arXiv subjects

Robert P. Behringer

Publications and source records attributed to Robert P. Behringer.

At least 19 recordsLinked to original sources

arXiv2019

Dynamics of a grain-scale intruder in a two-dimensional granular medium with and without basal friction

We report on a series of experiments in which a grain-sized intruder is pushed by a spring through a 2D granular material comprised of photoelastic disks in a Couette geometry. We study the intruder dynamics as a function of packing fraction for two types of supporting substrates: a frictional glass plate and a layer of water for which basal friction forces are negligible. We observe two dynamical regimes: intermittent flow, in which the intruder moves freely most of the time but occasionally gets stuck, and stick-slip dynamics, in which the intruder advances via a sequence of distinct, rapid events. When basal friction is present, we observe a smooth crossover between the two regimes as a function of packing fraction, and we find that reducing the interparticle friction coefficient causes the stick-slip regime to shift to higher packing fractions. When basal friction is eliminated, we observe intermittent flow at all accessible packing fractions. For all cases, we present results for the statistics of stick events, the intruder velocity, and the force exerted on the intruder by the grains. Our results indicate the qualitative importance of basal friction at high packing fractions and suggest a possible connection between intruder dynamics in a static material and clogging dynamics in granular flows.

cond-mat.soft↗

arXiv2019

Shear jammed, fragile, and steady states in homogeneously strained granular materials

We study the jamming phase diagram of sheared granular material using a novel Couette shear set-up with multi-ring bottom. The set-up uses small basal friction forces to apply a volume-conserving linear shear with no shear band to a granular system composed of frictional photoelastic discs. The set-up can generate arbitrarily large shear strain due to its circular geometry, and the shear direction can be reversed, allowing us to measure a feature that distinguishes shear-jammed from fragile states. We report systematic measurements of the stress, strain and contact network structure at phase boundaries that have been difficult to access by traditional experimental techniques, including the yield stress curve and the jamming curve close to $ϕ_{SJ}\approx 0.74$, the smallest packing fraction supporting a shear-jammed state. We observe fragile states created under large shear strain over a range of $ϕ< ϕ_{SJ}$. We also find a transition in the character of the quasi-static steady flow centered around $ϕ_{SJ}$ on the yield curve as a function of packing fraction. Near $ϕ_{SJ}$, the average contact number, fabric anisotropy, and non-rattler fraction all show a change of slope. Above $ϕ_{F}\approx 0.7$ the steady flow shows measurable deviations from the basal linear shear profile, and above $ϕ_c\approx 0.78$ the flow is localized in a shear band.

cond-mat.soft↗

arXiv2019

Jamming transition in non-spherical particle systems: pentagons vs. disks

We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles with static friction coefficient $μ\approx 1$. (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, $Z_{nr}$ , reaches 3, and the dependence of $Z_{nr}$ on the packing fraction $ϕ$ changes again when $Z_{nr}$ reaches 4. (2) Though the packing fractions $ϕ_{c1}$ and $ϕ_{c2}$ at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of $ϕ_{c1}$ and $ϕ_{c2}$ for pentagons are around 1% smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs comparing to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution.

cond-mat.soft↗

arXiv2019

Dynamics of oblique impact in a photoelastic granular medium

When a solid projectile impacts a granular target, it experiences a drag force and abruptly comes to rest as its momentum transfers to the grains. An empirical drag force law successfully describes the force experienced by the projectile, and the corresponding grain-scale mechanisms have been deciphered for normal impacts. However, there is little work exploring non-normal impacts. Accordingly, we extend studies to explore oblique impact, in which a significant horizontal component of the drag force is present. In our experiments, a projectile impacts a quasi-two-dimensional bed of bidisperse photoelastic grains. We use high-speed imaging to measure high-resolution position data of the projectile trajectory and simultaneously visualize particle-scale force propagation in the granular medium. When the impact angle becomes important, the spatial structure of the stress response reveals relatively weak force chain propagation in the horizontal direction. Based on these observations, we describe the decrease of the inertial drag force with impact angle.

