Session J13: Granular Flows II

Faraday Waves in Granular Particles Subject to Combined Gas Flow and Vibration

Experiments show that an analog of the Faraday wave instability forms in granular particles subject to combined vertical vibration and vertical gas flow. As compared to vibration alone, combined gas flow and vibration induces waves at lower vibration strengths and allows waves to persist at higher granular layer heights. Results across different vibration and gas flow conditions for the onset of waves are collapsed by introducing a non-dimensional velocity which incorporates the effects of gas flow and vibration. Continuum numerical simulations using a recently developed granular rheology model are able to reproduce wave patterns in grains subject to vibration with and without gas flow. Simulation results show that the added drag force in cases with gas flow causes more uniform forces and coordination motion among particles throughout the layer, which allow waves to persist at higher layer heights when gas flow is used.   

Evolution of Rayleigh-Taylor instability at the interface between a granular suspension and a clear fluid

We report the characteristics of Rayleigh–Taylor instabilities (RTI) occurring at the interface between a suspension of granular particles and a clear fluid. The time evolution of these instabilities is studied numerically using coupled lattice Boltzmann and discrete element methods with a focus on the overall growth rate (σ) of the instabilities and their average wave number (k). Special attention is paid to the effects of two parameters, the solid fraction (0.10 ≤ φ₀ ≤ 0.40) of the granular suspension and the solid-to-fluid density ratio (1.5 ≤ R ≤ 2.7). Perturbations at the interface are observed to undergo a period of linear growth, the duration of which decreases with φ₀ and scales with the particle shear time d/w_∞, where d is the particle diameter and w_∞ is the terminal velocity. For φ₀ > 0.10, the transition from linear to nonlinear growth occurs when the characteristic steepness of the perturbations is around 29%. At this transition, the average wave number is approximately 0.67 d^-1 for φ₀ > 0.10 and appears independent of R. For a given φ₀, the growth rate is found to be inversely proportional to the particle shear time, i.e., σ ∝ (d/w_∞)^-1; at a given R, σ increases monotonically with φ₀, largely consistent with a linear stability analysis (LSA) in which the granular suspension is approximated as a continuum. These results reveal the relevance of the time scale d/w_∞ to the evolution of interfacial granular RTI, highlight the various effects of φ₀ and R on these instabilities, and demonstrate modest applicability of the continuum-based LSA for the particle-laden problem.   

Cross-stream oscillation in gravity flow through a vertical channel

The gravity flow of cohesionless granular material between two vertical walls separated by width 2W has been simulated using the discrete element method. Periodic boundary conditions are applied in the flow (vertical) and other horizontal directions. The mass flow rate is controlled by specifying the average solids fraction Φ^a, the ratio of volume of the particles to volume of the channel. There is no flow for Φ^a>Φ^a_max=0.62. As Φ^a reduces, the flow becomes dilute and material flows faster. A steady fully developed state can be achieved only for a narrow range Φ^a_max≥Φ^a≥Φ^a_c. When Φ^a is decreased below Φ^a_c, the flow is unstable and oscillates between the side walls for Φ^a_c>Φ^a≥Φ^a_min. For Φ^a<Φ^a_min, the material is in free fall under gravity. In oscillatory regime, the horizontal coordinate of centre of mass of the flowing material oscillates with a non-zero amplitude and frequency in the cross-stream direction, analogous to a spring-mass system resulting in higher fluctuations in wall stresses. The phenomenon resembles the ‘clustering instability’ in granular flows. If the normal component of interparticle contact force depends only on a elastic spring, the cross-stream oscillation is absent; it is independent of nature of wall-particle interactions, except for frictionless walls.     

Periodic, Unsteady Velocity Characteristics within Rotating Triangular Tumblers of Variable Fill Levels

Rotating tumblers are used in a wide variety of industrial applications from mixing and deburring to flow regulation and storage. Almost all model tumblers previously analyzed, both theoretically and experimentally, had circular cross sections that produced consistent flowing layer dimensions and steady state flow. In contrast, tumblers with triangular cross sections produced unsteady flow as a direct result of the dynamic dimensions of the flowing surface. Although unsteady, the flow produced in triangular tumblers is periodic every 120$^\circ$ of rotation after an initial start-up period. The mechanisms by which the flow characteristics vary as a triangular tumbler rotates and the number of tumbler walls in contact with the flowing layer change, is poorly understood. The primary objective of this work is to determine the effect of orientation, fill level, and tumbler size on flow velocities and flowing layer dimensions. High speed imaging with particle tracking velocimetry are used in experiments exploring the flow in the central region of the tumblers. Results indicate that fill level is the dominant feature on the velocity profile while tumbler size affects velocity amplitudes through the instantaneous dimension at each orientation. Normalization of various flow characteristics reveals a phase shift relation for velocity as a function of tumbler orientation as both fill level and tumbler dimension change.   

