A study on the validity of the multi-sphere Discrete Element Method

Emerging Process Modeling Capabilities for Dry Powder Operations for Inhaled Formulations

Dry powder inhaler (DPI) products are commonly formulated as a mixture of micronized drug particles and large carrier particles, with or without additional fine particle excipients, followed by final powder filling into dose containment systems such as capsules, blisters, or reservoirs. DPI product manufacturing consists of a series of unit operations, including particle size reduction, blending, and filling. This review provides an overview of the relevant critical process parameters used for jet milling, high-shear blending, and dosator/drum capsule filling operations across commonly utilized instruments. Further, this review describes the recent achievements regarding the application of empirical and mechanistic models, especially discrete element method (DEM) simulation, in DPI process development. Although to date only limited modeling/simulation work has been accomplished, in the authors' perspective, process design and development are destined to be more modeling/simulation driven with the emphasis on evaluating the impact of material attributes/process parameters on process performance. The advancement of computational power is expected to enable modeling/simulation approaches to tackle more complex problems with better accuracy when dealing with real-world DPI process operations.

The Effect of Particle Shape on the Compaction of Realistic Non-Spherical Particles—A Multi-Contact DEM Study

The purpose of this study was to investigate the deformation behavior of non-spherical particles during high-load compaction using the multi-contact discrete element method (MC-DEM). To account for non-spherical particles, the bonded multi-sphere method (BMS), which incorporates intragranular bonds between particles, and the conventional multi-sphere (CMS), where overlaps between particles are allowed to form a rigid body, were used. Several test cases were performed to justify the conclusions of this study. The bonded multi-sphere method was first employed to study the compression of a single rubber sphere. This method’s ability to naturally handle large elastic deformations is demonstrated by its agreement with experimental data. This result was validated further through detailed finite element simulations (multiple particle finite element method (MPFEM)). Furthermore, the conventional multi-sphere (CMS) approach, in which overlaps between particles are allowed to form a rigid body, was used for the same objective, and revealed the limitations of this method in successfully capturing the compression behavior of a single rubber sphere. Finally, the uniaxial compaction of a microcrystalline cellulose-grade material, Avicel® PH 200 (FMC BioPolymer, Philadelphia, PA, USA), subjected to high confining conditions was studied using the BMS method. A series of simulation results was obtained with realistic non-spherical particles and compared with the experimental data. For a system composed of non-spherical particles, the multi-contact DEM showed very good agreement with experimental data.

Study on Verification Approach and Multicontact Points Issue When Modeling Cyperus esculentus Seeds Based on DEM

In this paper, the Multisphere (MS) models of three varieties of Cyperus esculentus seeds are modeled based on DEM. In addition, for comparison, other particle models based on automatic filing in EDEM software are also introduced. Then, the direct shear test, piling test, bulk density test, and rotating hub test are used to verify the feasibility of particle models of Cyperus esculentus seeds that we proposed. By comparing the simulated results and experimental results, combined with the CPU computation time, the proposed particle models achieved better simulation accuracy with fewer filing spheres. According to simulation results, some limitation was present when using one single verification test; varieties of verification tests used could improve the verification reliability, and a more appropriate particle model could be selected. Additionally, the issue of multicontact points in the MS model was studied. The Hertz Mindlin (no slip) (HM) model and Hertz Mindlin new restitution (HMNR) model were both considered in simulations for comparison. The rotating hub test and particle–wall impact test were used, and the influences of multiple contact points on the motion behavior of individual particles and particle assemblies were analyzed. Simulation results showed that the multiple contact points affected the motion behavior of individual particles; in contrast, the influence of multiple contact points on the motion behavior of the particle assembly was insignificant. Moreover, the relationships between moisture content of seeds and Young’s modulus, Young’s modulus, and the number of contact points were also considered. Young’s modulus decreased with increasing moisture content. The number of contact points increased with a decreasing Young’s modulus.

A DEM-Based Modeling Method and Simulation Parameter Selection for Cyperus esculentus Seeds

To build a DEM model of Cyperus esculentus seed particles, the shape and size of the Cyperus esculentus seed particles were measured and analyzed. The results showed that the dispersity in size had a normal distribution. Additionally, a certain functional relationship between the primary dimension and secondary dimensions was determined. The width of the seed was the primary dimension, and the other secondary dimensions (length and thickness) were calculated based on their relationships with the primary dimension. On this basis, an approach for modeling Cyperus esculentus seed particles based on the multi-sphere (MS) method was proposed. The discrete element analysis models of three varieties of Cyperus esculentus seeds were established with different numbers of filing spheres. Moreover, to obtain more accurate simulation parameters, first, a range of values of the simulation parameters was obtained by the experimental method. Second, the Plackett–Burman (PB) test and the path of steepest ascent method were both adopted to correct and calibrate the simulation parameters, which were difficult to obtain through experiments, and simulation of the direct shear test was used for calibration. All of the methods guaranteed that the selected parameters were reasonable. The test results showed that the static friction coefficient of seed–seed had a significant effect on the simulation results. Finally, piling tests and the bulk density test were used for modeling verification. By comparing the simulated results and experimental results in the piling tests and bulk density test, when the number of filing spheres increased, the simulated results were close to those obtained experimentally. Therefore, the feasibility and validity of the modeling method for Cyperus esculentus seed particles that we proposed and the simulation parameters that were obtained were verified.

