Kinetic Theory of Polydisperse Granular Mixtures: Influence of the Partial Temperatures on Transport Properties—A Review

Abstract

It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently adapted to account for inelastic collisions. A surprising result (compared to its molecular gas counterpart) for granular mixtures is the failure of the energy equipartition, even in homogeneous states. This means that the partial temperatures Ti (measuring the mean kinetic energy of each species) are different to the (total) granular temperature T. The goal of this paper is to provide an overview on the effect of different partial temperatures on the transport properties of the mixture. Our analysis addresses first the impact of energy nonequipartition on transport which is only due to the inelastic character of collisions. This effect (which is absent for elastic collisions) is shown to be significant in important problems in granular mixtures such as thermal diffusion segregation. Then, an independent source of energy nonequipartition due to the existence of a divergence of the flow velocity is studied. This effect (which was already analyzed in several pioneering works on dense hard-sphere molecular mixtures) affects to the bulk viscosity coefficient. Analytical (approximate) results are compared against Monte Carlo and molecular dynamics simulations, showing the reliability of kinetic theory for describing granular flows.

High-Degree Collisional Moments of Inelastic Maxwell Mixtures—Application to the Homogeneous Cooling and Uniform Shear Flow States

“…and three different values of the mass ratio: m 1 /m 2 = 5 (circles), m 1 /m 2 = 5 (triangles), and m 1 /m 2 = 0.5 (squares). The lines correspond to the theoretical results obtained here for IMM while the symbols refer to the results obtained from the DSMC method for IHS [32]. The theoretical lines have been obtained from the condition…”

“…Theoretical results for IMM [with the choice (41)] are compared against Monte Carlo simulations carried out in Ref. [32] for IHS. Figure 1 highlights one of the most characteristic features of granular mixtures (as compared with molecular mixtures): the partial temperatures are different even in homogenous states.…”

Connecting micro- and macroscopic variables in the design of a granular stirrer using simulations

“…The cause can also have a more subtle origin like a difference in the friction coefficient (Ciamarra et al, 2006;Gillemot et al, 2017). For dilute to moderately dense media, the kinetic theory can be used to explain segregation and mixing using a granular temperature proportional to the fluctuations of the velocities, as shown in García-Chamorro et al (2022).…”