Decompaction and fluidization of a saturated and confined granular medium by injection of a viscous liquid or gas

Unstable Invasion of Sedimenting Granular Suspensions

We investigate the development of mobility inversion and fingering when a granular suspension is injected radially between horizontal parallel plates of a cell filled with a miscible fluid. While the suspension spreads uniformly when the suspension and the displaced fluid densities are exactly matched, even a small density difference is found to result in a dense granular front which develops fingers with angular spacing that increase with granular volume fraction and decrease with injection rate. We show that the timescale over which the instability develops is given by the volume fraction dependent settling timescale of the grains in the cell. We then show that the mobility inversion and the nonequilibrium Korteweg surface tension due to granular volume fraction gradients determine the number of fingers at the onset of the instability in these miscible suspensions.

Pressure evolution and deformation of confined granular media during pneumatic fracturing

By means of digital image correlation, we experimentally characterize the deformation of a dry granular medium confined inside a Hele-Shaw cell due to air injection at a constant overpressure high enough to deform it (from 50 to 250 kPa). Air injection at these overpressures leads to the formation of so-called pneumatic fractures, i.e., channels empty of beads, and we discuss the typical deformations of the medium surrounding these structures. In addition we simulate the diffusion of the fluid overpressure into the medium, comparing it with the Laplacian solution over time and relating pressure gradients with corresponding granular displacements. In the compacting medium we show that the diffusing pressure field becomes similar to the Laplace solution on the order of a characteristic time given by the properties of the pore fluid, the granular medium, and the system size. However, before the diffusing pressure approaches the Laplace solution on the system scale, we find that it resembles the Laplacian field near the channels, with the highest pressure gradients on the most advanced channel tips and a screened pressure gradient behind them. We show that the granular displacements more or less always move in the direction against the local pressure gradients, and when comparing granular velocities with pressure gradients in the zone ahead of channels, we observe a Bingham type of rheology for the granular paste (the mix of air and beads), with an effective viscosity μ_{B} and displacement thresholds ∇[over ⃗]P_{c} evolving during mobilization and compaction of the medium. Such a rheology, with disorder in the displacement thresholds, could be responsible for placing the pattern growth at moderate injection pressures in a universality class like the dielectric breakdown model with η=2, where fractal dimensions are found between 1.5 and 1.6 for the patterns.

Mechanism behind Erosive Bursts In Porous Media

Erosion and deposition during flow through porous media can lead to large erosive bursts that manifest as jumps in permeability and pressure loss. Here we reveal that the cause of these bursts is the reopening of clogged pores when the pressure difference between two opposite sites of the pore surpasses a certain threshold. We perform numerical simulations of flow through porous media and compare our predictions to experimental results, recovering with excellent agreement shape and power-law distribution of pressure loss jumps, and the behavior of the permeability jumps as a function of particle concentration. Furthermore, we find that erosive bursts only occur for pressure gradient thresholds within the range of two critical values, independent of how the flow is driven. Our findings provide a better understanding of sudden sand production in oil wells and breakthrough in filtration.

Pneumatic fractures in confined granular media

We perform experiments where air is injected at a constant overpressure P_{in}, ranging from 5 to 250 kPa, into a dry granular medium confined within a horizontal linear Hele-Shaw cell. The setup allows us to explore compacted configurations by preventing decompaction at the outer boundary, i.e., the cell outlet has a semipermeable filter such that beads are stopped while air can pass. We study the emerging patterns and dynamic growth of channels in the granular media due to fluid flow, by analyzing images captured with a high speed camera (1000 images/s). We identify four qualitatively different flow regimes, depending on the imposed overpressure, ranging from no channel formation for P_{in} below 10 kPa, to large thick channels formed by erosion and fingers merging for high P_{in} around 200 kPa. The flow regimes where channels form are characterized by typical finger thickness, final depth into the medium, and growth dynamics. The shape of the finger tips during growth is studied by looking at the finger width w as function of distance d from the tip. The tip profile is found to follow w(d)∝d^{β}, where β=0.68 is a typical value for all experiments, also over time. This indicates a singularity in the curvature d^{2}d/dw^{2}∼κ∼d^{1-2β}, but not of the slope dw/dd∼d^{β-1}, i.e., more rounded tips rather than pointy cusps, as they would be for the case β>1. For increasing P_{in}, the channels generally grow faster and deeper into the medium. We show that the channel length along the flow direction has a linear growth with time initially, followed by a power-law decay of growth velocity with time as the channel approaches its final length. A closer look reveals that the initial growth velocity v_{0} is found to scale with injection pressure as v_{0}∝P_{in}^{3/2}, while at a critical time t_{c} there is a cross-over to the behavior v(t)∝t^{-α}, where α is close to 2.5 for all experiments. Finally, we explore the fractal dimension of the fully developed patterns. For example, for patterns resulting from intermediate P_{in} around 100-150 kPa, we find that the box-counting dimensions lie within the range D_{B}∈[1.53,1.62], similar to viscous fingering fractals in porous media.

