Session M24: Granular Flows Beyond Simple Mechanical Models I

Mechanics of Deformation in 3D Granular Materials Using X-ray Measurements

Granular materials deform in complex ways, including through particle deformation, local particle rearrangements, inter-particle slip, and particle fracture. Discrete and continuum models have been proposed within the engineering and physics communities to capture the effects of these deformation mechanisms on mechanical and dynamical material properties. For instance, local particle rearrangements have been captured in glassy rheology models and shear transformation zone theories, while particle fractures have been captured in the continuum breakage mechanics framework. A major challenge remains the quantitative validation and calibration of these models using in-situ 3D experimental data.

In this talk, I will discuss our experiments combining in-situ X-ray computed tomography (XRCT) and 3D X-ray diffraction (3DXRD) during the deformation of granular materials. The samples we have studied to-date include tens to over 1,000 spherical and angular particles, each ranging in size from 100 to 400 μm, and each typically composed of single-crystal sapphire or quartz. We have subjected samples to a variety of loading conditions, including uniaxial compression and triaxial compression. XRCT measurements performed periodically during loading provide high-resolution 3D images of the evolving structure of granular materials during deformation. 3DXRD measurements provide the location (with several um precision), the orientation (with 0.05^○ precision) and the strain tensor (with 10^-4 resolution) in each of thousands of particles, from which the stress tensor of each particle can be computed. I will present examples of prior work studying local particle rearrangements and inter-particle slip. I will also discuss ongoing and future work on the impact of both structure and forces on ultrasound transmission and the quantitative details of local particle rearrangements.
  

Dimensionality and viscosity exponent in shear-driven jamming

Collections of bidisperse frictionless particles at zero temperature in three dimensions are simulated with a shear-driven dynamics with the aim to compare with behavior in two dimensions. Contrary to the prevailing picture, and in contrast to results from isotropic jamming from compression or quench, we find that the critical exponents in three dimensions are different from those in two dimensions and conclude that shear-driven jamming in two and three dimensions belong to different universality classes.   

Identification of a universal data collapse in the rheology of granular media

We propose a reduced description of nonlocal phenomena in dense granular flows where the shear stress ratio μ is not locally determined by the inertial number (dimensionless shear rate) I. The nonlocal granular fluidity (NGF) model has been proposed to describe nonlocality by introducing an implicit “fluidity” field and its diffusion. A recent study found the fluidity can be roughly expressed by two physical quantities: the particle velocity fluctuations δv and packing fraction. Here, we reduce the number of quantities from two to one revealing that only δv is needed to explain nonlocality. We perform DEM simulations in many geometries using 3D spheres and 2D discs with various surface frictions. For each granular material, we show there exists a clear constitutive equation that works across geometries, which directly relates three local dimensionless variables: μ, I, and the dimensionless granular temperature (dimensionless δv²) Θ. It allows us to consider the nonlocal phenomena as the result of various spatial distributions of the granular temperature, a field that is generated, diffuses, and dissipates similar to the implied behavior of the fluidity field in the NGF model. We also demonstrate how this μ-I-Θ relation can be applied in continuum simulations of granular flows.   

Nonlocal rheology of dense granular flows: the effect of particle and boundary properties

In granular rheology, one of the most promising recent advances has been the development of nonlocal rheologies, including the nonlocal rheology model proposed by Kamrin and Koval. This model extends a local Bagnold-type granular flow law to include a Laplacian term governing the diffusion of fluidity. It has been observed to successfully capture the dynamics of quasi-2D flows without the need to provide detailed particle dynamics, using a single set of experimentally-determined model parameters. For use as a modeling tool, the next step is to make predictions for particles with any particle shape/material, and to correctly model the response to various boundary conditions. We perform experiments to study particles of three different shapes and three different stiffnesses to explore their influence on the rheological parameters. We find that the nonlocal parameter varies with both particle shape and material, frictional parameter varies primarily with particle shapes, and the local parameter is approximately constant. Finally, we identify how the roughness of the boundary changes both the flow and the interparticle forces using photoelastic force measurements.   

