Experimental investigation of the impact breakage characteristics between grinding media and iron ore particle in ball mills

The particle breakage of the ball mill is an extremely complicated breakage process. It is difficult to quantify and describe the particle breakage behavior. In this study, a drop-ball experimental setup was developed to demonstrate the impact process of grinding media on ore particles. The quantitative analysis of the effects of particle size, impact energy, and the number of impacts on particle breakage behavior was performed separately. The results show that the breakage probability model and product size distribution model used can be excellent to predict the particle breakage behavior for the single-particle impact experiments. The breakage probability of particles is highly sensitive to impact energy and particle size, exponentially increasing with the increase of impact energy. In addition, the application of the t_n-t₁₀ relationship provides a convenient means to characterize and predict the particle size distribution. In multi-layer particle impact experiments, the captured thickness of ore particles is approximately 2 layers during the crushing process. The broken mass of iron ore particles is proportional to the number of concessive impacts at different impact energies. This paper provides theoretical and methodological support for the evaluation and optimization of particle breakage in ball mills.     

Effect of lognormal particle size distributions on particle spreading in additive manufacturing

Additive manufacturing (AM) has attracted much attention worldwide in various applications due to its convenience and flexibility to rapidly fabricate products, which is a key advantage compared to the traditional subtractive manufacturing. This discrete element method (DEM) study focusses on the impact of particle polydispersity during the particle spreading process on parameters that affect the quality of the final product, like packing and bed surface roughness. The particle systems include four lognormal particle size distribution (PSD) widths, which are benchmarked against the monodisperse system with the same mean particle diameter. The results reveal that: (i) the solid volume fraction of the initial packed particle bed in the delivery chamber increases then plateaus as the PSD width increases; (ii) regardless of PSD width, the solid volume fraction of the particle bed increases with spreading layer height before compression, but decreases with layer height after compression; (iii) the bed surface roughness increases with PSD width or layer height both before and after the compression of the spreading layer; (iv) the extent of increase in solid volume fraction during compression is correlated with the extent of decrease in bed surface roughness; and (v) the broader PSDs exhibit larger fluctuations of solid volume fraction of the particle bed and bed surface roughness due to greater variability in the arrangement of particles of different sizes. The results here have important implications on the design and operation of particle-based AM systems.     

Influence of particle breakage on the dynamic compression responses of brittle granular materials

The dynamic compression responses of dry quartz sand are tested with a modified spilt Hopkinson pressure bar (MSHPB), and the quasi-static compression responses are tested for comparison with a material testing system. In the experiments, the axial stress–strain responses and the confining pressure of the jacket are both measured. Comparison of the dynamic and the quasi-static axial stress–strain curves indicate that dry quartz sand exhibits obvious strain-rate effects. The grain size distributions of the samples after dynamic and quasi-static loading are obtained with the laser diffractometry technique to interpret the rate effects. Quantitative analyses of the grain size distributions show that at the same stress level, the particle breakage extent under quasi-static loading is larger than that under dynamic loading. Moreover, the experimental and the theoretical relationships of the particle breakage extent versus the plastic work show that the energy efficiency in particle breakage is higher under quasi-static loading, which is the intrinsic cause of the strain-rate effects of brittle granular materials. Using the discrete element method (DEM), the energy distributions in the brittle granular material under confined compression are discussed. It is observed that the input work is mainly transformed into the frictional dissipation, and the frictional dissipation under dynamic loading is higher than that under quasi-static loading corresponding to the same breakage extent. The reason is that more fragmentation debris is produced during dynamic breakage of single grains, which promotes particle rearrangement and the corresponding frictional dissipation significantly.     

