Rheological properties for inelastic Maxwell mixtures under shear flow

The Boltzmann equation for inelastic Maxwell models is considered to determine the rheological properties in a granular binary mixture in the simple shear flow state. The transport coefficients (shear viscosity and viscometric functions) are {\em exactly} evaluated in terms of the coefficients of restitution, the (reduced) shear rate and the parameters of the mixture (particle masses, diameters and concentration). The results show that in general, for a given value of the coefficients of restitution, the above transport properties decrease with increasing shear rate

Kovacs-like memory effect in driven granular gases

While memory effects have been reported for dense enough disordered systems such as glasses, we show here by a combination of analytical and simulation techniques that they are also intrinsic to the dynamics of dilute granular gases. By means of a certain driving protocol, we prepare the gas in a state where the granular temperature $T$ coincides with its long time limit. However, $T$ does not subsequently remain constant, but exhibits a non-monotonic evolution before reaching its non-equilibrium steady value. The corresponding so-called Kovacs hump displays a normal behavior for weak dissipation (as observed in molecular systems), but is reversed under strong dissipation, where it thus becomes anomalous.Comment: 5 pages, to appear in Physical Review Letter

Random inelasticity and velocity fluctuations in a driven granular gas

We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show that in its simplest version, the ``stochastic thermostat'' model of heated inelastic hard spheres, contrary to what has been hitherto stated, is incompatible with the experimental data, although predicting a reminiscent high velocity stretched exponential behavior with an exponent 3/2. The experimental observations lead to refine a recently proposed random restitution coefficient model. Very good agreement is then found with experimental velocity distributions within this framework, which appears self-consistent and further provides relevant probes to investigate the universality of the velocity statistics.Comment: 5 pages, 5 eps figure

Lack of energy equipartition in homogeneous heated binary granular mixtures

We consider the problem of determining the granular temperatures of the components of a homogeneous binary heated mixture of inelastic hard spheres, in the framework of Enskog kinetic theory. Equations are derived for the temperatures of each species and their ratio, which is different from unity, as may be expected since the system is out of equilibrium. We focus on the particular heating mechanism where the inelastic energy loss is compensated by an injection through a random external force (``stochastic thermostat''). The influence of various parameters and their possible experimental relevance is discussed.Comment: 8 pages, 9 eps figures, to be published in Granular Matte

Free cooling and inelastic collapse of granular gases in high dimensions

The connection between granular gases and sticky gases has recently been considered, leading to the conjecture that inelastic collapse is avoided for space dimensions higher than 4. We report Molecular Dynamics simulations of hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular medium is monitored throughout the cooling process. The behaviour is found to be very similar to that of a two-dimensional system, with a shearing-like instability of the velocity field and inelastic collapse when collisions are inelastic enough, showing that the connection with sticky gases needs to be revised.Comment: 6 pages, 6 figures (7 postscript files), submitted to EPJ

Effective charge of cylindrical and spherical colloids immersed in an electrolyte: the quasi-planar limit

We consider the non-linear Poisson-Boltzmann theory for a single cylindrical or spherical macro-ion in symmetric 1:1, together with asymmetric 1:2 and 2:1 electrolytes. We focus on the regime where $\kappa a$, the ratio of the macro-ion radius $a$ over the inverse Debye length in the bulk electrolyte, is large. Analyzing the structure of the analytical expansion emerging from a multiple scale analysis, we uncover a hidden structure for the electrostatic potential. This structure, which appears after a heuristic resummation, suggests a new and convenient expansion scheme that we present and work out in detail. We show that novel exact results can thereby be obtained, in particular pertaining to effective charge properties, in complete agreement with the direct numerical solution to the problem