Assessing mixing characteristics of particle-mixing and granulation devices

The mixing of particulates such as powders is an important process in many industries including pharmaceuticals, plastics, household products (such as detergents) and food processing. The quality of products depends on the degree of mixing of their constituent materials which in turn depends on both geometric design and operating conditions. Unfortunately, due to lack of understanding of the interaction between mixer geometry and the granular material, limited progress has been made in optimizing mixer design. The discrete element method (DEM) is a computational technique that allows particle systems to be simulated and mixing to be predicted. Simulation is an effective way of acquiring information on the performance of different mixers that is difficult and/or expensive to obtain using traditional experimental approaches. Here we demonstrate how DEM can be used to unravel flow dynamics and assess mixing in several different types of devices. These devices used for mixing and/or granulation of particulates, are classified broadly as gravity controlled, bladed and high shear. We also explore the role of particle shape in mixing performance and use DEM to test whether Froude number scaling is suitable for predicting scale performance of rotating mixers.     

Numerical simulation of tetrahedral particle mixing and motion in rotating drums

A regular tetrahedron is the simplest three-dimensional structure and has the largest non-sphericity. Mixing of tetrahedral particles in a thin drum mixer was studied by the soft-sphere-imbedded pseudo-hard particle model and compared with that of spherical particles. The two particle types were simulated with different rotation speeds and drum filling levels. The Lacey mixing index and Shannon information entropy were used to explore the effects of sphericity on the mixing and motion of particles. Moreover, the probability density functions and mean values and variances of motion velocities, including translational and rotational, were computed to quantify the differences between the motion features of tetrahedra and spheres. We found that the flow regime depended on the particle shape in addition to the rotation speed and filling level of the drum. The mixing of tetrahedral particles was better than that of spherical particles in the rolling and cascading regimes at a high filling level, whereas it may be poorer when the filling level was low. The Shannon information entropy is better than the Lacey mixing index to evaluate mixing because it can reflect the real change of flow regime from the cataracting to the centrifugal regime, whereas the mixing index cannot.     

Use of multiscale particle simulations in the design of nuclear plant decommissioning

The application of a digital modelling method that can faithfully take account of three-dimensional shape and inherent physical and chemical properties of each particulate component provides an essential tool in decommissioning design. This is useful in handling of high, medium and low level radioactive waste. The processes involve making decisions on where to cut existing plant components and then how to pack these components into boxes, which are then cemented and kept for long term storage as the level of radioactive declines with time. We illustrate the utility of the method and its ability to take data at plant scale (m-scale) and then deduce behaviours at sub millimetre scale in the packed containers. A variety of modelling approaches are used as a part of this approach including cutting algorithms, geometric and dynamic (distinct element) force models, and lattice Boltzmann methods. These methods are applicable to other complex particulate systems including simulation of waste, building recycling, heap leaching and related minerals processes. The paper introduces the basic concepts of this multi-scale and multi-model approach.     

Simulation and calibration of granules using the discrete element method

The discrete element method (DEM), developed by Cundall and Strack (1979) to solve geomechanical problems, is used to simulate the mechanical behavior of granules. According to the DEM, an individual granule can be modeled as a realistic mechanical system consisting of primary particles bonded by interaction forces.Granulometric properties of the model material, zeolite 4A, have been measured to determine their macro properties. To investigate the compression behavior, a compression test was performed using a strength tester on single granules between two pistons. A modeled granule consisting of more than 22,000 primary particles was generated. The micro properties of the modeled granule have been precisely set to allow its macro properties to be equivalent to the macro properties of zeolite 4A granules. To calibrate the mechanical properties, diametrical compression was simulated using two rigid walls stressed at a constant stressing velocity. The force–displacement curve of the modeled granule at compression has been calibrated by the experimental curve of zeolite 4A.     

