Session P24: Granular Flows Beyond Simple Mechanical Models II

Flow-Arrest Transition in Granular Materials

Flowing granular materials can abruptly arrest if the applied stresses are smaller than a friction-dependent critical value. Such a phenomenon is commonly observed in geophysical scenarios and industrial practice, often with deleterious consequences. However, the statistical and rheological properties of this non-equilibrium transition are not well-understood. In this talk, I will describe our stress-controlled granular simulations that indicate a highly stochastic nature of this transition with long-tailed distributions of flowing times before arrest, which diverge as a power law at a critical stress ratio. We construct a flow-arrest state diagram that clearly distinguishes between shear flow and shear arrest in granular systems in terms of microstructural and rheological properties, with inter-particle friction being an important ingredient. Furthermore, granular flows in the vicinity of this transition exhibit rheological features that are not captured by the traditional μ(I) model, such as the presence of normal stress differences. I will describe our recently developed 3D constitutive model that captures these features and is fully compatible with more complex flow scenarios beyond simple shear, such as extensional and so-called triaxial flows.   

Shear thickening and jamming of dense suspensions: the importance of rolling friction

The mechanism of shear thickening in dense suspensions has been linked to a stress-controlled transition from a lubricated ``frictionless'' to an unlubricated ``frictional'' rheology. Recent particle simulations that constrain the sliding motion between particles have been successful to reproduce both the discontinuous shear thickening (DST) and shear jamming (SJ) observed experimentally but cannot account for the surprisingly low SJ volume fraction (often below 50%) measured in real-life suspensions in which particles are rough. However, an additional way to build up and maintain stress-carrying paths across a suspension, particularly relevant to rough particles, is by constraining particle rolling. We show via simulations that using rolling friction together with sliding friction can significantly decrease the volume fraction required for the onset of DST and SJ leading to enhanced shear thickening. Moreover, rolling friction drastically affects the structure of the underlying network of frictional particle-particle contacts, while from a dynamical perspective it leads to an increase in the velocity correlation length, in part responsible for the increased dissipation.   

Tuning Solvent Chemistry to Suppress Shear-Jamming in Dense Suspensions

Mechanical stress can transform a free flowing suspension of solid particles in a Newtonian liquid into a shear jammed, solid-like state. While recent work highlighted how particle surface chemistry contributes to the shear jamming transition,[1] much less is known about the suspending liquid. We here report both steady state rheology and the transient impact response tracked by high-speed ultrasound imaging [2] for silica nanoparticles dispersed in polyethylene glycols (PEGs) of varied chain lengths. For suspensions with identical silica volume fractions and impact conditions, decreasing the solvent molecular weight (MW) suppresses shear jamming. We attribute these results to stronger solvation layers in low MW PEG which keep contacts between particles lubricated even under high stress.

[1] N. James, E. Han, R. Lopez, J. Jure H Jaeger, “Interparticle hydrogen bonding can elicit shear jamming in dense suspensions”, Nature Materials volume 17, 965–970 (2018)
[2] E. Han, L. Zhao, N. Ha, S. Hseih, D. Szyld, H. Jaeger, “Dynamic jamming of dense suspensions under tilted impact”, Phys. Rev. Fluids 4, 063304 (2019)
  

Yielding and Rigidity of Sheared Columns of Hexapod Granules

Granular packings of non-convex or elongated particles can form free-standing structures like walls or arches. For some particle shapes, such as staples, the rigidity arises from interlocking of pairs of particles, but the origins of rigidity for non-interlocking particles remain unclear. We report on experiments and numerical simulations of sheared columns of “hexapods,” particles consisting of three mutually orthogonal rods whose centers coincide. We vary the length-to-diameter ratio, α, of the rods and subject the packings to quasistatic direct shear. For small α, we observe a finite yield stress. For large α, however, column is rigid against shear, and stresses within it increase with increasing strain. Analysis of X-ray micro-computed tomography data collected during the shear, reveals that the stiffening is associated with a tilted, oblate cluster of hexapods near the nominal shear plane in which particle deformation and average contact number both increase. Simulation results show that geometric cohesion effects are negligible for small α. For large α (α=10), we directly observe that particles are collectively under tension even though they do not interlock pairwise. The tensile stress counteracts the tendency to dilate in direction normal to the shear plane.   

Chaotic particle dynamics above and below yield in a 2D jammed material

Amorphous materials, often fail catastrophically, just beyond yield. This is a problem not just in design engineering (harnessing high strength glasses without the chance of ruinous breakdowns), but also in predicting the failure of non-constrained, natural systems (averting damage caused by mudslides). The yielding transition has previously been observed in both experiments and simulations to present via the emergence of specific particle trajectories, known as reversibly or irreversibly plastic. Here we present detailed quantification of Lagrangian properties (displacement lengths, arc-lengths, and enclosed area) of experimentally obtained particle trajectories for the purpose of illuminating where plasticity occurs in space and time both above and below yield. Our findings suggest plastic trajectories, both reversible and irreversible, predominantly occur in specific regions as a function of the strain amplitude, but not time. These findings imply that the yield transition is of the first order and that mean field and thermodynamic models are attainable. In this direction, we introduce a non-dimensional measure of plastic dissipation that applies both above and below yield and captures the rheological yield point.   