Alternative approach for defining the particle population requirements for static image analysis based particle characterization methods

For image based particle characterisation approaches one of the most common discussion points is determining the number of particles required to have statistical confidence that the measurement is able to adequately describe the distribution of the sample. This topic becomes significantly more challenging when applied to the extraction of single component size distributions from multi-component samples.The aim of this work was to propose a means to accurately assess the particle number requirements using a method specific approach. The method applies a sub-sampling method to the original imaged dataset in order to provide an understanding of the impact of sub-sampling on the ability to accurately reproduce the original distribution.The method was applied to understand the particle number requirements for two batches of theophylline anhydrous with varied particle size distributions, using the input size distribution to guide the requirements for the subsequent multi-component samples of both materials.The results demonstrate the utility of the method to determine the appropriate number of particles required to recreate the size distributions. Whilst the minimum number of particles required to be sampled can be estimated, how those particles are sampled can also affect the validity of the measurement and must be taken into consideration.     

Experimental identification of entropy model of comminution process

The entropy model based on population balance enables theoretical prediction of particle size distribution of comminution product. Selection and breakage functions occur in this model. The form of the selection function was determined experimentally. Informational entropy was used for the breakage function determination. Parameters of both functions can be estimated from experiments. The parameter identification of the entropy model was carried out on the basis of research on limestone comminution. Grinding tests were carried out in a laboratory fluidised bed jet mill. The results of the experimental identification confirm the accuracy of the entropy model.     

A general approach for the characterization of fragmentation problems

A general approach for the quantitative and systematic characterization of fragmentation problems, which is based on the Weibull statistics, is presented. A model, initially developed for materials stressed under impact with respect to their breakage probability, has been successfully applied to the characterization of compressive comminution, fragmentation of nanoparticle agglomerates and destroying of adhesive bonds. The experimental results from the slow compression comminution and from the comminution by falling weight match for various materials and particle sizes exactly to the master curve deduced for impact comminution. However, the material parameters determined for compression comminution are not identical for one and the same material to that determined by impact comminution. This indicates that the two model parameters are not pure material characteristics as assumed from the impact experiments, but depend on the stress mechanism. The dependence of the fragmentation degree on the particle size and the energy input observed when impacting particles in the micrometer to millimeter range has been proven also for nanoparticle agglomerates. Furthermore, a model analogous to that for breakage has been deduced for the quantification of the failure of adhesive bonds.     

Fracture mechanisms and particle shape formation during size reduction of a model food material

The importance of particle shape to powder properties warrants examination of the effect of size reduction on particle shape formation. In this study, a model food material (dried gelatinized starch) was comminuted in an impact breakage gun, a hammer mill (with and without a screen) and in a blender. After sieving, particle shape at selected sizes was assessed as deviation from sphericity. Generally, particle shapes were elongated at smaller size, except for those produced by unscreened hammer milling. Particle shapes were unaffected by impact velocity in the gun, but were rounded by increased milling. Fractography was used to demonstrate how elongated particles formed. During fracture, fracture fronts were disturbed by air holes in the material, creating cleavage steps. Subsequent undercutting of the steps as fracture planes spread released the elongated particles. Such particle formation mechanisms may account for anomalous size distribution results at early stages of grinding. Particle shape differences between mills and single impact breakage were ascribed to particle selection mechanisms surmised to be operating in the mill. Both material properties and the size reduction method were shown to affect particle shape, thus fracture progress in a given material should be studied if particles of specific shapes are to be produced by comminution.     

Evaluation of direct quadrature method of moment for the internally circulating fluidized bed simulation with ultrafine particles

In the framework of the Euler-Euler gas–solid two-fluid model, the particle population balance equation is solved by the direct quadrature method of moment. The dynamic process of ultrafine particle movement and aggregation in an internally circulating fluidized bed is simulated. The distribution of the concentration and velocity of the agglomerates in the flow process is given, and the changes of the moments in the bed are shown. The effects of different breakage coefficients and inlet gas rates on the concentration distribution of agglomerates are compared. The results show that the particle size decreases with the increase of breakage coefficient, and the time required to reach steady fluidization state increases; the higher the inlet velocity, the better the effect of circulating particles in the bed. When there is a certain gas velocity difference between the two sides, the effect of circulating particles in the bed is better.     

