Simulation of density segregation in vibrated beds

Modifying self-assembly and species separation in three-dimensional systems of shape-anisotropic particles

The behaviors of large, dynamic assemblies of macroscopic particles are of direct relevance to geophysical and industrial processes and may also be used as easily studied analogs to micro- or nano-scale systems, or model systems for microbiological, zoological, and even anthropological phenomena. We study vibrated mixtures of elongated particles, demonstrating that the inclusion of differing particle "species" may profoundly alter a system's dynamics and physical structure in various diverse manners. The phase behavior observed suggests that our system, despite its athermal nature, obeys a minimum free energy principle analogous to that observed for thermodynamic systems. We demonstrate that systems of exclusively spherical objects, which form the basis of numerous theoretical frameworks in many scientific disciplines, represent only a narrow region of a wide, multidimensional phase space. Thus, our results raise significant questions as to whether such models can accurately describe the behaviors of systems outside this highly specialized case.

Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow

We study in this work a steady shearing laminar flow with null heat flux (usually called "uniform shear flow") in a gas-solid suspension at low density. The solid particles are modeled as a gas of smooth hard spheres with inelastic collisions while the influence of the surrounding interstitial fluid on the dynamics of grains is modeled by means of a volume drag force, in the context of a rheological model for suspensions. The model is solved by means of three different but complementary routes, two of them being theoretical (Grad's moment method applied to the corresponding Boltzmann equation and an exact solution of a kinetic model adapted to granular suspensions) and the other being computational (Monte Carlo simulations of the Boltzmann equation). Unlike in previous studies on granular sheared suspensions, the collisional moment associated with the momentum transfer is determined in Grad's solution by including all the quadratic terms in the stress tensor. This theoretical enhancement allows for the detection and evaluation of the normal stress differences in the plane normal to the laminar flow. In addition, the exact solution of the kinetic model gives the explicit form of the velocity moments of the velocity distribution function. Comparison between our theoretical and numerical results shows in general a good agreement for the non-Newtonian rheological properties, the kurtosis (fourth velocity moment of the distribution function), and the velocity distribution of the kinetic model for quite strong inelasticity and not too large values of the (scaled) friction coefficient characterizing the viscous drag force. This shows the accuracy of our analytical results that allows us to describe in detail the flow dynamics of the granular sheared suspension.

Shear-induced segregation of particles by material density

Recently, shear rate gradients and associated gradients in velocity fluctuations (e.g., granular temperatures or kinetic stresses) have been shown to drive segregation of different-sized particles in a manner that reverses at relatively high solids fractions (〈f〉>0.50). Here we investigate these effects in mixtures of particles differing in material density through computational and theoretical studies of particles sheared in a vertical chute where we vary the solids fraction from 〈f〉=0.2 to 0.6. We find that in sparse flows, 〈f〉=0.2 to 0.4, the heavier (denser) particles segregate to lower shear rates similarly to the heavier (larger) particles in mixtures of particles differing only in size. However, there is no segregation reversal at high f in mixtures of particles differing in density. At all solids fractions, heavier (denser) particles segregate to regions of lower shear rates and lower granular temperatures, in contrast with segregation of different-sized particles at high f, where the heavier (larger) particles segregate to the region of higher shear rates. Kinetic theory predicts well the segregation for both types of systems at low f but breaks down at higher f's. Our recently proposed mixture theory for high f granular mixtures captures the segregation trends well via the independent partitioning of kinetic and contact stresses between the two species. In light of these results, we discuss possible directions forward for a model framework that encompasses segregation effects more broadly in these systems.

Maximizing energy transfer in vibrofluidized granular systems

Using discrete particle simulations validated by experimental data acquired using the positron emission particle tracking technique, we study the efficiency of energy transfer from a vibrating wall to a system of discrete, macroscopic particles. We demonstrate that even for a fixed input energy from the wall, energy conveyed to the granular system under excitation may vary significantly dependent on the frequency and amplitude of the driving oscillations. We investigate the manner in which the efficiency with which energy is transferred to the system depends on the system variables and determine the key control parameters governing the optimization of this energy transfer. A mechanism capable of explaining our results is proposed, and the implications of our findings in the research field of granular dynamics as well as their possible utilization in industrial applications are discussed.

Competition between geometrically induced and density-driven segregation mechanisms in vibrofluidized granular systems

The behaviors of granular systems are sensitive to a wide variety of particle properties, including size, density, elasticity, and shape. Differences in any of these properties between particles in a granular mixture may lead to segregation, or "demixing," a process of great industrial relevance. Despite the known influence of particle geometry in granular systems, a considerable fraction of research into these systems concerns only uniformly spherical particles. We address, for the case of vertically vibrated granular systems, the important question of whether the introduction of differing particle geometries entirely invalidates our existing knowledge based on purely spherical granulates, or whether current models may simply be adapted to account for the effects of particle shape. We demonstrate that while shape effects can indeed influence the dynamical and segregative behaviors of a granular system, the segregative mechanisms associated with particle geometry are decidedly secondary to those related to particle density. The relevant control parameters determining the extent of geometrically induced segregation are established. Finally, a manner in which shape effects may be accounted for in simulations utilizing purely spherical particles is proposed.

