The kinetics of a collection of inelastically colliding smooth disks in a plane, in a state of constant shear rate, is studied by performing an analysis of the pertinent Boltzmann equation. The fact that the granular temperature T satisfies T∝γ2ℓ2/ε, where ℓ is the mean free path, γ is the shear rate and ε≡1−e2, where e is the coefficient of normal restitution, leads to the observation that when γ∝√ε the limit ε→0 of the above problem corresponds to a system of elastically colliding particles in equilibrium (at temperature T). This observation enables the construction of a systematic perturbative expansion (for the single particle distribution function) in powers of √ε , in which the equilibrium (Maxwellian) distribution function serves as zeroth order. The limitations of this expansion are discussed alongside possible generalizations. Explicit expressions for the single particle distribution function to O(ε) and expressions for the corresponding stress tensor are obtained. The phenomenon of normal stress difference is shown to be of O(ε), i.e. of second (Burnett) order in the shear-rate and its calculated magnitude compares well with results of numerical simulations. A comparison of the present theory with that of Jenkins and Richman is presented as well.

It is shown that a vertically vibrated binary granular gas mixture of light and heavy particles can segregate (in the presence of gravity) in such a way that the bottom and top layers are composed mostly of light particles, even if all other parameters (including size) are the same for both species. The corresponding concentration profile possesses certain universal properties. It is also shown that such mixtures can segregate when the only difference between the species is the value of the coefficient of restitution. These findings follow from a set of hydrodynamic equations for granular gas mixtures which we derived from the pertinent Boltzmann equation. The above results comprise the second part of this article, the first part of which is devoted to a brief and somewhat biased review of the main physical properties of granular gases. This includes their (generic) tendency to coagulate into clusters and other micro- and macrostructures. A fundamental property of granular materials in general, and granular gases in particular, is the lack of scale separation; an explanation and some consequences are presented. The answer to the basic question of whether the dynamics of granular gases lends itself to description by (appropriate) hydrodynamic equations seems to be positive, though some restrictions apply.

Hydrodynamic equations for nearly smooth granular gases are derived from the pertinent Boltzmann equation. The angular velocity distribution field needs to be included in the set of hydrodynamic fields. The angular velocity distribution is strongly non-Maxwellian for the homogeneous cooling state and any homogeneous steady state. In the case of steady wall-bounded shear flows the average spin (created at the boundaries) has a finite penetration length into the bulk.

A novel computer-aided method for solving kinetic equations has been developed and implemented in a study of the Boltzmann equation corresponding to elastic and inelastic hard spheres. Accurate results are obtained for the linear transport coefficients for all physical values of the coefficient of normal restitution, α. These coefficients are bounded and nonsingular even in the limit of vanishing α. Using the new method we also calculated the full homogeneous cooling state (HCS) distribution function (after replacing the standard divergent expansion by a convergent one) and confirmed the conjecture that it possesses an exponential tail. Further implications and applications of these results are outlined.

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