Session L33: Granular Flows: Applications of Mixing, Blending, Segregation, Locomotion and Drag

River erosion by groundwater seepage

The shear stress exerted by rivers on their banks is well known to drive erosion, over time sculpting the landscape through which they flow. These rivers are ultimately fed by groundwater flow from their surrounding catchments, and as this flow enters the river through the bank it exerts a pressure force on the sediment, further enhancing the erosion. Here we demonstrate the interplay between river and seepage driven erosion from the source of a river and along its length through a series of idealised, 2D experiments with a monodisperse granular bank. These experiments are interpreted both through a classical analysis of erosion, and through a boundary-layer analysis treating the granular bank using the mu(I) rheology. We use these approaches to understand the sediment flux, and to show that for a given water flux the model river attains an ultimate steady state in which the seepage and river shear stresses are equal to the critical (or yield) stress along the river profile.   

Pumping of granular materials via horizontal multimodal vibrations

Recent experimental work demonstrated that dual-frequency, horizontal vibrations cause dry granular materials to pump in a desired direction within a lab-on-a-chip device. Here we present numerical predictions of the pumping velocity by applying Coulomb’s friction law with a shooting method over one period of the vibrational motion. At sufficiently fast vibrations, the steady velocity is predicted to be a unique function of the vibratory amplitude ratio, frequency modes, and phase lag between the two modes. At sufficiently slow vibrations and for certain ranges of frictional coefficients, however, multiple solutions are obtained. Furthermore, for some frequency mode ratios and relatively low amplitudes, granules with slightly different friction coefficients are predicted to move in opposite directions. We present experimental tests of these predictions, and we discuss the implications for manipulate granular materials on the millimeter to micrometer scale for lab-on-a-chip applications.   

Active Intruder Dynamics in Granular Beds

We will discuss the dynamics of magnetoelastic robots driven by an oscillating magnetic field in a granular bed as a function of the elasticity of the robot and the properties of granular medium.  Our research draws inspiration from biomimetic soft robot designs that imitate how biological organisms respond to stimuli and their surroundings. The body changes shape from reciprocal rigid rod rotation to showing traveling wave as the applied field and the frequency is increased depending on the body elasticity. Depending on the lift generated due to the overburden pressure gradient, we find that the robot can rise through the bed and then crawl over the surface, or burrow through the bed. The rise time depends on many factors including the oscillating frequency and the body elasticity. While burrowing through the bed, we find that its speed is consistent with a model adapted from Lighthill’s elongated body theory of fish locomotion [1]. We will discuss the observed behavior as a function of experimental parameters, and compare and contrast behavior with intruder dynamics in vibrated granular beds.   

Influence of an Intruder Particle on Wave-like Behavior in Vertically Vibrated Granular Matter

Pattern-forming behavior is widely observed in granular matter, particularly when vertically vibrated, and the study of granular matter is relevant due both to its wide-ranging applications in various industries as well as for its mathematical properties. The existence of surface waves in a bath of vertically vibrated granular matter is well known, as is the segregation of polydisperse mixtures of particles. Of particular interest is the behavior of a single large particle, known as an intruder, in a bath of otherwise monodisperse smaller particles. In this work, we use particle-tracking software to track an intruder in a bath of vertically vibrated granular matter. We systematically vary the shaking amplitude and frequency as well as the bath depth and intruder size and density. By computing the radial distribution of and pairwise distances between coarse-grained bath particles, we show that the intruder is responsible for additional wave-like behavior of the bath particles beyond what they experience from the vertical vibration alone. We also establish the nature of wave-like interactions between multiple intruders mediated by the bath particles. This study sheds light on the interplay between an intruder particle and the collective wave-like behavior in vertically vibrated granular matter.    

On the Geometry of the Particle Free Sifting Threshold

The propagation of fine particles through the interstices in a bed of static large particles due to gravity is known as free sifting. It is governed by the geometrical trapping threshold, R_t = 6.464, defined as the ratio of the large bed spherical particle diameter to the diameter of the largest fine particle that can pass through the throat between three touching bed particles. However, R_t is idealized for uniform rigid particles.  In practice, the free sifting threshold depends on the deformation of the bed particles (or overlap in simulations) and the size distribution of the bed particles. Simple geometric arguments show that the size ratio necessary for fine particles to pass through a bed of large particles can increase well beyond R_t for particle overlap of just a few percent and bed particle distributions with particle size variations of only 10-20%.  Simulations for common conditions and materials demonstrate how fine particle trapping can occur even for situations where the fine particle to bed particle diameter ratio is well above R_t = 6.464.    

