Session R36: Continuum Descriptions of Discrete Materials II

Dynamic shear jamming in dense suspensions

Shear a dense suspension of cornstarch and water hard enough, and the system seems to solidify as a result. Indeed, previous studies have shown that a jamming front propagates through these systems until, after interaction with boundaries, a jammed solid spans across the system. Because these fully jammed states are only observed if the deformation is fast enough, a natural question to ask is how this phenomenon is related to the discontinuous shear thickening (DST) behavior of these suspensions. We present a single experimental setup in which we on the one hand can measure the rheological flow curves, but on the other hand also determine if the suspension is in a jammed state. This we do by using a large-gap cylindrical Couette cell, where we control the applied shear stress using a rheometer. Because our setup only applies shear, the jammed states we observe are shear-jammed, and cannot be a result of an overall increase in packing fraction. We probe for jammed states by dropping small steel spheres on the surface of the suspension, and identify elastic responses. Our experiments reveal a clear distinction between the onset of DST and Shear-Jammed states, which have qualitatively different trends with packing fraction close to the isotropic jamming point.   

Rheological behavior of partially-wet granular matter

The topic of wet granular material modeling is an open area of study. In this talk we present a comprehensive continuum model for wet granular matter, which is informed by a novel Discrete Element Method (DEM), which tracks the fluid content coating each grain as well as a variable fluid-bridge volume. We have devloped a DEM simulation method with a history-dependent potential based on the Hertz-Mindlin contact in compression and evolving capillary forces in tension. The capillary bridge in the simulations forms based on the volume of the fluid on each particle. First, we determine the cohesive force between grains, which is a function of grain separation, bridge volume, grain geometry, and fluid properties. The volume of the bridges also evolves in time, which affects the cut-off distance in bridges and the force-separation function. The other important factor which has been considered in the model is the particle roughness, which has a significant effect on the capillary force function. The effect of fluid viscosity is also considered. The second step in this work is to utilize the DEM results to identify a constitutive model that can explain the plastic behavior (flow rule) of a dense granular assembly under varying degrees of wetness.   

Effect of friction on shear jamming

Shear jamming of granular materials was first found for systems of frictional disks, with a static friction coefficient $\mu \approx 0.6$ (Bi et al. Nature (2011)). Jamming by shear is obtained by starting from a zero-stress state with a packing fraction $\phi$ between $\phi_J$ (isotropic jamming) and a lowest $\phi_S$ for shear jamming. This phenomenon is associated with strong anisotropy in stress and the contact network in the form of force chains, which are stabilized and/or enhanced by the presence of friction. Whether shear jamming occurs for frictionless particles is under debate. The issue we address experimentally is how changing friction affects shear jamming. By applying a homogeneous simple shear, we study the effect of friction by using photoelastic disks either wrapped with Teflon to reduce friction or with fine teeth on the edge to increase friction. Shear jamming is still observed; however, the difference $\phi_J-\phi_S$ is smaller with lower friction. We also observe larger fluctuations due to initial configurations both at the lowest and the highest friction systems studied. Ongoing work is to use particles made of gelatin to reduce the friction coefficient to the order of 0.01.   

Frictionless Shear Jamming, a finite-size phenomenon

Athermal frictionless spheres jam as their density is increased. A few years ago, it was shown that at sufficiently high density, an initially unjammed system of frictional particles can jam under shear. Here we study shear jamming in packings of frictionless particles, and show that it is a finite-size effect with scalings that can be understood within a generalized scaling theory.   

Slow Relaxations in Fluid-Driven Granular Flows

Particles in a pack may appear frozen, but exhibit very slow dynamics (creep). To probe long-time dynamics, we construct an annular chamber that mimics an infinitely-long river channel. We drive the packs with a laminar flow and record dynamics by laser scanned particle tracking. The dynamics of ``bed load'' grains near the surface exhibit relatively fast shear and their velocity profile as a function of depth can be well-described by a local \(\mu(I)\)-rheology. However, grains deep in the pack, which appear frozen by eye, exhibit slow creep dynamics that are not captured by the local model. This transition between bed load and creep occurs at a critical value of the local relaxation time. We find that the timescale for heterogeneous dynamics increases monotonically as a function of depth, but the length scale characterized by the domain size of the heterogeneities achieves a maximum at the transition to creeping. We explore the relation between the important length and time scales of the flow in the creep phase using nonlocal rheology.   