Cratering by impact

The impact of projectiles with a granular ground is common in nature and spans over a large range of scales. At small scales, it happens every time that cm-size drops and seeds fall on the ground, forming cm-size craters and involving low energies (of the order of 1E(-7) J). At large scales, it happens when km-size (or larger) asteroids collide with planets and moons, involving high energies (1E16 to 1E20 J, or even higher). Although high-energy impacts imply melting and evaporation of part of the material, the granular mechanisms for cratering remain valid across scales by assuring that the collisions happen within the same regime. We investigated cratering by performing DEM (discrete element method) computations, where we varied the projectile and grain properties for different available energies. We found that the solid friction and packing fraction affect the crater morphology, that the projectile rebounds by the end of its motion, and that the penetration depth increases considerably with the angular velocity of the projectile. Besides, we propose a scaling that can unify existing correlations for penetration. Those findings answer questions hitherto open, and shed new light on the mechanics of cratering.   

Erosion of cohesive grains by an impinging turbulent jet

A common method to clean surfaces is to use a turbulent jet of a gas to trigger the erosion and transport of surface contaminants. The onset of erosion, the subsequent transport and the resulting morphology of the eroded region are all modified by the presence of interparticle cohesive forces or surface adhesion. We perform experiments of a turbulent round jet of air impinging a granular bed. We finely tune the cohesion force between the grains and report the effects of cohesion in such an erosion process. First, we show that results for the onset of erosion can be rationalized by a cohesive Shields number that accounts for the interparticle cohesion force. Despite the complex nature of a turbulent jet, we provide a scaling law to correlate the erosion threshold, based on the outlet velocity at the nozzle, to a local cohesive Shields number. Beyond the onset of erosion, a crater is observed in the granular bed where erosion has locally removed the grains. The morphology of the observed craters is analyzed in detail as dependent on the local cohesive Shields number, and different types of craters are compared to similar experiments for cohesionless grains. Finally, we also consider the effects of the angle of impingement and the thickness of the cohesive granular bed on the mass removal.   

Author not Attending

Unlike fluids, no established principles govern the stress in static granular media under gravity, though they are encountered widely in nature and industry. Experiments have show that the stress depends strongly on how the grain assembly is created and the nature of confining boundaries. Non-trivial stress variation even in simple geometries have posed long-standing challenges to continuum modelling. We have studied the problem computationally by creating gravity-deposited grain packings and studying force transmission in the grain contact network. We determine the paths of load transmission averaged over an ensemble of realizations, or 'force lines', and show that they encode preparation history. We hypothesize that the weight of each particle is transmitted by biased random walks to the particles below, and validate the hypothesis by showing excellent agreement between the ensemble-averaged random walks and force lines. This identification leads to a closure relation for the static stress, that yields a parabolic partial differential equation for the vertical normal stress. The predictions of the model are shown to compare very well with the stress obtained from particle dynamics simulations.   

Not Participating

We use a densely packed double emulsion as a model soft granular material to produce freely-floating clusters of sizes of 20-40 grains (droplets). Despite the lack of an energetic potential, we report the occurrence of crystalline-like structures within such clusters. These structures can occur spontaneously during the formation of the clusters, but can also form within previously amorphously arranged structures due to flow, an effect we attribute to the input of noise and shear to the clusters from the surrounding flow. We find differences between the behaviours of two groups of droplets: those within the rim of the cluster and those within the inner part of the cluster. This largely stems from an intriguing competition between the tendency of the grains within the cluster to form the preferential crystal structure and effects on the surface of the cluster, such as the tendency of the cluster to minimize its surface area with the surrounding fluid due to surface tension and an attraction between the grains and the surface of the cluster, which leads to a series of consequences, including crowding and elongation of grains at the surface of the cluster.   