Beyond Spheres: Mixing and Segregation of Aspherical Binary Granular Materials in Vibrated Gas–Fluidized Beds

Granular flows are ubiquitous, with applications ranging from mining to polymers to carbon sequestration to food–processing. Mining ore segregation requires immense water solvents, making the process unsustainable. Free–bubbling flow regimes within gas–fluidized beds are chaotic and recent research (e.g., Guo et al., 2021, PNAS 118, e2108647118) has shown that it can be ordered into periodic, structured, rising bubbles by vertically vibrating the fluidized bed. We extend this phenomenon to aspherical grains and demonstrate that this dynamic structuring persists in unary and binary systems of different density and particle size ratios. The study also investigates the effects of vibrational stress on mixing and segregation. Optically imaged experiment data for various initial particle arrangements of spherical and aspherical particles is post–processed to quantify bubble dynamics and mixing characteristics. Results from NETL's CFD–SuperDEM simulations are compared with experimental findings. The ability to mix or segregate particles is crucial, and findings from this work offer valuable insights into the mining industry's future.   

Segregation-rheology feedback in bidisperse granular flow: a coupled Stokes' problem

The feedback between particle-size segregation and rheology in bidisperse granular flows is studied numerically using the Stokes' problem configuration. A method of lines scheme solves the coupled momentum and segregation equations for an initially-graded particle bulk that suddenly is subjected to an upper plate movement at constant velocity. We show that the velocity profiles develop quickly into a short-lived steady state, decoupled from segregation yet determined by the particles' size ratio. From this transitory state, the velocity profile morphs due to the particles' relative movement, which redistributes the bulk's frictional response, hence its rheology. Additionally, we change the particles' friction via a frictional-coefficient ratio, in analogy with the particles' size ratio and the asymmetric coefficient. While positive values of this ratio exacerbate the size-ratio-induced non-linearity, negative values neutralize this behavior. The numerical solutions adjust well to the here-developed analytical solutions for the velocity profiles, which can be obtained from the steady-state conditions of the momentum and segregation equations for the short-lived and definitive steady states, respectively.   

Fine particle transport in granular beds

Predicting segregation and mixing of size-bidisperse granular material is challenging in many industrial applications and natural phenomena. Existing models accurately describe segregation of mixtures with large-to-small particle diameter ratios, R<3, but do not work nearly as well for larger R where segregation behavior changes significantly due to free sifting (i.e., small particles percolate downward even in the absence of shear). Here we study segregation in mixtures with large size ratios, 4<R<10, by analyzing the diffusion and transport mechanisms of "fine" particles in a bed of large particles using DEM simulations. Additionally, we explore the influence of gravitational acceleration, particle inelasticity, and granular temperature in terms of constrictions in the large particle bed. While for R>7, the primary mode of transport is free sifting, we observe that an increase in the fluctuation velocity of fine particles significantly reduces their percolation velocity. For mixtures with intermediate size ratios, the flow behavior not only depends on fluctuation velocity but also on the constriction size distribution in the bed. This investigation illuminates the influence of relevant variables on percolation velocity and offers insights into potential strategies for its control.   

Application of Granular Flows over Rotating Drum using Graph Neural Networks

Discrete element method (DEM) has been widely used in various industrial and research fields for evaluating granular flows. However, DEM has the drawback of requiring high computational cost for simulating large-scale problems. This high computational cost is primarily due to time step and the number of particles. The numerical stability of DEM is dependent on simulation time step, hence large-scale problems require a small time step. Likewise, the number of particles in large-scale problems is huge. Here we apply Graph Neural Networks (GNNs) to reproduce granular flows which can alleviate high computational cost by utilizing generalization. The GNN models are trained with various rotating drum simulations. The GNN models are evaluated in a rotating drum and show the ability to accurately predict the simulation results. The GNN model is also able to accurately predict the different granular flow regimes. The application of GNNs has the potential to give benefits towards the development of large-scale DEM.   

Vibrational manipulation of dry granular materials in lab-on-a-chip devices

An unresolved challenge in lab-on-a-chip technology involves dry granular materials that are typically moved in labs by hand using a scoop or spatula. To date no facile technology exists to manipulate dry granular materials at the small length scales necessary for lab-on-a-chip devices. Here, we present vibrational techniques to pump, mix, and separate dry granular materials using multifrequency vibrations applied to a solid substrate with a standard audio system. The direction and velocity of the granular flow are tuned by modulating the sign and amplitude, respectively, of the vibratory waveform, with typical pumping velocities of centimeters per second. Different granular materials are mixed by combining them at Y-shaped junctions, and mixtures of granules with different friction coefficients are separated by judicious choice of the vibratory waveform. We demonstrate that the observed velocities accord with a theory valid for sufficiently large or fast vibrations, and we discuss the implications for using vibrational manipulation in conjunction with established microfluidic technologies to fully realize a complete laboratory at submillimeter length scales.