Session J29: Focus Session: Granular Flows I

Lateral stripe state in rapid granular flow on an inclined plane

Recently longitudinal vortices were reported in a rapid, dilute flow of sand down a rough inclined plane [1]. We present experimental results, showing that a robust stripe state develops at moderate plane inclinations in denser flows, with a structure substantially different from the one observed in dilute flows. We characterize this new type of stripes by measuring velocity profiles, height profiles, light transmission, and average density of the flow. As opposed to the stripes observed in the dilute regime, here the fast moving region corresponds to the maximum of the height profile. The stripe state is detected in the flow of various materials such as sand of different sizes, glass beads of different sizes, and copper particles of various shapes. We show that by increasing plane inclination we get back the dilute regime and the previously reported stripe structure. For sand particles with the diameter of d=0.4 mm the flow properties were extensively measured at six downstream locations. For this case we find an explicit correspondence between the accelerating nature of the flow and the formation of stripes in the dense regime. \vskip 5pt\noindent [1] Y. Forterre and O. Pouliquen, Phys. Rev. Lett. 86, 5886 (2001).   

Universality of granular impact dynamics

We dropped projectiles into granular media from various heights, and measured the dynamics by an optical method with 100 nanometer and 20 microsecond resolution. Data were obtained for 11 different projectiles (including cylinder as well as spheres) and 4 different granular media. The results can all be explained by a stopping force consisting of the sum of two terms: an inertial drag, proportional to velocity squared and independent of depth, and a frictional drag, proportional to depth and independent of speed. The latter scales as the square-root of projectile density and hence is not simply Coulomb friction. We also demonstrate that this stopping force law can explain seemingly-contradictory penetration and dynamics data reported by other researchers.   

The Liquid Nature of a Granular Jet Hitting a Fixed Target

We perform the granular analog to the 'water bell' experiment [1]. A column of dry spherical glass beads is accelerated by pressurized air through a glass tube to form a high-speed granular jet. When this jet collides with a stationary target disc, we observe the formation of granular sheets and cones enveloping the target similar to those seen when water jets hit a target and subsequently form water bells. The opening angle of the cones is measured as a function of the speed and diameter of the initial granular column and the diameter of the target disc. Under these conditions, dry granular material behaves similarly to a fluid with zero surface tension, i.e., a fluid with infinite Weber number. By decreasing the flux and increasing the size of the granular particles, we observe that the structure formed by the jet becomes more diffuse and the dynamics changes as the particulate nature of the material becomes more apparent. Furthermore, we measure the force impulse exerted on the target during the collision and relate it to the granular ripples formed on the thin ejected granular sheet. [1] C. Clanet, J. Fluid Mech. 430, 111 (2001).   

Rapid Granular Flows: From Kinetic Theory to Hydrodynamics

Rapid granular flows are defined as flows in which the time scales for the particle interactions are small compared to the inverse of the strain rate, so that the particle interactions can be treated as instantaneous collisions. We first show, using Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between $0.5$ and $0.6$ are rapid granular flows. Since collisions are instantaneous, a kinetic theory approach for the constitutive relations is most appropriate, and we present kinetic theory results for different microscopic models for particle interaction. The significant difference between granular flows and normal fluids is that energy is not conserved in a granular flow. The differences in the hydrodynamic modes caused by the non-conserved nature of energy are discussed. Going beyond the Boltzmann equation, the effect of correlations is studied using the ring kinetic approximation, and it is shown that the divergences in the viscometric coefficients, which are present for elastic fluids, are not present for granular flows because energy is not conserved. The hydrodynamic model is applied to the flow down an inclined plane. Since energy is not a conserved variable, the hydrodynamic fields in the bulk of a granular flow are obtained from the mass and momentum conservation equations alone. Energy becomes a relevant variable only in thin `boundary layers' at the boundaries of the flow where there is a balance between the rates of conduction and dissipation. We show that such a hydrodynamic model can predict the salient features of a chute flow, including the flow initiation when the angle of inclination is increased above the `friction angle', the striking lack of observable variation of the volume fraction with height, the observation of a steady flow only for certain restitution coefficients, and the density variations in the boundary layers.   

Kinetic theory of hydrodynamic response functions for a dense granular fluid

The general response functions characterizing the response of a homogeneous isolated granular fluid to small spatial perturbations in the hydrodynamic fields have been described recently [1]. These response functions are time correlation functions for the Homogeneous Cooling State. Special cases of this class of time correlation functions are the Green - Kubo expressions for the hydrodynamic transport coefficients. In this work, these functions are expressed in terms of reduced singe particle functions that are expected to obey a linear kinetic equation. The functional assumption required to obtain such a kinetic equation and its relationship to the well studied Boltzmann and Enskog kinetic theories of a granular fluid are illustrated in the particular context of the shear viscosity of this fluid. [1] J. W. Dufty, A. Baskaran and J. J. Brey, J. Stat. Mech. L08002 (2006).   

Velocity correlations in dense granular flows observed with internal imaging

We measure the velocity fluctuations in uniform dense granular flows inside a silo using a fluorescent refractive index matched interstitial fluid. The measurements are made in the uniform plug flow region where the flow is dominated by grains in enduring contacts and fluctuations scale with the distance traveled, independent of flow rate. The distributions of the horizontal and vertical displacements for short time scales show fat tails compared to a Gaussian indicating large fluctuations in particle displacements and possible cage breaking. The mean square displacements show an inflection point supporting the presence of caging dynamics. 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 dense liquids. Weak spatial velocity correlations are observed in the bulk over several grain diameters. The observed correlations are qualitatively different at the boundaries where significant structural ordering in the flowing granular layer is observed.   

