Theory for size segregation in flowing granular mixtures based on computation of forces on a single large particle.

We measure the upward force acting on a single, unconstrained, large particle in a granular medium of small particles flowing over inclined plane using discrete element method (DEM) simulation. Based on the computed force, we obtain an expression for the flux of large particles in a binary mixture of large and small particles and predict the equilibrium concentration profile and the velocity profile of the flowing layer. The theoretical predictions are in very good agreement with the DEM simulation results for a wide range of concentrations of large particles and inclination angles.

Global organization of three-dimensional, volume-preserving flows: Constraints, degenerate points, and Lagrangian structure.

Global organization of three-dimensional (3D) Lagrangian chaotic transport is difficult to infer without extensive computation. For 3D time-periodic flows with one invariant, we show how constraints on deformation that arise from volume-preservation and periodic lines result in resonant degenerate points that periodically have zero net deformation. These points organize all Lagrangian transport in such flows through coordination of lower-order and higher-order periodic lines and prefigure unique transport structures that arise after perturbation and breaking of the invariant.

Theoretical calculation of the buoyancy force on a particle in flowing granular mixtures.

Simulations and experiments of granular mixtures comprising two different sizes flowing over an inclined plane under the influence of gravity show segregation, where large particles rise to the free surface. The segregation results from differential forces acting on the particles. The buoyancy force experienced by the particles is an important component of the total force acting on the particles and, in this work, we theoretically calculate the buoyant force on intruder particles of different sizes in a flowing granular medium.

Breakage of vesicles in a simple shear flow.

The breakage of micron-size SOPC lipid vesicles in an aqueous suspension was studied in a simple shear flow over a range of shear rates (1000 s-1 to 4000 s-1). Evolution of the vesicle size distribution with time was determined using optical microscopy. The number average vesicle diameter was found to reduce continuously with time; at the highest shear rate (4000 s-1), the reduction was 38% after 6 h of shearing.

Anomalous toluene transport in model segmented polyurethane-urea/clay nanocomposites.

The kinetics of liquid solvent sorption in polymeric systems and their nanocomposites often deviate from normal Fickian behaviour. This needs to be understood and interpreted, in terms of their underlying mechanistic origins. In the present study, the results of time dependent toluene sorption measurements in model segmented polyurethane-urea/clay nanocomposites have been analysed at room temperature.

Sidewall-friction-driven ordering transition in granular channel flows: Implications for granular rheology.

We report a transition from a disordered state to an ordered state in the flow of nearly monodisperse granular matter flowing in an inclined channel with planar slide walls and a bumpy base, using discrete element method simulations. For low particle-sidewall friction coefficients, the flowing particles are disordered, however, for high sidewall friction, an ordered state is obtained, characterized by a layering of the particles and hexagonal packing of the particles in each layer. The extent of ordering, quantified by the local bond-orientational order parameter, varies in the cross section of the channel, with the highest ordering near the sidewalls.

Characterizing the nanoclay induced constrained amorphous region in model segmented polyurethane-urea/clay nanocomposites and its implications on gas barrier properties.

There has been an increasing recognition of the fact that purely geometric factors associated with clay platelet dispersion in a polymer matrix cannot adequately explain the barrier properties of polymer/clay nanocomposites. The objective of the present work is to understand the nanoclay induced structural changes in a polyurethane-urea matrix and clay dispersion at different length scales using segment-specific characterization techniques and implications of the same in gas barrier properties using He, N2 and CO2 as probe molecules. Wide angle X-ray diffraction (WAXD) and positron annihilation life time spectroscopy (PALS) studies revealed nanoclay induced alterations in the chain packing of the amorphous soft segments of the polyurethane matrix at a molecular scale of a few Angstroms.

Field induced gradient simulations: a high throughput method for computing chemical potentials in multicomponent systems.

We present a simulation method for direct computation of chemical potentials in multicomponent systems. The method involves application of a field to generate spatial gradients in the species number densities at equilibrium, from which the chemical potential of each species is theoretically estimated. A single simulation yields results over a range of thermodynamic states, as in high throughput experiments, and the method remains computationally efficient even at high number densities since it does not involve particle insertion at high densities.

Numerical simulation of the sedimentation of a sphere in a sheared granular fluid: a granular Stokes experiment.

We study, computationally, the sedimentation of a sphere of higher mass in a steady, gravity-driven granular flow of otherwise identical spheres, on a rough inclined plane. Taking a hydrodynamic approach at the scale of the particle, we find the drag force to be given by a modified Stokes law and the buoyancy force by the Archimedes principle, with excluded volume effects taken into account. We also find significant differences between the hydrodynamic case and the granular case, which are highlighted.

Gradient Monte Carlo simulations: hard spheres in spatially varying temperature and gravitational fields.

