Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas

We investigate the evolution of the velocity distribution function of a granular gas composed of viscoelastic particles in the homogeneous cooling state, i.e. before clustering occurs. The deviation of the velocity distribution function from the Maxwellian distribution is quantified by a Sonine polynomials expansion. The first non-vanishing Sonine coefficient a_2(t), reveals a complex time dependence which allows to assign the granular gas the property of an age. We discuss t...

The importance of roughness in the modeling of granular gases has been increasingly considered in recent years. In this paper, a freely evolving homogeneous granular gas of inelastic and rough hard disks or spheres is studied under the assumptions of the Boltzmann kinetic equation. The homogeneous base state reached by the system is studied from a theoretical point of view using a Sonine approximation, in contrast to a previous Maxwellian approach. A general theoretical descr...

We present experimental results on the velocity statistics of a uniformly heated granular fluid, in a quasi-2D configuration. We find the base state, as measured by the single particle velocity distribution $f(c)$, to be universal over a wide range of filling fractions and only weakly dependent on all other system parameters. There is a consistent overpopulation in the distribution's tails, which scale as $f\propto\exp(\mathrm{const.}\times c^{-3/2})$. More importantly, the h...

The transport coefficients for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal ($\alpha$) and tangential ($\beta$) restitution are obtained in a unified framework as functions of the number of translational ($d_t$) and rotational ($d_r$) degrees of freedom. The derivation is carried out by means of the Chapman--Enskog method with a Sonine-like approximation in which, in contrast to previous approaches, the reference dist...

The Chapman--Enskog solution to the Enskog kinetic equation of polydisperse granular mixtures is revisited to determine the first-order contributions $\varpi_i$ to the partial temperatures. As expected, these quantities (which were neglected in previous attempts) are given in terms of the solution to a set of coupled integro-differential equations analogous to those for elastic collisions. The solubility condition for this set of equations is confirmed and the coefficients $\...

The Enskog kinetic theory for moderately dense granular suspensions is considered as a model to determine the Navier-Stokes transport coefficients. The influence of the interstitial gas on solid particles is modeled by a viscous drag force term plus a stochastic Langevin-like term. The suspension model is solved by means of the Chapman--Enskog method conveniently adapted to dissipative dynamics. The momentum and heat fluxes as well as the cooling rate are obtained to first or...

The Boltzmann kinetic equation is considered to evaluate the first-order contributions $T_i^{(1)}$ to the partial temperatures in binary granular suspensions at low density. The influence of the surrounding gas on the solid particles is modeled via a drag force proportional to the particle velocity plus a stochastic Langevin-like term. The Boltzmann equation is solved by means of the Chapman--Enskog expansion around the local version of the reference homogeneous base state. T...

The time evolution and stationary values of the entropy per particle of a homogeneous freely cooling granular gas, relative to the maximum entropy consistent with the instantaneous translational and rotational temperatures, is analyzed by means of a Sonine approximation involving fourth-degree cumulants. The results show a rich variety of dependencies of the relative entropy on time and on the coefficients of normal and tangential restitution, including a peculiar behavior in...

Under many conditions, macroscopic grains flow like a fluid; kinetic theory pred icts continuum equations of motion for this granular fluid. In order to test the theory, we perform event driven molecular simulations of a two-dimensional gas of inelastic hard disks, driven by contact with a heat bath. Even for strong dissipation, high densities, and small numbers of particles, we find that continuum theory describes the system well. With a bath that heats the gas homogeneously...

Direct Monte Carlo simulations of the Enskog-Boltzmann equation for a spatially uniform system of smooth inelastic spheres are performed. In order to reach a steady state, the particles are assumed to be under the action of an external driving force which does work to compensate for the collisional loss of energy. Three different types of external driving are considered: (a) a stochastic force, (b) a deterministic force proportional to the particle velocity and (c) a determin...