Wavelength Scaling and Square/Stripe and Grain Mobility Transitions in Vertically Oscillated Granular Layers

Laboratory experiments are conducted to examine granular wave patterns near onset as a function of the container oscillation frequency f and amplitude A, layer depth H, and grain diameter D. The primary transition from a flat grain layer to standing waves occurs when the layer remains dilated after making contact with the container. With a flat layer and increasing dimensionless peak container acceleration G = 4 pi^2 f^2 A/g (g is the acceleration due to gravity), the wave transition occurs for G=2.6, but with decreasing G the waves persist to G=2.2. For 2.2<G<3.8, patterns are squares for f<f_ss and stripes for f>f_ss; H determines the square/stripe transition frequency f_ss=0.33(g/H)^0.5. The dispersion relations for layers with varying H collapse onto the curve L/H=1.0+1.1[f(H/g)^0.5]^(-1.32 +/- 0.03) (L is the wavelength) when the peak container velocity v exceeds a critical value v_gm of approximately 3 (Dg)^0.5. Local collision pressure measurements suggest that v_gm is associated with a transition in the horizontal grain mobility: for v>v_gm, there is a hydrodynamic-like horizontal sloshing motion, while for v<v_gm, the grains are essentially immobile and the stripe pattern apparently arises from a bending of the granular layer. For f at v_gm less than f_ss and v<v_gm, patterns are tenuous and disordered.Comment: 21 pages, 15 figures, submitted to Physica

Shocks in supersonic sand

We measure time-averaged velocity, density, and temperature fields for steady granular flow past a wedge and calculate a speed of granular pressure disturbances (sound speed) equal to 10% of the flow speed. The flow is supersonic, forming shocks nearly identical to those in a supersonic gas. Molecular dynamics simulations of Newton's laws and Monte Carlo simulations of the Boltzmann equation yield fields in quantitative agreement with experiment. A numerical solution of Navier-Stokes-like equations agrees with a molecular dynamics simulation for experimental conditions excluding wall friction.Comment: 4 pages, 5 figure

Phase Bubbles and Spatiotemporal Chaos in Granular Patterns

We use inelastic hard sphere molecular dynamics simulations and laboratory experiments to study patterns in vertically oscillated granular layers. The simulations and experiments reveal that {\em phase bubbles} spontaneously nucleate in the patterns when the container acceleration amplitude exceeds a critical value, about $7g$, where the pattern is approximately hexagonal, oscillating at one-fourth the driving frequency ($f/4$). A phase bubble is a localized region that oscillates with a phase opposite (differing by $\pi$) to that of the surrounding pattern; a localized phase shift is often called an {\em arching} in studies of two-dimensional systems. The simulations show that the formation of phase bubbles is triggered by undulation at the bottom of the layer on a large length scale compared to the wavelength of the pattern. Once formed, a phase bubble shrinks as if it had a surface tension, and disappears in tens to hundreds of cycles. We find that there is an oscillatory momentum transfer across a kink, and this shrinking is caused by a net collisional momentum inward across the boundary enclosing the bubble. At increasing acceleration amplitudes, the patterns evolve into randomly moving labyrinthian kinks (spatiotemporal chaos). We observe in the simulations that $f/3$ and $f/6$ subharmonic patterns emerge as primary instabilities, but that they are unstable to the undulation of the layer. Our experiments confirm the existence of transient $f/3$ and $f/6$ patterns.Comment: 6 pages, 12 figures, submitted to Phys. Rev. E on July 1st, 2001. for better quality figures, visit http://chaos.ph.utexas.edu/research/moo

Continuum-type stability balloon in oscillated granular layers

The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe patterns in a vertically oscillated granular layer. Molecular dynamics simulations show that the mechanism of the skew-varicose instability in granular patterns is similar to that in convection. These results suggest that pattern formation in granular media can be described by continuum models analogous to those used in fluid systems.Comment: 4 pages, 6 ps figs, submitted to PR

Transport Coefficients for Granular Media from Molecular Dynamics Simulations

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, 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.Comment: 14 pages, 17 figures, 39 references, submitted to PRE feb 199