Center of mass scaling in three-dimensional binary granular systems

Using a combination of experimental results acquired through positron emission particle tracking and simulational results obtained via the discrete particle method, we determine a scaling relationship for the center of mass height of a vibrofluidized three-dimensional, bidisperse granular system. We find the scaling to be dependent on the characteristic velocity with which the system is driven, the depth of the granular bed, and the elasticities of the particles involved, as well as the degree of segregation exhibited by the system and the ratio of masses between particle species. The scaling is observed to be robust over a significant range of system parameters.

Effects of packing density on the segregative behaviors of granular systems

We present results concerning the important role of system packing in the processes of density- and inelasticity-induced segregation in vibrofluidized binary granular beds. Data are acquired through a combination of experimental results acquired from positron emission particle tracking and simulations performed using the discrete particle method. It is found that segregation due to inelasticity differences between particle species is most pronounced in moderately dense systems, yet still exerts a significant effect in all but the highest density systems. Results concerning segregation due to disparities in particles' material densities show that the maximal degree to which a system can achieve segregation is directly related to the density of the system, while the rate at which segregation occurs shows an inverse relation. Based on this observation, a method of minimizing the time and energy requirements associated with producing a fully segregated system is proposed.

Energy non-equipartition in strongly convective granular systems

Using positron emission particle tracking, the effects of convective motion and the resulting segregative behaviour on the partition of kinetic energy between the components of a bidisperse granular system are, for the first time, systematically investigated. It is found that the distribution of energy between the two system components, which are equal in size but differ in their material properties, is strongly dependent on the degree of segregation observed in the granular bed. The results obtained demonstrate that the difference in energy obtained by dissimilar particle species is not an innate property of the materials in question, but can in fact be altered through variation of the relevant system parameters. The existence of a relationship between the convective and segregative properties of a granular system and the degree of energy equipartition within the system implies the possibility of extending existing theory into the convective regime. Thus, our findings represent an incremental step towards the definition of a granular analogy to temperature that can be applied to more generalised systems and, through this, an improved understanding of inhomogeneous granular systems in general.

Influence of thermal convection on density segregation in a vibrated binary granular system

Using a combination of experimental results and discrete particle method simulations, the role of buoyancy-driven convection in the segregative behavior of a three-dimensional, binary granular system is investigated. A relationship between convective motion and segregation intensity is presented, and a qualitative explanation for this behavior is proposed. This study also provides an insight into the role of diffusive behavior in the segregation of a granular bed in the convective regime. The results of this work strongly imply the possibility that, for an adequately fluidized granular bed, the degree of segregation may be indirectly controlled through the adjustment of the system's driving parameters, or the dissipative properties of the system's side-boundaries.

Adapting Data Processing To Compare Model and Experiment Accurately: A Discrete Element Model and Magnetic Resonance Measurements of a 3D Cylindrical Fluidized Bed

Discrete element modeling is being used increasingly to simulate flow in fluidized beds. These models require complex measurement techniques to provide validation for the approximations inherent in the model. This paper introduces the idea of modeling the experiment to ensure that the validation is accurate. Specifically, a 3D, cylindrical gas-fluidized bed was simulated using a discrete element model (DEM) for particle motion coupled with computational fluid dynamics (CFD) to describe the flow of gas. The results for time-averaged, axial velocity during bubbling fluidization were compared with those from magnetic resonance (MR) experiments made on the bed. The DEM-CFD data were postprocessed with various methods to produce time-averaged velocity maps for comparison with the MR results, including a method which closely matched the pulse sequence and data processing procedure used in the MR experiments. The DEM-CFD results processed with the MR-type time-averaging closely matched experimental MR results, validating the DEM-CFD model. Analysis of different averaging procedures confirmed that MR time-averages of dynamic systems correspond to particle-weighted averaging, rather than frame-weighted averaging, and also demonstrated that the use of Gaussian slices in MR imaging of dynamic systems is valid.

Experimental study on the effect of surface roughness of the intruder on the Brazil nut problem in a vertically vibrated bed

This study experimentally investigates the influence of intruder surface roughness in the Brazil nut effect in a quasi-two-dimensional vertical vibration granular bed. The intruder dynamics are determined using a particle-tracking method. The results show that surface roughness has a crucial role in the intruder rise dynamics; a rougher intruder has more difficulty rising in the bed because of higher kinetic energy dissipation. This study determined that penetration length and drag length are reduced and drag is enhanced as intruder surface roughness increases. The exponential decay of the penetration length with vibration frequency is shown. The results also show that at higher dimensionless vibration acceleration and lower vibration frequency the variation in rise time between smooth and rough intruders is negligible.