Breakage probability of irregularly shaped particles

The investigation of breakage probability by compression of single particles was carried out. The spherical glass particles and irregularly shaped particles of NaCl, sugar, basalt and marble were subjected to a breakage test. The breakage test includes the compression up to breakage of 100 particles to obtain the distribution of the breakage probability depending on the breakage force or compression work. The breakage test was conducted for five particle size fractions from each individual material, at two stressing rates. Thus obtained 50 breakage force distributions and corresponding 50 breakage work distributions were fitted with log-normal distribution function.Usually, the breakage probability distribution can be found by means of stress or energy approach. The first one uses the stress to calculate the breakage probability distribution. The second approach uses the mass-related work done to break the particle. We prefer to use the breakage force and energy as essential variables. The correlation between the force and energy at their breakage points is obtained by integrating the characteristic force–displacement curve, i.e. the constitutive function of elastic–plastic mechanical behavior of the particle. The irregularly shaped particle is approximated by comparatively “large” hemispherical asperities. In terms of elastic–plastic deformation of the contacting asperities with the plate, a transition from elastic to inelastic deformation behavior was considered. Thus, one may apply the model of soft contact behavior of comparatively stiff hemispheres. Based on this model a relationship between the breakage force distributions and corresponding energy distributions was analyzed. Every tested material exhibits a linear relationship between average breakage energy and average breakage force calculated for every size fraction.For future consideration both force and energy distributions were normalized by division by average force or energy, consequently. The relationship between the fit parameters of normalized energy distribution and corresponding fit parameters of normalized force distribution was established. The mean value and standard deviation of normalized force distribution can be found from mean value and standard deviation of normalized energy distribution by means of system of two linear equations. The coefficients of those linear equations remain the same for all of the above tested materials; particle size fractions and stressing rates. As a result the simple transformation algorithm of distributions is developed. According to this algorithm the force distribution can be transformed into energy distribution and vice versa.     

Laboratory methods for assessing API sensitivity to mechanical stress during agitated drying

Two distinct laboratory methods have been developed to assess the propensity of active pharmaceutical ingredients to undergo particle breakage during agitated drying operations. In the first method, mechanical stress is applied to particles by mechanical agitation of powders compressed under an applied normal force. For the second, particles experience stresses as they are carried within a pressurized gas stream. These methods are simple, relatively compound-sparing, and are used to rank materials according to a quantitative breakage classification scale as hard, medium, or easy to break. Based on the results obtained using these methods at laboratory scale, recommendations and precautions for processing at larger scale are made. In this paper, these methods are described in detail, and the results, obtained for several pharmaceutical compounds, are presented.     

Numerical simulation of particle breakage of angular particles using combined DEM and FEM

One of the effective parameters of the behavior of rockfill materials is particle breakage. As a result of particle breakage, both the stress–strain and deformability of materials change significantly. In this article, a novel approach for the two-dimensional numerical simulation of the phenomenon in rockfill (sharp-edge particles) has been developed using combined DEM and FEM. All particles are simulated by the discrete element method (DEM) as an assembly and after each step of DEM analysis, each particle is separately modeled by FEM to determine its possible breakage. If the particle fulfilled the proposed breakage criteria, the breakage path is assumed to be a straight line and is determined by a full finite element stress–strain analysis within that particle and two new particles are generated, replacing the original particle. These procedures are carried out on all particles in each time step of the DEM analysis. Novel approach for the numeric of breakage appears to produce reassuring physically consistent results that improve earlier made unnecessary simplistic assumptions about breakage. To evaluate the effect of particle breakage on rockfill's behavior, two test series with and without breakable particles have been simulated under a biaxial test with different confining pressures. Results indicate that particle breakage reduces the internal friction but increases the deformability of rockfill. Review of the v–p variation of the simulated samples shows that the specific volume has initially been reduced with the increase of mean pressures and then followed by an increase. Also, the increase of stress level reduces the growing length of the v–p path and it means that the dilation is reduced. Generally, any increase of confining stress decreases the internal friction angle of the assembly and the sample fail at higher values of axial stresses and promotes an increase in the deformability. The comparison between the simulations and the reported experimental data shows that the numerical simulation and experimental results are qualitatively in agreement. Overall the presented results show that the proposed model is capable with more accuracy to simulate the particle breakage in rockfill.     

