Anthony D. Rosato

Monte Carlo simulation of particulate matter segregation

Abstract Size segregation occurs when particulate matter is subjected to some form of shaking or vibration. This segregation has been the subject of much interest to industries dealing with granular materials. We present the results of new Monte Carlo simulations, which provide insight into the essentially geometric origin of the segregation effect. Results show excellent agreement with segregation observed in experimental systems by other researchers.

A perspective on vibration-induced size segregation of granular materials

Abstract Segregation of particulate mixtures is a problem of great consequence in industries involved with the handling and processing of granular materials in which homogeneity is generally required. While there are several factors that may be responsible for segregation in bulk solids, it is well accepted that nonuniformity in particle size is a fundamental contributor. When the granular material is exposed to vibrations, the question of whether or not convection is an essential ingredient for size segregation is addressed by distinguishing between the situation where vibrations are not sufficiently energetic to promote a mean flow of the bulk solid, and those cases where a convective flow does occur. Based on experimental and simulation results in the literature, as well as dynamical systems analysis of a recent model of a binary granular mixture, it is proposed that “void-filling” beneath large particles is a universal mechanism promoting segregation, while convection essentially provides a means of mixing enhancement.

Convection related phenomena in granular dynamics simulations of vibrated beds

Three-dimensional discrete element simulations are carried out to investigate the behavior of a shallow bed of inelastic, frictional spheres (of uniform diameter d), which are energized by vertical sinusoidal oscillations of a plane floor at amplitude a and frequency ω=2πf. We investigate the long-term and instantaneous velocity fields as well as the evolution of the pressure tensor. Results show that the onset of convection reported in the literature is not only determined by the floor acceleration, but also the ratio a/d. In a wide bed (L/d∼100) narrow persistent vortices appear near vertical sidewalls, while no distinct pattern is found within the central region. A large sphere within the bed is convected upward to the surface and either “segregates” itself from the bulk, or becomes reentrained, depending on the width of the downward velocity field near the wall relative to the sphere size. An inspection of the bed microstructure reveals internal vortex-like cells spanning its width giving rise to arch...

Macroscopic behavior of vibrating beds of smooth inelastic spheres

Three‐dimensional granular dynamics simulations are carried out to investigate macroscopic behavior of granular materials subjected to vibrations. Particles, idealized as smooth inelastic, uniform spheres, are gravitationally loaded into a rectangular periodic cell having an open top and plane floor. Vibrations to the bed are subsequently imposed through the sinusoidally oscillated floor. Significant differences in the character of the bed are found, depending on the strength of the applied floor accelerations Γ=aω2, even if the boundary input energy is fixed. At high acceleration values, a dense upper region is supported on a fluidized low‐density region near the floor. The temperature is maximum at the floor and monotonically attenuates upward, while the solids fraction profile peaks at some intermediate depth. When lower accelerations are applied, the granular temperature no longer decreases monotonically from the bottom to the top and the solids fraction depth profile bulges at approximately three diameters from the floor. The surface of the bed appears chaotic and fluidized, where a low solids fraction and high temperature occurs. The bed height, which remains almost constant below 1.2g, undergoes a pronounced expansion when 1.2g≤Γ≤2.0g, and subsequently flattens out at Γ≂2.8g. Computed granular temperature and solids fraction depth profiles are in good agreement with recent kinetic theory predictions when the acceleration is large enough, while bed expansion at lower accelerations is quantitatively consistent with existing experimental data.

Vibratory particle size sorting in multi-component systems

Particle size segregation of granular mixtures due to shaking or vibrations has been observed in industries concerned with the handling and processing of particulates. Upon introducing the concept of relative concentrations between each size species, this paper presents a segregation model from which generalized expressions are derived for the instantaneous rate of change of concentration of each size species. The expressions are specialized to a ternary system. A Monte Carlo computer simulation study is done to simulate size sorting in a ternary system at a fixed shaking amplitude. The results of the simulations show good agreement with model predictions regarding the influence of particle size ratios. The most striking effect is a reversal of sorting order between the small and large particles with a change of size ratios. This reversal, which occurs in the simulated system, is clearly explained by the model.

Microstructure evolution in compacted granular beds

Abstract In this paper, the densification process experienced by a bed of frictional, inelastic spheres of diameter d in a rectangular vessel whose floor is subjected to high frequency (ω) and low amplitude (a/d≠0.1) sinusoidal oscillations is modeled using discrete element simulations. Our recent experimental observations as well as those in the literature motivate this investigation. Beginning with an initial random assembly resulting from gravity deposition, the floor motion activates the system so as to induce the formation of a distinct microstructure in the absence of a mean flow field. This is accompanied by an increase in coordination number and bulk solids fraction whose evolution is strongly dependent on the magnitude of the acceleration amplitude Γ≡aω2/g.

Magnetic resonance imaging of vibrating granular beds by spatial scanning

Nuclear magnetic resonance is becoming an important experimental technique to study the behavior of moving granular materials because of its unique ability to measure concentration, velocity, and dissipation within the bulk granular materials rather than only on the surface. Of all the common motions of such assemblies of particles, the most difficult to measure is the vibrating bed because of the unsteady motion. This paper demonstrates a nuclear magnetic resonance imaging method to study highly energetic vibrating granular beds by spatial scanning. In contrast to Fourier imaging, spatial scanning prevents scattering of image intensities caused by unsteady motion. Two-dimensional images of a vibrating bed undergoing period doubling were obtained. A band of high shear was identified by reduced image intensity. It traveled back and forth across the bed with each cycle of up and down motion of the bed. Further studies of vibrating beds with the sequence modified for velocity encoding and velocity compensati...

New Mathematical Models for Particle Flow Dynamics

A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of infinite-dimensional dynamical systems models) on the Newtonian equations of motion of a many-particle system incorporating widely used inelastic particle-particle force formulas. By using Taylor series expansions, these models can be approximated by a system of partial differential equations of the Navier-Stokes type. The exact or approximate governing equations obtained are far from simple, but they are less complicated than most of the continuum models now being used to predict particle flow behavior. Solutions of the new models for granular flows down inclined planes and in vibrating beds are compared with known experimental and analytical results and good agreement is obtained.

Resonance effects on the dynamics of dense granular beds: achieving optimal energy transfer in vibrated granular systems

Using a combination of experimental techniques and discrete particle method simulations, we investigate the resonant behaviour of a dense, vibrated granular system. We demonstrate that a bed of particles driven by a vibrating plate may exhibit marked differences in its internal energy dependent on the specific frequency at which it is driven, even if the energy corresponding to the oscillations driving the system is held constant and the acceleration provided by the base remains consistently significantly higher than the gravitational acceleration, g. We show that these differences in the efficiency of energy transfer to the granular system can be explained by the existence of resonances between the beds bulk motion and that of the oscillating plate driving the system. We systematically study the dependency of the observed resonant behaviour on the systems main, controllable parameters and, based on the results obtained, propose a simple empirical model capable of determining, for a given system, the points in parameter space for which optimal energy transfer may be achieved.

Influence of initial conditions on granular dynamics near the jamming transition

In this paper, we compare the behaviours of two vibrofluidized granular systems, identical in terms of their composition, geometry and driving parameters, differing only in their initial conditions. It is found that, by increasing the strength with which a system is initially excited, considerable differences in system composition and dynamics persist even after the driving is returned to its typical value. The observed changes in particle mobility and packing density are shown to result in marked differences in segregative behaviour for equivalent steadystate systems distinguished only by the history of their driving. The ability to significantly increase the rate of segregation in a granular system simply through the application of a short burst of intense vibration clearly has potential industrial applications.