cond-mat.soft↗

arXiv2018

Vibration can enhance stick-slip behavior for granular friction

We experimentally study the frictional behavior of a two-dimensional slider pulled slowly over a granular substrate comprised of photoelastic disks. The slider is vibrated at frequencies ranging from 0 to 30 Hz in a direction parallel to sliding. The applied vibrations have constant peak acceleration, which results in constant average friction levels. Surprisingly, we find that stick-slip behavior, where stress slowly builds up and is released in intermittent slips, is enhanced as the frequency of vibration is increased. Our results suggest that increasing the frequency of vibration may help to combine many smaller rearrangements into fewer, but larger, avalanche-like slips, a mechanism unique to granular systems. We also examine the manner in which the self affine character of the force curves evolves with frequency, and we find additional support for this interpretation.

cond-mat.soft↗

arXiv2018

Thermal Marangoni-driven Dynamics of Spinning Liquid Films

Spin coating of thin films of viscous liquids on a rotating substrate is a core technological component of semiconductor microchip fabrication. The thinning dynamics is influenced by many physical processes. Specifically temperature gradients affect thin liquid films through their influence on the local fluid surface tension. We show here experimentally and numerically that adding a static temperature gradient has a significant effect on the equilibrium film thickness and height profile reached in spin coating. Our results suggest that thermal gradients can be used to control film height profile dynamics.

physics.flu-dyn↗

arXiv2018

Characterizing Granular Networks Using Topological Metrics

We carry out a direct comparison of experimental and numerical realizations of the exact same granular system as it undergoes shear jamming. We adjust the numerical methods used to optimally represent the experimental settings and outcomes up to microscopic contact force dynamics. Measures presented here range form microscopic, through mesoscopic to system-wide characteristics of the system. Topological properties of the mesoscopic force networks provide a key link between micro and macro scales. We report two main findings: the number of particles in the packing that have at least two contacts is a good predictor for the mechanical state of the system, regardless of strain history and packing density. All measures explored in both experiments and numerics, including stress tensor derived measures and contact numbers depend in a universal manner on the fraction of non-rattler particles, $f_{NR}$. The force network topology also tends to show this universality, yet the shape of the master curve depends much more on the details of the numerical simulations. In particular we show that adding force noise to the numerical data set can significantly alter the topological features in the data. We conclude that both $f_{NR}$ and topological metrics are useful measures to consider when quantifying the state of a granular system.

cond-mat.soft↗

arXiv2017

`Sinking' in a bed of grains activated by shearing

We show how a weak force, $f$, enables intruder motion through dense granular materials subject to external mechanical excitations, in the present case stepwise shearing. A force acts on a Teflon disc in a two dimensional system of photoelastic discs. This force is much smaller than the smallest force needed to move the disc without any external excitation. In a cycle, material + intruder are sheared quasi-statically from $γ= 0$ to $γ_{max}$, and then backwards to $γ= 0$. During various cycle phases, fragile and jammed states form. Net intruder motion, $δ$, occurs during fragile periods generated by shear reversals. $δ$ per cycle, e.g. the quasistatic rate $c$, is constant, linearly dependent on $γ_{max}$ and $f$. It vanishes as, $c \propto (ϕ_c - ϕ)^a$, with $a \simeq 3$ and $ϕ_c \simeq ϕ_J$, reflecting the stiffening of granular systems under shear as $ϕ\rightarrow ϕ_J$. The intruder motion induces large scale grain circulation. In the intruder frame, this motion is a granular analogue to fluid flow past a cylinder, where $f$ is the drag force exerted by the flow.

cond-mat.soft↗

arXiv2017

Topology of Force Networks in Granular Media under Impact

We investigate the evolution of the force network in experimental systems of two-dimensional granular materials under impact. We use the first Betti number, $β_1$, and persistence diagrams, as measures of the topological properties of the force network. We show that the structure of the network has a complex, hysteretic dependence on both the intruder acceleration and the total force response of the granular material. $β_1$ can also distinguish between the nonlinear formation and relaxation of the force network. In addition, using the persistence diagram of the force network, we show that the size of the loops in the force network has a Poisson-like distribution, the characteristic size of which changes over the course of the impact.

