Session D8: Focus Session: Granular Flows: Vibrated

Particle kinematics in a 3-dimensional vibration-fluidized granular medium

We report a study by high speed video imaging of particle motions in the bulk of a three dimensional granular gas. We fluidise with intense vertical vibration, delrin spheres of diameter, d=1.6 mm confined in a 3-dimensional volume (32d)$^3$. We isolate particles moving in a thin slice of this volume by illuminating with a laser sheet. We have developed a new algorithm to track with sub-pixel precision particles that are only partially illuminated or eclipsed by other particles. We will present data in the low-volume fraction regime for spatial profiles of the the kinetic temperature and number density, as well as for the velocity distribution. These results will be compared to predictions from hydrodynamic models.   

Heating mechanism affects equipartition in a binary granular system

Two species of particles in a binary granular system typically do not have the same mean kinetic energy, in contrast to the equipartition of energy required in equilibrium. We investigate the role of the heating mechanism in determining the extent of this non-equipartition of kinetic energy. In most experiments, different species of particle are unequally heated at the boundaries. We show by event-driven simulations that this differential heating at the boundary influences the level of non-equipartition even in the bulk of the system. This conclusion is fortified by studying a numerical model and a solvable stochastic model without spatial degrees of freedom. In both cases, even in the limit where heating events are rare compared to collisions, the effect of the heating mechanism persists.   

Energy fluctuation, diffusivity and mobility in a 2D vibrated granular packing

We present an experimental realization of a 2D vibrated granular packing. The new agitation method allows a spatially non synchronized influx of energy and the study of the vibrated packing at steady state. By image analysis of fast-camera movies, we obtain the velocity fluctuation spectra at different vertical levels and then, we separate the agitation velocities from the velocity fluctuations corresponding to the ``thermalized'' degrees of freedom. By measuring the corresponding particle diffusivities, we show that, in spite a large heterogeneity and anisotropy of the vibration, a relation between diffusivity and ``thermalized'' kinetic energy can be identified. We relate this type of fluctuation-dissipation relation to the mobility of macroscopic intruders of different sizes and weight moving in the vibrated granular packing.   

``Free Energy" in Vibrated Granular Non-Equilibrium Steady-States.

Equilibrium statistical mechanics is generally not applicable to systems with energy input and dissipation present, and identifying relevant tools for understanding these far-from- equilibrium systems poses a serious challenge. Excited granular materials or granular fluids have become a canonical system to explore such ideas since they are inherently dissipative due to inter-particle frictional contacts and inelastic collisions. Granular materials also have far reaching practical importance in a number of industries, but accumulated ad-hoc knowledge is often the only design tool. An important feature of granular fluids is that the driving and dissipation mechanisms can be made to balance such that a Non-Equilibrium Steady-State (NESS) is achieved. We present strong experimental evidence for a NESS first-order phase transition in a vibrated two-dimensional granular fluid. The phase transition between a gas and a crystal is characterized by a discontinuous change in both density and temperature and exhibits rate dependent hysteresis. We measure a ``free energy''-like function for the system and compare and contrast this type of transition with an equilibrium first-order phase transition and a hysteretic backward bifurcation in a nonlinear pattern forming system.   

Singular Energy Distributions in Granular Media

We study the kinetic theory of driven and undriven granular gases, taking into account both translational and rotational degrees of freedom. We obtain the high-energy tail of the stationary bivariate energy distribution, depending on the total energy $E$ and the ratio $x=\sqrt{E_w/E}$ of rotational energy $E_w$ to total energy. Extremely energetic particles have a unique and well-defined distribution $f(x)$ which has several remarkable features: $x$ is not uniformly distributed as in molecular gases; $f(x)$ is not smooth but has multiple singularities. The latter behavior is sensitive to material properties such as the collision parameters, the moment of inertia and the collision rate. Interestingly, there are preferred ratios of rotational-to-total energy. In general, $f(x)$ is strongly correlated with energy and the deviations from a uniform distribution grow with energy. We also solve for the energy distribution of freely cooling Maxwell Molecules and find qualitatively similar behavior.   

Breathing Phenomena in Driven, Confined, Granular Chains

We consider a tapered granular alignment where the spherical grains progressively shrink in radius by a factor $q$. The system has a hard wall at one end and a piston at the other. We assume that the piston can be used to impart a force $F$ (time- dependent or otherwise) to an edge grain in the system. Extensive particle dynamics simulations and theoretical analysis reveal that such a system could revert back and forth between an oversqueezed state and a dilated state - i.e., ``breathe." The breathing is strongly dependent on the driving. When driven with a constant force, we show that $TF^ {1/6}$ is a constant for fixed $q$. More complex dynamics including nonlinear-resonance is observed when $F=F(t)$. The talk shall discuss the observed dynamical responses of the system.   

