Statistics of particle velocities in dense granular flows

Micromechanical origin of heat transfer to granular flow

Heat transfer across a granular flow is comprised of two resistances in series : near the wall and within the bulk particle bed, neither of which is well understood due to the lack of experimental probes to separate their respective contribution. Here, we use a frequency modulated photothermal technique to separately quantify the thermal resistances in the near-wall and the bulk bed regions of particles in flowing states. Compared to the stationary state, the flowing leads to a higher near-wall resistance and a lower thermal conductivity of bulk beds. Coupled with discrete element method simulation, we show that the near-wall resistance can be explained by particle diffusion in granular flows.

Toward a 3D physical model of diffusive polymer chains

Recent studies in polymer physics have created macro-scale analogs to solute microscopic polymer chains like DNA by inducing diffusive motion on a chain of beads. These bead chains have persistence lengths of O(10) links and undergo diffusive motion under random fluctuations like vibration. We present a bead chain model within a new stochastic forcing system: an air fluidizing bed of granular media. A chain of spherical 6 mm resin beads crimped onto silk thread are buffeted randomly by the multiphase flow of grains and low density rising air "bubbles". We "thermalize" bead chains of various lengths at different fluidizing airflow rates, while X-ray imaging captures a projection of the chains' dynamics within the media. With modern 3D printing techniques, we can better represent complex polymers by geometrically varying bead connections and their relative strength, e.g., mimicking the variable stiffness between adjacent nucleotide pairs of DNA. We also develop Discrete Element Method (DEM) simulations to study the 3D motion of the bead chain, where the bead chain is represented by simulated spherical particles connected by linear and angular spring-like bonds. In experiment, we find that the velocity distributions of the beads follow exponential distributions rather than the Gaussian distributions expected from polymers in solution. Through use of the DEM simulation, we find that this difference can likely be attributed to the distributions of the forces imparted onto the chain from the fluidized bed environment. We anticipate expanding this study in the future to explore a wide range of chain composition and confinement geometry, which will provide insights into the physics of large biopolymers.

Collisional regime during the discharge of a two-dimensional silo

The present work reports an investigation into the collisional dynamics of particles in the vicinity of the outlet of a two-dimensional silo using molecular dynamics simulations. Most studies on this granular system focus in the bulk of the medium. In this region, contacts are permanent or long-lived, so continuous approximations are able to yield results for velocity distributions or mass flow. Close to the exit, however, the density of the medium decreases and contacts are instantaneous. Thus, the collisional nature of the dynamics becomes significant, warranting a dedicated investigation as carried out in this work. More interesting, the vicinity of the outlet is the region where the arches that block the flow for small apertures are formed. It is found that the transition from the clogging regime (at small apertures) to the continuous flow regime is smooth in collisional variables. Furthermore, the dynamics of particles as reflected by the distributions of the velocities is as well unaffected. This result implies that there is no critical outlet size that separates both regimes, as had been proposed in the literature. Instead, the results achieved support the alternative picture in which a clog is possible for any outlet size.

Anomalous diffusion in a bench-scale pulsed fluidized bed

We present our analysis on microrheology of a bench-scale pulsed fluidized bed, which represents a weakly confined system. Nonlinear gas-particle and particle-particle interactions resulting from pulsed flow are associated with harmonic and subharmonic modes. While periodic structured bubble patterns are observed at the mesoscale, particle-scale measurements reveal anomalous diffusion in the driven granular medium. We use single-particle tracks to analyze ergodicity and ageing properties at two pulsing frequencies having remarkably different mesoscale features. The scaling of ensemble-averaged mean-squared displacement is not unique. The distribution of time-averaged mean-squared displacements is non-Gaussian, asymmetric, and has a finite trivial contribution from particles in crowded quasistatic surroundings. Results indicate weak ergodicity breaking, which along with ageing characterizes the nonstationary and out-of-equilibrium dynamics.

Poiseuille Flow of Soft Polycrystals in 2D Rough Channels

Polycrystals are partially ordered solids where crystalline order extends over mesoscopic length scales, namely, the grain size. We study the Poisuielle flow of such materials in a rough channel. In general, similar to yield stress fluids, three distinct dynamical states, namely, flowing, stick-slip, and jammed can be observed, with a yield threshold dependent on channel width. Importantly, the interplay between the finite channel width, and the intrinsic ordering scale (the grain size) leads to a new type of spatiotemporal heterogeneity. In wide channels, although the average flow profile remains pluglike, at the underlying granular level, there is vigorous grain remodeling activity resulting from the velocity heterogeneity among the grains. As the channel width approaches typical grain size, the flowing polycrystalline state breaks up into a spatially heterogeneous mixture of flowing liquid like patches and chunks of nearly static grains. Despite these static grains, the average velocity still shows a parabolic profile, dominated by the moving liquidlike patches. However, the solid-liquid front moves at nearly constant speed in the opposite direction of the external drive.

