Torque about electrostatically charged spheres makes them more attractive.

The strength of interparticle interactions in a granular system controls how a collection of insulating particles flow, cohere and fragment. Forces due to electrostatic charging, particularly in free-fall or low gravity environments, can dominate the static and dynamic interactions with important implications for understanding natural and industrial processes. Here we show that shaking of homogeneous, spherical particles can result in a non-uniform surface charge distribution. The measured dipole moment and torque for each particle are found to be strongly correlated. However, our model shows that to predict the torque and force requires one to consider the full surface charge distribution. This overlooked torque is not only significant, but would amplify attractive interactions through particle reorientation.

Collective behavior of composite active particles.

We describe simulations of active Brownian particles carried out to explore how dynamics and clustering are influenced by particle shape. Our particles are composed of four disks, held together by springs, whose relative size can be varied. These composite objects can be tuned smoothly from having a predominantly concave to a convex surface. We show that even two of these composite particles can exhibit collective motion which modifies the effective Peclet number. We then investigate how particle geometry can be used to explain the phase behavior of many such particles.

Reduced Thermodynamic Description of Phase Separation in a Quasi-One-Dimensional Granular Gas.

We describe simulations of a quasi-one-dimensional, vibrated granular gas which exhibits an apparent phase separation into a liquidlike phase and a gaslike phase. In thermal equilibrium, such a phase separation in one dimension is prohibited by entropic considerations. We propose that the granular gas minimizes a function of the conserved mechanical variables alone: the particle number and volume. Simulations in small cells can be used to extract the equation of state and predict the coexisting pressure and densities, as confirmation of the minimization principle. Fluctuations in the system manifest themselves as persistent density waves but they do not destroy the phase-separated state.

The minimization of mechanical work in vibrated granular matter.

Experiments and computer simulations are carried out to investigate phase separation in a granular gas under vibration. The densities of the dilute and the dense phase are found to follow a lever rule and obey an equation of state. Here we show that the Maxwell equal-areas construction predicts the coexisting pressure and binodal densities remarkably well, even though the system is far from thermal equilibrium. This construction can be linked to the minimization of mechanical work associated with density fluctuations without invoking any concept related to equilibrium-like free energies.

Propulsion of a Two-Sphere Swimmer.

We describe experiments and simulations demonstrating the propulsion of a neutrally buoyant swimmer that consists of a pair of spheres attached by a spring, immersed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There appears to be a critical onset value of the streaming Reynolds number for swimming to occur. We observe a change in the streaming flows as the Reynolds number increases, from that generated by two independent oscillating spheres to a collective flow pattern around the swimmer as a whole. The mechanism for swimming is traced to a strengthening of a jet of fluid in the wake of the swimmer.

Spontaneous orbiting of two spheres levitated in a vibrated liquid.

In the absence of gravity, particles can form a suspension in a liquid irrespective of the difference in density between the solid and the liquid. If such a suspension is subjected to vibration, there is relative motion between the particles and the fluid which can lead to self-organization and pattern formation. Here, we describe experiments carried out to investigate the behavior of two identical spheres suspended magnetically in a fluid, mimicking weightless conditions. Under vibration, the spheres mutually attract and, for sufficiently large vibration amplitudes, the spheres are observed to spontaneously orbit each other. The collapse of the experimental data onto a single curve indicates that the instability occurs at a critical value of the streaming Reynolds number. Simulations reproduce the observed behavior qualitatively and quantitatively, and are used to identify the features of the flow that are responsible for this instability.

Emergent surface tension in vibrated, noncohesive granular media.

We describe experiments and simulations carried out to investigate spinodal decomposition in a vibrated, dry granular system. The dynamics is found to be similar to that of systems evolving under curvature-driven diffusion, which suggests the presence of an effective surface tension. By studying quasi-2D droplets in the steady state, we find behavior consistent with Laplace's equation, demonstrating the existence of an actual surface tension. Detailed measurements of the pressure tensor in the interfacial region show that the surface tension results predominantly from an anisotropy in the kinetic energy part of the pressure tensor, in contrast to thermodynamic systems where it arises from either the attractive interaction between particles or entropic considerations.

Liquid-gas phase separation in confined vibrated dry granular matter.

