Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session A59: Rheology and Flow of Particulate Matter IFocus

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Sponsoring Units: GSOFT GSNP Chair: Jeffrey Morris, City College of New York Room: BCEC 257B 
Monday, March 4, 2019 8:00AM  8:36AM 
A59.00001: Toward General Rheological Models of Dry and FluidSaturated Granular Media Invited Speaker: Ken Kamrin Dry and fluidsaturated granular media display multiple modeling challenges from a continuum perspective. Foremost is the search for quantitative and robust constitutive models, in order to robustly predict the flow and stress fields in a flowing body. However, a major challenge is also to find methods to implement these theories in nontrivial geometries up to huge deformations. Methods able to do this are needed not just to implement models in realistic settings of practical interest, but also to test the versatility and correctness of any proposed model, especially models that employ higherorder effects. In this talk we will discuss various continuum modeling approaches for dry and for fluidsaturated granular media. We will also present two numerical technqiues for running these models in general geometries. Key challenges on the modeling front include the importance (or lack thereof) of grain size, the various influences of an interstitial fluid phase, and modeling the granular ``phase transition’’ between solidlike, denseflowing, and disconnected gaslike regions of material. 
Monday, March 4, 2019 8:36AM  8:48AM 
A59.00002: Continuum modeling of flow and sizesegregation in dense, bidisperse granular mixtures Daren Liu, David Henann Dense granular systems, consisting of particles of disparate sizes, segregate based on size during flow, resulting in complex, coupled segregation and flow patterns. In this talk, we study sizesegregation in three dense granular flow configurations: (1) gravitydriven flow down a long vertical chute with rough parallel walls, (2) annular shear flow with rough inner and outer walls, and (3) planar shear flow with gravity. We perform twodimensional discrete element method (DEM) simulations of flow of dense, bidisperse granular systems in all three configurations, while varying system parameters, such as the flow rate, flow configuration size, fraction of large/small grains, and grainsize ratio, and we study the effects of these parameters on the segregation dynamics. Our simulations inform continuum constitutive equations for both the sizesegregation flux as well as the diffusion flux. When coupled with the nonlocal granular fluidity model  a nonlocal continuum model for dense granular flow  we show that both the flow field and segregation dynamics may be simultaneously captured using this closed, coupled, continuum system of equations. 
Monday, March 4, 2019 8:48AM  9:00AM 
A59.00003: Nearcontact dynamics of a spherewall collision in a viscous medum Sumit Kumar Birwa, Narayanan Menon, Rama Govindarajan As a sphere falling under gravity through a viscous medium approaches a wall, there is a large increase in the pressure in the thin layer of fluid being squeezed out between the sphere and wall. At low enough Stokes number, this leads to settling, and above a threshold Stokes number, the sphere bounces. Our earlier experiments have shown that even near this threshold, bouncing involves direct mechanical contact with the bottom plate [SK Birwa et al., Physical Review Fluids, 3(4), 044302, (2018)]. This is in contradiction with lubrication theory (LT) which says that the pressure diverges in the fluid and contact is not made in finite time. To study this difference, we conduct experiments to measure optically and interferometrically the dynamics of a sphere until the micrometer scale preceding the normal collision. The sphere is found to be decelerating slower than predicted by LT. We present an attempt to go beyond LT by accounting for the inertial terms neglected while making the boundary layer approximation, and by defining an appropriate nonorthogonal coordinate system. We obtain a single parametric differential equation which provides us with the timeevolution of the velocity profiles at different radii. 