cond-mat.soft↗

arXiv2017

Local and global avalanches in a 2D sheared granular medium

We present the experimental and numerical studies of a 2D sheared amorphous material constituted of bidisperse photo-elastic disks. We analyze the statistics of avalanches during shear including the local and global fluctuations in energy and changes in particle positions and orientations. We find scale free distributions for these global and local avalanches denoted by power-laws whose cut-offs vary with inter-particle friction and packing fraction. Different exponents are found for these power-laws depending on the quantity from which variations are extracted. An asymmetry in time of the avalanche shapes is evidenced along with the fact that avalanches are mainly triggered from the shear bands. A simple relation independent from the intensity, is found between the number of local avalanches and the global avalanches they form. We also compare these experimental and numerical results for both local and global fluctuations to predictions from meanfield and depinning theories.

cond-mat.soft↗

arXiv2017

Force and Mass Dynamics in Non-Newtonian Suspensions

Above a certain solid fraction, dense granular suspensions in water exhibit non-Newtonian behavior, including impact-activated solidification. Although it has been suggested that solidification depends on boundary interactions, quantitative experiments on the boundary forces have not been reported. Using high-speed video, tracer particles, and photoelastic boundaries, we determine the impactor kinematics and the magnitude and timings of impactor-driven events in the body and at the boundaries of cornstarch suspensions. We observe mass shocks in the suspension during impact. The shockfront dynamics are strongly correlated to those of the intruder. However, the total momentum associated with this shock never approaches the initial impactor momentum. We also observe a faster second front, associated with the propagation of pressure to the boundaries of the suspension. The two fronts depend differently on the initial impactor speed, $v_0$, and the suspension packing fraction. The speed of the pressure wave is at least an order of magnitude smaller than (linear) ultrasound speeds obtained for much higher frequencies, pointing to complex amplitude and frequency response of cornstarch suspensions to compressive strains.

cond-mat.soft↗

arXiv2016

Granular Impact: A Grain-scale Approach

This work summarizes a series of studies on two-dimensional granular impact, where an intruding object strikes a granular material at high speed. Many previous studies on granular impact have used a macroscopic force law, which is dominated by an inertial drag term proportional to the intruder velocity squared. The primary focus here is on the microscopic force response of the granular material, and how the grain-scale effects give rise to this inertial drag term. We show that the inertial drag arises from intermittent collisions with force-chain-like structures. We construct a simple collisional model to explain the inertial drag, as well as off-axis instability and rotations. Finally, we show how the granular response changes when the intruder speed approaches $d/t_c$, leading to a failure of the inertial drag description in this regime. Here, $d$ is the mean particle diameter and $t_c$ the characteristic momentum-transfer time between two grains.

cond-mat.soft↗

arXiv2016

Collisional Model of Energy Dissipation in 3D Granular Impact

We study the dynamic process occurring when a granular assembly is displaced by a solid impactor. The momentum transfer from the impactor to the target is shown to occur through sporadic, normal collisions of high force carrying grains at the intruder surface. We therefore describe the stopping force of the impact through a collisional based model. To verify the model in impact experiments, we determine the forces acting on an intruder decelerating through a dense granular medium using high-speed imaging of its trajectory. By varying the intruder shape and granular target, intruder-grain interactions are inferred from the consequent path. As a result, we connect the drag to the effect of intruder shape and grain density based on a proposed collisional model.

cond-mat.soft↗

arXiv2016

Steady Flow Dynamics during Granular Impact

We study experimentally and computationally the dynamics of granular flow during impacts, where intruders strike a collection of disks from above. In the regime where granular force dynamics are much more rapid than the intruder motion, we find that the particle flow near the intruder is proportional to the instantaneous intruder speed; it is essentially constant when normalized by that speed. The granular flow is nearly divergence-free and remains in balance with the intruder, despite the latter's rapid deceleration. Simulations indicate that this observation is insensitive to grain properties, which can be explained by the separation of time scales between intergrain force dynamics and intruder dynamics. Assuming there is a comparable separation of time scales, we expect our results are applicable to a broad class of dynamic or transient granular flows. Our results suggest that descriptions of static-in-time granular flows might be extended or modified to describe these dynamic flows. Additionally, we find that accurate grain-grain interactions are not necessary to correctly capture the granular flow in this regime.