Dissipation and velocity distribution at the shear-driven jamming transition

We investigate energy dissipation and the distribution of particle velocities at the jamming transition for overdamped shear-driven frictionless disks in two dimensions at zero temperature. We find that the dissipation is caused by the fastest particles and that the fraction of particles responsible for the dissipation decreases towards zero as jamming is approached. These particles belong to an algebraic tail of the velocity distribution that approaches ∼v^{-3} as jamming is approached. We further find that different measures of the velocity diverge differently, which means that concepts such as typical velocity may no longer be used, a finding that should have implications for analytical approaches to shear-driven jamming.

Shear-Rate-Independent Diffusion in Granular Flows

We computationally study the behavior of the diffusion coefficient D in granular flows of monodisperse and bidisperse particles spanning regions of relatively high and low shear rate in open and closed laterally confined heaps. Measurements of D at various flow rates, streamwise positions, and depths collapse onto a single curve when plotted as a function of γd2, where d is the local mean particle diameter and γ is the local shear rate. When γ is large, D is proportional to γd2, as in previous studies. However, for γd2 below a critical value, D is independent of γd2. The acceleration due to gravity g and particle stiffness (or, equivalently, the binary collision time t(c)) together determine the transition in D between regimes. This suggests that while shear rate and particle size determine diffusion at relatively high shear rates in surface-driven flows, diffusion at low shear rates is an elastic phenomenon with time and length scales dependent on gravity (sqrt d/g) and particle stiffness (t(c)sqrt(dg), respectively.

Fluctuations of grains inside a discharging two-dimensional silo

We present experimental data corresponding to a two-dimensional dense granular flow, namely, the gravity-driven discharge of grains from a small opening in a silo. We study the local velocity field at the scale of single grains at different places with the help of particle-tracking techniques. From these data, the velocity profiles can be obtained and the validity of some long-standing approaches can be assessed. Moreover, the fluctuations of the velocities are taken into consideration to characterize the features of the advective motion (due to the gravity force) and the diffusive motion, which shows nontrivial behavior.

Constitutive relations in dense granular flows

We use simulations to investigate constitutive relations in dry granular flow. Our system is comprised of polydisperse sets of spherical grains falling down a vertical chute under the influence of gravity. Three phases or states of granular matter are observed: a free-fall dilute granular gas region at the top of the chute, a granular fluid in the middle and then a glassy region at the bottom. We examine a complete closed set of constitutive relations capable of describing the local stresses, heat flow, and dissipation in the different regions. While the pressure can be reasonably described by hard sphere gas models, the transport coefficients cannot. Transport coefficients such as viscosity and heat conductivity increase with decreasing temperature in the fluid and glassy phases. The glass exhibits signs of a finite yield stress and we show that the static sand pile is a limit of our glassy state.

Unusual diffusion in a quasi-two-dimensional granular gas

We have studied diffusion in a quasi-two-dimensional granular gas composed of plastic balls confined in a vertically vibrating thin box. The horizontal motion of the balls in the box is found to follow the Langevin equation with the top and bottom of the box acting on the balls with a viscous drag like that in a fluid. Surprisingly, we find that both the granular temperature and the diffusion constant increase with the number of balls (N) in the box for small N . The unusual diffusion can be explained by a two-state model, in which a ball is in contact with two effective temperature baths due to collisions with the top or bottom of the box and collisions with other balls.

Slip velocity and stresses in granular Poiseuille flow via event-driven simulation

Event-driven simulations of inelastic smooth hard disks are used to probe the slip velocity and rheology in gravity-driven granular Poiseuille flow. It is shown that both the slip velocity (U(w)) and its gradient (dU(w)/dy) depend crucially on the mean density, wall roughness, and inelastic dissipation. While the gradient of slip velocity follows a single power-law relation with Knudsen number, the variation in U(w) with Kn shows three distinct regimes in terms of Knudsen number. An interesting possibility of Knudsen-number-dependent specularity coefficient emerges from a comparison of our results with a first-order transport theory for the slip velocity. Simulation results on stresses are compared with kinetic-theory predictions, with reasonable agreement of our data in the quasielastic limit. The deviation of simulations from theory increases with increasing dissipation which is tied to the increasing magnitude of the first normal stress difference (N(1)) that shows interesting nonmonotonic behavior with density. As in simple shear flow, there is a sign change of N(1) at some critical density and its collisional component and the related collisional anisotropy are responsible for this sign reversal.

Growing length scale in gravity-driven dense granular flow

We report simulations of a two-dimensional, dense, bidisperse system of inelastic hard disks falling down a vertical tube under the influence of gravity. We examine the approach to jamming as the average flow of particles down the tube is slowed by making the outlet narrower. Defining coarse-grained velocity and stress fields, we study two-point temporal and spatial correlation functions of these fields in a region of the tube where the time-averaged velocity is spatially uniform. We find that fluctuations in both velocity and stress become increasingly correlated as the system approaches jamming. We extract a growing length scale and time scale from these correlations.

