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Register a new userSegregation induced by inelasticity in a vibrofluidized granular mixture
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R. Brito
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We investigate the segregation of a dense binary mixture of granular particles that only differ in their restitution coefficient. The mixture is vertically vibrated in the presence of gravity. We find a partial segregation of the species, where most dissipative particles submerge in the less dissipative ones. The segregation occurs even if one type of the particles is elastic. In order to have a complete description of the system, we study the structure of the fluid at microscopic scale (few particle diameters). The density and temperature pair distribution functions show strong enhancements respect the equilibrium ones at the same density. In particular, there is an increase in the probability that the more inelastic particles group together in pairs (microsegregation). Microscopically the segregation is buoyancy driven, by the appearance of a dense and cold region around the more inelastic particles.
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The segregation of large spheres in a granular bed under vertical vibrations is studied. In our experiments we systematically measure rise times as a function of density, diameter and depth; for two different sinusoidal excitations. The measurements reveal that: at low frequencies, inertia and convection are the only mechanisms behind segregation. Inertia (convection) dominates when the relative density is greater (less) than one. At high frequencies, where convection is suppressed, fluidization of the granular bed causes either buoyancy or sinkage and segregation occurs.
The spontaneous symmetry breaking taking place in the direction perpendicular to the energy flux in a dilute vibrofluidized granular system is investigated, using both a hydrodynamic description and simulation methods. The latter include molecular dynamics and direct Monte Carlo simulation of the Boltzmann equation. A marginal stability analysis of the hydrodynamic equations, carried out in the WKB approximation, is shown to be in good agreement with the simulation results. The shape of the hydrodynamic profiles beyond the bifurcation is discussed.
A solution of the inelastic Enskog equation that goes beyond the weak dissipation limit and applies for moderate densities is used to determine the thermal diffusion factor of an intruder immersed in a dense granular gas under gravity. This factor provides a segregation criterion that shows the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the system (masses, sizes, density and coefficients of restitution). The form of the phase-diagrams for the BNE/RBNE transition depends sensitively on the value of gravity relative to the thermal gradient, so that it is possible to switch between both states for given values of the parameters of the system. Two specific limits are considered with detail: (i) absence of gravity, and (ii) homogeneous temperature. In the latter case, after some approximations, our results are consistent with previous theoretical results derived from the Enskog equation. Our results also indicate that the influence of dissipation on thermal diffusion is more important in the absence of gravity than in the opposite limit. The present analysis extends previous theoretical results derived in the dilute limit case [V. Garzo, Europhys. Lett. {bf 75}, 521 (2006)] and is consistent with the findings of some recent experimental results.
Modeling collective motion in non-conservative systems, such as granular materials, is difficult since a general microscopic-to-macroscopic approach is not available: there is no Hamiltonian, no known stationary densities in phase space, not a known small set of relevant variables. Phenomenological coarse-grained models are a good alternative, provided that one has identified a few slow observables and collected a sufficient amount of data for their dynamics. Here we study the case of a vibrofluidized dense granular material. The experimental study of a tracer, dispersed into the media, showed the evidence of many time scales: fast ballistic, intermediate caged, slow superdiffusive, very slow diffusive. A numerical investigation has demonstrated that tracers superdiffusion is related to slow rotating drifts of the granular medium. Here we offer a deeper insight into the slow scales of the granular medium, and propose a new phenomenological model for such a secular dynamics. Based upon the model for the granular medium, we also introduce a model for the tracer (fast and slow) dynamics, which consists in a stochastic system of equations for three coupled variables, and is therefore more refined and successful than previous models.
A collisional model of a confined quasi-two-dimensional granular mixture is considered to analyze homogeneous steady states. The model includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical direction to the horizontal degrees of freedom of grains. The set of Enskog kinetic equations for the velocity distribution functions of each component is derived first to analyze the homogeneous state. As in the one-component case, an exact scaling solution is found where the time dependence of the distribution functions occurs entirely through the granular temperature $T$. As expected, the kinetic partial temperatures $T_i$ of each component are different and hence, energy equipartition is broken down. In the steady state, explicit expressions for the temperature $T$ and the ratio of partial kinetic temperatures $T_i/T_j$ are obtained by considering Maxwellian distributions defined at the partial temperatures $T_i$. The (scaled) granular temperature and the temperature ratios are given in terms of the coefficients of restitution, the solid volume fraction, the (scaled) parameters of the collisional model, and the ratios of mass, concentration, and diameters. In the case of a binary mixture, the theoretical predictions are exhaustively compared with both direct simulation Monte Carlo and molecular dynamics simulations with a good agreement. The deviations are identified to be originated in the non-Gaussianity of the velocity distributions and on microsegregation patterns, which induce spatial correlations not captured in the Enskog theory.
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