Segregation mechanisms in a numerical model of a binary granular mixture

Jammed disks of two sizes and weights in a channel: Alternating sequences

Disks of two sizes and weights in alternating sequence are confined to a long and narrow channel. The axis of the channel is horizontal and its plane vertical. The channel is closed off by pistons that freeze jammed microstates out of loose disk configurations subject to moderate pressure, gravity, and random agitations. Disk sizes and channel width are such that under jamming no disk remains loose and all disks touch one wall. We present exact results for the characterization of jammed macrostates including volume and entropy. The rigorous analysis divides the disk sequences of jammed microstates into overlapping tiles from which we construct a small number of species of statistically interacting particles. Jammed macrostates depend on dimensionless control parameters inferred from ratios between measures of expansion work against the pistons, gravitational potential energy, and intensity of random agitations. These control parameters enter the configurational statistics via the activation energies prior to jamming of the particles. The range of disk weights naturally divides into regimes where qualitatively different features come into play. We sketch a path toward generalizations that include random sequences under a modified jamming protocol.

Demixing of active particles in the presence of external fields

Self-propelled active particles are inherently out of equilibrium as they collect energy from their surroundings and transform it into directed motion. A recent theoretical study suggests that binary mixtures of active particles with distinct effective diffusion coefficients exhibit dynamical demixing when their diffusion coefficients differ by more than one order of magnitude. Here, we show that this difference may be reduced drastically in the presence of external fields even when the response to the field is the same for both species. We investigate this demixing as a function of the ratio of the diffusion coefficients and discuss the implications of the results for active systems.

Exploiting non-equilibrium phase separation for self-assembly

Demixing can occur in systems of two or more particle species that experience different driving forces, e.g., mixtures of self-propelled active particles or of oppositely charged colloids subject to an electric field. Here we show with macroscopic experiments and computer simulations that the forces underlying such non-equilibrium segregation can be used to control the self-assembly of particles that lack attractive interactions. We demonstrate that, depending on the direction, amplitude and frequency of a periodic external force acting on one particle species, the structures formed by a second, undriven species can range from compact clusters to elongated, string-like patterns.

(Ir)reversibility in dense granular systems driven by oscillating forces

We use computer simulations to study highly dense systems of granular particles that are driven by oscillating forces. We implement different dissipation mechanisms that are used to extract the injected energy. In particular, the action of a simple local Stokes' drag is compared with non-linear and history-dependent frictional forces that act either between particle pairs or between particles and an external container wall. The Stokes' drag leads to particle motion that is periodic with the driving force, even at high densities around close packing where particles undergo frequent collisions. With the introduction of inter-particle frictional forces this "interacting absorbing state" is destroyed and particles start to diffuse around. By reducing the density of the material we go through another transition to a "non-interacting" absorbing state, where particles independently follow the force-induced oscillations without collisions. In the system with particle-wall frictional interactions this transition has signs of a discontinuous phase transition. It is accompanied by a diverging relaxation time, but not by a vanishing order parameter, which rather jumps to zero at the transition.

The timescales of granular segregation in horizontally shaken monolayers

The results of an experimental investigation of segregation phenomenon in thin layers of a binary multi-particle system on a horizontal vibrating tray are discussed. Complex structures are observed to emerge from initially mixed states and result from interaction of individual particles. Qualitatively different segregation states are found which have disparate timescales and these are shown to have a systematic dependence on the control parameters.

The nature of the laning transition in two dimensions

If a binary colloidal mixture is oppositely driven by an external field, a transition towards a laned state occurs at sufficiently large drives, where particles driven alike form elongated structures ('lanes') characterized by a large correlation length ξ along the drive. Here we perform extensive Brownian dynamics computer simulations on a two-dimensional equimolar binary Yukawa system driven by a constant force that acts oppositely on the two species. We systematically address finite-size effects on lane formation by exploring large systems up to 262,144 particles under various boundary conditions. It is found that the correlation length ξ along the field depends exponentially on the driving force (or Peclet number). Conversely, in a finite system, ξ reaches a fraction of the system size at a driving force which is logarithmic in the system size, implying massive finite-size corrections. For a fixed finite drive, ξ does not diverge in the thermodynamic limit. Therefore, though laning has a signature as a sharp transition in a finite system, it is a smooth crossover in the thermodynamic limit.

Microscopic theory for anisotropic pair correlations in driven binary mixtures

A self-consistent microscopic approach to calculate non-equilibrium pair correlations in strongly interacting driven binary mixtures is presented. The theory is derived from the many-body Smoluchowski equation for interacting Brownian particles by employing Kirkwood's superposition approximation as a closure relation. It is shown that the pair correlations can exhibit notable anisotropy and a strong tendency to laning in the driving direction. Furthermore, there are strong indications that pair correlations are characterized by a long-range decay along the drive. The theoretical results are in good quantitative agreement with the complementary Brownian dynamics computer simulations.

Segregation-pattern reorientation of a granular mixture on a horizontally oscillating tray

Reorientation of the segregation pattern of a binary granular mixture on a two-dimensional horizontally oscillating tray is numerically realized. The mixture consists of large and heavy particles and small and light particles, and the segregation pattern shows a transition between a striped pattern perpendicular to the oscillation and one parallel to the oscillating direction according to the change of area fractions of the two types of particle. The transition mechanism is discussed on the basis of a simplified one-dimensional dynamics.