Velocity fluctuations in dense granular flows

We use simulations to investigate velocity fluctuations in dry granular flow. Our system is comprised of mono- and polydisperse sets of spherical grains falling down a vertical chute under the influence of gravity. We find three different classes of velocity distributions depending on factors such as the local density. The class of the velocity distribution depends on whether the grains are in a free-fall, fluid, or glassy state. The analytic form of the distributions match those that have been found by other authors in fairly diverse systems. Here, we have all three present in a single system in steady state. Power-law tails that match recent experiments are also found but in a transition area suggesting they may be an artifact of crossover from one class of velocity distribution to another. We find evidence that the transition from one class to another may correspond to a second order dynamical phase transition in the limit that the vertical flow speed goes to zero.

Random walks with random velocities

We consider a random walk model that takes into account the velocity distribution of random walkers. Random motion with alternating velocities is inherent to various physical and biological systems. Moreover, the velocity distribution is often the first characteristic that is experimentally accessible. Here, we derive transport equations describing the dispersal process in the model and solve them analytically. The asymptotic properties of solutions are presented in the form of a phase diagram that shows all possible scaling regimes, including superdiffusive, ballistic, and superballistic motion. The theoretical results of this work are in excellent agreement with accompanying numerical simulations.

Response to perturbations for granular flow in a hopper

We experimentally investigate the response to perturbations of circular symmetry for dense granular flow inside a three-dimensional right-conical hopper. These experiments consist of particle tracking velocimetry for the flow at the outer boundary of the hopper. We are able to test commonly used constitutive relations and observe granular flow phenomena that we can model numerically. Unperturbed conical hopper flow has been described as a radial velocity field with no azimuthal component. Guided by numerical models based upon continuum descriptions, we find experimental evidence for secondary, azimuthal circulation in response to perturbation of the symmetry with respect to gravity by tilting. For small perturbations we can discriminate between constitutive relations, based upon the agreement between the numerical predictions they produce and our experimental results. We find that the secondary circulation can be suppressed as wall friction is varied, also in agreement with numerical predictions. For large tilt angles we observe the abrupt onset of circulation for parameters where circulation was previously suppressed. Finally, we observe that for large tilt angles the fluctuations in velocity grow, independent of the onset of circulation.

Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction

Combining analytical and numerical methods, we study within the framework of the homogeneous nonlinear Boltzmann equation a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism: namely, a deterministic nonlinear friction force. We derive analytically the high-energy tail of the velocity distribution and compare the theoretical predictions with high-precision numerical simulations. Stretched exponential forms are obtained when the nonequilibrium steady state is stable. We derive subleading corrections and emphasize their relevance. In marginal stability cases, power-law behaviors arise, with exponents obtained as the roots of transcendental equations. We also consider some simple Bhatnagar-Gross-Krook models, driven by similar heating devices, to test the robustness of our predictions.

Velocity correlations in dense granular flows observed with internal imaging

We show that the velocity correlations in uniform dense granular flows inside a silo are similar to the hydrodynamic response of an elastic hard-sphere liquid. The measurements are made using a fluorescent refractive-index-matched interstitial fluid in a regime where the flow is dominated by grains in enduring contact and fluctuations scale with the distance traveled, independent of flow rate. The velocity autocorrelation function of the grains in the bulk shows a negative correlation at short time and slow oscillatory decay to zero similar to simple liquids. Weak spatial velocity correlations are observed over several grain diameters. The mean square displacements show an inflection point indicative of caging dynamics. The observed correlations are qualitatively different at the boundaries.

Anomalous diffusion in silo drainage

The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained at the beginning of the discharge reveal non-Gaussian statistics and superdiffusive behaviors. When the stationary flow is developed, the PDFs at shorter temporal scales are non-Gaussian too. For big orifices a well-defined transition between ballistic and diffusive regime is observed. In the case of a small outlet orifice, no well-defined transition is observed. We use a nonlinear diffusion equation introduced in the framework of non-extensive thermodynamics in order to describe the movements of the grains. The solution of this equation gives a well-defined relationship (gamma = 2/(3 - q)) between the anomalous diffusion exponent gamma and the entropic parameter q introduced by the non-extensive formalism to fit the PDF of the fluctuations.

Velocity statistics in dissipative, dense granular media

We use a two-dimensional random-force model to investigate the velocity distributions in driven granular media. In general, the shape of the distribution is found to depend on the degree of dissipation and the packing fraction but, in highly dissipative systems, the velocity distributions have tails close to exponential. We show that these arise from the dynamics of single particles traveling in dilute regions and influenced predominantly by the random force. A self-consistent kinetic theory is developed to describe this behavior.

Velocity distribution and the effect of wall roughness in granular Poiseuille flow

From event-driven simulations of a gravity-driven channel flow of inelastic hard disks, we show that the velocity distribution function remains close to a Gaussian for a wide range densities (even when the Knudsen number is of order 1) if the walls are smooth and the particle collisions are nearly elastic. For dense flows, a transition from a Gaussian to a power-law distribution for the high-velocity tails occurs with increasing dissipation in the center of the channel, irrespective of wall roughness. For a rough wall, the near-wall distribution functions are distinctly different from those in the bulk, even in the quasielastic limit.