Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session A09: Nonlinear Response of Complex Granular Materials IFocus Recordings Available
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Sponsoring Units: GSNP DSOFT DFD Chair: Ishan Srivastava, Lawrence Berkeley National Laboratory Room: McCormick Place W-180 |
Monday, March 14, 2022 8:00AM - 8:36AM |
A09.00001: Predicting size and density segregation in granular flows Invited Speaker: Richard M Lueptow As large and small particles flow, small particles fall between large particles to segregate in lower portions of a dense granular flow while displacing large particles upward, a process known as "percolation." Similarly, heavy particles segregate below light particles as they flow due to "buoyancy." The degree of segregation depends on the flow conditions and the differences between particles. We address granular segregation in two ways. The first approach is a continuum segregation model based on the advection-diffusion equation with a term added to account for particle segregation. The model can predict mixing and segregation in both steady and transient flows for a variety of flow geometries and for a range of particle systems including multiple individual particle sizes, polydisperse particle size distributions, mixtures of particles varying in both size and density, and non-spherical particles. Furthermore, the model's segregation velocity can be used to "design" non-segregating particle mixtures by adjusting particle size, density, and concentration. The second approach is to consider the physics of granular segregation at the particle level via discrete particle simulations. The result is the ability to predict the segregation force acting on an intruder particle as well as whether a single intruder particle will rise or sink in a bed of other particles. These results have recently been extended from single intruder particles to cooperative phenomena in particle mixtures. The ongoing challenge is to connect particle level forces to parameters in the continuum segregation model as well as to integrate the segregation model into constitutive models for granular flow. |
Monday, March 14, 2022 8:36AM - 8:48AM |
A09.00002: A three-dimensional continuum model for coupled size segregation and flow in dense, bidisperse granular materials David Henann, Harkirat Singh, Shihong Li, Daren Liu When a non-monodisperse granular system undergoes flow, particles of similar sizes tend to gather together, a phenomenon known as size segregation, which can result in complex, non-homogeneous fields for the average particle size. The ability to predict how granular mixtures segregate is important in the design of industrial processes and the understanding of geophysical phenomena. At the continuum level, the two main drivers of size segregation are pressure gradients and strain-rate gradients. In this talk, we discuss a continuum model for the dynamics of segregation in bidisperse, dense granular flows that accounts for both driving mechanisms. Combined with the nonlocal granular fluidity (NGF) model (a nonlocal continuum model for dense granular flow), the coupled model is capable of quantitatively predicting segregation fields in quasi-one-dimensional flow configurations, such as vertical chute flow and inclined plane flow. Moreover, we have developed a finite-element-based numerical approach for solving the segregation dynamics equation (SDE) and the NGF model simultaneously. Our implementation is applied to a few three-dimensional inhomogeneous flow configurations: notably, annular shear flow with gravity and split-bottom flow with gravity, and we show that the coupled continuum model is capable of qualitatively capturing the segregation dynamics observed in three-dimensional discrete-element method simulations. |
Monday, March 14, 2022 8:48AM - 9:00AM |
A09.00003: Modeling size segregation driven by pressure gradients in three-dimensional, dense, bidisperse granular mixtures Harkirat Singh, David Henann Dense granular systems that consist of particles of disparate size segregate based on size during flow, and size-based segregation in granular mixtures is a longstanding problem in industrial and geophysical processes. The two primary driving forces of size segregation are pressure gradients and shear strain-rate gradients, which we study using three-dimensional discrete-element method (DEM) simulations of dense, bidisperse spheres. In this study, we consider a granular flow configuration called antiplane shear flow (ASF) in which gravitational pressure gradients are perpendicular to the plane of shear, which allows for the isolation of pressure gradient driven segregation from strain-rate gradient driven segregation. Moreover, we consider inclined plane flow (IPF), in which gravitational pressure gradients are within the plane of shear. Based on DEM simulation data, we propose a three-dimensional constitutive equation for the relative flux of large and small particles due to pressure gradients, which accounts for the orientation of the pressure gradient vector relative to the stretching tensor (i.e., the strain-rate tensor). When coupled with the nonlocal granular fluidity model (a nonlocal continuum model for dense granular flow) we show that segregation dynamics may be captured using the continuum model across all considered variations in driving conditions and mixture properties for ASF and IPF. |