DEM analysis of the effect of electrostatic interaction on particle mixing for carrier-based dry powder inhaler formulations

Particle interactions play a significant role in controlling the performance of dry powder inhalers (DPIs), which mainly arise through van der Waals potentials, electrostatic interactions, and capillary forces. Our aim is to investigate the influence of electrostatic charge on the performance of DPIs as a basis for improving the formulation of the particle ingredients. The mixing process of carrier and active pharmaceutical ingredient (API) particles in a vibrating container is investigated using a discrete element method (DEM). The number of API particles attaching to the carrier particle (i.e., contact number) increases with increasing charge and decreases with increasing container size. The contact number decreases with increasing vibrational velocity amplitude and frequency. Moreover, a mechanism governed by the electrostatic force is proposed for the mixing process. This mechanism is different from that previously proposed for the mixing process governed by van der Waals forces, indicating that long-range and short-range adhesive forces can result in different mixing behaviours.     

The effect of side walls on particles mixing in rotating drums

In this paper, we study the effects of the presence and shape of side walls and of the overall length of rotating cylindrical drums on the mixing of particles with differing sizes by application of the discrete element method (DEM). By varying the semi-axis of the spheroidally shaped side walls and the length of the overall drum, we observe the formation of circulation patterns near the side walls. Although there is a vast amount of literature studying mixing regimes in rotating drums, little is known about the effect of the side walls of the drum on particle mixing. The results of our study demonstrate that introducing curved side walls induces a strong circulation pattern near these side walls, but has, paradoxically, a negative impact on mixing and actually promotes segregation. The cause for this segregation is the difference in velocity of differently sized particles near the curved side walls. Large particles accumulate at the curved side walls, whereas small particles move away from the curved side walls. When the length of the drum is increased, the overall effect of the side walls is decreased, although it does remain observable, even in very large drums.     

Using the discrete element method to assess the mixing of polydisperse solid particles in a rotary drum

Despite the wide applications of powder and solid mixing in industry, knowledge on the mixing of polydisperse solid particles in rotary drum blenders is lacking. This study investigates the mixing of monodisperse, bidisperse, tridisperse, and polydisperse solid particles in a rotary drum using the discrete element method. To validate the model developed in this study, experimental and simulation results were compared. The validated model was then employed to investigate the effects of the drum rotational speed, particle size, and initial loading method on the mixing quality. The degree of mixing of polydisperse particles was smaller than that for monodisperse particles owing to the segregation phenomenon. The mixing index increased from an initial value to a maximum and decreased slightly before reaching a plateau for bidisperse, tridisperse, and polydisperse particles as a direct result of the segregation of particles of different sizes. Final mixing indices were higher for polydisperse particles than for tridisperse and bidisperse particles. Additionally, segregation was weakened by introducing additional particles of intermediate size. The best mixing of bidisperse and tridisperse particles was achieved for top–bottom smaller-to-larger initial loading, while that of polydisperse systems was achieved using top–bottom smaller-to-larger and top–bottom larger-to-smaller initial loading methods.     

Segregation of particulate solids: Experiments and DEM simulations

Segregation of granular materials is a complex phenomenon, difficult to measure quantitatively and to predict. Discrete element method (DEM) can be a useful tool to predict segregation effects and to support the industrial design. In this context, a very challenging idea is the characterization of the granular solids to provide the key parameters needed for a successful DEM simulation of segregation processes. Rolling friction, sliding friction and the coefficient of restitution are the critical parameters to be studied. These microscopic simulation parameters are calibrated by comparing the macroscopic behavior of granular matter in standard bulk experiments, which have the advantage of being highly repeatable and reliable.An experimental method is presented to characterize free surface segregation. The effects of different particle properties, particularly, shape and size, on segregation of cohesionless materials were investigated. From the experiments, particle size demonstrated a stronger effect on segregation than particle shape. Finally, the corresponding DEM simulations of the segregation experiments were presented. The parameters obtained by calibration were validated by the comparison of the modeled segregation behavior with the experimental results. Thus, calibrated DEM simulations are capable of predicting segregation effects.     

