Dynamics of electrostatically driven granular media: effects of humidity

Anomalous flocking in nonpolar granular Brownian vibrators

Using Brownian vibrators, we investigated the structures and dynamics of quasi-2d granular materials, with packing fractions (ϕ) ranging from 0.111 to 0.832. Our observations revealed a remarkable large-scale flocking behavior in hard granular disk systems, encompassing four distinct phases: granular fluid, flocking fluid, poly-crystal, and crystal. Anomalous flocking emerges at ϕ = 0.317, coinciding with a peak in local density fluctuations, and ceased at ϕ = 0.713 as the system transitioned into a poly-crystal state. The poly-crystal and crystal phases resembled equilibrium hard disks, while the granular and flocking fluids differed significantly from equilibrium systems and previous experiments involving uniformly driven spheres. This disparity suggests that collective motion arises from a competition controlled by volume fraction, involving an active force and an effective attractive interaction resulting from inelastic particle collisions. Remarkably, these findings align with recent theoretical research on the flocking motion of spherical active particles without alignment mechanisms.

Cohesion-controlled granular material

We present a simple method to prepare a granular material with a controlled cohesion between particles. The granular material is made of spherical glass beads coated with a polyborosiloxane polymer. This material is proved to be stable in time and nonsensitive to temperature and humidity. The interparticle force is measured and related to the size of the grain and the polymer coating thickness. Classical measurements (packing fraction, repose angle, macroscopic cohesion) are performed with this cohesion-controlled granular material. This model material opens many perspectives to study in a controlled manner the flow of cohesive grains.

Double origin of stochastic granular tribocharging

The mechanisms underlying triboelectric charging have a stochastic nature. We investigate how this randomness affects the distributions of charges generated on granular particles during either a single or many collisions. The charge distributions we find in our experiments are more heavy-tailed than normal distributions with an exponential decay of the probability, they are asymmetric, and exhibit charges of both signs. Moreover, we find a linear correlation between the width and mean of these distributions. We rationalize these findings with a model for triboelectric charging which combines stochastic charge separation during contact and stochastic charge recombination after separation of the surfaces. Our results further imply that subsequent charging events are not statistically independent.

Influence of humidity on tribo-electric charging and segregation in shaken granular media

We study the effect of humidity on the charge accumulation of polymer granulates shaken vertically in a stainless steel container. This setup allows us to control the humidity level from 5% to 100%RH while performing automated charge measurements in a Faraday cup directly connected to the shaking container. We find that samples of approximately 2000 polymer spheres become highly charged at low humidity levels (<30%RH), but acquire almost no charge for humidity levels above 80%RH. The transition between these two regimes does depend on the material, as does the sign of the charge. For the latter we find a correlation with the contact angle of the polymer with only very hydrophilic particles attaining positive charges. We show that this humidity dependence of tribo-charging can be used to control segregation in shaken binary mixtures.

Antiphase synchronization of electrically shaken conducting beads

When a spherical conducting bead is placed in an electrode, it experiences an electric force. In a plane capacitor, it can undergo a periodic bouncing between the electrodes. Using a fast video camera, we measured the acceleration of the bead and the period of its motion as a function of the applied voltage. A mathematical model based on the hypothesis of electrostatic equilibrium is proposed to describe the dynamics of the system. We observe a stabilization of the trajectories: A bead bouncing between two electrodes tends to oscillate on a quasivertical trajectory, whatever its initial horizontal velocity. When two identical beads are placed together in a capacitor, they oscillate at the same frequency and an antiphase synchronization effect occurs. We propose a simple mechanism based on a Kuramoto-like model to explain it.

Brownian motion of a self-propelled particle

Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the 'active' particle is driven along its internal orientation axis. We calculate the first four moments of the probability distribution function for displacements as a function of time for a spherical particle with isotropic translational diffusion, as well as for an anisotropic ellipsoidal particle. In both cases the translational and rotational motion is either unconfined or confined to one or two dimensions. A significant non-Gaussian behaviour at finite times t is signalled by a non-vanishing kurtosis γ(t). To delimit the super-diffusive regime, which occurs at intermediate times, two timescales are identified. For certain model situations a characteristic t(3) behaviour of the mean-square displacement is observed. Comparing the dynamics of real and artificial microswimmers, like bacteria or catalytically driven Janus particles, to our analytical expressions reveals whether their motion is Brownian or not.

Effect of an electric field on an intermittent granular flow

Granular gravity driven flows of glass beads have been observed in a silo with a flat bottom. A dc high electric field has been applied perpendicularly to the silo to tune the cohesion. The outlet mass flow has been measured. An image subtraction technique has been applied to visualize the flow geometry and a spatiotemporal analysis of the flow dynamics has been performed. The outlet mass flow is independent of voltage, but a transition from funnel flow to rathole flow is observed. This transition is of probabilistic nature and an intermediate situation exists between the funnel and the rathole situations. At a given voltage, two kinds of flow dynamics can occur: a continuous flow or an intermittent flow. The electric field increases the probability to observe an intermittent flow.

Far-from-equilibrium Ostwald ripening in electrostatically driven granular powders

We report an experimental study of cluster size distributions in electrostatically driven granular submonolayers. The cluster size distribution in this far-from-equilibrium process exhibits dynamic scaling behavior characteristic of the (nearly equilibrium) Ostwald ripening, controlled by the attachment and detachment of the "gas" particles. The scaled size distribution, however, is different from the classical Wagner distribution obtained in the limit of a vanishingly small area fraction of the clusters. A much better agreement is found with the theory of Phys. Rev. E 65, 046117 (2002)] which accounts for the cluster merger.

Coarsening of granular clusters: Two types of scaling behaviors

We report on an experimental study of small cluster dynamics during the coarsening process in driven granular submonolayers of 120-microm bronze particles. The techniques of electrostatic and vertical mechanical vibration were employed to excite the granular gas. We measure the scaling exponent for the evaporation of small clusters during coarsening. It was found that the surface area of small clusters S vs time t behaves as S to (t(0)-t)(2/3) for lower frequencies and S to (t(0)-t) for higher frequencies. We argue that the change in the scaling exponent is related to the transition from three-dimensional (3D) to 2D character of motion in the granular gas.

Velocity fluctuations in electrostatically driven granular media

We study experimentally the particle velocity fluctuations in an electrostatically driven dilute granular gas. The velocity distributions have strong deviations from a Maxwellian form over a wide range of parameters. We have found that the tails of the distribution functions are consistent with a stretched exponential law with typical exponents of the order 3/2. Molecular dynamic simulations shows qualitative agreement with experimental data. Our results suggest that this non-Gaussian behavior is typical of most inelastic gases with both short- and long-range interactions.

Phase separation and coarsening in electrostatically driven granular media

A continuum model for the phase separation and coarsening in electrostatically driven granular media is formulated in terms of a Ginzburg-Landau equation subject to conservation of the total number of grains. In the regime of well-developed clusters, the continuum model is used to derive "sharp-interface" equations that govern the dynamics of the interphase boundary. The model captures the essential physics of this system.