Investigation of f/2 and f/4 Waves in Granular Beds Subject to Vertical, Sinusoidal Oscillations

When a deep bed of granular material is subject to vertical, sinusoidal oscillations, a number of phenomena appear including two regimes of standing surface waves that form at one-half and one-quarter of the oscillation forcing frequency. These waves are referred to as f/2 and f/4 waves where f is the oscillation frequency. This paper presents the results from experiments and computer simulations designed to study the wavelength and wave amplitude dependence of the surface waves on the vibration parameters, collision coefficient of restriction, and the particle bed depth

Effects of vertical vibration on hopper flows of granular material

This paper examines the flow of granular material through a wedge-shaped hopper subject to vertical, sinusoidal oscillations. Experiments and discrete element computer simulations were conducted to investigate particle trajectories within and mass discharge rates from the hopper. With the hopper exit closed, side wall convection cells are observed in both the experiments and simulations. The convection cells are oriented such that particles move up along the inclined walls of the hopper and down along the centerline. Results from the computer simulation indicate that the convection cells are a result of the dilation of the granular bed during free fall and interaction with hopper walls. Measurements of the mean mass discharge rate for various vibration parameters were also made in both the experiments and simulations. The ratio of the mass discharge rate for a vibrating hopper to the mass discharge rate for a non-vibrating hopper scales with the oscillation velocity amplitude and exhibits a maximum value just greater than one for oscillation velocity amplitudes less than 0.5. The ratio is less than one for larger velocity amplitudes. A simple model taking into account the change in the effective gravity acting on the granular material over an oscillation cycle is examined. A significant deficiency in the model is that is assumes no material discharges from the hopper during part of each oscillation cycle for acceleration amplitudes greater than gravitational acceleration. Data from the simulations indicate that although the discharge rate from the hopper varies throughout an oscillation cycle, it never equals zero. The simulation was also used to examine particle horizontal position and velocity profiles at the hopper exit. Lastly, preliminary observations of the effects of localized vibration on a granular material in a closed hopper are presented

A study on the sensitivity of Drucker–Prager cap model parameters during die compaction of pharmaceutical powders

In powder die compaction, the characteristics of the end product are dictated by the mechanical properties of the powder being processed. A commonly used constitutive model describing the behavior of pharmaceutical powders during compaction is the modified-Drucker Prager Cap (DPC) model. The experiments used to measure DPC parameters are time consuming and, hence, limit the model’s wide-spread use in industry. In the interest of potentially simplifying the DPC parameter measurement procedures, it is of interest to understand the influence each of the model parameters has on the prediction of a tablet’s density field. In this study, a 2 k–p statistical analysis is performed on intratablet density gradients obtained from finite element simulation of powder compaction using a range of DPC parameters. The high and low values for the material parameters are selected based on literature reported values for pharmaceutical powders

Effect of Conveying and Distributive Mixing Elements on Breakage Phenomenon in Twin Screw Granulation

Twin screw wet granulation (TSG) is gaining more attention and becoming an important process in the pharmaceutical industry. The process is widely implemented because of its flexibility, short residence time, and small equipment footprint. Past studies have shown that screw elements can have a significant impact on the performance of the TSG process. In addition, these studies identified that breakage of wet mass is a significant step in the process. Currently there is no literature that focuses on the effect of each screw element on the breakage process. In this work, experiments have been designed to isolate the breakage process and study the different breakage effects between distributing mixing elements (DMEs) and conveying elements (CEs) in TSG. Cylindrical pellets were made using different model materials having a wide range of dynamic yield strength. The pellets were fed into the twin screw granulator, which then passed through the different screw elements. Pellet breakage probabilities were measured for each screw element configuration. As the strength of the pellets increases, the breakage probability in the CEs decreases. The breakage probability in the DMEs remains the same and shows 100% breakage, independent of the material strength. The experiments have aided in the understanding of the different breakage processes using CEs and DMEs. The breakage in CEs shows a strong dependence on material dynamic yield strength whereas the breakage in DMEs is not a function of the strength

Intrepid: A Mission to Pluto

A proposal for an exploratory spacecraft mission to Pluto/Charon system was written in response to the request for proposal for an unmannned probe to pluto (RFP). The design requirements of the RFP are presented and under the guidance of these requirements, the spacecraft Intrepid was designed. The RPF requirement that was of primary importance is the minimization of cost. Also, the reduction of flight time was of extreme importance because the atmosphere of Pluto is expected to collapse close to the Year 2020. If intrepid should arrive after the collapse, the mission would be a failure; for Pluto would be only a solid rock of ice. The topics presented include: (1) scientific instrumentation; (2) mission management, planning, and costing; (3) power and propulsion subsystem; (4) structural subsystem; (5) command, control, and communications; and (6) attitude and articulation control

Yielding and hardening of flexible fiber packings during triaxial compression

This paper examines the mechanical response of flexible fiber packings subject to triaxial compression. Short fibers yield in a manner similar to typical granular materials in which the deviatoric stress remains nearly constant with increasing strain after reaching a peak value. Interestingly, long fibers exhibit a hardening behavior, where the stress increases rapidly with increasing strain at large strains and the packing density continuously increases. Phase diagrams for classifying the bulk mechanical response as yielding, hardening, or a transition regime are generated as a function of the fiber aspect ratio, fiber-fiber friction coefficient, and confining pressure. Large fiber aspect ratio, large fiber-fiber friction coefficient, and large confining pressure promote hardening behavior. The hardening packings can support much larger loads than the yielding packings contributing to the stability and consolidation of the granular structure, but larger internal axial forces occur within fibers.Comment: 14 pages, 4 figure

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)