Numerical Study of Particle Damping Mechanism in Piston Vibration System via Particle Dynamics Simulation

Mechanical damping systems with granular particles as the damping media have promising applications in extreme temperature conditions. In particle-based damping systems, the mechanical energy is dissipated through the inelastic collision and friction of particles. In the past, many experiments have been performed to investigate the particle damping problems. However, the detailed energy dissipation mechanism is still unclear due to the complex collision and flow behavior of dense particles. In this work, we use 3-D particle dynamics simulation to investigate the damping mechanism of an oscillating cylinder piston immerged in millimeter-size steel particles. The time evolution of the energy dissipation through the friction and inelastic collision is accurately monitored during the damping process. The contribution from the particle-particle interaction and particle-wall interaction is also separated for investigation. The effects of moisture, surface roughness, and density of particles are carefully investigated in the simulation. The comparison between the numerical simulation and experiment is also performed. The simulation results can help us understand the particle damping mechanism and design the new generation of particle damping devices.   

Breaking of granular jams with mechanical shocks

We studied the brief granular flows initiated by breaking the jamming in a hopper using mechanical shocks. Jamming near the orifice of a hopper prevents granular materials from flowing spontaneously under gravity. Controlled mechanical shocks were applied from the bottom of the hopper to break the jamming and to initiate brief flows. The magnitude and the duration of the flows were measured. Preliminary results show that the probability of initiating a flow increases with the intensity of the shock, and reaches almost 100{\%} at the highest shock intensities. We also investigated the flow probability as a function of the ratio between the diameters of the orifice and the bead. Statistical characteristics of the flow magnitude and duration evolve with shock intensity as well as the ratio between the diameters of the orifice and the bead. This research was supported by the NASA through grant NAG3-2384 and the NSF REU program through grant DMR 0305238.   

Spreading of a granular droplet

The influence of controlled vibrations on the granular rheology is investigated in a specifically designed experiment in which a granular film spreads under the action of horizontal vibrations. A nonlinear diffusion equation is derived theoretically that describes the evolution of the deposit shape. A self-similar parabolic shape (the``granular droplet'') and a spreading dynamics are predicted that both agree quantitatively with the experimental results. The theoretical analysis is used to extract effective friction coefficients between the base and the granular layer under sustained and controlled vibrations. A shear thickening regime characteristic of dense granular flows is evidenced at low vibration energy, both for glass beads and natural sand. Conversely, shear thinning is observed at high agitation.   

2D granular avalanches with imposed vibrations

We present work on a 2D free surface granular flow experiment under vertical vibration. The experiment consists of photoelastic grains in a 2D circular drum which is rotated at a constant rate (f $<$ 1 mHz). We measure time series of the slope, particle trajectories, and image the bulk force network. Avalanche and build-up distributions exhibit a power-law dependence as previously observed. We then vibrate the drum vertically to determine the effect of external vibrations on this ``unjamming'' transition. While larger vibrations destabilize the pile and decrease the maximum angle of repose, small vibrations lead to a strengthening of the pile and tend to increase the critical angle of failure. In the absence of vibration, when the drum is rotated opposite the direction of steady rotation, the critical angle of the first failure decreases slightly from the steady-state value due to the lack of an established steady-state force network.   

Bouncing trimer

Trimers are composed of three stainless steel beads (1 cm of diameter) forming a solid equilateral triangle (2.5 cm of side). They are placed on a plate of an electromagnetic shaker. The system is shaken vertically. According to the acceleration, the trimer may spin, jump once every two periods or even every threee periods. Between these stable regimes, the system is chaotic. By measuring the time delay between two successive shocks (bead-plate), a mapping of the different regimes has been constructed. The spinning, 2-period and 3-period orbits occurs for the same acceleration whatever the frequency. However, the spin speed has been measured with respect of the frequency.   

Dynamics of a single particle on a 2D driven granular lattice

Previous measurements have demonstrated interesting behavior in a novel bi-layer granular gas experiment of mechanically shaken particles. The results are of importance because the two layers are in ``thermal contact'' and yet have very different dynamical behaviors. The lower layer of particles demonstrates velocity statistics that are strongly correlated and non-Gaussian, while the upper layer of particles concurrently demonstrates a lack of correlations and Gaussian velocity statistics. Details of the collisions within each layer (intralayer) and between the layers (interlayer) are clearly of interest to understand the simultaneous behavior. Measurements are made for a single particle in the upper layer to examine the effects of interlayer collisions. In addition, velocity statistics in both layers are analyzed to determine effects of the sidewalls.   

Structure and dynamics of a vibrated granular bead-chain

We investigate the dynamics of a vibrated granular bead-chain with experiments and numerical simulations of random-walk models of polymers. Experiments are conducted with a chain composed of hollow 3~mm steel beads connected by flexible links confined to move on a 300~mm diameter rough circular bed. Observations made with digital imaging. We analyze the radius of gyration $R_g$, the structure factor of the chain configurations, and the diffusion of the center of mass. We find that $R_g$ and the structure factor scale with the exponent $\nu \sim 3/4$, consistent with the two dimensional self-avoiding random-walk model. Further, we observe confinement effects in the scaling of $R_g$ as the chain length increases relative to the size of the container. We perform simulations of non-self-avoiding walks confined to the same sized domain and find good agreement with experiment. The simulations show confinement effects dominate over self-avoided crossings in the experiments even when the length of chain is smaller than system size. We then experimentally examine the chain dynamics and find that the center of mass diffusion scales inversely as the length of the chain, consistent with the Rouse model of polymers. We observe an exponential decay in the the dynamical structure factor and compare this exponent with the measurement of the center of mass diffusion.