Monday, March 4, 2019 9:00AM  9:12AM 
A59.00004: Normal Stresses in SteadyState and Transient Frictional Granular Flows Ishan Srivastava, Jeremy Lechman, Gary Grest, Leonardo Silbert Steady flow of sheared frictional granular matter is welldescribed by a plastic yield criterion along with a ratedependent viscoplastic rheology. However, existing constitutive formulations focus exclusively on steadystate simple shear rheology. Using stresscontrolled discrete element simulations, we highlight that normal stresses are crucial in the rheology of granular matter, both in steady flow above yield stress and transient creep flow below yield stress. The evolution of shear and normal stress components with strain rate is described in terms of frictiondependent viscometric flow functions, and the effect of friction on the directionality of stress and strain rate tensors is assessed. Additionally, correlations between the evolution of bulk stress tensor and granular fabric—both in transient and steadystate flows—are also described. These results provide important inputs toward formulating rheological constitutive equations that predict stresses during arbitrary deformations of frictional granular matter. 
Monday, March 4, 2019 9:12AM  9:24AM 
A59.00005: Dynamics of the granular fluidity field Seongmin Kim, Ken Kamrin A collection of denselypacked solid grains such as sand, rice, and sugar can flow like liquids. A key issue for dense granular flows is rheology: what is the relation between stress and strain rate? The mu(I) rheology postulates a local rheology for steadystate inertial flows. Modified from the local rheology, the nonlocal granular fluidity (NGF) model has been proposed to explain nonlocal phenomena due to finite grain size. In the NGF model, an order parameter called ‘granular fluidity’ diffuses away following a partial differential equation in a form of the reactiondiffusion equation. This PDE, however, has only been verified in steadystates. Using the discrete element method, we observe dynamics of the order parameter in different configurations and verify the PDE of the NGF model in transient states. 
Monday, March 4, 2019 9:24AM  9:36AM 
A59.00006: Fluiddriven transport of spherical sediment particles: from discrete simulations to continuum modeling Qiong Zhang, Ken Kamrin Empirical bedload transport expressions commonly over or underpredict sediment flux by more than a factor of two, even under controlled laboratory conditions. In this work, the discrete element method and lattice boltzmann method are coupled together to simulate 3D fluiddriven transport problems of spherical particles. After comparisons with flume experiments are made to test the numerical simulations, the grainscale physics is studied, such as the flow field around individual particles and higher order descriptions of the granular motion. A more robust continuum model, unifying empirical models under various conditions and in different regimes, is further proposed based on the new grainscale understanding of the mechanisms. 
Monday, March 4, 2019 9:36AM  9:48AM 
A59.00007: Dynamics of ultrasonically levitated granular rafts Melody Lim, Anton A Souslov, Vincenzo Vitelli, Heinrich M Jaeger Macroscopic particles in an acoustic trap can selfassemble into closepacked granular rafts consisting of hundreds of particles. These rafts are formed and stabilised due to a sonic depletion force mediated by scattering, which establishes shortrange attractions between the constituent particles [1]. We show that this cohesive granular material displays fluidlike behaviour, forming circular “granular droplets” with an emergent surface tension and viscosity. These droplets interact with the acoustic field, inducing forces and torques that drive the droplets to merge, deform, and breakup. We focus on a rotational instability that provides a persistent torque to objects moving in the acoustic field. As the angular momentum of a granular droplet is increased, it deforms from a circle to an ellipse, eventually pinching off into two separate droplets. We use hydrodynamic models for rotating liquid drops to describe the granular dynamics and extract the droplet surface tension. 
Monday, March 4, 2019 9:48AM  10:00AM 
A59.00008: Material stability and localization in the nonlocal granular fluidity model for dense granular flow SHIHONG LI A common and successful continuum model for steady, dense granular flows is the inertial rheology. Recent work has shown that under certain conditions, the inertial rheology displays a linear instability in which short wavelength perturbations grow at an unbounded rate  i.e., a Hadamard instability. This observation indicates that the inertial rheology is capable of describing strain localization; however, it also raises concerns regarding the robustness of numerical solutions. It has been shown that the inclusion of higherorder velocity gradients into the rheology can suppress the Hadamard instability, while not precluding the modeling of strain localization into diffuse shear bands. In this talk, we consider the nonlocal granular fluidity (NGF) model  which also involves higherorder flow gradients and has been shown to quantitatively describe a wide variety of steady, dense flows  and show that the NGF model successfully regularizes the Hadamard instability of the inertial rheology. We further apply the NGF model to the problem of strain localization in quasistatic planestrain compression using nonlinear finiteelement simulations in order to demonstrate that the model is capable of describing diffuse strain localization in a meshindependent manner. 