Flow of interacting colloidal suspensions through a narrow channel

In this work we numerically study the constitutive behavior of interacting colloidal suspensions at intermediate and high concentrations. The influence of the interaction potential strength on the system's response is examined, in suspensions flowing through narrow channels at low Reynold's numbers. Using Lattice Boltzmann methods, we analyze the rheological response of a colloidal suspension once the steady state is established. In dilute suspensions we always recover a newtonian behavior. At higher volume fractions, the range and strength of the interaction potential has a stronger impact in the behavior of the suspension. While for short range potentials, the non-newtonian response mostly depends on colloid concentration and confinement distance, for a Lennard-Jones potential we identify two rheological responses depending on the potential strength, $\xi_{LJ}$, at a given concentration. For weak $\xi_{LJ}$ the effective viscosity, $\eta_{eff}$ , decreases until a minimum is reached. On the contrary, at large values of $\xi_{LJ}$ the effective viscosity $\eta_{eff}$ increases when increasing the strength of interaction. This behavior has been correlated with the local structure of this complex fluid.   

Impact Fragmentation and Crushing of Concrete and Other Solids Due to Kinetic Energy of High Shear Strain Rate

While numerous studies have dealt with dynamic crack propagation, they have not led to a macroscopic continuum model usable in FE analysis. Recent work on such a model is reviewed. The key idea is that comminution under high-rate shear is driven by the release local kinetic (rather than strain) energy of the shear strain rate field in forming finite-size fragments. At strain rates \textgreater 103/s, this energy exceeds the maximum possible elastic strain energy by orders of magnitude. It is found that the particle size scales as the -2/3 power of the shear strain rate and as the 2/3 power of interface fracture energy, and the released and dissipated kinetic energy as the 2/3 power of the shear strain rate. These results explain the long debated phenomenon of ``dynamic overstress''. In FE simulations, this kinetic energy of strain rate field can be dissipated either by equivalent viscosity or by the work of increased strength limits. In simulating the impact of missiles into concrete walls, both approaches give nearly equivalent results. A dimensionless indicator of the comminution intensity is also formulated. The theory was inspired by noting that the local kinetic energy of shear strain rate plays a role analogous to the local kinetic energy of eddies in turbulent flow.   

Explaination of nonlocal granular fluidity in terms of microscopic fluctuations

A recently proposed granular constitutive law has shown capability to predict nonlocal granular rheology using a variable denoted “granular fluidity”. This work is aimed at finding the microscopic physical meaning of fluidity in terms of fluctuations such as fluctuation of normalized shear stress and fluctuation of velocity. We try to predict the fluidity as a function of the fluctuation of normalized shear stress, and also test Eyring equation and kinetic theory based on the theoretical prediction proposed in other work. We find a consistent definition for the fluidity to be proportional to the product of the velocity fluctuations and some function of packing fraction divided by the average diameter of the grains. This definition shows predictive ability in multiple geometries for which flow behavior is nonlocal. It is notable that the fluidity is well-defined as a function of kinematic state variables, as one would hope for a quantity of this nature.   

Mesoscale poroelasticity of heterogeneous media

Poroelastic behavior of heterogeneous media is revisited. Lattice Element Method (LEM) is used to model interaction between solid constituents due to a pressurized pore space. Exploring beyond mean-field based theories in continuum microporomechanics, local textural variations and its contribution to the global anisotropic poroelastic behavior of real multiphase porous media are captured. To this end, statistical distributions of mesoscale poroelastic coefficients from numerical simulations on X-ray microscopy scans of two different organic-rich shales with different microtextures are presented. The results are compared with predictions using mean-field based tools of continuum micromechanics. The textural dependency of strain localization and stress chain formation captured in this framework promises a powerful tool for modeling poroelastic response of complex porous composites and a path to incorporate local textural and elastic variations into a continuum description.   

Low-frequency oscillations in vibrated granular columns.

We present simulations, experiments and theoretical treatments of vertically vibrated granular media. The systems considered are quasi-one-dimensional. This column geometry makes it possible to study collective oscillations of the grains with a characteristic frequency that is much lower than the frequency of energy injection (LFOs). Using event-driven molecular dynamics simulations we see that LFOs become slower and more pronounced as the shaking of the container increases. Experimental observations, using the positron emission particle tracking technique, agree well with the simulated data. The conditions necessary for the existence of LFOs are derived from a granular continuum model, which is able to relate the column density profile with the measured characteristic frequencies   