Monday, March 14, 2022 9:00AM - 9:12AM |
A09.00004: Drag on a sphere in granular shear flows Lu Jing, Julio M Ottino, Richard M Lueptow, Paul B Umbanhowar Drag in granular media has significant implications for granular rheology, particle segregation, impact and penetration, and even robotic locomotion. Extensive research has focused on the drag force on intruders in static or vibrofluidized granular beds, but the fundamental characteristics and scaling laws for particle drag in flowing granular materials remain largely unknown. Here, we use discrete element method simulations to study the drag force on a driven intruder particle in an otherwise size- and density-monodisperse granular shear flow, in the absence of gravity. For a wide range of applied intruder forces and flow conditions (shear rate and overburden pressure), the intruder particle velocity is constant (i.e., the drag force exerted by its neighbouring particles counterbalances the applied driving force) and the drag force is proportional to the velocity. The linear force-velocity relation can be cast into a modified Stokes' drag model with a drag coefficient dependent on the intruder size and density, as well as the flow inertial number. Intriguingly, changing the direction of the applied force with respect to the shear flow also affects the drag coefficient, which is attributed to the anisotropic contact force orientation and drag-induced lift effects in granular shear flows. Finally, our drag model accurately predicts the dependence of the segregation velocity on particle size and density ratios, as observed previously in gravity-driven granular segregation studies. |
Monday, March 14, 2022 9:12AM - 9:48AM |
A09.00005: Rheology of inertial viscohesive granular flows: insights from numerical simulations Invited Speaker: Franck Radjai In the presence of cohesive and viscous interactions between particles (wet particles, sticky particles), a granular flow is governed by several characteristic time and stress scales that determine its rheological properties (shear stress, packing fraction, effective viscosities) and texture variables (coordination number, contact network anisotropy). In this talk, based on extensive discrete element simulations, we show that the shear strength is proportional to the total confining stress (sum of external and cohesive stresses) and a unique function of the inertial, Stokes and cohesion numbers. This function extends therefore the inertial number used previously for dry cohesionless granular flows and suspensions to more complex flows. We also show that a similar scaling describes the texture parameters. Lastly, we discuss its relevance to non-Brownian suspensions. |
Monday, March 14, 2022 9:48AM - 10:00AM |
A09.00006: Fluctuations and power-law scaling in granular flow simulations Andrew P Santos, Ishan Srivastava, Leo Silbert, Jeremy Lechman, Gary S Grest Accurate and general constitutive models of granular material flow would aid experimental flow characterization measurements, but yet remain elusive. Further development of these models requires understanding higher-order flow properties and fluctuations in steady granular flow. We perform particle-based stress-controlled discrete element modeling simulations of frictionless particles. The average values and fluctuations of steady flow properties, such as shear stress, pressure, strain rate and normal stress differences are presented. The number of particles is varied from 3x102 to 105 and the pressure up to 6 orders of magnitude. We find that the critical shear stress ratio measured from arrest and taken from fits to the disagree for small system sizes. Sufficiently large system sizes allow us to identify a non-monotonic dependence in the second normal difference with strain rate. We show how fluctuations of flow properties, such as normal stresses differences, scale and normalize with system size, pressure and strain rate. |
Monday, March 14, 2022 10:00AM - 10:12AM |