DEM investigation on the breakage of spherical aggregate under multi-contact loadings

Particle crushing is commonly encountered during the storage, transportation, and handling of granular assemblies. This work is aimed at ascertaining the applicability of four particle breakage criteria frequently mentioned in literature. Discrete element method (DEM) simulations were conducted to investigate the crushing of spherical aggregates under multicontact loadings. Mean and major principal stress criteria, octahedral shear stress criterion, and maximal contact force (MCF) criterion were then evaluated based on the obtained DEM results. It is found that the first three parameters all vary with the number of loading contacts, demonstrating they cannot predict the crushing of particles under arbitrary loading configuration. Simulation results indicate that the MCF at crushing is related to the number and the spatial arrangement of loading contacts. Thus, strictly speaking, this parameter cannot uniquely define particle breakage either. The influences of the microstructural heterogeneity on the breakage strength of particle and also on the applicability of MCF criterion are discussed.     

Simulation of dry powder inhalers: Combining micro‐scale,meso‐scale and macro‐scale modeling

The flow of carrier particles, coated with active drug particles, is studied in a prototype dry powder inhaler. A novel, multiscale approach consisting of a discrete element model (DEM) to describe the particles coupled with a dynamic large eddy simulation (LES) model to describe the dynamic nature of the flow is applied. The model consists of three different scales: the micro‐scale, the meso‐scale, and the macro‐scale. At the micro‐scale, the interactions of the small active drug particles with larger carrier particles, with the wall, with the air flow, and with each other is thoroughly studied using discrete element modeling and detailed computational fluid dynamics (CFD), i.e., resolving the flow structures around the particles. This has led to the development of coarse‐grained models, describing the interaction of the small active drug particles at the larger scales. At the meso‐scale the larger carrier particles, and all of their interactions are modeled individually using DEM and CFD‐LES. Collisions are modeled using a visco‐elastic model to describe the local deformation at each point of particle‐particle contact in conjunction with a model to account for cohesion. At the macro‐scale, simulations of a complete prototype inhaler are carried out. By combining the relevant information of each of the scales, simulations of the inhalation of one dose from a prototype inhaler using a patient relevant air flow profile show that fines leave the inhaler faster than the carrier particles. The results also show that collisions are not important for particle‐particle momentum exchange initially but become more important as the particles accelerate. It is shown that for the studied prototype inhaler the total release efficiency of the fine particles is between 10 and 30%, depending on the Hamaker constant, using typical settings for the properties of both particles. The results are also used to study regions of recirculation, where carrier particles can become trapped, and regions where fines adhere to the wall of the device. © 2016 American Institute of Chemical Engineers AIChE J, 63: 501–516, 2017     

Revealing cracking and breakage behaviours of gibbsite particles

Mitigating gibbsite particle cracking and breakage during industrial alumina production can increase the quality of smelter grade alumina product by reducing the ultrafine particle content. Therefore, it is essential to investigate the particle cracking during static calcination and the breakage of calcined gibbsite particles under external force. In this work, we investigated the impact of the calcination ramping rate and the crystallite size on gibbsite particle cracking during static calcination. A slow ramping rate and a large pristine crystallite size tend to increase particle cracking. Apart from the study of particle cracking behaviour, we also investigated the breakage of calcined gibbsite particle under external force. Cracks on the particle surface can initiate breakage within the crystallite and along the grain boundary under external force. The breakage within crystallite occurs as the cleavage of the crystallite, while the breakage along the grain boundary leads to the shedding of a whole crystallite. We further explored the factors influencing the strength of calcined gibbsite particles. With increasing calcination temperature, the strength of particle increases when gibbsite converts to boehmite, and then decreases when boehmite converts into amorphous alumina. Particles containing smaller crystallites and calcined with fast ramping rates exhibit higher resistance to breakage.     

A two-dimensional study of the rupture of funicular liquid bridges

An analysis of the rupture behaviour of liquid bridges in simple granular systems is reported. Wet granules present a complex structure in which primary particles are held together at a microscopic scale by means of capillary forces mediated by a liquid binder. These capillary interactions control the mechanical properties of the particle assemblies as well as the kinetics and pathways of granule growth. The evaluation of the interaction between contacting particles by means of the interstitial liquid binder in its various possible configurations has recently been reported for two-dimensional systems of contacting particles (J. Colloid Interface Sci. 220 (1999) 42). In the current work particle separation forces and bridge rupture have been examined for the symmetric separation pathways in all possible wetted states of triplets of particles. The separation force and the energy of the system due to the liquid capillary action have been calculated during the process of separation, which is assumed to occur slowly through a sequence of equilibrium configurations. A wide range of behaviour is found for the rupture processes of the different liquid configurations.     

