Phenomenological modeling of the compaction dynamics of shaken granular systems

Improved compaction of dried tannery wastewater sludge

We quantitatively studied the advantages of improving the compaction of a powder waste by several techniques, including its pelletization. The goal is increasing the mass storage capacity in a given storage volume, and reducing the permeability of air and moisture, that may trigger exothermic spontaneous reactions in organic waste, particularly as powders. The study is based on dried sludges from a wastewater treatment, mainly from tanneries, but the indications are valid and useful for any waste in the form of powder, suitable to pelletization. Measurements of bulk density have been carried out at the industrial and laboratory scale, using different packing procedures, amenable to industrial processes. Waste as powder, pellets and their mixtures have been considered. The bulk density of waste as powder increases from 0.64 t/m(3) (simply poured) to 0.74 t/m(3) (tapped) and finally to 0.82 t/m(3) by a suitable, yet simple, packing procedure that we called dispersion filling, with a net gain of 28% in the compaction by simply modifying the collection procedure. Pelletization increases compaction by definition, but the packing of pellets is relatively coarse. Some increase in bulk density of pellets can be achieved by tapping; vibration and dispersion filling are not efficient with pellets. Mixtures of powder and pellets is the optimal packing policy. The best compaction result was achieved by controlled vibration of a 30/70 wt% mixture of powders and pellets, leading to a final bulk density of 1t/m(3), i.e. an improvement of compaction by more than 54% with respect to simply poured powders, but also larger than 35% compared to just pellets. That means increasing the mass storage capacity by a factor of 1.56. Interestingly, vibration can be the most or the least effective procedure to improve compaction of mixtures, depending on characteristics of vibration. The optimal packing (30/70 wt% powders/pellets) proved to effectively mitigate the onset of smouldering, leading to self-heating, according to standard tests, whereas the pure pelletization totally removes the self-heating hazard.

Strong interlocking of nonconvex particles in random packings

We present a numerical study of random packings made of nonconvex grains. These particles are built by the agglomeration of overlapping spheres in order to control their sphericity φ. The contact number C is found to be much larger than the coordination number Z, providing a significant difference with convex grains. The packing properties are found to be highly dependent on the morphological parameters of the grains : packing fractions as low as 0.3 have been reached. More importantly, the way nonconvex grains develop multiple contacts, i.e., interlocking, is found to be a relevant effect in such packings. Interlocking provides more stability to loose packings.

Microstructure evolution in density relaxation by tapping

The density relaxation phenomenon is modeled using both Monte Carlo and discrete element simulations to investigate the effects of regular taps applied to a vessel having a planar floor filled with monodisperse spheres. Results suggest the existence of a critical tap intensity which produces a maximum bulk solids fraction. We find that the mechanism responsible for the relaxation phenomenon is an evolving ordered packing structure propagating upwards from the plane floor.

Cluster kinetics of density relaxation in granular materials

Of the many complex processes of granular materials, vibrational settling and compaction are common phenomena that have attracted much attention. In this work, we investigate vibrational, or tapping, compaction, and propose that the underlying kinetics involves clusters fragmenting and aggregating, and individual grains attaching and dissociating at cluster surfaces. The periodic vibrations cause cluster breakage and interchange between individual free grains and the clusters. The population balance equations for the concurrent kinetics are solved by a moment method, yielding easily solved differential equations. The compaction ratio defined in terms of the mass moments agrees well with experimental data [Knight et al., Phys. Rev. E. 51, 3957 (1995); Nowak et al., ibid. 57, 1972 (1998)] and other models. A change in tapping acceleration can produce reversible or irreversible transitions between densities, depending on the number of clusters that have evolved.

Microscopic two-dimensional lattice model of dimer granular compaction with friction

We study by Monte Carlo simulation the compaction dynamics of hard dimers in two dimensions under the action of gravity, subjected to vertical and horizontal shaking, considering also the case in which a friction force acts for horizontal displacements of the dimers. These forces are modeled by introducing effective probabilities for all kinds of moves of the particles. We analyze the dynamics for different values of the time tau during which the shaking is applied to the system and for different intensities of the forces. It turns out that the density evolution in time follows a stretched exponential behavior if tau is not very large, while a power law tail develops for larger values of tau. Moreover, in the absence of friction, a critical value tau(*) exists, which signals the crossover between two different regimes: for tau<tau(*) the asymptotic density scales with a power law of tau, while for tau>tau(*) it reaches logarithmically a maximal saturation value. Such behavior smears out when a finite friction force is present. In this situation the dynamics is slower and lower asymptotic densities are attained. In particular, for significant friction forces, the final density decreases linearly with the friction coefficient. We also compare the frictionless single tap dynamics to the sequential tapping dynamics, observing in the latter case an inverse logarithmic behavior of the density evolution, as found in the experiments.