A new phase transition is observed experimentally in a dry granular gas subject to vertical vibration between two horizontal plates. Molecular dynamics simulations of this system allow us to investigate the observed phase separation in detail. We find a high-density, low temperature liquid, coexisting with a low-density, high temperature gas moving coherently. The importance of the coherent motion for phase separation is investigated using frequency modulation.

Partition instability in water-immersed granular systems.

It is well known that a system of grains, vibrated vertically in a cell divided into linked columns, may spontaneously move into just one of the columns due to the inelastic nature of their collisions. Here we study the behavior of a water-immersed system of spherical barium titanate particles in a rectangular cell which is divided into two columns, linked by two connecting holes, one at the top and one at the bottom of the cell. Under vibration the grains spontaneously move into just one of the columns via a gradual transfer of grains through the connecting hole at the base of the cell. We have developed numerical simulations that are able to reproduce this behavior and provide detailed information on the instability mechanism. We use this knowledge to propose a simple analytical model for this fluid-driven partition instability based on two coupled granular beds vibrated within an incompressible fluid.

Chain formation of spheres in oscillatory fluid flows.

A collection of spherical particles subjected to horizontal oscillatory fluid flow is known to form chains perpendicular to the direction of the oscillation. We have developed computer simulations to model such a system and have validated them against experiments carried out in a small fluid-filled cell. In both experiment and simulation we find that the particles go through the same stages of evolution from a dispersed initial configuration to an ordered chain structure. We then use our computer simulations to investigate in detail the interactions responsible for chain formation and the interaction between fully formed chains.

Influence of magnetic cohesion on the stability of granular slopes.

We use a molecular dynamics model to simulate the formation and evolution of a granular pile in two dimensions in order to gain a better understanding of the role of magnetic interactions in avalanche dynamics. We find that the angle of repose increases only slowly with magnetic field; the increase in angle is small even for intergrain cohesive forces many times stronger than gravity. The magnetic forces within the bulk of the pile partially cancel as a result of the anisotropic nature of the dipole-dipole interaction between grains. However, we show that this cancellation effect is not sufficiently strong to explain the discrepancy between the angle of repose in wet systems and magnetically cohesive systems. In our simulations we observe shearing deep within the pile, and we argue that it is this motion that prevents the angle of repose from increasing dramatically. We also investigate different implementations of friction with the front and back walls of the container, and conclude that the nature of the friction dramatically affects the influence of magnetic cohesion on the angle of repose.

Migration of an asymmetric dimer in oscillatory fluid flow.

We describe the motion of an asymmetric dimer across a horizontal surface when exposed to an oscillatory fluid flow. The dimer consists of two spheres of distinct sizes, rigidly attached to each other. The dimer is found to move in a direction perpendicular to the fluid flow, with the smaller sphere foremost. We have determined how the speed depends upon the vibratory conditions, on the fluid viscosity, and on the dimer size and aspect ratio. Computer simulations are used to give an insight into the mechanism responsible for the motion. We use a scaling argument based on the asymmetry of the streaming flow to predict the approximate dependence of the migration speed on the system parameters.

Interaction between intruders in vibrated granular beds.

Two neutrally buoyant intruder particles in a granular bed fluidized by vertical, sinusoidal vibration are known to interact with each other over a range of about five intruder diameters. Using molecular dynamics simulations, we investigate in detail the spatial and temporal nature of this interaction. We show that the force of attraction between intruders can be calculated from the local density and kinetic energy using a simple equation of state. Moreover, the interaction can be changed from attractive to repulsive by reducing the coefficient of restitution between the intruders and host particles, one of the key results of this work.

Magneto-vibratory separation of glass and bronze granular mixtures immersed in a paramagnetic liquid.

A fluid-immersed granular mixture may spontaneously separate when subjected to vertical vibration, separation occurring when the ratio of particle inertia to fluid drag is sufficiently different between the component species of the mixture. Here, we describe how fluid-driven separation is influenced by magneto-Archimedes buoyancy, the additional buoyancy force experienced by a body immersed in a paramagnetic fluid when a strong inhomogeneous magnetic field is applied. In our experiments glass and bronze mixtures immersed in paramagnetic aqueous solutions of MnCl2 have been subjected to sinusoidal vertical vibration. In the absence of a magnetic field the separation is similar to that observed when the interstitial fluid is water. However, at modest applied magnetic fields, magneto-Archimedes buoyancy may balance the inertia/fluid-drag separation mechanism, or it may dominate the separation process. We identify the vibratory and magnetic conditions for four granular configurations, each having distinctive granular convection. Abrupt transitions between these states occur at well-defined values of the magnetic and vibrational parameters. In order to gain insight into the dynamics of the separation process we use computer simulations based on solutions of the Navier-Stokes' equations. The simulations reproduce the experimental results revealing the important role of convection and gap formation in the stability of the different states.