There are many physical situations where particles experience external fields or are in a nonisothermal environment. Monte Carlo (MC) simulations can be useful to understand such experimental systems at steady state. Within this context, we formulate a general framework to study these systems via inhomogeneous MC simulations incorporating spatially varying temperature and gravitational fields.

Steady flow of smooth, inelastic particles on a bumpy inclined plane: hard and soft particle simulations.

We study smooth, slightly inelastic particles flowing under gravity on a bumpy inclined plane using event-driven and discrete-element simulations. Shallow layers (ten particle diameters) are used to enable simulation using the event-driven method within reasonable computational times. Steady flows are obtained in a narrow range of angles (13 degrees-14.

Granular flow in rotating cylinders with noncircular cross sections.

An experimental and theoretical study is carried out of the flow of granular material in cylinders with different cross-sectional shapes rotated about their axes. The flow of particles in such geometries is confined to a shallow layer at the free surface. The length and thickness of the layer shrink and expand periodically with rotation of the cylinder, resulting in chaotic advection and improved mixing of passive tracers.

Solid-fluid transition in a granular shear flow.

The rheology of a granular shear flow is studied in a quasi-2D rotating cylinder. Measurements are carried out near the midpoint along the length of the surface flowing layer where the flow is steady and nonaccelerating. Streakline photography and image analysis are used to obtain particle velocities and positions.

Sensitivity of granular segregation of mixtures in quasi-two-dimensional fluidized layers.

Size segregation is studied using a quasi-two-dimensional rotating cylinder system for mixtures of different size, near-spherical particles. Flow occurs only in a thin surface layer, whereas the remaining particles rotate as a fixed bed. In most of the systems studied, the measured radial weight fraction profiles in the bed show significant double segregation (a core of small particles as well as a thin layer of small particles at the periphery).

Mixing and segregation of granular materials in chute flows.

Mixing of granular solids is invariably accompanied by segregation, however, the fundamentals of the process are not well understood. We analyze density and size segregation in a chute flow of cohesionless spherical particles by means of computations and theory based on the transport equations for a mixture of nearly elastic particles. Computations for elastic particles (Monte Carlo simulations), nearly elastic particles, and inelastic, frictional particles (particle dynamics simulations) are carried out.

Chaotic mixing of granular materials in two-dimensional tumbling mixers.

We consider the mixing of similar, cohesionless granular materials in quasi-two-dimensional rotating containers by means of theory and experiment. A mathematical model is presented for the flow in containers of arbitrary shape but which are symmetric with respect to rotation by 180 degrees and half-filled with solids. The flow comprises a thin cascading layer at the flat free surface, and a fixed bed which rotates as a solid body.

Open problems in active chaotic flows: Competition between chaos and order in granular materials.

There are many systems where interaction among the elementary building blocks-no matter how well understood-does not even give a glimpse of the behavior of the global system itself. Characteristic for these systems is the ability to display structure without any external organizing principle being applied. They self-organize as a consequence of synthesis and collective phenomena and the behavior cannot be understood in terms of the systems' constitutive elements alone.

Scaling relations for granular flow in quasi-two-dimensional rotating cylinders.

An experimental study of the flow of different materials (steel balls, glass beads, and sand) in quasi-two-dimensional rotating cylinders is carried out using flow visualization. The flow in the rotating cylinder comprises of a thin-flowing surface layer with the remaining particles rotating as a fixed bed. Experimental results indicate that the scaled layer thickness increases with increasing Froude number (Fr=omega(2)R/g, where omega is the angular speed, R is the cylinder radius, and g the acceleration due to gravity) and with increase in size ratio (s=d/R, where d is the particle diameter).

Self-organization in granular slurries.

We report the existence of self-organization in wet granular media or slurries, mixtures of particles of different sizes dispersed in a lower density liquid. As in the case of dry granular mixtures, axial banding (alternating bands rich in small and large particles in a long rotating cylinder) and radial segregation (in quasi-2D containers) are observed in slurries. However, when compared with the dry counterpart axial segregation is significantly faster and the spectrum of outcomes is richer.

Segregation-driven organization in chaotic granular flows.

An important industrial problem that provides fascinating puzzles in pattern formation is the tendency for granular mixtures to de-mix or segregate. Small differences in either size or density lead to flow-induced segregation. Similar to fluids, noncohesive granular materials can display chaotic advection; when this happens chaos and segregation compete with each other, giving rise to a wealth of experimental outcomes.

Visualization of three-dimensional chaos.

Most chaotic mixing experiments have been restricted to two-dimensional, time-periodic flows, and this has shaped advances in theory as well. A prototypical, bounded, three-dimensional flow with a moderate Reynolds number is presented; this system lends itself to detailed experimental observation and allows for high-precision computational inspection. The flow structure, captured by means of cuts with a laser sheet (experimental Poincare section), was visualized with the use of continuously injected fluorescent dye streams and revealed detailed chaotic structures with high-period islands.