Glassy systems under time-dependent driving forces: application to slow granular rheology

We study the dynamics of a glassy model with infinite range interactions externally driven by an oscillatory force. We find a well-defined transition in the (temperature-amplitude-frequency) phase diagram between (i) a "glassy" state characterized by the slow relaxation of one-time quantities, aging in two-time quantities and a modification of the equilibrium fluctuation-dissipation relation; and (ii) a "liquid" state with a finite relaxation time. In the glassy phase, the degrees of freedom governing the slow relaxation are thermalized to an effective temperature. Using Monte Carlo simulations, we investigate the effect of trapping regions in phase space on the driven dynamics. We find that it alternates between periods of rapid motion and periods of trapping. These results confirm the strong analogies between the slow granular rheology and the dynamics of glasses. They also provide a theoretical underpinning to earlier attempts to present a thermodynamic description of moderately driven granular materials.

Phenomenological glass model for vibratory granular compaction

A model for weakly excited granular media is derived by combining the free volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)]. This is made possible by relating the granular excitation parameter Gamma, defined as the peak acceleration of the driving pulse scaled by gravity, to a temperaturelike parameter eta(Gamma). The resulting master equation is formally identical to that of Bouchaud's trap model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are shown to compare favorably with a range of known experimental behavior. This includes the logarithmic densification and power spectrum of fluctuations under constant eta, the annealing curve when eta is varied cyclically in time, and memory effects observed for a discontinuous shift in eta. Finally, we discuss the physical interpretation of the model parameters and suggest further experiments for this class of systems.

Adsorption-desorption model and its application to vibrated granular materials

We investigate both analytically and by numerical simulation the kinetics of a microscopic model of hard rods adsorbing on a linear substrate, a model that is relevant for compaction of granular materials. The computer simulations use an event-driven algorithm that is particularly efficient at very long times. For a small, but finite desorption rate, the system reaches an equilibrium state very slowly, and the long-time kinetics display three successive regimes: an algebraic one where the density varies as 1/t, a logarithmic one where the density varies as 1/ln(t), followed by a terminal exponential approach. The characteristic relaxation time of the final regime, though incorrectly predicted by mean field arguments, can be obtained with a systematic gap-distribution approach. The density fluctuations at equilibrium are also investigated, and the associated time-dependent correlation function exhibits a power law regime followed by a final exponential decay. Finally, we show that denser particle packings can be obtained by varying the desorption rate during the process.

Swirling granular solidlike clusters

Experiments and three-dimensional numerical simulations are presented to elucidate the dynamics of granular material in a cylindrical dish driven by a horizontal, periodic motion. The following phenomena are obtained both in the experiments and in the simulations: First, for large particle numbers N the particles describe hypocycloidal trajectories. In this state the particles are embedded in a solidlike cluster ("pancake") which counter-rotates with respect to the external driving (reptation). Self-organization within the cluster occurs such that the probability distribution of the particles consists of concentric rings. Second, the system undergoes phase transitions. These can be identified by changes of the quantity dE(kin)/dN (E(kin) is the mean kinetic energy) between zero (rotation), positive (reptation), and negative values (appearance of the totality of concentric rings).

Minimal relaxation law for compaction of tapped granular matter

Granular systems can compact under the influence of sufficiently strong, successive tapping. Recent experimental investigations show that the packing fraction obeys a very slow relaxation to a final, dense packing fraction that is basically proportional to the inverse of the logarithm of the tap number or time. We provide a simple macromechanical argument that explains this inverse logarithmic relaxation in time in all functional details. By considering the asymptotic limits of the resulting relaxation law, we show that the relaxational dynamics of the compaction process can be interpreted as a combination of a biased void diffusion for short times and a collective reorganization for large times.