Competition of mixing and segregation in rotating cylinders

Using discrete element methods, we study numerically the dynamics of the size segregation process of binary particle mixtures in three-dimensional rotating drums, operated in the continuous flow regime. Particle rotations are included and we focus on different volume filling fractions of the drum to study the interplay between the competing phenomena of mixing and segregation. It is found that segregation is best for a more than half-filled drum due to the non-zero width of the fluidized layer. For different particle size ratios, it is found that radial segregation occurs for any arbitrary small particle size difference and the final amount of segregation shows a linear dependence on the size ratio of the two particle species. To quantify the interplay between segregation and mixing, we investigate the dynamics of the center of mass positions for each particle component. Starting with initially separated particle groups we find that no mixing of the component is necessary in order to obtain a radially segregated core.Comment: 9 pages, 12 figures (EPIC/EEPIC & EPS, macros included), submitted to Physics of Fluid

An exactly solvable model for driven dissipative systems

We introduce a solvable stochastic model inspired by granular gases for driven dissipative systems. We characterize far from equilibrium steady states of such systems through the non-Boltzmann energy distribution and compare different measures of effective temperatures. As an example we demonstrate that fluctuation-dissipation relations hold, however with an effective temperature differing from the effective temperature defined from the average energy.Comment: Some further clarifications. No changes in results or conclusion

Phase separation of a driven granular gas in annular geometry

This work investigates phase separation of a monodisperse gas of inelastically colliding hard disks confined in a two-dimensional annulus, the inner circle of which represents a "thermal wall". When described by granular hydrodynamic equations, the basic steady state of this system is an azimuthally symmetric state of increased particle density at the exterior circle of the annulus. When the inelastic energy loss is sufficiently large, hydrodynamics predicts spontaneous symmetry breaking of the annular state, analogous to the van der Waals-like phase separation phenomenon previously found in a driven granular gas in rectangular geometry. At a fixed aspect ratio of the annulus, the phase separation involves a "spinodal interval" of particle area fractions, where the gas has negative compressibility in the azimuthal direction. The heat conduction in the azimuthal direction tends to suppress the instability, as corroborated by a marginal stability analysis of the basic steady state with respect to small perturbations. To test and complement our theoretical predictions we performed event-driven molecular dynamics (MD) simulations of this system. We clearly identify the transition to phase separated states in the MD simulations, despite large fluctuations present, by measuring the probability distribution of the amplitude of the fundamental Fourier mode of the azimuthal spectrum of the particle density. We find that the instability region, predicted from hydrodynamics, is always located within the phase separation region observed in the MD simulations. This implies the presence of a binodal (coexistence) region, where the annular state is metastable. The phase separation persists when the driving and elastic walls are interchanged, and also when the elastic wall is replaced by weakly inelastic one.Comment: 9 pages, 10 figures, to be published in PR

On the Shape of the Tail of a Two Dimensional Sand Pile

We study the shape of the tail of a heap of granular material. A simple theoretical argument shows that the tail adds a logarithmic correction to the slope given by the angle of repose. This expression is in good agreement with experiments. We present a cellular automaton that contains gravity, dissipation and surface roughness and its simulation also gives the predicted shape.Comment: LaTeX file 4 pages, 4 PS figures, also available at http://pmmh.espci.fr

Force Dynamics in Weakly Vibrated Granular Packings

The oscillatory force F_b^ac on the bottom of a rigid, vertically vibrated, grain filled column, reveals rich granular dynamics, even when the peak acceleration of the vibrations is signicantly less than the gravitational acceleration at the earth's surface. For loose packings or high frequencies, F_b^ac 's dynamics are dominated by grain motion. For moderate driving conditions in more compact samples, grain motion is virtually absent, but F_b^ac nevertheless exhibits strongly nonlinear and hysteretic behavior, evidencing a granular regime dominated by nontrivial force-network dynamics.Comment: 4 pages, 5 figure

Avalanche Mixing of Granular Solids

Mixing of two fractions of a granular material in a slowly rotating two-dimensional drum is considered. The rotation is around the axis of the upright drum. The drum is filled partially, and mixing occurs only at a free surface of the material. We propose a simple theory of the mixing process which describes a real experiment surprisingly well. A geometrical approach without appealing to ideas of self-organized criticality is used. The dependence of the mixing time on the drum filling is calculated. The mixing time is infinite in the case of the half-filled drum. We describe singular behaviour of the mixing near this critical point.Comment: 9 pages (LaTeX) and 2 Postscript figures, to be published in Europhys. Let

Mixing and condensation in a wet granular medium

We have studied the effect of small amounts of added liquid on the dynamic behavior of a granular system consisting of a mixture of glass beads of two different sizes. Segregation of the large beads to the top of the sample is found to depend in a nontrivial way on the liquid content. A transition to viscoplastic behavior occurs at a critical liquid content, which depends upon the bead size. We show that this transition can be interpreted as a condensation due to the hysteretic liquid bridge forces connecting the beads, and provide the corresponding phase diagram.Comment: submitted to PR

Piling and avalanches of magnetized particles

We performed computer simulations based on a two-dimensional Distinct Element Method to study granular systems of magnetized spherical particles. We measured the angle of repose and the surface roughness of particle piles, and we studied the effect of magnetization on avalanching. We report linear dependence of both angle of repose and surface roughness on the ratio $f$ of the magnetic dipole interaction and the gravitational force (\emph{interparticle force ratio}). There is a difference in avalanche formation at small and at large interparticle force ratios. The transition is at $f_c \approx 7$. For $f < f_c$ the particles forming the avalanches leave the system in a quasi-continuous granular flow (\emph{granular regime}), while for $f > f_c$ the avalanches are formed by long particle clusters (\emph{correlated regime}). The transition is not sharp. We give plausible estimates for $f_c$ based on stability criteria.Comment: 9 pages, 7 figure

Diffusion of a granular pulse in a rotating drum

The diffusion of a pulse of small grains in an horizontal rotating drum is studied through discrete elements methods simulations. We present a theoretical analysis of the diffusion process in a one-dimensional confined space in order to elucidate the effect of the confining end-plate of the drum. We then show that the diffusion is neither subdiffusive nor superdiffusive but normal. This is demonstrated by rescaling the concentration profiles obtained at various stages and by studying the time evolution of the mean squared deviation. Finally we study the self-diffusion of both large and small grains and we show that it is normal and that the diffusion coefficient is independent of the grain size