Energy nonequipartition in gas mixtures of inelastic rough hard spheres: The tracer limit

Rotational and translational motions in a homogeneously cooling granular gas

A granular gas composed of monodisperse spherical particles was studied in microgravity experiments in a drop tower. Translations and rotations of the particles were extracted from optical video data. Equipartition is violated, the rotational degrees of freedom were excited only to roughly 2/3 of the translational ones. After stopping the mechanical excitation, we observed granular cooling of the ensemble for a period of three times the Haff time, where the kinetic energy dropped to about 5% of its initial value. The cooling rates of all observable degrees of freedom were comparable, and the ratio of rotational and translational kinetic energies fluctuated around a constant value. The distributions of translational and rotational velocity components showed slight but systematic deviations from Gaussians at the start of cooling.

Cooling of a granular gas mixture in microgravity

Granular gases are fascinating non-equilibrium systems with interesting features such as spontaneous clustering and non-Gaussian velocity distributions. Mixtures of different components represent a much more natural composition than monodisperse ensembles but attracted comparably little attention so far. We present the observation and characterization of a mixture of rod-like particles with different sizes and masses in a drop tower experiment. Kinetic energy decay rates during granular cooling and collision rates were determined and Haff's law for homogeneous granular cooling was confirmed. Thereby, energy equipartition between the mixture components and between individual degrees of freedom is violated. Heavier particles keep a slightly higher average kinetic energy than lighter ones. Experimental results are supported by numerical simulations.

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

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.

Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture

A collisional model of a confined quasi-two-dimensional granular mixture is considered to analyze homogeneous steady states. The model includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical direction to the horizontal degrees of freedom of grains. The set of Enskog kinetic equations for the velocity distribution functions of each component is derived first to analyze the homogeneous state. As in the one-component case, an exact scaling solution is found where the time dependence of the distribution functions occurs entirely through the granular temperature T. As expected, the kinetic partial temperatures T_{i} of each component are different and, hence, energy equipartition is broken down. In the steady state, explicit expressions for the temperature T and the ratio of partial kinetic temperatures T_{i}/T_{j} are obtained by considering Maxwellian distributions defined at the partial temperatures T_{i}. The (scaled) granular temperature and the temperature ratios are given in terms of the coefficients of restitution, the solid volume fraction, the (scaled) parameters of the collisional model, and the ratios of mass, concentration, and diameters. In the case of a binary mixture, the theoretical predictions are exhaustively compared with both direct simulation Monte Carlo and molecular dynamics simulations with a good agreement. The deviations are identified to be originated in the non-Gaussianity of the velocity distributions and on microsegregation patterns, which induce spatial correlations not captured in the Enskog theory.

Induced correlations and rupture of molecular chaos by anisotropic dissipative Janus hard disks

A system of smooth "frozen" Janus-type disks is studied. Such disks cannot rotate and are divided by their diameter into two sides of different inelasticities. Taking as a reference a system of colored elastic disks, we find differences in the behavior of the collisions once the anisotropy is included. A homogeneous state, akin to the homogeneous cooling state of granular gases, is seen to arise and the singular behavior of both the collisions and the precollisional correlations are highlighted.

Impact of roughness on the instability of a free-cooling granular gas

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results for the transport coefficients derived from the Boltzmann equation for inelastic rough hard spheres [Phys. Rev. E 90, 022205 (2014)PLEEE81539-375510.1103/PhysRevE.90.022205], which take into account the complete nonlinear dependence of the transport coefficients and the cooling rate on the coefficients of normal and tangential restitution. As expected, linear stability analysis shows that a doubly degenerate transversal (shear) mode and a longitudinal ("heat") mode are unstable with respect to long enough wavelength excitations. The instability is driven by the shear mode above a certain inelasticity threshold; at larger inelasticity, however, the instability is driven by the heat mode for an inelasticity-dependent range of medium roughness. Comparison with the case of a granular gas of inelastic smooth spheres confirms previous simulation results about the dual role played by surface friction: while small and large levels of roughness make the system less unstable than the frictionless system, the opposite happens at medium roughness. On the other hand, such an intermediate window of roughness values shrinks as inelasticity increases and eventually disappears at a certain value, beyond which the rough-sphere gas is always less unstable than the smooth-sphere gas. A comparison with some preliminary simulation results shows a very good agreement for conditions of practical interest.

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

A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It is found that disks typically present a stronger rotational-translational nonequipartition but a weaker component-component nonequipartition than spheres. A noteworthy "mimicry" effect is unveiled, according to which a polydisperse gas of disks having common values of the coefficient of restitution and of the reduced moment of inertia can be made indistinguishable from a monodisperse gas in what concerns the degree of rotational-translational energy nonequipartition. This effect requires the mass of a disk of component i to be approximately proportional to 2σ_{i}+〈σ〉, where σ_{i} is the diameter of the disk and 〈σ〉 is the mean diameter.