A09.00007: Transient rheology and the direct velocity effect in simulated sheared granular materials Behrooz Ferdowsi, Allan M Rubin, Benjamin M Alessio Here we use short-range molecular dynamics simulations to examine the transient rheology of confined sheared granular materials in response to perturbations in sliding velocity within the quasi-static shearing regime (inertial number 10-8 to 10-1). The granular systems are composed of spherical and disk-shaped grains that interact with each other via the Hertzian and Hookean contact laws in normal direction and a constant grain-grain friction coefficient in tangential direction. We find that sheared layers show an immediate transient effect (“direct velocity effect”) following velocity perturbations, the size of which depends on the ratio of fluctuating kinetic energy (δEk) to the stored elastic potential energy (UE) of the layer. The Hookean simulations in low-sliding velocity show low δEk values and no appreciable direct velocity effect. Our observations can be explained by a modified version of a thermally-activated creep model for the direct velocity effect seen in crystalline materials, that instead uses energetic terms measured and estimated for the granular layer. Using these findings, we can begin to explain a possible source for a similar transient friction effect seen in fault rocks and other geological shear zones, referred to as the rate- and state-dependent friction. |
Monday, March 14, 2022 10:12AM - 10:24AM |
A09.00008: Flow, arrest, and dynamics near the jamming transition in sheared granular materials Joel T Clemmer, Ishan Srivastava, Gary S Grest, Jeremy Lechman With a decreasing pressure-normalized shear stress or stress ratio, the strain rate in granular materials decreases and approaches zero as the system nears a critical stress ratio. This critical stress ratio is the threshold for the system to flow and depends not only on material properties such as the friction coefficient but also on the type of flow, whether a planar pure or simple shear flow or a non-planar triaxial flow. Using discrete element method simulations of large systems, we characterize how the critical stress ratio depends on these parameters and then discuss the dynamics of granular systems both above this critical stress ratio where the system flows at a near-quasistatic rate and below where the system eventually arrests. Near this limit, the system experiences bursts of motion and spatial inhomogeneities. We isolate these events to examine the spatial-temporal rearrangement of grains and explore their statistics. |
Monday, March 14, 2022 10:24AM - 10:36AM |
A09.00009: Pinned Bubble Dynamics in Locally Fluidized Granular Media Andras Karsai, Daniel I Goldman Recent studies of soft robot movement in sand have revealed that local high Reynolds number airflows can aid in intrusion, but the multiphase flow phenomena that emerge beneath the surface remain unexplored. We experimentally study the simplest version of such dynamics, the grain flow and structure formation created by a downward impinging buried air jet in a granular medium at different depths and flow rates. By bringing the probe to a clear sidewall, we observe rich phenomenology and a diversity of states including pinned granular bubbles and breaching cavities. For certain parameters of depth and airflow, bubbles can display a regular oscillation in their surfaces; we refer to these as "bubblators" and their dynamics are due to a creeping boundary flow that creates damped travelling vertical dunes along the bubblators length. A dimensional model based on self-similar turbulent jets captures the frequency scaling of these oscillations. We also find that pinned bubbles and bubblators can also be stably transported through space simply by moving the inlet source. |
Monday, March 14, 2022 10:36AM - 10:48AM |
A09.00010: Transient analysis of granular materials flowing over an inclined plane. Satyabrata Patro, Anubhav Majumdar, Sumit Kumar, Anurag Tripathi The popular inertial number based rheology of dense granular flows as proposed by Jop et. al. (2006) [Nature. 441, 727–730] is able to describe the flow behavior in various configurations. In comparison to the steady-state flow behavior, relatively little attention has been given to the transient study of the granular flow. In this study, we numerically solve the unsteady state momentum balance equations along with a viscoplastic rheological constitutive model given by the μ - I rheology and predict the transient flow profiles of the velocity, solids fraction, inertial number, shear stress, pressure, and shear rate. We also compute these flow properties by performing two-dimensional discrete element method (DEM) simulations of slightly polydisperse particles flowing down a rough and bumpy inclined surface. At any given inclination, the particles which were initially at a settled state start to flow under the influence of gravity. The predicted profiles obtained by using the unsteady state momentum balance equations from the numerical results at different instants are compared with the DEM simulations. The validity of the numerical method for low as well as moderate inertial numbers will be discussed in this work. The applicability of the inertial number based μ - I rheology at the moderate and high inertial numbers and its detailed study will be the main focus of this work. |
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