Local plastic deformation in sheared highly polydisperse foams

We simulate the shear of dense two-dimensional foams using the Durian bubble model with a Lees-Edwards boundary condition. In particular, we study highly polydisperse systems with the largest bubble diameters being as much as ten times the smallest diameter. The high polydispersity requires us to rethink the conventional ideas that are applied to study the local plastic deformation of systems with comparable sizes of droplets, such as D²_min which highlights locally nonaffine motion (Falk & Langer, PRE 1998). We modify the conventional definition of "local" in the calculation of D²_min to consider the existence of big droplets and study how the "local" rearrangements differ for large and small droplets. More specifically, we find the large droplets follow the mean shear, while the small droplets have significant nonaffine motions and move more erratically. We demonstrate an optimal definition of local that best distinguishes the local nonaffine motions from the bulk shear.   

Generalized Granular Resistive Force Theory for Rate-Dependent Intrusions

The resistive forces during intrusion into granular media can be described accurately by reduced-order models like Resistive Force Theory, but rate effects may emerge as intrusion speed increase. We demonstrate with both rapid plate drag data and freely locomoting rigid wheel experiments how such rate-dependent dynamics diverge from the quasistatic limit. Additional forces from a continuum momentum balance are sufficient for describing the forces in rapid plate drag, but do not capture the effects of rapid rotational shear in the wheeled locomotion experiments. A frictional flow continuum model captures these phenomena without needing to account for micro-inertial effects such as frictional dependence on grain inertia. Based on the observed physics of the flow model simulation, we propose a modified RFT for arbitrary intruders that reconciles both cases using a geometry-dependent modification and an additional macro-inertial resistance, extending RFT beyond describing quasistatic intruding bodies.   

Stick-slip and intermittent flow dynamics of a single-grain intruder driven through a granular medium with and without basal friction

We report on experiments in which a grain-sized intruder is pushed by a spring through a quasi-2D granular material in an annular geometry. We study intruder dynamics as a function of packing fraction for two types of supporting substrates: a frictional glass plate and a layer of water, which completely removes basal friction. In the presence of basal friction, we observe a novel crossover with increasing packing fraction from intermittent flow to stick-slip dynamics. In intermittent flow, the intruder only occasionally gets stuck by the medium; in stick-slip, the intruder advances via a sequence of distinct, rapid slip events. With lower interparticle friction, the crossover packing fraction shifts to higher values; when basal friction is removed, no crossover to stick-slip dynamics is observed. We characterize the dynamics using statistics of the intruder velocity, the force of the medium on the intruder, and the waiting times between sticking periods. Our results indicate the qualitative importance of basal friction and suggest a possible connection between intruder dynamics in a static material and clogging dynamics in granular flows.   

Intruder dynamics in a 2D granular system: Effects of dynamic and static basal friction

We discuss the results of simulations of an intruder pulled through a 2D granular system by a spring, using a model designed to lend insight into the experimental findings described by Kozlowski et al. [Phys. Rev. E 100, 032905 (2019)]. In that previous study, the presence of basal friction between the grains and the base was observed to change the intruder dynamics from clogging to stick–slip. Here we first show that our simulation results are in excellent agreement with the experimental data for a variety of experimentally accessible friction coefficients governing interactions of particles with each other and with boundaries. We then use simulations to explore a broader range of parameter space, focusing on the friction between the particles and the base. We consider a range of friction coefficients, which are difficult to vary smoothly in experiments. The simulations show that dynamic friction strongly affects the stick–slip behavior when the coefficient is decreased below 0.1, while static friction plays only a marginal role.
  

Drafting of intruders in dry and fluid-saturated granular beds

We discuss an experimental study of the drag experienced by two vertical rods as they follow each other around a circular track while being dragged across a granular bed. We systematically measure the drag experienced as a function of rod speed, separation distance, penetration depth, and the properties of the interstitial fluid. As in drafting in air and fluids, we find significant separation effects on the total drag experienced in comparison with that of a single rod [1]. The drag ratio is observed to decrease monotonically as the separation distance is decreased over a scale set by the penetration depth in a dry granular bed essentially independent of their speed. A complex rate-dependence is observed in a liquid-saturated granular bed at separation distances comparable to the penetration depth. A peak in drag is observed when the distance of separation is comparable to the penetration depth which is greater than the drag of experienced at large separation distance. We will discuss our results in light of resistive force theory, and nondimensional inertial and viscous numbers used to characterize granular mediums.

