Breakage Modeling of Needle-Shaped Particles Using The Discrete Element Method

This paper models the breakage of large aspect ratio particles in an attrition cell using discrete element method (DEM) and population balance (PB) models. The particles are modeled in DEM as sphero-cylinders. The stresses within each particle are calculated along the particle length using beam theory and the particle breaks into two parts if the stress exceeds a critical value. Thus, the size distribution changes with time within the DEM model. The DEM model is validated against previously published experimental data. The simulations demonstrate that particle breakage occurs primarily in front of the attrition cell blades, with the breakage rate decreasing as the particle sizes decrease. Increasing the particle elastic modulus, decreasing the particle yield strength, and increasing the attrition cell lid stress also increase the rate of breakage. Particles break most frequently at their center and the daughter size distribution normalized by the initial particle size is fit well with a Gaussian distribution. Parametric studies in which the initial particle size distribution varies demonstrate that the particle sizes approach a distribution that is independent of the initial state after a sufficient amount of work is done on the particle bed. A correlation for the specific breakage rate is developed from the DEM simulations and used within a PB model along with the daughter size distribution fit. The PB model also clearly shows that the particle size distribution becomes independent of the initial size distribution and after a sufficiently long time, is fit well with a log-normal distribution

Comparisons of intra-tablet coating variability using DEM simulations, asymptotic limit models, and experiments

This is the final version. It first appeared at http://www.sciencedirect.com/science/article/pii/S0009250915001852.Discrete element method (DEM) computer simulations are used to investigate intra-tablet coating thickness variability. Two new post-processing algorithms are presented. The first algorithm uses an image-based method to track the exposure to a simulated spray of small area panels on each tablet׳s surface so that the distribution of spray exposure times over the tablet׳s surface can be determined directly from DEM data. The second algorithm predicts the asymptotic limit of intra-tablet coating uniformity. This second algorithm includes the influence of tablet orientation and shadowing when considering exposure to the spray, averaged over many tablets. The DEM simulations produce the first direct evidence that non-spherical tablets approach asymptotic intra-tablet coating variability values. The asymptotic limits are predicted well using the new asymptotic prediction model. In general, tablet caps have thicker coatings than tablet bands. Moreover, tablets that have a more elongated shape tend to have less coating on the smaller radius of curvature portions of the bands. Of particular importance in this new asymptotic modeling approach is the inclusion of shadowing effects. When shadowing is not included and only tablet orientation is considered, the predictions over-predict the asymptotic intra-tablet coating variability values and also change the observed rank order of the asymptotic values for different tablet shapes. The asymptotic intra-tablet coating variability values using the new algorithm correlate reasonably well with tablet sphericity, with increasing sphericity improving coating uniformity. This paper also presents the first attempt to directly compare experimental and simulated coating thickness distributions. The asymptotic coating thickness predictions compare well qualitatively with terahertz thickness measurements made on tablets from coating experiments. Unfortunately, only qualitative comparisons could be made due to the limited number of tablets sampled experimentally and differences in spray zone areas and flux distributions. The tablets in the experiments, however, displayed similar features as those found in the simulations.The authors would like to thank Bob Green from Pfizer for manufacturing the tablets used in this study. R. Kumar and C. Wassgren are grateful to the National Science Foundation Engineering Research Center for Structured Organic Particulate Systems (NSF ERC-SOPS, 0951845-EEC) for financial support. K. Su and J.A. Zeitler would like to acknowledge the UK Engineering and Physical Science Research Council (EP/L019922/1 and EP/K503721/1)

Effect of particle shape on flow in discrete element method simulation of a rotary batch seed coater

In the seed processing industry, rotary batch seed coaters are widely used for providing a protective coating layer (consisting of various ingredients including fertilisers and crop protection chemicals) on the seeds. Seed motion and mixing are important in ensuring uniform coating. In the rotary batch seed coater, the base of a cylindrical vessel rotates, whilst the cylindrical wall is stationary and two baffles turn the bed over for mixing. In the present study, the Discrete Element Method (DEM) is used to simulate the effect of particle shape on motion and mixing in this device. Corn seed is used as a model material and the effect of its shape on motion is analysed by considering two approaches: (1) manipulation of rolling friction to account for shape as it is commonly used in the field; (2) approximation of the actual shape by a number of overlapping spheres of various sizes. The geometry of corn seeds is captured using X-ray microtomography and then the ASG2013 software (Cogency, South Africa) is used to generate and optimise the arrangement of the overlapping spheres. A comparison is made of the predicted tangential and radial velocity distributions of the particles from DEM and those measured experimentally. It is concluded that for rapid shearing systems with short collisional contacts a small number of clumped spheres suffice to provide a reasonable agreement with experimental results. Equally well, manipulating the rolling friction coefficient can provide results that match experiments but its most suitable value is unknown a priori, hence the approach is empirical rather than predictive