Drag on a circular intruder traversing a shape-heterogeneous granular mixture

The main aim of our work is to explore the effect of particle shape heterogeneity on the dynamics of an intruder moving through a two-dimensional mixture of dumbbells and disks. In spite of similar physical conditions (the mass of the dumbbell is the same as that of the disk) and the same area fraction, we noticed a significant difference in the drag experienced by the intruder as the mixture concentration varies. The propagation of stress from the intruder to the granular grains manifests in the form of force chains, and interestingly these force chains can vary significantly depending on the shape of the grains. These differences, however, appear to be suppressed in the frictionless case where the force chains cannot extend very far from the initial point of contact. Apart from particle shape, the effect of the area fraction of the system and the size of the intruder have also been explored. As the area fraction increases, the drag force on the intruder increases owing to the increase in the contact forces. Finally, we present the velocity and stress fields at different dumbbell fractions and for various intruder diameters to show the effect of the moving intruder on its surrounding particles.

A Review of the Application of Discrete Element Method in Agricultural Engineering: A Case Study of Soybean

The discrete element method has become a common method for analyzing the contact interaction between particulate materials and between particles and mechanical components. It has been widely used in agricultural engineering and other fields. Taking soybean as an example, soybean seed particles always have contact effects between particles and mechanical components in the process of planting, harvesting, threshing, separation, cleaning, and processing. The discrete element method can be used to obtain information on the contact forces between seed particles and mechanical parts, as well as the velocity and displacement of seed particle motion from a microscopic perspective. This paper summarizes the application of the discrete element method in soybean cultivation and production processes in recent years. This will help future researchers to conduct relevant test studies, develop and improve existing research methods. It can also serve as a guide and reference for the production and processing of other granular materials and the optimization of agricultural machinery components.

Determination of mechanical properties of Zanthoxylum armatum using the discrete element method

Using the discrete element method (DEM) to investigate the behavior of particles is a crucial strategy in the research and development of novel equipment. Green pepper (Zanthoxylum armatum) is a globally renewable plant-derived medicinal and food homologous commodity with a wide range of uses and great demand, but the mechanical properties needed to develop its processing equipment are scare. Thus, this case of study aimed to systematically explore the necessary input parameters to model green pepper, and to provide new insights for the guidance of future industrial applications worldwide. On the basis of the experimental measured physical properties, the contact properties of green pepper on zinc-coated steel were fist calibrated, and then used to determine the contact properties between particles. The differences between the experimental and simulation results were analyzed for selection and verification of the contact properties accurately. Difference analysis confirmed that the coefficient of restitution, coefficient of static friction and coefficient of rolling friction for contact between the particle and zinc-coated steel have values of 0.392, 0.650, and 0.168, and those coefficients for particle-to-particle contact have values of 0.199, 0.710, and 0.184, respectively. Discoveries in this work may contribute to the research and development of production equipment for green pepper.

Simulation and Analysis of the Working Process of Soil Covering and Compacting of Precision Seeding Units Based on the Coupling Model of DEM with MBD

In precision seeding, the final displacements of the seeds are determined as a working result of the profiling mechanism, opener, seed-metering device, covering apparatus and compacting machine. For a better understanding of the disturbance of seed displacement during soil covering and compaction in the actual working process, experiments and simulations have been performed. In this paper, a type of soybean seeding monomer was taken as the research object, and a soil bin test of soil covering and compacting was executed. The experimental results showed that the traction velocity and the open angle of the covering discs had a significant influence on the changes in the horizontal and vertical displacements of seeds during the soil covering processing. With an increasing traction velocity, the vertical displacements of seeds increased after soil covering; in contrast, the horizontal displacements decreased. When the covering apparatus had a larger open angle it had a smaller disturbance influence on the soil. Therefore, with an increase in the opening angle, the changes in the vertical and horizontal displacements of seeds showed a decreasing trend. Inversely, in the process of compacting, the forward velocity had little effect on the three-dimensional displacement change in the seeds after compacting. The analysis model of the precision seeding unit was established based on the coupling model of the DEM (discrete element method) with MBDs (multi-body dynamics). The process of soil covering and compacting was simulated and analyzed. The comparison between the experimental results and the simulated results showed that the trend was similar, and the two results were close. Thus, the feasibility and applicability of the coupling method were verified. It also provided a new method for the design and optimization of covering and compacting components of a precise seeding monomer.