Lubrication forces in dense granular flow with interstitial fluid: A simulation study with Discrete Element Method

Using three-dimensional molecular dynamics simulations, we study steady gravity-driven flows of frictional inelastic spheres of diameter $d$ and density $\rho _g$ down an incline, interacting through two-body lubrication forces in addition to granular contact forces. Scaling arguments suggest that, in 3D, these forces constitute the dominant perturbation of an interstitial fluid for small Reynolds number \textit{Re} and low fluid density$\rho$. Two important parameters that characterize the strength of the lubrication forces are fluid viscosity and grain roughness. We observe that incline flows with lubrication forces exhibit a packing density that \textit{decreases} with increasing distance from the surface. As the incline angle is increased, this results in a severely dilated basal layer that looks like ``hydroplaning'' similar to that observed in geological subaqueous debris flows. This is surprising since the model explicitly disallows any buildup of fluid pressure in the base of the flow, and suggests that hydroplaning might have other contributing factors besides this traditional explanation. The local packing density is still determined by the dimensionless strain rate $I\equiv \dot {\gamma }{\kern 1pt}d\sqrt {\rho _g /p} $, where $p$ is the average normal stress, obeying a ``dilatancy law'' similar to dry granular flows.   

Geometrical Mechanism for Solid-Fluid transition in a Granular system

We report an experimental investigation of the geometrical mechanism for solid-fluid transition in a quasi-two dimensional granular system. We demonstrate the presence of geometrical structures resembling plane tilings composed of squares and equilateral triangles in our quasi-2D granular fluid. We further show that this tiling structure manifests itself in distinct features in the bond-length and bond-angle distribution functions. These experimental observations coupled with a number of previously reported theoretical and simulation studies strongly support the proposed square-triangle tiling mechanism for 2D melting. These findings present a possible way to explain the observed phase transitions in non-equilibrium granular systems using entropic-like arguments similar to those used for equilibrium hard sphere/disk systems.   

Swirling Motion in the System of Vibrated Elongated Particles

We study large-scale collective motion emerging in a monolayer of vertically vibrated elongated particles. The motion is characterized by recurring swirls with the characteristic scale exceeding several times the size of individual particle. Our experiments identified small horizontal component of the oscillatory acceleration of the vibrating plate in a combination with orientation-dependent bottom friction as a source for the swirls formation. We developed a continuum model operating with velocity field and local alignment tensor which is in a qualitative agreement with the experiment.   

Angle of Repose of Small, Conducting and Non-Conducting Plates

We have investigated the behavior of granular collections consisting of laser-cut shapes from conducting and non-conducting paper, with various cross-sectional shapes (square, rectangular, triangular, circular) and in several sizes and aspect ratios. In particular we have measured the Angle of Repose of piles consisting of large numbers of these particles. While the shape of these particles would suggest that these should behave as thin plates, making quite shallow piles, instead we find that the piles are not shallow, and that the piling is remarkably robust to external disturbances. We will compare our results for various types of materials in various shapes, and also compare these results with what we have observed for larger, symmetric particles.   

Large scale surface flow generation in driven suspensions of magnetic microparticles: Experiment, theoretical model and simulations

Nontrivially ordered dynamic self-assembled snake-like structures are formed in an ensemble of magnetic microparticles suspended over a fluid surface and energized by an external alternating magnetic field. Formation and existence of such structures is always accompanied by flows which form vortices. These large-scale vortices can be very fast and are crucial for snake formation/destruction. We introduce theoretical model based on Ginzburg-Landau equation for parametrically excited surface waves coupled to conservation law for particle density and Navier-Stokes equation for water flows. The developed model successfully describes snake generation, accounts for flows and reproduces most experimental results observed.   

The Behavior of Ultrafine Particles in the Absence and Presence of External Fields

Length scales of particles and their surrounding medium strongly determines the nature of their interactions with one another and their responses to external fields. We are interested in systems of ultrafine particles (0.1 - 1.0 micron) such as volcanic ash, solid aerosols, or fine powders for pharmaceutical ihalation applications. We develop a numerical model for these systems using the Derjaguin-Muller-Toporov (DMT) adhesion theory along with the van der Waals attraction between the particles and their contact mechanical interactions. We study the dynamics of these systems in the absence and presence of gravity by controlling the particle size, and thereby, the surface properties of the particles. Finally, we explore the response of these systems to external fields by studying the evolution of the internal microstructure under contant load and shear strain.   

Quasi-equilibrium in tapered chains

The approach to equilibrium in 1d lattices is interesting for granular media since temperature is not well-defined and various authors have reported a violation of equipartition. We extend our previous work on shock mitigation in tapered chains to look at energy sharing among spheres and how the system appraoches a so-called quasi-equilibrium. An overlap potential of adjacent particles is used to model the elastic response of spheres under loading and has the form, $V\sim\delta^n$. For spheres, $n=5/2$ and is known as the Hertz potential. We can also compare results when $n=2$ which resembles spring-like behavior. It should be noted however, that in both cases the potential has no restoration term and vanishes when adjacent spheres lose contact. We present the velocity statistics for a variety of Hertzian chain configurations as well as fluctuations for the system's total kinetic energy for both $n=2$ and $n=2.5$. We find that most particles in these systems exhibit Gaussian velocity distributions and that the kinetic energy fluctuations of the system depend strongly on system size and weakly on tapering of the spheres. Fluctuations do not damp out over long time however, indicating that the steady-state is a type of quasi-equilibrium. Mathematical fits of the mean fluctuations are further provided as functions of system size, tapering, and $n$.