cond-mat.soft↗

arXiv2015

Packings of 3D stars: Stability and structure

We describe a series of experiments involving the creation of cylindrical packings of star-shaped particles, and an exploration of the stability of these packings. The stars cover a broad range of arm sizes and frictional properties. We carried out three different kinds of experiments, all of which involve columns that are prepared by raining star particles one-by-one into hollow cylinders. As an additional part of the protocol, we sometimes vibrated the column before removing the confining cylinder. We rate stability in terms of r, the ratio of the mass of particles that fall off a pile when it collapsed, to the total particle mass. The first experiment involved the intrinsic stability of the pile when the confining cylinder was removed. The second kind of experiment involved adding a uniform load to the top of the column, and then determining the collapse properties. A third experiment involved testing stability to tipping of the piles. We find a stability diagram relating the pile height, h, vs. pile diameter, delta, where the stable and unstable regimes are separated by a boundary that is roughly a power-law in h vs. delta with an exponent that is less than one. Increasing friction and vibration both tend to stabilize piles, while increasing particle size can destabilize the system under certain conditions.

cond-mat.soft↗

arXiv2015

Self-organized magnetic particles to tune the mechanical behaviour of a granular system

Above a certain density a granular material jams. This property can be controlled by either tuning a global property, such as the packing fraction or by applying shear strain, or at the micro-scale by tuning grain shape, inter-particle friction or externally controlled organization. Here, we introduce a novel way to change a local granular property by adding a weak anisotropic magnetic interaction between particles. We measure the evolution of the pressure, $P$, and coordination number, $Z$, for a packing of 2D photo-elastic disks, subject to uniaxial compression. Some of the particles have embedded cuboidal magnets. The strength of the magnetic interactions between particles are too weak to have a strong direct effect on $P$ or $Z$ when the system is jammed. However, the magnetic interactions play an important role in the evolution of latent force networks when systems containing a large enough fraction of the particles with magnets are driven through unjammed states. In this case, a statistically stable network of magnetic chains self-organizes and overlaps with force chains, strengthening the granular medium. We believe this property can be used to reversibly control mechanical properties of granular materials.

cond-mat.soft↗

arXiv2015

Orientation, Flow, and Clogging in a Two-Dimensional Hopper: Ellipses vs. Disks

Two-dimensional (2D) hopper flow of disks has been extensively studied. Here, we investigate hopper flow of ellipses with aspect ratio $α= 2$, and we contrast that behavior to the flow of disks. We use a quasi-2D hopper containing photoelastic particles to obtain stress/force information. We simultaneously measure the particle motion and stress. We determine several properties, including discharge rates, jamming probabilities, and the number of particles in clogging arches. For both particle types, the size of the opening, $D$, relative to the size of particles, $\ell$ is an important dimensionless measure. The orientation of the ellipses plays an important role in flow rheology and clogging. The alignment of contacting ellipses enhances the probability of forming stable arches. This study offers insight for applications involving the flow of granular materials consisting of ellipsoidal shapes, and possibly other non-spherical shapes.

cond-mat.soft↗

arXiv2015

Obtaining Self-similar Scalings in Focusing Flows

The surface structure of converging thin fluid films displays self-similar behavior, as was shown in the work by Diez et al [Q. Appl. Math 210, 155, 1990]. Extracting the related similarity scaling exponents from either numerical or experimental data is non-trivial. Here we provide two such methods. We apply them to experimental and numerical data on converging fluid films driven by both surface tension and gravitational forcing. In the limit of pure gravitational driving, we recover Diez' semi-analytic result, but our methods also allow us to explore the entire regime of mixed capillary and gravitational driving, up to entirely surface tension driven flows. We find scaling forms of smoothly varying exponents up to surprisingly small Bond numbers. Our experimental results are in reasonable agreement with our numerical simulations, which confirm theoretically obtained relations between the scaling exponents.

physics.flu-dyn↗