Self-organized patterns in collections of chains

Results are presented of an experimental investigation into patterned segregation in thin layers of poppy seeds and short lengths of metal chains subjected to vibration. Critical phenomena are uncovered and both continuous and discontinuous transitions are observed. A phase diagram for the behavior is mapped out and a tricritical point that separates hysteretic from continuous segregation is identified. Remarkable similarities are found between the observed behavior in this driven granular system and phase separation phenomena in mixtures where the dynamics of the constituent components are markedly different.

Influence of hydrodynamic interactions on lane formation in oppositely charged driven colloids

The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are considered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic interactions strongly disfavor laning. In the steady state of lanes, a macroscopic phase separation of lanes is observed. This is in marked contrast to the simple Brownian case where a finite size of lanes was obtained in the steady state. For strong Coulomb interactions between the colloidal particles a lateral square lattice of oppositely driven lanes is stable similar to the simple Brownian dynamics. In an electric field, on the other hand, the behavior is found in qualitative and quantitative accordance with the case of neglected hydrodynamics.

Segregation in a noninteracting binary mixture

Process of stripe formation is analyzed numerically in a binary mixture. The system consists of particles of two sizes, without any direct mutual interactions. Overlapping of large particles, surrounded by a dense system of small particles, induces indirect entropy driven interactions between large particles. Under an influence of an external driving force the system orders and stripes are formed. Mean width of stripes grows logarithmically with time, in contrast to a typical power law temporal increase observed for driven interacting lattice gas systems. We describe the mechanism responsible for this behavior and attribute the logarithmic growth to a random walk of large particles in a random potential created by the site blocking due to the small ones.

Depletion force in a bidisperse granular layer

We demonstrate the effect of the depletion force in experiments and simulations of vertically vibrated mixtures of large and small steel spheres. The system exhibits size segregation and a large increase in the pair correlation function of the large spheres for short distances that can be accurately described using a combination of the depletion potential derived for equilibrium colloidal systems and a Boltzmann factor. The Boltzmann factor defines an effective temperature for the system, which we compare to other measures of temperature.

Lane formation in oppositely charged colloids driven by an electric field: chaining and two-dimensional crystallization

A binary mixture of oppositely charged colloids which is driven by an external electric field is studied by extensive Brownian dynamics computer simulations, ignoring hydrodynamic interactions. The particle interaction is modeled via a screened Coulomb potential together with a steric repulsion. A strong electric field leads to lane formation of oppositely driven lanes. Each lane comprises particles of the same charge. A nonequilibrium "phase diagram" classifying different steady states is obtained as a function of the colloidal volume fraction and the Coulomb coupling. Different steady states are characterized by structural correlations perpendicular and parallel to the applied field. We find a variety of different phases involving lane chains at small volume fraction and low screening, and lanes with two-dimensional crystalline order perpendicular to the field at high volume fraction. The lateral crystalline order can be a square, triangular, or rhombic lattice. In between there is a lateral network structure. These predictions can be verified in real-space experiments on oppositely charged colloids.

Phenomenology and theory of horizontally oscillated granular mixtures

We overview the physics of a granular mixture subject to horizontal oscillations, recently investigated via experiments and molecular dynamics simulations. First we discuss the rich phenomenology exhibited by this system, which encompasses both segregation and dynamical instabilities. Then we show that the phenomenology can be explained via an effective interaction approach, by which the driven, non-thermal, granular mixture in mapped into a monodispersed thermal system of particles interacting via an effective potential. After determining the effective interaction we discuss its microscopic origin and investigate how it induces the observed phenomenology. Finally, as much as in thermal fluids, from the effective interaction we derive a Cahn-Hilliard dynamics equation, which appears to capture the essential characteristics of the dynamics of the granular mixture.

Phases of granular segregation in a binary mixture

We present results from an extensive experimental investigation into granular segregation of a shallow binary mixture in which particles are driven by frictional interactions with the surface of a vibrating horizontal tray. Three distinct phases of the mixture are established viz. binary gas (unsegregated), segregation liquid, and segregation crystal. Their ranges of existence are mapped out as a function of the system's primary control parameters using a number of measures based on Voronoi tessellation. We study the associated transitions and show that segregation can be suppressed as the total filling fraction of the granular layer, C, is decreased below a critical value, Cc, or if the dimensionless acceleration of the driving, gamma, is increased above a value gammac.

Dynamically induced effective interaction in periodically driven granular mixtures

We show that a granular mixture subject to horizontal oscillations can be reduced to a monodisperse system of particles interacting via an effective interaction. This interaction is attractive at short distances and strongly anisotropic, and its features explain the system rich phenomenology, including segregation and stripe pattern formation. Finally, we show that a modified Cahn-Hilliard equation, which takes into account the characteristics of the effective interaction, is capable of describing the dynamics of the mixture.

Shear instabilities in granular mixtures

Dynamical instabilities in fluid mechanics are responsible for a variety of important common phenomena, such as waves on the sea surface or Taylor vortices in Couette flow. In granular media dynamical instabilities have just begun to be discovered. Here we show by means of molecular dynamics simulation the existence of a new dynamical instability of a granular mixture under oscillating horizontal shear, which leads to the formation of a striped pattern where the components are segregated. We investigate the properties of such a Kelvin-Helmholtz-like instability and show how it is connected to pattern formation in granular flow and segregation.