Intruder clustering in three-dimensional granular beds.

We present results of computer simulations for neutrally buoyant intruders in a vertically vibrated three-dimensional granular bed of smaller host particles. Under sinusoidal excitation, pairs of intruders interact over a distance of several intruder diameters; a group of intruders forms a cluster. The strength of the interaction grows as the number of intruders is increased. We show that the tendency to cluster may be manipulated through the use of nonsinusoidal excitation, which allows partial mixing. Finally, we investigate the effects of walls on the clustering of intruders.

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.

Interaction of spheres in oscillatory fluid flows.

Rigid spherical particles in oscillating fluid flows form interesting structures as a result of fluid mediated interactions. Here we show that spheres under horizontal vibration align themselves at right angles to the oscillation and sit with a gap between them. The details of this behavior have been investigated through experiments and simulations. We have carried out experiments in which a pair of stainless steel spheres is shaken horizontally in a cell filled with glycerol-water fluid mixtures of three different viscosities, at various frequencies and amplitudes of oscillation. There is an equilibrium gap between the particles resulting from a long-range attraction and a short-range repulsion. The size of the gap was found to depend on the fluid viscosity and the vibratory parameters, and we have identified two distinct scaling regimes for the dependence of the gap on the system parameters. Using a Navier-Stokes solver the same system was simulated. The interaction force between the spheres was measured and the streaming flows induced by the motion were determined.

Stochastic dynamics of a rod bouncing upon a vibrating surface.

We describe the behavior of a rod bouncing upon a horizontal surface which is undergoing sinusoidal vertical vibration. The predictions of computer simulations are compared with experiments in which a stainless-steel rod bounces upon a metal-coated glass surface. We find that, as the dimensionless acceleration parameter Gamma is increased appreciably above unity, the motion of a long rod passes from periodic or near-periodic motion into stochastic dynamics. Within this stochastic regime the statistics of the times between impacts follow distributions with tails of approximately Gaussian form while the probability distributions of the angles at impact have tails that are close to exponential. We determine the dependence of each distribution upon the length of the rod, upon frequency, and on Gamma. The statistics of the total energy and of the translational and rotational components each approximately follow a Boltzmann distribution in their tails, the translational and rotational energy components being strongly correlated. The time-averaged mean vertical translational energy is significantly larger than the mean rotational energy, and both are considerably larger than the energy associated with horizontal motion.

Traveling waves in a water-immersed binary granular system vibrated within an annular cell.

It has been known since the time of Faraday that vertically vibrated fine grains may spontaneously form piles through their interaction with a fluid. More recently, it has been observed that a fine binary mixture may separate under vertical vibration through the differential influence of the fluid on the two granular components. Here, we report a detailed study of a system of water-immersed bronze and glass grains held between two coaxial cylinders. Under vertical vibration, the bronze separates to form a layer above the glass, which itself breaks symmetry to form a pile. Symmetry is broken a second time by the bronze forming layers of different thicknesses upon the two slopes of the glass pile. The pile then travels as a wave with the thicker bronze layer upon its leading surface. We examine the conditions for these traveling waves and determine how their speed varies with particle size, frequency, and amplitude of vibration. A model is developed which provides a semiquantitative account of the wave motion.

Separation of binary granular mixtures under vibration and differential magnetic levitation force.

The application of both a strong magnetic field and a magnetic field gradient to a diamagnetic or paramagnetic material can produce a vertical force that acts in concert with the force of gravity. We consider a binary granular mixture in which the two components have different magnetic susceptibilities and therefore experience different effective forces of gravity when subjected to an inhomogeneous magnetic field. Under vertical vibration, such a mixture may rapidly separate into regions almost pure in the two components. We investigate the conditions for this behavior, studying the speed and completeness of separation as a function of differential effective gravity and the frequency and amplitude of vibration. The influence of the cohesive magnetic dipole-dipole interactions on the separation process is also investigated. In our studies insight is gained through the use of a molecular dynamics simulation model.