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Register a new userPatterns and Collective Behavior in Granular Media: Theoretical Concepts
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Granular materials are ubiquitous in our daily lives. While they have been a subject of intensive engineering research for centuries, in the last decade granular matter attracted significant attention of physicists. Yet despite a major efforts by many groups, the theoretical description of granular systems remains largely a plethora of different, often contradicting concepts and approaches. Authors give an overview of various theoretical models emerged in the physics of granular matter, with the focus on the onset of collective behavior and pattern formation. Their aim is two-fold: to identify general principles common for granular systems and other complex non-equilibrium systems, and to elucidate important distinctions between collective behavior in granular and continuum pattern-forming systems.
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We perform the analog to the water bell experiment using non-cohesive granular material. When a jet of granular material, many particles wide, rebounds from a fixed cylindrical target, it deforms into a sharply-defined sheet or cone with a shape that mimics a liquid with zero surface tension. The particulate nature of granular material becomes apparent when the number of particles in the cross-section of the jet is decreased and the emerging sheets and cones broaden and gradually disintegrate into a broad spray. This experiment has its counterpart in the behavior of the quark-gluon plasma generated by collisions of gold ions at the Relativistic Heavy Ion Collider. There a high density of inter-particle collisions gives rise to collective behavior that has also been described as a liquid.
Porous media with hierarchical structures are commonly encountered in both natural and synthetic materials, e.g., fractured rock formations, porous electrodes and fibrous materials, which generally consist of two or more distinguishable levels of pore structure with different characteristic lengths. The multiphase flow behaviours in hierarchical porous media have remained elusive. In this study, we investigate the influences of hierarchical structures in porous media on the dynamics of immiscible fingering during fluid-fluid displacement. By conducting a series of numerical simulations, we found that the immiscible fingering can be suppressed due to the existence of secondary porous structures. To characterise the fingering dynamics in hierarchical porous media, a phase diagram is constructed by introducing a scaling parameter, i.e., the ratio of time scales considering the combined effect of characteristic pore sizes and wettability. The findings present in this work provide a basis for further research on the application of hierarchical porous media for controlling immiscible fingerings.
We use a computational model to investigate the emergence of interaction forces between pairs of intruders in a horizontally vibrated granular fluid. The time evolution of a pair of particles shows a maximum of the likelihood to find the pair at contact in the direction of shaking. This relative interaction is further studied by fixing the intruders in the simulation box where we identify effective mechanical forces, and torques between particles and quantify an emergent long range attractive force as a function of the shaking relative angle, amplitude, and the packing density of grains. We determine the local density and kinetic energy profiles of granular particles along the axis of the dimer to find no gradients in the density fields and additive gradients in the kinetic energies.
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.
Recent experiments with rotational diffusion of a probe in a vibrated granular media revealed a rich scenario, ranging from the dilute gas to the dense liquid with cage effects and an unexpected superdiffusive behavior at large times. Here we setup a simulation that reproduces quantitatively the experimental observations and allows us to investigate the properties of the host granular medium, a task not feasible in the experiment. We discover a persistent collective rotational mode which emerges at high density and low granular temperature: a macroscopic fraction of the medium slowly rotates, randomly switching direction after very long times. Such a rotational mode of the host medium is the origin of probes superdiffusion. Collective motion is accompanied by a kind of dynamical heterogeneity at intermediate times (in the cage stage) followed by a strong reduction of fluctuations at late times, when superdiffusion sets in.
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