Implementation of rotational resistance models: A critical appraisal

Contact models that simulate rotational resistance at particle contacts have been proposed as a means to capture the effect of shape in DEM simulations. This contribution critically explores some key issues related to the implementation of rotational resistance models; these include the need for physically meaningful model parameters, the impact of the model on the overall numerical stability/critical time increment for the DEM model, model validation, and the assessment of model performance relative to real physical materials. The discussion is centred around a rotational resistance model that captures the resistance provided by interlocking asperities on the particle surface. An expression for the maximum permissible integration time step to ensure numerical stability is derived for DEM simulations when rotational resistance is incorporated. Analytical solutions for some single-contact scenarios are derived for model validation. The ability of this type of model to provide additional fundamental insight into granular material behaviour is demonstrated using particle-scale analysis of triaxial compression simulations to examine the roles that contact rolling and sliding have on the stability of strong force chains.     

Time-averaged flow characteristics and mixing properties of double-concentric jets

We examined the flow behaviors and mixing characteristics of double-concentric jets using laser-assisted smoke flow visualization method to analyze typical flow patterns and binary boundary detection technique to investigate jet spread width. Time-averaged velocity vectors, streamline patterns, velocity distributions, turbulence properties, and vorticity contours were analyzed using Particle Image Velocimetry (PIV). Topological flow patterns were analyzed to interpret the vortical flow structures. Mixing properties were investigated using a tracer-gas concentration detection method. Four characteristic modes were observed: annular flow dominated mode, transition mode, central jet dominated mode-low shear, and central jet dominated mode-high shear. The jets’ mixing properties were enhanced by two major phenomena: the merging of annular flow and central jet at the centerline and the large turbulence fluctuations produced in the flow field. The merging of the jets induced stagnation points on the central axis in the annular flow dominated mode, which caused reverse flow on the central axis and drastic turbulence fluctuations of the near field region. When the central jet penetrated the recirculation region in the other three modes, the stagnation points on the central axis and the reverse flow vanished. Therefore, the mixing behaviors were prominently enhanced in the annular flow dominated mode.     

Scaling granular material with polygonal particles in discrete element modeling

Despite advancements in computational resources, the discrete element method (DEM) still requires considerable computational time to solve detailed problems, especially when it comes to the large-scale models. In addition to the geometry scale of the problem, the particle shape has a dramatic effect on the computational cost of DEM. Therefore, many studies have been performed with simplified spherical particles or clumps. Particle scaling is an approach to increase the particle size to reduce the number of particles in the DEM. Although several particle scaling methods have been introduced, there are still some disagreements regarding their applicability to certain aspects of problems. In this study, the effect of particle scalping on the shear behavior of granular material is explored. Real granular particles were scanned and imported as polygonal particles in the direct shear test. The effect of particle size distribution, particle angularity, and the amount of scalping were investigated. The results show that particle scalping can simulate the correct shear behavior of the model with significant improvement in computational time. Also, the accuracy of the scalping method depends on the particle angularity and particle size range.     

DEM simulation of influence of parameters on energy and degree of mixing

Powder mixing is being modeled using a simulation based on Newtonian mechanics. Variables under consideration include particle friction and the amplitude, frequency, and direction of shaking. Trajectories for each particle were recorded, and a mixing degree was calculated for each simulation, for which the average energy transferred into the powder system was recorded and compared to the resulting mixing degree. Mixing of particles originally located near the bottom was studied separately, as was the mixing of particles near the surface. This study shows that choosing the proper mixing parameters not only enhances the final result of mixing, but also yields good results with less strain on the material mixed and on the mixing device.     

Scale effects on strength of geomaterials, case study: Coal

Scale effects on the strength of coal are studied using a discrete element model. The key point of the model is its capability to discriminate between the “strictly sample size” effect and the “Discrete Fracture Network (DFN) density” effect on the mechanical response. Simulations of true triaxial compression tests are carried out to identify their respective roles. The possible bias due to the discretization size distribution of the discrete element model is investigated in detail by considering low-resolution configurations. The model is shown to be capable of quantitatively reproducing the dependency of the maximum strength on the size of the sample. This relationship mainly relies on the DFN density. For all given sizes, as long as the DFN density remains constant with a uniform distribution or if discontinuities are absent in the considered medium, the maximum strength of the material remains constant.     