Continuum model and simulation of segregating rods

Most studies of segregation of flowing granular materials focus on spherical particles, even though particles are often non-spherical in practical granular systems. Here we focus on the segregation of rod-like (cylindrical) particles of the same diameter but different lengths using continuum theory and DEM simulations based on super-ellipsoids. In the flowing layer of a bounded heap flow, a bidisperse mixture of long and short rods segregates such that the shorter rods percolate toward the lower portion of the flowing layer while longer rods rise toward the upper portion of the flowing layer, much like smaller spherical particles segregate from larger spherical particles. The rods tend to deposit on the underlying bed of particles in the heap such that they are aligned with the flow with the smaller rods deposited upstream of the larger rods due to segregation. The percolation velocities related to segregation for long and short rods depend on the local shear rate and the concentration of the other particle species, just as is the case for small and large spherical particles. Using this percolation velocity and an appropriate value for collisional diffusion, the advection-diffusion-segregation continuum model successfully predicts the segregation of rod-like particles.   

Flow and packing properties of frictional shapes from spheres to cubes

Though grains in many applications are aspherical and rough, many computational studies of granular flow and packing focus on ideal spherical particles, often without friction. Following Latham [1], we optimally represent arbitrary shapes using overlapping spheres of different sizes. We use discrete element simulations to study the packing and flow of frictional granular superquadric (superball) shapes ranging from spheres to cuboids. When packing particles, friction becomes more important as particle shape becomes more angular. This leads to a larger density change between frictional and frictionless packings. Friction and shape are also important to granular flow. For a planar-shear flow different shapes have similar flow behavior in the zero-friction limit. However, with increasing friction particle shape couples to the tangential frictional forces and becomes more important. Flow results are compared with continuum theories of granular materials. Results from simulations of anisotropic particles and mixtures of shapes will also be discussed. \\[4pt] [1] X. Garcia, J. Xiang, J.-P. Latham, and J. P. Harrison, G\'{e}otechnique 59, 779 (2009).   

Scaling Relations for Wheeled Locomotion in Granular Media

Vehicular wheel design for use on granular material has not currently been perfected. Resistive Force Theory (RFT) is a reduced-order empirical model for granular drag, which shows promise to help simulate and understand locomotion processes to design more efficient wheels. Here we explore the fundamental scaling relations derived from RFT and their experimental validation. Similar to the non-dimensional scaling relations in fluid mechanics, the relative simplicity of RFT asserts that only one material parameter, the "grain-structure coefficient", is required, which reduces the complexity of the non-dimensional groups implied by the system. Therefore, wheels with differing input design parameters like size, mass, shape and even gravity, can be tested and their performance related to each other in predictable ways. We experimentally confirmed these relations by testing with 3D printed wheel geometries in a controlled sand bed.   

Scaling of heat transfer in granular material in rotating drums

Several industrial processes involve thermal treatment of granular materials and powders, in devices such as rotating drums, to bring about a desired chemical and/or physical transformation. Developing a better understanding of the heat transfer process can significantly improve the quality of the end product and efficiency. However, there is a lack of predictive models, for example, to predict the evolution of the distribution and average of the particles' temperature, particularly for the purposes of scale-up from laboratory scale experiments to manufacturing scale productions. We used discrete element method (DEM) based simulations to study the distribution of particles' temperature in rotating drums at low temperature. Various physical, mechanical, and thermal properties of particles were considered in the simulations and in the analysis. In addition, the effect of operating conditions such as size of drum, material fill level, and speed of rotation on the heat transfer were investigated. Based on the simulations, we identified timescales relevant to the heat transfer process and developed a relationship between these timescales that can be used to predict the average temperature of particles. We also found that the evolution of the temperature distribution, since different particles may have different temperatures, can be predicted based on these timescales. These findings can be used to predict the required time to heat up all particles to the desired temperature.   

Structural evolution of Colloidal Gels under Flow

Colloidal suspensions are ubiquitous in different industrial applications ranging from cosmetic and food industries to soft robotics and aerospace. Owing to the fact that mechanical properties of colloidal gels are controlled by its microstructure and network topology, we trace the particles in the networks formed under different attraction potentials and try to find a universal behavior in yielding of colloidal gels. Many authors have implemented different simulation techniques such as molecular dynamics (MD) and Brownian dynamics (BD) to capture better picture during phase separation and yielding mechanism in colloidal system with short-ranged attractive force. However, BD neglects multi-body hydrodynamic interactions (HI) which are believed to be responsible for the second yielding of colloidal gels. We envision using dissipative particle dynamics (DPD) with modified depletion potential and hydrodynamic interactions, as a coarse-grain model, can provide a robust simulation package to address the gel formation process and yielding in short ranged-attractive colloidal systems. The behavior of colloidal gels with different attraction potentials under flow is examined and structural fingerprints of yielding in these systems will be discussed.