Modeling Food Particle Systems: A Review of Current Progress and Challenges

For many years, food engineers have attempted to describe physical phenomena such as heat and mass transfer in food via mathematical models. Still, the impact and benefits of computer-aided engineering are less established in food than in most other industries today. Complexity in the structure and composition of food matrices are largely responsible for this gap. During processing of food, its temperature, moisture, and structure can change continuously, along with its physical properties. We summarize the knowledge foundation, recent progress, and remaining limitations in modeling food particle systems in four relevant areas: flowability, size reduction, drying, and granulation and agglomeration. Our goal is to enable researchers in academia and industry dealing with food powders to identify approaches to address their challenges with adequate model systems or through structural and compositional simplifications. With advances in computer simulation capacity, detailed particle-scale models are now available for many applications. Here, we discuss aspects that require further attention, especially related to physics-based contact models for discrete-element models of food particle systems.

A Comparative Study on the Modelling of Soybean Particles Based on the Discrete Element Method

To solve the poor universality in the existing modelling approaches of soybean particles, we proposed a soybean particle modelling approach by combining five, nine, and 13 balls. The soybean seeds from three varieties (Suinong42, Jidou17, and Zhongdou39 with a sphericity of 94.78%, 86.86%, and 80.6%, respectively) are chosen as the study objects. By the comparisons between the simulation results and the test results in the “self-flow screening” and “piling angle” tests, it is concluded that the soybean particle modelling approach we presented in this paper is a universal modelling approach appropriate for soybean particles with different sphericities. The five-ball model is appropriate for the soybean particles with high sphericity, and the nine- or 13-ball models are applicable to those with low sphericity. The soybean particle modelling approach we presented is also compared with the ellipsoidal equation modelling approach for soybean particles and with the modelling approaches presented by other researchers. From an overall perspective, the soybean particle modelling approach we presented is better than the ellipsoidal equation modelling approach and those modelling approaches presented by other researchers. Additionally, it is shown that the multiple contacts issue in the multi-ball model has a little influence on the simulation results of soybean particle models. The study in this paper provides a new modelling approach for soybean particles in the DEM simulation of the contacts between soybean particles and the related machines.

Self-assembly and entropic effects in pear-shaped colloid systems. I. Shape sensitivity of bilayer phases in colloidal pear-shaped particle systems

The role of particle shape in self-assembly processes is a double-edged sword. On the one hand, particle shape and particle elongation are often considered the most fundamental determinants of soft matter structure formation. On the other hand, structure formation is often highly sensitive to details of shape. Here, we address the question of particle shape sensitivity for the self-assembly of hard pear-shaped particles by studying two models for this system: (a) the pear hard Gaussian overlap (PHGO) and (b) the hard pears of revolution (HPR) model. Hard pear-shaped particles, given by the PHGO model, are known to form a bicontinuous gyroid phase spontaneously. However, this model does not replicate an additive object perfectly and, hence, varies slightly in shape from a "true" pear-shape. Therefore, we investigate in the first part of this series the stability of the gyroid phase in pear-shaped particle systems. We show, based on the HPR phase diagram, that the gyroid phase does not form in pears with such a "true" hard pear-shaped potential. Moreover, we acquire first indications from the HPR and PHGO pair-correlation functions that the formation of the gyroid is probably attributed to the small non-additive properties of the PHGO potential.

A New Approach to Explore the Surface Profile of Clay Soil Using White Light Interferometry

In order to have a better understanding of the real contact area of granular materials, the white light interference method is applied to explore the real surface morphology of clay soils under high stress. Analysis of the surface profile indicates that there exists a support point height z₀ with the highest distribution frequency. A concept of a real contact region (from z₀ to z₀ + d₉₀; d₉₀ represents the particle size corresponding to 90% of the volume fraction) is proposed by combining a surface profile with the particle size distribution of clay soil. It was found that under the compressive stress of 106 MPa–529 MPa, the actual contact area ratio of clay soil varies between 0.375 and 0.431. This demonstrates an increasing trend with the rise of stress. On the contrary, the apparent porosity decreases with an increasing stress, varying between 0.554 and 0.525. In addition, as the compressive stress increases, the cumulative frequency of apparent profile height (from z₀ − d₉₀ to z₀ + d₉₀) has a concentrated tendency with a limited value of 0.9.