Shear flow of assemblies of cohesive granular materials under constant applied normal stress

We have studied plane shear flow of nearly homogeneous assemblies of uniformly sized, spherical, cohesive particles in periodic domains under constant applied normal stress. Our focus has been on (a) exploration of the effect of inter-particle attractive forces on the flow behavior manifested by dense assemblies under constant applied normal stress, and (b) comparison of the rheological characteristics observed under constant-applied normal stress and constant-volume conditions. As a model problem, the cohesion resulting from van der Waals force acting between particles is considered. Simulations were performed for different strengths of cohesion, shear rates, and applied stresses. From each simulation, the volume fraction, shear stress and the average coordination number have been extracted. We find that cohesive assemblies sheared under constant applied normal stress shear differently from those sheared at constant volume only in the dynamic sense, while the time-averaged rheological characteristics are essentially indistinguishable. At constant volume, the fluctuations in shear stress are larger than, but have the same dependence on cohesion as under constant applied normal stress. This study has also exposed a pronounced dependence of the apparent coefficient of friction on particle volume fraction in the quasi-static flow regime.     

Viscosities and Sintering Rates of a Two-Dimensional Granular Composite

The effective sintering rates and viscosities of two-dimensional granular composites are studied using discrete computational models. The composites consist of randomly mixed soft and hard spheres on a triangular lattice. The numerical formulation is based on a requirement of quasistatic equilibrium for each particle in the packing, Two distinct models are employed: the truss model in which only force equilibrium is enforced for each particle, and the beam model in which force and moment equilibrium are enforced for each particle. The differences between the two models are illustrated by the specific problem studied. The effective composite properties display a transition from soft to hard behavior at a well-defined fraction of hard particles. If contacts between hard particles resist interpenetration, shear, and bending ( bonded case), the transition coincides with the site percolation threshold. If contacts between hard particles can slide and bend but resist inter-penetration ( sliding case), the transition coincides with percolation of triangular units. Thresholds and scaling of effective viscosities and sintering rates are computed. Because of the mathematical analogy between linear viscous and elastic deformations, these results can also be used to predict the effective moduli and coefficients of thermal expansion of such composites.     

Utilization of a Radial Temperature Model for Heat Conduction within Spherical Particles to Model Granular Assemblies

A heat transfer (DEM) model for application in the particle based discrete element simulation method is presented. It utilizes an analytical solution of the heat diffusion equation for a solid spherical particle to obtain temporal and radial solutions of the temperature distributions within the particles. This radial temperature model avoids the shortcomings of the usual assumption of spatially uniform temperature profiles in particles. The concept is designed to minimize computing power and memory requirement in order to allow the computation of granular assemblies consisting of a large number of particles. Results obtained for a particle subject to transient convective boundary conditions are compared with a Crank‐Nicholson implicit scheme as numerical reference solution. A first implementation of the radial temperature model in a discrete element code reveals the additional computational cost as negligible compared to the demands of contact identification and force calculation.     

Influences of loading rate and preloading on the mechanical properties of dry elasto‐plastic granules under compression

To ensure high quality of granular products post‐industrial operations, it is necessary to precisely define their micro–macro mechanical properties. However, such an endeavor is arduous, owing to their highly inhomogeneous, anisotropic and history‐dependent nature. In this article, we present the distributed granular micromechanical and macromechanical, energetic and breakage characteristics using statistical distributions. We describe the material behavior of elastoplastic zeolite 4AK granules under uniaxial compressive loading until primary breakage, and localized cyclic loading up to different maximum force levels, at different displacement‐controlled loading rates. The observed force‐displacement behavior had been approximated and further evaluated using well‐known contact models. The results provide the basis for a detailed analysis of the viscous behavior of zeolite 4AK granules in the moist and wet states, indicating that higher compressive loads are required at higher displacement‐controlled loading rates to realize equivalent deformation and breakage probability achieved by loads at lower displacement‐controlled loading rates. © 2014 American Institute of Chemical Engineers AIChE J 60: 4037–4050, 2014     

Analysis of catalyst particle strength by impact testing: The effect of manufacturing process parameters on the particle strength

The mechanical strength of porous alumina catalyst carrier beads, used in the reforming units with continuous catalytic regeneration, was measured by impact testing. With this testing method particle strength can be measured at higher strain rates than the traditional crushing test method, hence providing a better simulation of pneumatic conveying and chute flow conditions, and also a large number of particles can be tested quickly. This is important for particles with a brittle failure mode such as the alumina particles used in this work as a wide distribution of mechanical strength usually prevails. Extensive impact testing was carried out first with an industrial sample, in order to understand the failure mechanism of this type of particles and to develop a methodology for analysing the extent of breakage by impact. Then the method was used to analyse the effect of a number of process parameters, such as filler, macroporosity and drying procedure on the particle strength with the aim of optimising the manufacturing process. The impact test results were then used to test the model of breakage behaviour of particulate solids proposed by Vogel and Peukert [Vogel and Peukert, Breakage behaviour of different materials—construction of a mastercurve for the breakage probability. Powder Technol., 129 (2003) pp. 101-110].     

