Dino Risso

Thermal convection in fluidized granular systems

Thermal convection is observed in molecular dynamic simulations of a fluidized granular system of nearly elastic hard disks moving under gravity, inside a square box. Boundaries introduce no shearing or time dependence, but the energy injection comes from a slip (shear-free) thermalizing base. The top wall is perfectly elastic and lateral boundaries are either elastic or periodic. The spontaneous temperature gradient appearing in the system due to the inelastic collisions, combined with gravity, produces a buoyancy force that, when dissipation is large enough, triggers convection.

Sudden Chain Energy Transfer Events in Vibrated granular Media

In a mixture of two species of grains of equal size but different mass, placed in a vertically vibrated shallow box, there is spontaneous segregation. Once the system is at least partly segregated and clusters of the heavy particles have formed, there are sudden peaks of the horizontal kinetic energy of the heavy particles, that is otherwise small. Together with the energy peaks the clusters rapidly expand and the segregation is partially lost. The process repeats once segregation has taken place again, either randomly or with some regularity in time depending on the experimental or numerical parameters. An explanation for these events is provided based on the existence of a fixed point for an isolated particle bouncing with only vertical motion. The horizontal energy peaks occur when the energy stored in the vertical motion is partly transferred into horizontal energy through a chain reaction of collisions between heavy particles.

Segregation in quasi-two-dimensional granular systems

Segregation for two granular species is studied numerically in a vertically vibrated quasi-two-dimensional (quasi-2D) box. The height of the box is smaller than two particle diameters so that particles are limited to a submonolayer. Two cases are considered: grains that differ in their density but have equal size, and grains that have equal density but different diameters, while keeping the quasi-2D condition. It is observed that in both cases, for vibration frequencies beyond a certain threshold—which depends on the density or diameter ratios—segregation takes place in the lateral directions. In the quasi-2D geometry, gravity does not play a direct role in the in-plane dynamics and gravity does not point to the segregation directions; hence, several known segregation mechanisms that rely on gravity are discarded. The segregation we observe is dominated by a lack of equipartition between the two species; the light particles exert a larger pressure than the heavier ones, inducing the latter to form clusters. This energy difference in the horizontal direction is due to the existence of a fixed point characterized by vertical motion and hence vanishing horizontal energy. Heavier and bigger grains are more rapidly attracted to the fixed point and the perturbations are less efficient in taking them off the fixed point when compared to the lighter grains. As a consequence, heavier and bigger grains have less horizontal agitation than lighter ones. Although limited by finite size effects, the simulations suggest that the two cases we consider differ in the transition character: one is continuous and the other is discontinuous. In the cases where grains differ in mass on varying the control parameter, partial segregation is first observed, presenting many clusters of heavier particles. Eventually, a global cluster is formed with impurities; namely lighter particles are present inside. The transition looks continuous when characterized by several segregation order parameters. On the other hand, when grains differ in size, there is no partial segregation and the global cluster has a much smaller concentration of impurities. The segregation order parameters change discontinuously and metastability is observed.

Hydrodynamic theory for granular gases

A granular gas subjected to a permanent injection of energy is described by means of hydrodynamic equations derived from a moment expansion method. The method uses as reference function not a Maxwellian distribution f(M) but a distribution f(0)=Phif(M), such that Phi adds a fourth cumulant kappa to the velocity distribution. The formalism is applied to a stationary conductive case showing that the theory fits extraordinarily well the results coming from our Newtonian molecular dynamic simulations once we determine kappa as a function of the inelasticity of the particle-particle collisions. The shape of kappa is independent of the size N of the system.

Two-dimensional gas of disks: Thermal conductivity

The phenomenon of heat conduction in a two-dimensional gas ofN hard disks is studied in the hydrostatic regime by means of nonequilibrium molecular dynamics (N ranging from 100 to 8000). For systems withN≥1500 the temperature and density profiles observed are in excellent agreement with the continuous theory, but the conductivityk differs from the one derived from Enskogs theory in a systematic way. This difference seems to slowly decrease with increasing density.

Hydrodynamic modes in a confined granular fluid.

Confined granular fluids, placed in a shallow box that is vibrated vertically, can achieve homogeneous stationary states due to energy injection mechanisms that take place throughout the system. These states can be stable even at high densities and inelasticities allowing for a detailed analysis of the hydrodynamic modes that govern the dynamics of granular fluids. By analyzing the decay of the time correlation functions it is shown that there is a crossover from a quasielastic regime in which energy evolves as a slow mode to an inelastic regime with energy slaved to the other conserved fields. The two regimes have well differentiated transport properties and in the inelastic regime the dynamics can be described by a reduced hydrodynamics with modified longitudinal viscosity and sound speed. The crossover between the two regimes takes place at a wave vector that is proportional to the inelasticity. A two-dimensional granular model, with collisions that mimic the energy transfers that take place in a confined system, is studied by means of microscopic simulations. The results show excellent agreement with the theoretical framework and allow validation of hydrodynamiclike models.

Buoyancy driven convection and hysteresis in granular gases: numerical solution

Granular gas-dynamic equations are written down and numerically integrated to study convection. For a two-dimensional gas of inelastic hard disks in a square box and under the effect of gravity, the equations predict buoyancy driven convection triggered by the dynamically created “temperature”-gradient, in coincidence with what has been seen in molecular dynamics simulations and in real 3D experiments. Three states are observed: conductive, one-convective roll and two-convective rolls states. The numerical solution predicts a hysteresis cycle between the last two states.

Nonlinear transport laws for low density fluids

Hydrodynamics equations derived directly from Boltzmann’s equation and specialized to sheared planar flow are shown to yield approximate nonlinear laws of heat transport and of viscous flow. The law of viscous flow predicts non-Newtonian effects including shear thinning and the law of heat transport is more general than Fourier’s law: it is not linear and it implies heat flow parallel to the isotherms. These nonlinear transport laws are faithfully corroborated by molecular dynamic simulations based on straightforward Newtonian dynamics.

Shear viscosity of a model for confined granular media

The shear viscosity in the dilute regime of a model for confined granular matter is studied by simulations and kinetic theory. The model consists on projecting into two dimensions the motion of vibrofluidized granular matter in shallow boxes by modifying the collision rule: besides the restitution coefficient that accounts for the energy dissipation, there is a separation velocity that is added in each collision in the normal direction. The two mechanisms balance on average, producing stationary homogeneous states. Molecular dynamics simulations show that in the steady state the distribution function departs from a Maxwellian, with cumulants that remain small in the whole range of inelasticities. The shear viscosity normalized with stationary temperature presents a clear dependence with the inelasticity, taking smaller values compared to the elastic case. A Boltzmann-like equation is built and analyzed using linear response theory. It is found that the predictions show an excellent agreement with the simulations when the correct stationary distribution is used but a Maxwellian approximation fails in predicting the inelasticity dependence of the viscosity. These results confirm that transport coefficients depend strongly on the mechanisms that drive them to stationary states.

Energy bursts in vibrated shallow granular systems

In a mixture of two species of inelastic spheres of equal size but different mass, placed in a vertically vibrated shallow box (large horizontal dimensions and height comparable to the grains’ size), there is spontaneous segregation. Once the system is at least partly segregated energy bursts recurrently take place: the horizontal kinetic energy of the heavy particles, that normally is small, suddenly increases an order of magnitude. An explanation of these events is provided based on the existence of a fixed point for an isolated particle bouncing with only vertical motion between the top and bottom plates. Energy bursts occur when clusters of heavy particles start a chain reaction of collisions that transfer vertical energy to horizontal energy producing an expansion of the cluster.