DEM simulation of the shear behaviour of breakable granular materials with various angularities

Particle shape is an important factor that affects particle breakage and the mechanical behaviour of granular materials. This report explored the effect of angularity on the mechanical behaviour of breakable granular materials under triaxial tests. Various angular particles are generated using the quasi-spherical polyhedron method. The angularity α is defined as the mean exterior angle of touching faces in a particle model. A breakable particle is constructed as an aggregate composed of coplanar and glued Voronoi polyhedra. After being prepared under the densest conditions, all assemblies were subjected to triaxial compression until a critical state was reached. The macroscopic characteristics, including the shear strength and dilatancy response, were investigated. Then, particle breakage characteristics, including the extent of particle breakage, breakage pattern and correlation between the particle breakage and energy input, were evaluated. Furthermore, the microscopic characteristics, including the contact force and fabric anisotropy, were examined to probe the microscopic origins of the shear strength. As α increases, the peak shear strength increases first and then remains constant, while the critical shear strength generally increases. Assemblies with larger angularity tend to cause more serious particle breakage. The relative breakage is linearly correlated with α under shear loading. Compared with unbreakable particles, the peak shear strength and the critical volumetric strain decline, and the degree of decline linearly increases with increasing α.     

Towards realistic characterisation of chemical reactors: An in-depth analysis of catalytic particle beds produced by sieving

Optimization of large-scale fixed particle bed catalytic reactors requires extensive insight into the multi-scale bed structure, even down to the micrometre scale. Theoretical studies of chemical reactors provide a time- and cost-effective means to supporting the optimisation process. However, they rely on simplified assumptions for the particles, e.g. homogeneous perfect spheres. In practise, the preparation of catalytic particles cannot attain this level of uniformity. Typical preparation techniques, such as sieving, are conducted with the aim of obtaining particle size distributions within a pre-defined range, governed by the sizes of the sieves. However, such methods offer limited control in the actual particle sizes and shapes. This paper evaluates the impact of sieving on the resulting particles and overall structural morphology of catalytic beds. The bed structure is quantified using micro-focus computed tomography (µ-CT), enabling the non-destructive examination and analysis of over 150 thousand particles, in terms of particle size, shape, uniformity, and interparticle porosity. Furthermore, the chemical performance of the resulting beds is compared. The detailed characterisation achieved paves the way for the evolution of more rigorous computational models coupling intricate, localised hydrodynamics with realistic chemical processes. Validation of such models at the lab-scale will accelerate the development of more accurate large-scale models.     

Realizing fragment spawning and fragment growth in the parallelized Discrete Element Method (DEM) during modelling of comminution

The particle based Discrete Element Method (DEM) can be applied to examine comminution processes. In this study, a DEM framework has been extended to model particle breakage without mass loss. After a breakage event occurs, spherical particles, as often considered in the DEM, are replaced by size reduced spherical fragments. During the following time steps, the fragments grow to their desired sizes, so that the mass loss can be counterbalanced. Previously defined overlaps with adjacent unbroken and broken particles (fragments) as well as walls are allowed. The breakage model has been realized in a parallelized DEM framework because comminution processes are often attributed to large numbers of particles and by parallelization the computational time can be reduced efficiently. An oedometer (one-dimensional compression in axial direction of a confined particle bed) has been modelled to investigate the parallelization efficiency and the influence of the permitted overlaps during the growth process on the growth duration. A simplified roller mill has been considered to examine the applicability of the breakage procedure considering parallelization. The results show that parallelization reduces computational time considerably. The breakage procedure is suitable to model comminution processes involving even densely packed particle systems and is superior to existing approaches.     