Validation of a discrete element model using magnetic resonance measurements

The discrete element model(DEM)is a very promising modelling strategy for two-phase granular systems.However,owing to a lack of experimental measurements,validation of numerical simulations of two-phase granular systems is still an important issue.In this study,a small two-dimensional gas- fluidized bed was simulated using a discrete element model.The dimensions of the simulated bed were 44 mm×10 mm×120 mm and the fluidized particles had a diameter dp=1.2 mm and density p=1000 kg/m3.The comparison between D...     

Effect of particle size distribution on micro- and macromechanical response of granular packings under compression

The role of particle size heterogeneity on micro- and macromechanical properties of assemblies of spherical particles was studied using DEM simulations. The response to an imposed load of a granular material composed of non-uniformly sized spheres subjected to uniaxial confined compression was investigated. A range of geometrical and micro-mechanical properties of granular packings (e.g., void fraction, contact force distribution, average coordination number and degree of mobilisation of friction at contacts between particles) were examined, and provided a more accurate interpretation of the macroscopic behaviour of mixtures than has previously been available. The macromechanical study included stress transmission, stiffness and angle of internal friction of the granular assemblies.The degree of polydispersity showed slight effect on both, the void fraction and the elastic properties of the system. The tendency for increase in the lateral-to-vertical pressure ratios was observed with an increasing degree of particle size heterogeneity; however, the different pressure ratios calculated for samples with various degrees of polydispersity lay within the range of data scatter.     

Effects of dual jets distance on mixing characteristics and flow path within a cavity in supersonic crossflow

A rectangular open cavity with upstream dual injectors at a freestream Mach number of 1.9 was investigated experimentally. To evaluate the effect of the distance between the jets, the flow characteristics were investigated using the high-speed schlieren photography, particle image velocimetry, and surface oil flow techniques. The dual jet distances of 18 and 54 mm were used. Unstable flow occurs over the cavity in all cases and is not improved by changing the distance between the dual jets. Although the distance between the dual jets does not influence the flow stability, the flow field varies decidedly depending on the dual jets distance. The enhancement of air mixing depends on the distance between the jets. A long dual jets distance was found to yield better mixing characteristics within the cavity than a short one. When the jets are further apart, the mainstream between two counter-rotating vortex pairs behind the jets flows strongly into the cavity because of the increased blow-down occurring between the vortex pairs. Additionally, a counterflow with a low velocity magnitude occurs behind the jets. Hence, mixing is enhanced within the cavity by effects of the opposed flow. When the jet pairs are closer to each other, the counter-rotating vortex pairs are in contact; as a result, the blow-down effect does not occur between them. The flow drawn into the cavity from the mainstream is supplied from the sides of the test section into the cavity.     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity,residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient,the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But,the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter,respectively.In addition,the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.     

DEM simulation of particle percolation in a packed bed

The phenomenon of spontaneous particle percolation under gravity is investigated by means of the discrete element method. Percolation behaviors such as percolation velocity, residence time distribution and radial dispersion are examined under various conditions. It is shown that the vertical velocity of a percolating particle moving down through a packing of larger particles decreases with increasing the restitution coefficient between particles and diameter ratio of the percolating to packing particles. With the increase of the restitution coefficient, the residence time and radial dispersion of the percolating particles increase. The packing height affects the residence time and radial dispersion. But, the effect can be eliminated in the analysis of the residence time and radial dispersion when they are normalized by the average residence time and the product of the packing height and packing particle diameter, respectively. In addition, the percolation velocity is shown to be related to the vertical acceleration of the percolating particle when an extra constant vertical force is applied. Increasing the feeding rate of percolating particles decreases the dispersion coefficient.