C. Bizon

Transport coefficients for granular media from molecular dynamics simulations

Under many conditions, macroscopic grains flow like a fluid; kinetic theory predicts 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, strong velocity correlations produce a slightly smaller energy loss due to inelastic collisions than that predicted by kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients are induced. Determination of the resulting fluxes allows calculation of the thermal conductivity and shear viscosity, which are compared to the predictions of granular kinetic theory, and which can be used in continuum modeling of granular flows. The shear viscosity is close to the prediction of kinetic theory, while the thermal conductivity can be overestimated by a factor of 2; in each case, transport is lowered with increasing inelasticity.

Plume dynamics in quasi-2D turbulent convection

We have studied turbulent convection in a vertical thin (Hele-Shaw) cell at very high Rayleigh numbers (up to 7x10(4) times the value for convective onset) through experiment, simulation, and analysis. Experimentally, convection is driven by an imposed concentration gradient in an isothermal cell. Model equations treat the fields in two dimensions, with the reduced dimension exerting its influence through a linear wall friction. Linear stability analysis of these equations demonstrates that as the thickness of the cell tends to zero, the critical Rayleigh number and wave number for convective onset do not depend on the velocity conditions at the top and bottom boundaries (i.e., no-slip or stress-free). At finite cell thickness delta, however, solutions with different boundary conditions behave differently. We simulate the model equations numerically for both types of boundary conditions. Time sequences of the full concentration fields from experiment and simulation display a large number of solutal plumes that are born in thin concentration boundary layers, merge to form vertical channels, and sometimes split at their tips via a Rayleigh-Taylor instability. Power spectra of the concentration field reveal scaling regions with slopes that depend on the Rayleigh number. We examine the scaling of nondimensional heat flux (the Nusselt number, Nu) and rms vertical velocity (the Peclet number, Pe) with the Rayleigh number (Ra(*)) for the simulations. Both no-slip and stress-free solutions exhibit the scaling NuRa(*) approximately Pe(2) that we develop from simple arguments involving dynamics in the interior, away from cell boundaries. In addition, for stress-free solutions a second relation, Nu approximately nPe, is dictated by stagnation-point flows occurring at the horizontal boundaries; n is the number of plumes per unit length. No-slip solutions exhibit no such organization of the boundary flow and the results appear to agree with Priestleys prediction of Nu approximately Ra(1/3). (c) 1997 American Institute of Physics.

Computational test of kinetic theory of granular media

Kinetic theory of granular media based on inelastic hard sphere interactions predicts continuum equations of motion similar to Navier–Stokes equations for fluids. We test these predictions using event-driven molecular dynamics simulations of uniformly excited inelastic hard spheres confined to move in a plane. The event-driven simulations have been previously shown to quantitatively reproduce the complex patterns that develop in shallow layers of vertically oscillated granular media. The test system consists of a periodic two-dimensional box filled with inelastic hard disks uniformly forced by small random accelerations in the absence of gravity. We describe the inelasticity of the particles by a velocity-dependent coefficient of restitution. Granular kinetic theory assumes that the velocities at collision are uncorrelated and close to a Maxwell–Boltzmann distribution. Our two-dimensional simulations verify that the velocity distribution is close to a Maxwell–Boltzmann distribution over 3 orders of magnitude in velocity, but we find that velocity correlations, of up to 40% of the temperature, exist between the velocity components parallel to the relative collision velocity. Despite the velocity correlations we find that the calculated transport coefficients compare well with kinetic theory predictions.

Velocity Correlations in Driven Two-Dimensional Granular Media

Simulations of volumetrically forced granular media in two dimensions produce s tates with nearly homogeneous density. In these states, long-range velocity correlations with a characteristic vortex structure develop; given sufficient time, the correlations fill the entire simulated area. These velocity correlations reduce the rate and violence of collisions, so that pressure is smaller for driven inelastic particles than for undriven elastic particles in the same thermodynamic state. As the simulation box size increases, the effects of veloc ity correlations on the pressure are enhanced rather than reduced.

Pattern Formation in Vertically Vibrated Granular Layers: Experiment and Simulation

We report on pattern formation in experiments and simulations of vertically vibrated granular layers. We find that initially flat vibrated layers lose stability to sub-harmonic standing wave patterns when the driving acceleration is increased to about 2.5 times gravity. Patterns can be squares, stripes, hexagons, or localized structures (oscillons), depending on frequency and acceleration. Event driven simulations show excellent qualitative and quantitative agreement with the experiments.