Temperature scaling in a dense vibrofluidized granular material

Anisotropic energy distribution in three-dimensional vibrofluidized granular systems

We examine the energy flows in a three-dimensional model of a granular system consisting of N inelastic hard spheres contained in an open cylinder of radius R under the influence of gravity. Energy is supplied to the system in the vertical direction by a vibrating base and is transferred to the perpendicular directions through particle-particle collisions. We examine how the local and global dissipation of energy by particle-particle and particle-wall collisions depends on the number of particles, the velocity of the vibrating base, and the restitution coefficients.

Coexistence of two granular temperatures in binary vibrofluidized beds

An investigation into the granular temperature distributions of a binary vibrofluidized granular bed has been conducted using positron emission particle tracking. By repeating each experiment with the tracer selected in turn from the two size components, the granular temperature and packing fraction distributions for each phase were determined. It was found that, for a range of size fractions, the granular temperature of the larger particles was higher than that of the smaller diameter grains, a result which was supported by a simple theoretical analysis based on the steady state energy equation.

Driven granular gases with gravity

We study fluidized granular gases in a stationary state determined by the balance between external driving and bulk dissipation. The two considered situations are inspired by recent experiments, where gravity plays a major role as a driving mechanism: in the first case, gravity acts only in one direction and the bottom wall is vibrated; in the second case, gravity acts in both directions and no vibrating walls are present. Simulations performed under the molecular chaos assumption show averaged profiles of density, velocity, and granular temperature that are in good agreement with the experiments. Moreover, we measure velocity distributions that show strong non-Gaussian behavior, as experiments pointed out, but also density correlations accounting for clustering, at odds with the experimental results. The hydrodynamics of the first model is discussed and an exact solution is found for the density and granular temperature as functions of the distance from the vibrating wall. The limitations of such a solution, in particular in a broad layer near the wall injecting energy, are discussed.

Hydrodynamics of an open vibrated granular system

Using the hydrodynamic description and molecular dynamics simulations, the steady state of a fluidized granular system in the presence of gravity is studied. For an open system, the density profile exhibits a maximum, while the temperature profile goes through a minimum at high altitude, beyond that the temperature increases with the height. The existence of the minimum is explained by the hydrodynamic equations if the presence of a collisionless boundary layer is taken into account. The energy dissipated by interparticle collisions is also computed. A good agreement is found between theory and simulation. The relationship with previous works is discussed.

Global equation of state of two-dimensional hard sphere systems

Hard sphere systems in two dimensions are examined for arbitrary density. Simulation results are compared to the theoretical predictions for both the low- and the high-density limit, where the system is either disordered or ordered, respectively. The pressure in the system increases with the density, except for an intermediate range of volume fractions 0.65< or =nu< or =0.75, where a disorder-order phase transition occurs. The proposed global equation of state (which describes the pressure for all densities) is applied to the situation of an extremely dense hard sphere gas in a gravitational field and shows reasonable agreement with both experimental and numerical data.

Liquid-solid transition of hard spheres under gravity

We investigate the liquid-solid transition of two-dimensional hard spheres in the presence of gravity. We determine the transition temperature and the fraction of particles in the solid regime as a function of temperature via event-driven molecular-dynamics simulations and compare them with the theoretical predictions. We then examine the configurational statistics of a vibrating bed from the viewpoint of the liquid-solid transition by explicitly determining the transition temperature and the effective temperature T of the bed, and present a relation between T and the vibration strength.

Boundary conditions and normal state for a vibrated granular fluid

The steady state of a fluidized granular system confined between a vibrating wall and a reflecting one is analyzed in detail. The relationship between the velocity of the wall and the hydrodynamic profiles is established. In the limit of a large system, a peculiar normal state, independent of the details of the boundaries, is reached in the bulk. This state has a uniform pressure and a constant temperature gradient. Both quantities are not independent, but verify a closed constitutive relationship. The generality of this state and the relevant role it is expected to play in the description of vibrated granular systems is discussed.