Session T33: Granular Flows: Fluctuations and Instabilities

Instabilities and avalanches in 2D hopper flows of soft-rigid granular mixtures

Handling granular material flows through narrow pathways can be critically important. In the pharmaceutical industry, for instance, powder ingredients or gel tablets can clog hopper exits and halt production. Previous work suggests that soft particle flows are less prone to clogging, but they also exhibit more complex flow features [1,2]. Unlike rigid particles that either flow smoothly or clog permanently, soft particles can flow intermittently by forming temporary clogs that can be spontaneously disrupted by gravity or other driving forces. This behavior is due to the deformability of soft particles that enables them to create self-destructing contacts. We study the transition between flow and clogging in mixtures of soft and rigid granular particles in a quasi-2D hourglass-shaped rotating hopper. We study the flow dynamics of soft-rigid mixtures using different particle sizes, measuring the outflow rate, avalanche size, and the time intervals between consecutive particle exits.  For each particle size, we investigate a range of mixing fractions. Preliminary results suggest that mixtures containing more rigid particles flow both faster and more smoothly.  Mixtures containing more soft particles exhibit slower and oscillating outflow velocities, especially when they contain smaller particles. Soft particles may become sticky when they are sufficiently small, which makes them more subject to intermittent flowing.  Interestingly, our results may provide insight into the collective dynamics that can result when two species flow at different velocities. 

 

 

1. Tao, Wilson, Weeks, PRE 104, 044909 (2021) 

2. Alborzi, Clark, Hashmi, Soft Matter 18, 4127 (2022).    

Experiments of gravitational instabilities at particle suspension-fluid interface

Experiments are conducted to understand the gravitational instabilities that occur at the interface of an overlying suspension of granular particles and a clear fluid, utilizing a sealed Hele–Shaw cell. Attention is paid to the influences of particle Reynolds number and particle packing on the growth of the interfacial disturbances. At the intersection of the fluid and densely packed particles, perturbations take on an asymmetrical cusp-like structure. In contrast, at the interface where the fluid meets loosely packed particles, the perturbations initially form a symmetrical, sinusoidal pattern, similar to the typical Rayleigh–Taylor instability. The growth rate of both types of instabilities is found to increase with the particle Reynolds number. Notably, symmetrical perturbations grow faster than their asymmetrical counterparts at equivalent Reynolds numbers. The experimental data are also viewed through the lens of linear stability analysis for single-phase fluids to test the latter's applicability to the two-phase problem.   

Understanding slow compression of frictional granular particles by network analysis

We will discuss frictional granular packings exposed to quasi-static compression rates. For frictionless packings, earlier work (Soft Matter, vol. 18, 1868 (2022)) has uncovered that the system evolution/response involves smooth evolution phases, intercepted by fast transitions (events). The general finding is that the force networks' static properties correlate closely with the pressure, while their evolution resembles the kinetic energy of the packings. The former represents reversible (elastic) particle deformations with affine and non-affine components, whereas the latter also involves much stronger, irreversible (plastic) rearrangements of the packings. Events are associated with jumps in the overall kinetic energy as well as dramatic changes in the force networks describing particle interactions. The frictional nature of particle interactions affects both their frequency and the relevant time scale. Often, events are followed by an unexpected slow-down during which the kinetic energy drops below its average value. We find that these slow-downs are associated with a significant decrease in the non-affine dynamics of the particles, and are strongly influenced by friction. Friction also has a strong influence on both static and dynamic properties of the force networks. Friction modifies the structure of the networks, both through influencing the typical number of contacts of a particle, and by influencing topological features of the resulting networks. Furthermore, friction modifies the dynamics of the networks, with larger values of friction leading to slower evolution of the more stable networks.   