基于颗粒尺度的离散颗粒传热模型

颗粒间传热在诸多工业过程中有着十分重要的作用。详细考虑颗粒间传热机理,对颗粒间各传热途径建模,包括颗粒内部导热、颗粒粗糙表面传热、颗粒表面气膜及接触颗粒间隙气膜传热,并与离散颗粒模型(DEM)耦合,建立颗粒尺度下离散颗粒传热模型。以固定床为对象,考察颗粒粒径、颗粒比热容、颗粒热导率及压缩负载对固定床有效传热系数的影响,并将本文计算值和文献的实验值及模型预测值对比,结果表明,该模型可定量预测固定床有效传热系数。本文建立的离散颗粒传热模型为合理预测颗粒体系内的传热提供了一种有效方法。     

Breakage model development and application with CFD for predicting breakage of whey protein precipitate particles

Particle breakage due to fluid flow through various geometries can have a major influence on the performance of particle/fluid processes and on the product quality characteristics of particle/fluid products. In this study, whey protein precipitate dispersions were used as a case study to investigate the effect of flow intensity and exposure time on the breakage of these precipitate particles. Computational fluid dynamic (CFD) simulations were performed to evaluate the turbulent eddy dissipation rate (TED) and associated exposure time along various flow geometries. The focus of this work is on the predictive modelling of particle breakage in particle/fluid systems. A number of breakage models were developed to relate TED and exposure time to particle breakage. The suitability of these breakage models was evaluated for their ability to predict the experimentally determined breakage of the whey protein precipitate particles. A “power-law threshold” breakage model was found to provide a satisfactory capability for predicting the breakage of the whey protein precipitate particles. The whey protein precipitate dispersions were propelled through a number of different geometries such as bends, tees and elbows, and the model accurately predicted the mean particle size attained after flow through these geometries.     

Determination of Breakage Parameters in Turbulent Fluid‐Fluid Breakage

Numerous sets of single‐particle breakage experiments are required in order to provide a sufficient database for improving the modeling of fluid particle breakage mechanisms. This work focuses on the interpretation of the physical breakage events captured on video. In order to extract the necessary information required for modeling the mechanisms of the fluid particle breakage events in turbulent flows, a well‐defined image analysis procedure is necessary. Two breakage event definitions are considered, namely, initial breakup and cascade breakup. The reported breakage time, the number of daughter particles created, and the daughter size distribution are significantly affected by the definition used. For each breakage event definition, an image analysis procedure is presented.     

Micro‐ and nanostructures of polylactide stereocomplexes and their biomedical applications

The discovery of stereocomplexation, secondary interaction between enantiomeric poly(l ‐lactide) (PLLA) and poly(d ‐lactide) (PDLA) provides a method for the creation of novel biomaterials with distinctive chemical and physical stability. Stereocomplexation opens a new way for the preparation of diverse micro‐ and nanostructures such as uniform microspheres, hollow particles, micelles, nanocrystals, nanofibres, nanotubes and polymerosomes. Herein, we describe the design of stereocomplex assemblies for specific applications and methods for their preparation. This review focuses primarily on the use of stereocomplex assemblies in biomedical applications due to the improved stability and physicochemical properties in comparison to enantiomeric polylactides. To make the polylactide stereocomplexes soluble in water and, as a consequence, to improve compatibility with the human body, various amphiphilic copolymers with PLLA and PDLA enantiomeric segments can be prepared. Stereocomplexation can facilitate their self‐assembly into micro‐ and nanoparticles, stabilize the particle size and morphology and can also have an influence on the in vivo degradation rate and cytotoxicity of these materials. Stimuli‐responsiveness in stereocomplex assemblies can be achieved by copolymerization of lactide with, for example, thermoresponsive N‐isopropylacrylamide or amino acids with pH‐sensitive pendant groups. Stereocomplex micro‐ and nanoparticles are used for encapsulation of various bioactive compounds: anticancer drugs, antibiotics and proteins. Finally, examples of materials in which high thermal and mechanical stabilities delivered as a result of stereocomplexation play a crucial role, i.e. hydrogels, nanofibres, microcellular foams and artificial skin, are described. The preparation of biomaterials and biomedical systems based on polylactide stereocomplex assemblies opens new opportunities in this field. © 2015 Society of Chemical Industry     

