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Register a new userDissipative lateral walls are sufficient to trigger convection in vibrated granular gases
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Buoyancy-driven (thermal) convection in dilute granular media, fluidized by a vibrating base, is known to appear without the need of lateral boundaries in a restricted region of parameters (inelasticity, gravity, intensity of energy injection). We have recently discovered a second buoyancy-driven convection effect which occurs at any value of the parameters, provided that the impact of particles with the lateral walls is inelastic (Pontuale et al., Phys. Rev. Lett. 117, 098006 (2016)). It is understood that this novel convection effect is strictly correlated to the existence of perpendicular energy fluxes: a vertical one, induced by both bulk and wall inelasticity, and a horizontal one, induced only by dissipation at the walls. Here we first review those previous results, and then present new experimental and numerical data concerning the variations of box geometry, intensity of energy injection, number of particles and width of the box.
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We consider a granular gas under the action of gravity, fluidized by a vibrating base. We show that a horizontal temperature gradient, here induced by limiting dissipative lateral walls (DLW), leads always to a granular thermal convection (DLW-TC) that is essentially different from ordinary buoyancy-driven convection (BD-TC). In an experiment where BD-TC is inhibited, by reducing gravity with an inclined plane, we always observe a DLW-TC cell next to each lateral wall. Such a cell squeezes towards the nearest wall as the gravity and/or the number of grains increase. Molecular dynamics simulations reproduce the experimental results and indicate that at large gravity or number of grains the DLW-TC is barely detectable.
We describe a series of experiments and computer simulations on vibrated granular media in a geometry chosen to eliminate gravitationally induced settling. The system consists of a collection of identical spherical particles on a horizontal plate vibrating vertically, with or without a confining lid. Previously reported results are reviewed, including the observation of homogeneous, disordered liquid-like states, an instability to a `collapse of motionless spheres on a perfect hexagonal lattice, and a fluctuating, hexagonally ordered state. In the presence of a confining lid we see a variety of solid phases at high densities and relatively high vibration amplitudes, several of which are reported for the first time in this article. The phase behavior of the system is closely related to that observed in confined hard-sphere colloidal suspensions in equilibrium, but with modifications due to the effects of the forcing and dissipation. We also review measurements of velocity distributions, which range from Maxwellian to strongly non-Maxwellian depending on the experimental parameter values. We describe measurements of spatial velocity correlations that show a clear dependence on the mechanism of energy injection. We also report new measurements of the velocity autocorrelation function in the granular layer and show that increased inelasticity leads to enhanced particle self-diffusion.
A vertically shaken granular medium hosts a blade rotating around a fixed vertical axis, which acts as a mesorheological probe. At high densities, independently from the shaking intensity, the blades dynamics show strong caging effects, marked by transient sub-diffusion and a maximum in the velocity power density spectrum (vpds), at a resonant frequency $sim 10$ Hz. Interpreting the data through a diffusing harmonic cage model allows us to retrieve the elastic constant of the granular medium and its collective diffusion coefficient. For high frequencies $f$, a tail $sim 1/f$ in the vpds reveals non-trivial correlations in the intra-cage micro-dynamics. At very long times (larger than $10$ s), a super-diffusive behavior emerges, ballistic in the most extreme cases. Consistently, the distribution of slow velocity inversion times $tau$ displays a power-law decay, likely due to persistent collective fluctuations of the host medium.
The role of forcing on the dynamics of a vertically shaken granular monolayer is investigated. Using a flat plate, surprising negative velocity correlations are measured. A mechanism for this anti-correlation is proposed with support from both experimental results and molecular dynamics simulations. Using a rough plate, velocity correlations are positive, and the velocity distribution evolves from a gaussian at very low densities to a broader distribution at high densities. These results are interpreted as a balance between stochastic forcing, interparticle collisions, and friction with the plate.
Using high-speed video and magnetic resonance imaging (MRI) we study the motion of a large sphere in a vertically vibrated bed of smaller grains. As previously reported we find a non-monotonic density dependence of the rise and sink time of the large sphere. We find that this density dependence is solely due to air drag. We investigate in detail how the motion of the intruder sphere is influenced by size of the background particles, initial vertical position in the bed, ambient pressure and convection. We explain our results in the framework of a simple model and find quantitative agreement in key aspects with numerical simulations to the model equations.
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