Probing non-locality in gravity-driven granular flows

Gravity-driven granular flows appear widely in nature, with avalanches, landslides and debris flows, changing the world around us and endangering lives. They are also crucial in countless important processes across many different types of industry, including pharmaceuticals, agriculture and construction. Despite their ubiquity, there are aspects of these flows that remain poorly understood. Specifically, we are interested in validating the concept of 'granular fluidity' that has been utilised in the development of theoretical non-local constitutive equations. Extensive experimental validation is currently lacking for these models, especially in determining the physical suitability of fluidity definitions. Using innovative experimental techniques that allow us to visualise the forces within a granular flow, we probe the origins of granular fluidity on a microscopic scale. Importantly, we show that boundary conditions have a significant impact on the flow and the suitability of the granular fluidity model used.   

Role of friction in granular Plateau-Rayleigh instability.

Streams of weakly cohesive granular materials exhibit liquid-like breakup into droplets. We numerically study such a granular analog of the Plateau-Rayleigh instability in a free-falling granular stream. We use a discrete element method (DEM) simulation with Johnson-Kendall-Robert (JKR) interactions between the grains, as well as sliding and rolling frictions. Our simulation results recover the experimentally observed w_min∝(t - t₀ )^2/3  for large (t - t₀), where w_min is the minimum width of the neck and t₀ is the rupture time. Interestingly, no breakup is observed for frictionless grains. This suggests that friction and the motion tangential to the stream direction play an important role in the granular Plateau-Rayleigh instability.   

Instability of a slider dragged on a granular bed

We report an instability of a slider slowly dragged at the surface of a granular bed in a quasistatic regime. The boat-shaped slider sits on the granular medium under its own weight and is free to translate vertically and to rotate around the pitch axis while a constant horizontal speed is imposed. For a wide range of parameters (mass, length, shape, velocity) a regular pattern of peaks and troughs spontaneously emerges as the slider travels forward. This instability is studied through experiments using a conveyor belt and by means of two-dimensional discrete elements method simulations. We show that the wavelength and amplitude of the pattern scale as the length of the slider. We also observe that the ripples disappear for low and high masses, indicating an optimal confining pressure. The effect of the shape, more specifically the inclination of the front spatula, is studied and found to drastically influence both the wavelength and the amplitude. Finally, we show that the mechanical details (friction, cohesion) of the contact point between the slider and the pulling device is critical and remains to be fully understood.   

The effects of cohesion on freely falling granular jets

Cohesive granular systems are hard to pour, which may be familiar from trouble controlling the pouring of powders such as flour while baking. Flow is often broken up into chunks ranging from the particle diameter to many times the particle size, causing both irregular flow and clogs near apertures. In this study, we describe the behavior of granular jets released from a circular aperture at the bottom of an axisymmetric silo. We perform experiments controlling the cohesive strength, the diameter of the grains, and the size of the aperture to construct a phase diagram describing the different flowing states observed. Cohesion arising from capillary bridges of water or mineral oil is compared with interparticle cohesion induced by a polymer coating. The profiles of the freely falling jets are described. The presence of interparticle cohesion causes the granular jet to break up into agglomerates. By controlling the added cohesion, the agglomeration can be controlled, evidencing a Rayleigh-Plateau like instability for a cohesive granular filament.   

Granular Flow through a Wedge-shaped Hopper: Discrete Element Method Simulations for the Smooth Wall, Radial Gravity Problem

The gravity flow of particulate solids occurs in various industries. The simplest version of the flow is a wedge-shaped, quasi-two-dimensional geometry with smooth walls and a gravitational force that is directed radially towards the apex of the wedge. Theoretical analysis of the flow using the Mohr-Coulomb criterion

was carried out in the classical work of Savage (1965) and using a critical state theory by Ravi Prakash and Rao (1988). Discrete Element Method simulations are carried out on particles for the smooth-wall radial gravity (SWRG) hopper to test the existing theories. Our computational results match the predictions of the theories of Savage and Rao, except for the region close to the exit, where both frictional and viscous effects are present. To further comprehend this behaviour, a parametric study is performed. The conclusion is that velocity increases as the flow rate increases but decreases as the wedge angle and friction coefficient increase. It is anticipated that stresses at the exit are caused by the transfer of momentum transfer between collisions. It is shown that viscosity and volume fraction have power law relations with the inertial number and data collapsed into a single curve.