Shocked granular flow over multiple obstacles

Interaction of supersonic granular flow [1] with obstacles in a confined channel generates shock waves characterised by a nearly parabolic front of agitating grains in the outer region and a heap of static grains in the inner region. The inner static heap results from granular collapse due to high volume fraction and enhanced collision rate near the obstacle [2]. The present work reports interesting flow structures when granular shock waves are formed on an array of three identical wedges placed in line transverse to the flow direction in a rectangular chute at different symmetrical spacings. It is observed that spacing has a profound influence, resulting in three types of flow structures [3,4]. The experimental data showed a strong dependence of normalised shock stand-off distance on Froude number and normalised spacing. The normalised shock stand-off distance also followed a linear trend for a range of Froude numbers. Due to structural changes in the dynamic heap [3], a non-intuitive behaviour with wedge spacing is observed. These features will be discussed in detail using high-resolution shadowgraphy and velocity field obtained from particle imaging velocimetry.   

Flow of non-spherical particles within a belt-driven hopper: simulations and experiments

The repeatable, steady mass flow rate of pellets is desired in order to maintain a consistent energy conversion or provide the required rate of reactant for a chemical process. A discrete element method was used to model pellet-shaped granular flow within a bottom-driven conveyor belt as a function of the exit area; the size of the opening fluctuates as a result of the conveyor flights passing through the exit. Simulations and experiments were evaluated to demonstrate that greater uniformity in mass flow rates are possible with smaller opening area. The limitation in exit size due to the flights passing through the exit causes some circulation within the hopper reducing the efficiency of the transport process. Larger openings resulted in gravity dominated flow rather than the control via the belt speed. Frequency analysis of the fluctuations of the mass flow rate indicate correlation with the velocity of the flights on the belt. Simulations also considered the orientation of the 3:1 aspect ratio pellets showing the pattern of plug flow transitioning to pseudo-stationary material on top of the storage hopper. The overlapping performance of experiments confirmed the predictive nature of simulations to aid design of future poly-disperse systems of non-uniform materials.   

From avalanches to stochastic self-assembly in low-dimensional soft granular flows.

Soft granular materials, that is materials consisting of close-packed deformable grains separated by thin fluid films, are ubiquitous in industry and nature (concentrated emulsions, foams, tissues). Rheology and flow of such materials is intrinsically complex and involves phenomena characteristic of either fluid or solid phases depending on the dynamic state of the system. In general, soft granular flows rely on overcoming of the local energy barriers via rearrangements. The multi-dimensional complex and constantly evolving energy landscape leads to stochastic dynamics and overall unpredictable behavior such as avalanches. Here, we exploit droplet microfluidics to not only study the soft granular flows at the micro- and meso-scale--with droplets as the model ‘grains’--but also to precisely control the interplay of rearrangements versus arrest in such types of systems. In particular, we generate regular yet disordered quasi-1D structures in which the spatial droplet patterns reflect the history of the rearrangements. Due to granularity, the patterns are transcriptable as digital sequences resembling, e.g., the DNA code. We discuss how such patterns could be used to store information, e.g., about the content of the droplets for applications in microfluidic assays. 

    

Tapped Granular Systems: Simulations and Machine Learning Approaches

We report on simulations of microstructure development in assemblies of monodisperse spheres in a tapped container.  The average solids fraction of an assembly was computed at a tap completion when its kinetic energy was essentially zero.  An ensemble of 25 realizations was evolved over the span of M =15,000 taps from which evolution curves of the solids fractions were obtained. Drastically different progressions of the individual realizations were observed that featured sporadic jumps in solids fraction over the duration of a small number of taps. This behavior is consistent with a collective reorganization process that has been previously reported in the literature. Visualizations further revealed the formation of crystalline regions separated by dislocations facilitating bulk sliding motion in the system through periodic boundaries. Simulations conducted at a higher tap acceleration promoted a larger frequency of jumps in density over the M taps, resulting in more of the realizations attaining an apparent final saturation density.

 

A recurrent neural network model developed with a 60% training set was used to forecast the ensemble-averaged density in the limit of a large number of taps. The model appeared to be able to capture jumps exhibited in the simulations beyond the training set.  Our findings suggest that it may be possible to analyze the evolution of granular microstructure by applying deep learning methods. The inclusion of physics-informed quantities into the learning feature space may provide an enhanced ability to understand the process towards the development of predictive surrogate models.