[1] Effective drag of a rod in fluid-saturated granular beds, Benjamin Allen and Arshad Kudrolli, Phys. Rev. E 100, 022901 (2019)   

Reduction in Resistive Forces by Directional Air Fluidization in Dry Granular Media

Directional fluidization applies the concept of granular air fluidization to vary the resistive forces locally around an intruder in a granular medium. We fabricated a cylindrical intruder (d = 30mm, length = 30 mm) capable of blowing air through a nozzle at varying flow rates (from 0 to 100 L/min) and angles relative to the direction of intruder motion in dry granular media. Varying the flow rate and angle affects the drag force parallel to the intruder’s direction of motion as well as the lift force in the vertical direction. Drag experiments were performed by forcing the intruder horizontally with a robot arm at a low speed (v ~= 10 mm/s) in 5 cm of dry sand with grain diameters ranging from 0.4-0.8 mm. Multi-axis force data demonstrated a consistent reduction in saturated drag forces that was sensitive to air flow rate but insensitive to blowing angle (BL). Saturated lift forces showed a greater dependence on BL, with more significant reductions coinciding with steeper angles (60 - 90 degree range). These results suggest a scheme for minimizing resistive forces in lift and drag by blowing air downwards and open a door for growing robot navigation in granular media.   

Properties of air-fluidized granular media

We study a 2D granular system of particles intercacting via a short-ranged potential, and thermalized homogeneously. This achieved by means of a turbulent air flow. Particles consist of 4 cm diameter ping-pong balls. We will show that, as packing fraction and air current are increased, the system can undergo transitions from gas to liquid, glass, and hexagonal phases.

The particles, placed on a metallic mesh and are subject to an uniform air flow from. This creates vortexes past the spheres, injecting energy. Air flow is adjusted so that particles remain in contact with the mesh, so that the dynamics are purely 2D. The system can be regarded as being under a stochastic white noise.

We perform several series of measurements with varying air flow intensity and density, detecting particle positions through a CV algorithm. We then carry out an analysis on single-particle trajectories and study configurational properties: pair correlation function, and order parameters.

We compare our granular temperature results against other 2D homogeneously driven granular systems.   

Granular chiral separation

Single helical granular particle (~5 mm), when placed in a slowly rotating tube, migrates laterally to different sides dependent on the chirality. First entrained by the rotating tube up to certain height, the particle suddenly starts to slide or roll down, during which process chiral separation is made possible as the particle only rolls at certain particle orientation and thus migrates in one direction exclusively. The intricate interplay between particle shape, which determines a critical slope of rolling, and static friction, which determines a critical slope of sliding, is found responsible for the chiral separation and its efficiency. We corroborate the experimental finding with theoretical predictions and extend the single particle phenomena to multi-particles.   

Super-Flory scaling in compressed micro-gel packings

We perform multi-body finite element simulations of packings of hydrogel particles immersed in a large solvent bath in 2D at various particle volume fraction, φ using the Flory-Rehner constitutive law to model the mechanics of the hydrogel network. The system becomes rigid with finite osmotic pressure, Π and zero-frequency storage modulus, G, only above the random close packing point. At large enough φ regions of pure solvent are completely eliminated, and we find a qualitative change in the G vs φ curve with a weaker dependence on φ. However, in this dense limit, G exceeds the modulus of a monolithic piece of hydrogel made of the same Flory-Rehner material and continues to increase with φ. This result is surprising as we observe strong inhomogeneous non-affine relaxation which helps to reduce the modulus, however, it is in agreement with experiments which also show super-Flory behavior. Furthermore, we show that the slip at the facets between particles is proportional to the transverse gradient of the applied deformation which strongly screens the stress near facets oriented along the applied shear. Our results on the deformation kinematics during shear suggest new measurements to attempt in experiments and should open the way to quantitative theories to estimate G at high φ.