients of restitution. Their quantitative variation across this parameter set is demonstrated using low-order Sonine polynomial approximations to solve the exact integral equations. The results are also used to quantify the violation of the Onsager reciprocal relations for a granular mixture. Finally, the stability of the homogeneous cooling state is discussed.

Rheology of Two- and Three-dimensional Granular Mixtures Under Uniform Shear Flow: Enskog Kinetic Theory Versus Molecular Dynamics Simulations

Abstract: The rheological properties for dilute and moderately dense granular binary mixtures of smooth, inelastic hard disks/spheres under uniform shear flow in steady state conditions are reported The results are based on the Enskog kinetic theory, numerically solved by a dense gas extension of the Direct Simulation Monte Carlo method for dilute gases These results are confronted to the ones also obtained by performing molecular dynamics (MD) simulations with good agreement for the lower densities and higher coefficients of restitution For increasing density and dissipation, the Enskog equation applies qualitatively, but the quantitative differences increase Possible reasons for deviations of Enskog from MD results are discussed, indicating non-Newtonian flow behavior and anisotropy as the most likely direction in which previous analytical approaches have to be extended