Two-state model to describe the rheological behavior of vibrated granular matter

Self-replicating segregation patterns in horizontally vibrated binary mixture of granules

Fluidized granular mixtures of various particle sizes exhibit intriguing patterns as different species segregate and condense. However, understanding the segregation dynamics is hindered by the inability to directly observe the time evolution of the internal structure. We discover self-replicating bands within a quasi-2D container subjected to horizontal agitation, resulting in steady surface waves. Through direct observation of surface flow and evolving internal structures, we reveal the crucial role of coupling among segregation, surface flow, and hysteresis in granular fluidity. We develop Bonhoeffer-van der Pol type equations grounded in experimental observations, reproducing complex band dynamics, such as replication, oscillation, and breathing. It suggests the similarity between pattern formation in granular segregation and that in reaction-diffusion systems.

How vertical oscillatory motion above a saturated sand bed leads to heap formation

We show how oscillations in fluid flow over a fluid-saturated and porous sediment bed leads to the development of a bedform. To understand the role of pressure fluctuations on the bed associated with flow oscillations, we analyze how the flow penetrates into and through the bed. We then calculate the corresponding vertical pressure gradients within the bed that tend to expand the bed along the vertical direction. When these pressure gradients are large enough, they facilitate small irreversible rearrangements of the grains within the bed, and so cause granular creep. We conjecture that this granular creep alternates with jamming to produce a granular ratchet that slowly lifts the surface of the bed locally where pressure gradients dominate, and depresses the surface where shear stresses dominate. We observe that the shape of the resulting heap exhibits a constant characteristic width. The height of this heap evolves approximately as the square root of time, in agreement with dimensional arguments predicated on a coarse-grained viscous deformation of the bed. The surface of the heap contracts initially with the square root of time, consistent with an incompressible analysis of the flow of grains within the heap. Near its peak the heap grows due to a dilatation of the bed, to inward radial flux, or to a combination of the two.

Particles bed morphology under an oscillating stiff and flexible plates

We analyse the different morphologies induced by an oscillating plate above an erodible bed. We present some data describing how the shape and the stiffness of the plate affects the main features of the generated heap. We investigate several configurations with different geometries, frequencies and the amplitudes. Some preliminary results are available, in which the role of the flexibility of the plate is taken in account. Unlike the rigid plate in which a proper oscillation induces the formation of one heap, the morphology of the bed is now characterized by more than one heap due to a different pressure profile induced by a flexible plate.

Bedforms Produced on a Particle Bed by Vertical Oscillations of a Plate

We describe a new mechanism that produces bedforms and characterize the conditions under which it operates. The mechanism is associated with pressure gradients generated in a fluid saturated particle bed by a plate oscillating in the water above it. These vertical pressure gradients cause oscillatory bed failure. This facilitates particle displacement in its interior and transport at and near its surface that contribute to the formation of a heap under the plate. Flows over erodible beds generally cause shear stresses on the bed and these induce bed failure. Failure driven by pressure gradients is different from this. We report on bedforms in a bed of glass beads associated with such fluctuating pressure gradients. We measure the development of the profiles of heaps as a function of time and determine the tangential and normal motion of areas on the beds surface and estimate the depth of penetration of the tangential transport. The measurements compare favorably with a simple model that describes the onset of failure due to oscillations in pressure.

Bulk and local rheology in a dense and vibrated granular suspension

In this paper, we investigate experimentally the dynamics of particles in dense granular suspensions when both shear and external vibrations are applied. We study in detail how vibrations affect particle reorganization at the local scale and modify the apparent rheology. The nonlocal nature of the rheology when no vibrations are applied is evidenced, in agreement with previous numerical studies from the literature. It is also shown that vibrations induce structural reorganizations, which tend to homogenize the system and cancel the nonlocal properties.

Unified rheology of vibro-fluidized dry granular media: From slow dense flows to fast gas-like regimes

Granular media take on great importance in industry and geophysics, posing a severe challenge to materials science. Their response properties elude known soft rheological models, even when the yield-stress discontinuity is blurred by vibro-fluidization. Here we propose a broad rheological scenario where average stress sums up a frictional contribution, generalizing conventional μ(I)-rheology, and a kinetic collisional term dominating at fast fluidization. Our conjecture fairly describes a wide series of experiments in a vibrofluidized vane setup, whose phenomenology includes velocity weakening, shear thinning, a discontinuous thinning transition, and gaseous shear thickening. The employed setup gives access to dynamic fluctuations, which exhibit a broad range of timescales. In the slow dense regime the frequency of cage-opening increases with stress and enhances, with respect to μ(I)-rheology, the decrease of viscosity. Diffusivity is exponential in the shear stress in both thinning and thickening regimes, with a huge growth near the transition.

Granular avalanches down inclined and vibrated planes

In this article, we study granular avalanches when external mechanical vibrations are applied. We identify conditions of flow arrest and compare with the ones classically observed for nonvibrating granular flows down inclines [Phys. Fluids 11, 542 (1999)PHFLE61070-663110.1063/1.869928]. We propose an empirical law to describe the thickness of the deposits with the inclination angle and the vibration intensity. The link between the surface velocity and the depth of the flow highlights a competition between gravity and vibrations induced flows. We identify two distinct regimes: (a) gravity-driven flows at large angles where vibrations do not modify dynamical properties but the deposits (scaling laws in this regime are in agreement with the literature for nonvibrating granular flows) and (b) vibrations-driven flows at small angles where no flow is possible without applied vibrations (in this last regime, the flow behavior can be properly described by a vibration induced activated process). We show, in this study, that granular flows down inclined planes can be finely tuned by external mechanical vibrations.

Model of heap formation in vibrated gravitational suspensions

In vertically vibrated dense suspensions, several localized structures have been discovered, such as heaps, stable holes, expanding holes, and replicating holes. Because an inclined free fluid surface is difficult to maintain because of gravitational pressure, the mechanism of those structures is not understood intuitively. In this paper, as a candidate for the driving mechanism, we focus on the boundary condition on a solid wall: the slip-nonslip switching boundary condition in synchronization with vertical vibration. By applying the lubrication approximation, we derived the time evolution equation of the fluid thickness from the Oldroyd-B fluid model. In our model we show that the initially flat fluid layer becomes unstable in a subcritical manner, and heaps and convectional flow appear. The obtained results are consistent with those observed experimentally. We also find that heaps climb a slope when the bottom is slightly inclined. We show that viscoelasticity enhances heap formation and climbing of a heap on the slope.

Vibration-induced compaction of granular suspensions

We investigate the compaction dynamics of vibrated granular suspensions using both digital imaging technique and MRI measurements. Starting from initialy loose packings, our experimental data suggest the existence of two stages in the compaction dynamics: a fast stage at short times where a rising compaction front propagates through the granular suspension and a slow stage at large times where the packing compacts slowly and homogeneously. The compaction dynamics in each stage can be well fitted to usual stretched exponential laws with stretching exponents equal to 2 and 0.45, respectively. The transition time between these two stages, τ c , depends on the fluid viscosity, vibration intensity and grain diameter. We show that τ c (-1) and the velocity of the front decrease roughly linearly with the lubrication Peclet number, Pe lub related to the competition between the lubrication stress induced by vibrations and the granular pressure.