Methods for traceability in food production processes involving bulk products

In food processing plants, raw materials are fed into the system in different supply-lots of product, and are processed through different stages. In these stages, raw or intermediate materials are mixed or combined together, and physico-chemical and/or microbiological processes such as heating, concentration, pasteurisation etc. take place. In this setting, traceability consists of the ability to determine for each portion of intermediate or final product, in any part of the plant, its relative composition in terms of supply-lots fed into the system as well as of new lots generated during the production process. Traceability becomes particularly difficult in the very common case when bulk products, such as liquids or grains, are involved in the production chain. Current traceability practices are in most cases unable to directly deal with bulk products, and typically resort to the definition of very large lots to compensate the lack of knowledge about lot composition. As demonstrated in recent food crises, this over-bounding approach has weaknesses in clearly identifying, immediately after risk assessment, the affected product lots, leading to unavoidably wide, expensive and highly impacting recalls. Motivated by these considerations, this paper presents a novel approach to manage traceability of bulk products during production, storage and delivery. It provides a tight definition of lots in terms of their composition and size, thus allowing strict control of the production and supply chain

Scaling of discrete elemnet model parameters for cohesionless and cohesive solid

One of the major shortcomings of discrete element modelling (DEM) is the computational cost required when the number of particles is huge, especially for fine powders and/or industry scale simulations. This study investigates the scaling of model parameters that is necessary to produce scale independent predictions for cohesionless and cohesive solid under quasi-static simulation of confined compression and unconfined compression to failure in uniaxial test. A bilinear elasto-plastic adhesive frictional contact model was used. The results show that contact stiffness (both normal and tangential) for loading and unloading scales linearly with the particle size and the adhesive force scales very well with the square of the particle size. This scaling law would allow scaled up particle DEM model to exhibit bulk mechanical loading response in uniaxial test that is similar to a material comprised of much smaller particles. This is a first step towards a mesoscopic representation of a cohesive powder that is phenomenological based to produce the key bulk characteristics of a cohesive solid and has the potential to gain considerable computational advantage for industry scale DEM simulations.Comment: accepted in Powder Technology, 32 pages, 14 figure

Granular Flow in Silo Discharge: Discrete Element Method Simulations and Model Assessment

Discharge dynamics of granular particles from a flat-bottomed silo is studied using both continuum modeling and three-dimensional (3D) discrete element method (DEM) simulations. Using DEM, the influence of microscopic parameters (interparticle friction coefficient, particle–wall friction coefficient and particle coefficient of restitution) and system parameters (orifice width) on the discharge rate is quantified. The spatial extent of different regimes (quasi-static, intermediate and inertial) of granular rheology are quantified using a regime map previously established from DEM data of homogeneously sheared granular flow. It is shown that all three regimes of granular rheology coexist during silo discharge, and the intermediate regime plays a significant role in discharge dynamics. A quantitative comparison between results of continuum and DEM simulations is performed by computing discharge rates, solid velocities, and solid stresses for a three-dimensional (3D) flat-bottomed silo. It is found that the three constitutive models investigated in this study overpredict the discharge rate when compared to DEM data. Contour plots of the error in solid stress prediction are compared with the spatial extent of different regimes of granular rheology to deduce that it is inaccurate modeling of the intermediate regime that is responsible for overprediction of the discharge rate

Modeling granular segregation during hopper discharge

Granular materials may readily segregate due to differences in particle properties such as size, shape, and density. This segregation may occur in many industrial processes involving granular materials and will occur even after a material has been uniformly blended. Segregation is typically problematic in that the quality of products is usually contingent upon maintaining some measure of blend homogeneity. The present work aims to investigate the causes and extent of segregation of granular materials during flow from a hopper. Segregation data are obtained from discharge of quasi-three-dimensional wedge-shaped hoppers and fully three-dimensional cylindrical hoppers. The granular material is modeled as bidisperse, inelastic, frictional spheres via the discrete element method (DEM) employing a soft-particle contact model. Complementary experimentation in small hoppers with bidisperse, glass beads provides data for validation purposes. These small-scale experiments allow for direct comparison with the computational data on a one-to-one basis. Results show the extent of segregation increases with particle diameter ratio while it decreases with increasing fines mass fraction and the ratio of hopper outlet size to particle size. Additionally, parameters such as the hopper aspect ratio and wall angle affect the shape of the segregation profile over the course of discharge. Further, the extent of segregation is observed to increase with both the particle-particle and particle-wall friction coefficients. A brief study of three different hopper fill methods shows that the initial state homogeneity has a pronounced effect on the discharge profile. The DEM data also permit visualization of the internal granular flow and microstructure. Colors are assigned to each particle based on a measured quantity such as the particle velocity, residence time, or the local mass fraction---a new color scheme developed in this work. Thus, the development of spatial concentration gradients during flow is observed, which provides novel insight as to how the fundamental segregation mechanisms manifest themselves in hopper geometries to yield the given discharge segregation results. Using the segregation results and flow visualizations, recommendations for reducing the extent of segregation during hopper flow from a product and process development standpoint are made

Motivation for Living the Religious Life as Treated in the Documents of Vatican II

Why does religious life exist today and why am I a part of it? A good number of religious women are seriously asking themselves this all-important question. The agonizing search for a satisfactory answer is forcing them to probe deep into the meaning of their own personal lives and al so into their hitherto unchallenged status quo. True, today, values never before questioned are being thoroughly scrutinized. Religious life does not escape this careful scrutiny. Rather it is being bombarded from all sides until the individual religious feels barraged both from within and without herself. At times she is on the defensive, at other times she is confused. She hears the cry, Adapt or die and she is in a quandry as to where she goes from here