The precursors to stick-slip events in sheared granular systems

The stick-slip transition of granular systems is related to earthquakes and avalanches, and therefore understanding the conditions leading to slip events is of general importance. Although stick-slip behavior has been studied extensively, what triggers a slip event still remains unclear. The purpose of our study is to explore the existence of precursors to slip events. For this purpose, we study a sheared system in a stick-slip regime via two-dimensional discrete element simulations. Particular focus is on the evolution of force networks before and during slip events. We will show that some features of force network evolution could be used to gain insight into the occurrence of a slip event.   

Jamming and tiling in fragmentation of rectangles

We investigate a stochastic process where a rectangle breaks into smaller rectangles through a series of horizontal and vertical fragmentation events. We focus on the case where both the vertical size and the horizontal size of a rectangle are discrete variables. Because of this constraint, the system reaches a jammed state where all rectangles are sticks, that is, rectangles with minimal width. Sticks are frozen as they can not break any further. The average number of sticks in the jammed state, S, grows as S≈A/(2π ln A)^1/2 with rectangle area A in the large-area limit, and remarkably, this behavior is independent of the aspect ratio. The distribution of stick length has a power-law tail, and further, its moments are characterized by a nonlinear spectrum of scaling exponents. We also study an asymmetric breakage process where vertical and horizontal fragmentation events are realized with different probabilities. In this case, there is a phase transition between a weakly asymmetric phase where the length distribution is independent of system size, and a strongly asymmetric phase where this distribution depends on system size.   

Contact breaking in packings of frictional disks

We employ discrete element modeling simulations of the geometrical asperity or "bumpy particle" model to study the nonlinear vibrational response of jammed packings of frictional disks. We first calculate the eigenmodes of the dynamical matrix for each bumpy-particle packing. We then perturb the packing by a given velocity along a single and multiple eigenmodes of the dynamical matrix, run the simulations at constant total energy, and measure the Fourier transform of the translational and rotational velocities of the particles. For small velocity perturbations, contacts do not break, and the peaks in the power spectrum occur at frequencies that match the eigenfrequencies of the dynamical matrix. We determine the characteristic temperature T_c above which the interparticle contact network breaks, and compare the density of vibrational modes from dynamical matrix to the power spectrum for T > T_c. We show that perturbing along eigenmodes with primarily translational velocities gives rise to qualitatively different behavior of the vibrational response compared to that after perturbing along eigenmodes with primarily rotational content.   

Modelling granular fragmentation in compacted systems

The jamming of hard particles in the zero-pressure limit has been well studied, however many applications are far from this limit. As pressure increases, granular rearrangement is no longer the only mechanism for densification as grains deform and fracture. This breakdown of granular matter, or comminution, produces irregular shapes and sizes and changes macroscopic properties including rheology. We explore the compaction of brittle granular systems using large-scale discrete element simulations. Each grain is composed of many small, fundamental particles. These particles are interconnected by bonds which break under sufficient stress allowing grains to fragment into smaller grains. During loading, we monitor the evolution of stress, porosity, and distributions of grain size and shape. We characterize trends and explore the effect of strain rate and material properties. We also identify the pressure at which individual grains fracture and compare to theoretical models.   

Electrostatic Attraction between Like-Charged Particles

A point charge Coulomb force model provides an inadequate description of the interaction between finite-sized particles. Experiments find that dielectric particles of like charge can polarize one another, causing effective attractive forces between them that lead to clumping. To more accurately model the origin of these attractive forces, we study the effective interaction between two dielectric spherical shells with like charge as a function of their size and charge ratios, and the dielectric constant of each. We base our work on a model developed by Bichoutskaia et. al. [1] in which the authors map a phase diagram of attractive interactions between like-charged spheres at touching. We extend the phase diagram to finite separations between the particles, determining the boundary at which the force becomes repulsive. Though a closed form expression for the force between particles does not exist, we find an effective force in certain parameter regimes that can be used as an input in simulations of charged granular particles. The form of this force is found to vary depending on whether we are in the small size ratio or the small charge ratio regime.
[1] Bichoutskaia et al, J. Chem Phys 133, 024105, (2010) https://doi.org/10.1063/1.3457157.   

Unforgettable random walks: forces and displacements distributions in granular systems.

Granular systems are known to exhibit memory effects characterized by the remembrance of the past states and preparation history, which affect its future evolution. At the same time there exist a consensus that the force distributions of granular systems follow exponential and gamma distributions; a hallmark of the memory independent Brownian motion. Both of these assertions are mutually contradicting. We resolve this incongruity by experimentally and numerically verifying that the forces, as well as translational and rotational displacements of dense granular systems are governed by log-normal and power law distributions; consequence of a history dependent geometrical Brownian motion. We show the latter to be a natural product of contacts that reign between particles.   

Weakening, compaction and creep from vibration in sheared granular materials

The strength and stability of granular materials like sands and powders corresponds to the strength and stability of soils, asphalt, building and industrial materials, gouge filled earthquake faults, hillslopes, and more. Passing vibrations and transient perturbations have been thought to play a role in determining dynamic friction during sliding in such systems as well as trigger failure in static grain packs. With laboratory experiments and discrete element method simulations, we show that low amplitude high frequency vibrations are capable of significantly reducing frictional resistance over a range of velocities in actively shearing systems. Near yield, coefficient of friction decreases with increasing acoustic energy raised to a power of -0.2. Susceptibility to creep, compaction and weakening depends on grain shape, vibration amplitude, frequency, system resonances and system pressure. Exposure to (and generation of) vibration during shear of granular materials is common in many industrial and transport processes, and granular materials’ susceptibility to vibrational weakening may play a pivotal role in these processes.