Comparison of Construction Method for DEM Simulation of Ellipsoidal Particles

Discrete element model was developed to simulate the ellipsoidal particles moving in the moving bed. Multi-element model was used to describe a ellipsoidal particle, the contact detection algorithm of ellipsoidal particle was developed, and both contact force and gravity force were considered in the models. The simulation results were validated by our experiment. Three algorithms for representing an ellipsoidal particle were compared in macro and micro aspects. The results show that there exists big difference in the microscopic parameters such as kinetic energy, rotational kinetic energy, deformation, contact force and collision number which leads to the difference of macroscopic parameters. The relative error in the discharge rate and tracer particle position is the largest between 3-tangent-element representation and experimental results. The flow pattern is similar for the 5-element and 3-intersection representations. The only difference is the discharge rate of 5-element representation is larger than the experimental value and that of the 3-intersection representation has the contrary result. Finally the 3-intersection- element representation is chosen in the simulation due to less computing time than that of the 5-element representation.     

椭球形颗粒动力效应模型(DEM)构建方法的比较(英文)

Discrete element model was developed to simulate the ellipsoidal particles moving in the moving bed.Multi-element model was used to describe a ellipsoidal particle,the contact detection algorithm of ellipsoidal particle was developed,and both contact force and gravity force were considered in the models.The simulation results were validated by our experiment.Three algorithms for representing an ellipsoidal particle were compared in macro and micro aspects.The results show that there exists big difference in the microscopic parameters such as kinetic energy,rotational kinetic energy,deformation,contact force and collision number which leads to the difference of macroscopic parameters.The relative error in the discharge rate and tracer particle position is the largest between 3-tangent-element representation and experimental results.The flow pattern is similar for the 5-element and 3-intersection representations.The only difference is the discharge rate of 5-element representation is larger than the experimental value and that of the 3-intersection representation has the contrary result.Finally the 3-intersectionelement representation is chosen in the simulation due to less computing time than that of the 5-element representation.     

Three dimensional discrete element modeling of granular media under cyclic constant volume loading: A micromechanical perspective

Discrete element modeling is employed to investigate the micromechanics of two granular assemblies subjected to constant-volume cyclic loading. For this purpose, two assemblies of spherical particles are modeled at the same confining pressure but with two different void ratios. The cyclic behaviors of the assemblies are inspected and the micromechanical parameters and their variations during cyclic loading are carefully observed and analyzed. The evolution of contact force networks with the progression of the loading cycles confirms that the contact force networks are hysteretic and their formation depends on the previous strain conditions of the assemblies. The distributions of the contact normals and their normal forces are also investigated to obtain a quantitative insight of the changes in the contact force networks. The probability distributions of the normal and tangential forces during cyclic loading are similar to the results of previous experimental studies that were conducted on two-dimensional specimens of granular materials. In addition, variations of the fabric tensors, which were calculated for strong contacts, are studied to trace the changes of the structural anisotropy of the specimens. The results suggest that the structural anisotropy of the specimens increases dramatically when they approach the state of liquefaction and that the degree of anisotropy is more profound in the strong contacts. Finally, the displacements of the particles during specific loading cycles are calculated to determine the relation between the movements of the particles and the changes in the macro-scale behavior of the two assemblies. The results of this study elaborate the origin of liquefaction phenomena with respect to the microstructure of the granular soils, showing the role of different mode of contacts failure in micro-scale (sliding and rolling) on the overall observed behavior of granular soils with two different relative densities, moreover the importance of strong and weak contacts in cyclic constant-volume loading of the media. It also emphasizes on the variation of structural anisotropy in undrained cyclic loading of granular media and its relationship with common soil behavior in macro-scale during liquefaction failure.     

Particle attrition mechanism with a sonic gas jet injected into a fluidized bed

High velocity gas jets in fluidized beds provide substantial particle attrition: they are used industrially to control the particle size in fluid bed cokers and to grind products such as toner, pharmaceutical or pigment powders. One method to control the size of the particles in the bed is to use an attrition nozzle, which injects high velocity gas and grinds the particles together. An important aspect of particle attrition is the understanding and modeling of the particle breakage mechanisms. The objective of this study is to develop a model to describe particle attrition when a sonic velocity gas jet is injected into a fluidized bed, and to verify the results using experimental data. The model predicts the particle size distribution of ground particles, the particle breakage frequency, and the proportion of original particles in the bed which were not ground. It was found that the particle breakage frequency can be used to predict the attrition results in different bed sizes. A correlation was also developed, which uses the attrition nozzle operating conditions such as gas density and equivalent speed of sound to predict the mass of particles broken per unit time.