Monday, March 4, 2019 10:00AM  10:12AM 
A59.00009: Suspension clogging fronts in a leaky pipe Jeremy S. Yodh, L Mahadevan A particle suspension flowing through a leaky microfluidic channel forms clogs that propagate backwards against the incident flow direction indefinitely. We study the speed and shape of clogs in such situations and show how we can control them. Further, we show that the particulate order in the clog can be controlled by tuning the geometry of the leaky walls. Time permitting, the implications of this for flow through parallel channels will also be addressed. 
Monday, March 4, 2019 10:12AM  10:24AM 
A59.00010: On the reversibility of granular rotations and translations Anton Peshkov, Michelle Girvan, Derek C. Richardson, Wolfgang Losert We analyze reversibility of both displacements and rotations of spherical grains in threedimensional compression experiments. Using transparent acrylic beads with cylindrical holes and index matching techniques, we are not only capable of tracking displacements but also, for the first time, analyze reversibility of rotations. We observe that for moderate compression amplitudes, up to the bead diameter, the translational displacements of the beads after each cycle become mostly reversible after an initial transient. By contrast, granular rotations are largely irreversible. We find a weak correlation between translational and rotational displacements, indicating that rotational reversibility depends on more subtle changes in contact distributions and contact forces between grains compared with displacement reversibility. 
Monday, March 4, 2019 10:24AM  10:36AM 
A59.00011: Drag and interactions of rigid bodies moving through submerged granular beds Benjamin Allen, Rausan Jewel, Arshad Kudrolli We discuss experimental investigation of the forces encountered by a rod moving through a fluidsaturated granular medium to understand the dynamics of intruders and organisms in sedimentary beds at the bottom of lakes and oceans. By dragging vertically oriented rods through a granular bed of glass spheres, immersed in a fluid, we probe the observed transition from a quasistatic granularlike response to a viscous fluidlike behavior of the medium with speed. The relative importance of inertia, gravitational, and viscous forces is probed in terms of the dimensionless Stokes number, inertial number, and viscous number by varying the rod speed, rod depth, rod diameter, and the viscosity of the fluid. We find that the measured drag is best scaled with the integrated hydrostatic pressure along the rod and the Stokes number at low drag speeds corresponding to the quasistatic region. The transition between the quasistatic and fluid behavior scales with the viscous number, which is the ratio of viscous stress and gravity. We further discuss the interaction of two intruders as a function of the distance of separation compared with their diameter and length. 
Monday, March 4, 2019 10:36AM  10:48AM 
A59.00012: Transition to Steady State in Sheared Dense Granular Materials HanHsin Lin, Melany Hunt Jamming and shearthinning are interesting, timedependent behaviors found in granular materials; however, most prior research has focused on the steadystate behavior under different shear rates. We study the transition phenomenon from unsteady to steady state by using a Couette cell and controlling the torque and speed of the inner cylinder. When controlling the torque, the system cannot reach a steady state when it is below a critical stress. When controlling the speed of the boundary, the shear stress at the wall increases slowly over a period of time that depends on the initial state of the bed, wall friction, shear rate, and flow along the free surface. At steady state, the stress decreases at the highest rotation speeds. Simulations show a recirculation cell driven by gravity and the free surface, which results in the increasing stress observed in the measurements. The effective friction of the inner wall matters. When using the smooth cylinder, the system needs more time to reach a steady state than using the rough cylinder. At steady state, its wall stress decreases more significantly at the highest rotation speeds compared to the rough cylinder. 
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