Kinetic Theory for Binary Granular Mixtures at Low Density

Abstract

Many features of granular media can be modelled as a fluid of hard spheres with inelastic collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations. At lowdensity, a fundamental basis for the derivation of the hydrodynamic equations and explicit expressions for the transport coefficients appearing in them is provided by the Boltzmann kinetic theory conveniently modified to account for inelastic binary collisions. The goal of this chapter is to give an overview of the recent advances made for binary granular gases by using kinetic theory tools. Some of the results presented here cover aspects such as transport properties, energy nonequipartition, instabilities, segregation or mixing, non-Newtonian behavior, . . . . In addition, comparison of the analytical results with those obtained from Monte Carlo and molecular dynamics simulations is also carried out, showing the reliability of kinetic theory to describe granular flows even for strong dissipation.

Energy production rates of multicomponent granular gases of rough particles. A unified view of hard-disk and hard-sphere systems

“…A "gas" made of identical and smooth hard disks or spheres with a constant coefficient of normal restitution is perhaps the simplest and most widely used model of a granular gas [1][2][3][4][5][6][7][8]. On the other hand, the mesoscopic or macroscopic nature of the "grains" may ask for a refinement of the model by allowing for particle-particle surface friction or "roughness" (usually accounted for by a constant coefficient of tangential restitution) , polydispersity (i.e., assuming that the particles belong to more than one component, each one characterized by different mechanical properties) [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66], or both [67][68][69][70][71][72][73][74].…”

Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases

“…In particular, there exists a vast literature about polydisperse systems of smooth disks or spheres [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], as well as about friction (or roughness) in monodisperse systems [10,. On the other hand, much fewer works have dealt with multicomponent gases of rough spheres [66][67][68][69][70][71][72].…”

Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases

“…The minimal version of the IHSM corresponds to a collection of smooth hard spheres or disks that undergo inelastic collisions, with a velocity-independent coefficient of normal restitution α [8,9]. More sophisticated models, close to the IHSM, consider particle rotations with coefficients of normal and tangential restitution [10][11][12][13][14][15][16], velocity-dependent coefficients of restitution [9,17,18], polydispersity [19], presence of an interstitial fluid [20][21][22][23], etc. Some conclusions of the research carried out along the last few years in the minimal version of the IHSM, and also in some others, are that the inelastic Boltzmann equation is able to describe dilute (and moderately dense) systems (the fundamental hydrodynamic variables being the same as that of the ordinary elastic case, i.e., density, velocity, and temperature) and the Navier-Stokes (NS) hydrodynamic equations provided by the CE method are applicable for a generality of accessible situations with small spatial gradients.…”