Channelization in porous media driven by erosion and deposition

We develop and validate a new model to study simultaneous erosion and deposition in three-dimensional porous media. We study the changes of the porous structure induced by the deposition and erosion of matter on the solid surface and find that when both processes are active, channelization in the porous structure always occurs. The channels can be stable or only temporary depending mainly on the driving mechanism. Whereas a fluid driven by a constant pressure drop in general does not form steady channels, imposing a constant flux always produces stable channels within the porous structure. Furthermore we investigate how changes of the local deposition and erosion properties affect the final state of the porous structure, finding that the larger the range of wall shear stress for which there is neither erosion nor deposition, the more steady channels are formed in the structure.

Bubbles trapped in a fluidized bed: Trajectories and contact area

This work investigates the dynamics of bubbles in a confined, immersed granular layer submitted to an ascending gas flow. In the stationary regime, a central fluidized zone of parabolic shape is observed, and the bubbles follow different dynamics: either the bubbles are initially formed outside the fluidized zone and do not exhibit any significant motion over the experimental time or they are located inside the fluidized bed, where they are entrained downwards and are, finally, captured by the central air channel. The dependence of the air volume trapped inside the fluidized zone, the bubble size, and the three-phase contact area on the gas injection flow rate and grain diameter are quantified. We find that the volume fraction of air trapped inside the fluidized region is roughly constant and of the order of 2%-3% when the gas flow rate and the grain size are varied. Contrary to intuition, the gas-liquid-solid contact area, normalized by the air injected into the system, decreases when the flow rate is increased, which may have significant importance in industrial applications.

Grains unchained: local fluidization of a granular packing by focused ultrasound

We report experimental results on the dynamics of a granular packing submitted to high-intensity focused ultrasound. Acoustic radiation pressure is shown to remotely induce local rearrangements within a pile as well as global motion around the focal spot in an initially jammed system. We demonstrate that this fluidization process is intermittent for a range of acoustic pressures and hysteretic when the pressure is cycled. Such a first-order-like unjamming transition is reproduced in numerical simulations in which the acoustic pressure field is modeled by a localized external force. Further analysis of the simulated packings suggests that in the intermittent regime unjamming is not associated with any noticeable prior structural signature. A simple two-state model based on effective temperatures is proposed to account for these findings.

Bubbles breaking the wall: Two-dimensional stress and stability analysis

Submerged granular material exhibits a wide range of behavior when the saturating fluid is slowly displaced by a gas phase. In confined systems, the moving interface between the invading gas and the fluid/grain mixture can cause beads to jam, and induce intermittency in the dynamics. Here, we study the stability of layers of saturated jammed beads around stuck air bubbles, and the deformation mechanism leading to air channel formations in these layers. We describe a two-dimensional extension of a previous model of the effective stress in the jammed packing. The effect of the tangential stress component on the yield stress is discussed, in particular how arching effects may impact the yield threshold. We further develop a linear stability analysis, to study undulations which develop under certain experimental conditions at the air-liquid interface. The linear analysis gives estimates for the most unstable wavelengths for the initial growth of the perturbations. The estimates correspond well with peak to peak length measurements of the experimentally observed undulations.

Dynamic aerofracture of dense granular packings

A transition in hydraulically induced granular displacement patterns is studied by means of discrete numerical molecular dynamics simulations. During this transition the patterns change from fractures and fingers to finely dispersed bubbles. The dynamics of the displacement patterns are studied in a rectangular Hele-Shaw cell filled with a dense but permeable two-dimensional granular layer. At one side of the cell the pressure of the compressible interstitial gas is increased. At the opposite side from the inlet of the cell a semipermeable boundary is located. This boundary is only permeable towards the gas phase while preventing grains from leaving the cell. The imposed pressure gradient compacts the grains. In the process we can identify and describe a mechanism that controls the transition of the emerging displacement patterns from fractures and fingers to finely dispersed bubbles as a function of the interstitial gas's properties and the characteristics of the granular phase.

Patterns and flow in frictional fluid dynamics

Pattern-forming processes in simple fluids and suspensions have been studied extensively, and the basic displacement structures, similar to viscous fingers and fractals in capillary dominated flows, have been identified. However, the fundamental displacement morphologies in frictional fluids and granular mixtures have not been mapped out. Here we consider Coulomb friction and compressibility in the fluid dynamics, and discover surprising responses including highly intermittent flow and a transition to quasi-continuodynamics. Moreover, by varying the injection rate over several orders of magnitude, we characterize new dynamic modes ranging from stick-slip bubbles at low rate to destabilized viscous fingers at high rate. We classify the fluid dynamics into frictional and viscous regimes, and present a unified description of emerging morphologies in granular mixtures in the form of extended phase diagrams.

Pattern-forming processes in simple fluids and suspensions are well understood, but displacement morphologies in frictional fluids and granular mixtures have not been studied extensively. Sandnes et al. consider the effects of Coulomb friction and compressibility on the fluid dynamics of granular mixtures.

Sedimentation instabilities: impact of the fluid compressibility and viscosity

The effect of an interstitial fluid on the mixing of sedimenting grains is studied numerically in a closed rectangular Hele-Shaw cell. We investigate the impact of the fluid compressibility and fluid viscosity on the dynamics and structures of the granular Rayleigh-Taylor instability. First we discuss the effect of the fluid compressibility on the initial fluid pressure evolution and on the dynamics of the particles. Here, the emerging patterns do not seem highly affected by the compressibility change studied. To characterize the patterns and motion the combined length of the particle trajectories in relation to the movement of the center of mass is analyzed, and the separation of particle pairs is measured as a function of the fluid viscosity.