DEM Simulation of Particle Comminutionin Jet Milling

A combined discrete element method (DEM) and CFD numerical model was developed to simulate particle comminution in a jet mill. The DEM was used to simulate the motion of the particles in the gas flow. For this, the compressible Reynolds Averaged Navier-Stokes (RANS) equations were used to describe the gas flow field inside a given size's jet mill. Ghadiri's models for breakage and chipping were implemented in the simulation to define the reduction of the particle's size during jet milling. The size distributions of the particles after grinding were obtained numerically. The prediction of the numerical simulation for the median particle size d 50 after grinding was qualitative compared with experimental results for the different operating conditions (i.e., feed rate, angle of grinding nozzles, volumetric rate of grinding air, etc.). The comparison shows good agreement with the experimental observation. The results shows that the feed rate, angle of feeding nozzle, and feeding air's flow rate have more influence on the breakage and chipping of particles in jet milling. In addition, a parametric study was performed to obtain the desired operation conditions.     

Dry Comminution of Silicon Carbide Particles in a Fluidized Bed Opposed Jet Mill: Kinetics of Batch Grinding

This study investigated the batch grinding kinetics of silicon carbide (SiC) particles in a fluidized bed opposed jet mill by population balance modeling. The selection and breakage functions were obtained by the first Kapur function method. The breakage behaviors for various SiC particles obtained under different experimental conditions (such as inlet air pressure, feed load, and distance between nozzle outlet and jet meeting point) in the jet mill were discussed. In addition, a polynomial model was proposed to predict the relation between the Kapur function and the particle size in the jet mill. The product size distributions obtained under various operating conditions from the jet mill could be simulated by modeling.     

DEM Simulation of Particle Comminutionin Jet Milling

A combined discrete element method (DEM) and CFD numerical model was developed to simulate particle comminution in a jet mill. The DEM was used to simulate the motion of the particles in the gas flow. For this, the compressible Reynolds Averaged Navier-Stokes (RANS) equations were used to describe the gas flow field inside a given size's jet mill. Ghadiri's models for breakage and chipping were implemented in the simulation to define the reduction of the particle's size during jet milling. The size distributions of the particles after grinding were obtained numerically. The prediction of the numerical simulation for the median particle size d 50 after grinding was qualitative compared with experimental results for the different operating conditions (i.e., feed rate, angle of grinding nozzles, volumetric rate of grinding air, etc.). The comparison shows good agreement with the experimental observation. The results shows that the feed rate, angle of feeding nozzle, and feeding air's flow rate have more influence on the breakage and chipping of particles in jet milling. In addition, a parametric study was performed to obtain the desired operation conditions.     

Breakage behaviour of single rice particles under compression and impact

Grain breakage is mainly caused by impact and compression load in harvest and processing. At present, the mechanism of grain breakage under loading, especially the statistics of breakage characteristics, is not clear. The analysis of breakage process of single particle provides a foundation for the understanding of breakage mechanisms. This paper aims to examine breakage behaviour of a single rice particle under compression and impact experiments. Firstly, the equivalent diameter (D_p) and moisture content (MC) of rice particles were regarded as important factors that may affect breakage. Then, by performing quasi-static compression and dynamic impact experiments under different values of D_p and MC, the detailed compression failure force, rice strength, breakage modes, breakage probability, and the breakage probability models were analyzed comprehensively. Furthermore, breakage processes of rice particles under these two breakage experiments were compared and discussed. Finally, the Weibull distribution of the compression breakage characteristics, the “non-size effect” of compression and impact breakage, the tensile failure forms, velocity threshold of impact breakage and the close relationship between the breakage characteristics under impact and compression were mainly found. The findings are useful for providing guidance for the revelation of breakage mechanism and optimizing related agricultural equipment design.     

The influence of particle orientation on the loading condition of pebbles in fluvial gravel

The loading conditions of pebbles in fluvial gravel deposits were studied with different degrees of preferred particle orientation. Sediments that are comprised of non-spherical particles often show a preferred particle orientation, due to dynamic sedimentation. Here, the impact of this effect on the loading conditions of the particles and its implication on particle breakage was investigated by using discrete element simulations in three dimensions. The numerical models are based on the size and shape distribution of pebbles from a natural gravel sample. In addition, the particle size in some of the models was chosen to be uniform, to study the influence of the particle size distribution on the loading condition. Fluvial pebbles, whose shapes can be at best approximated by ellipsoids, were efficiently simulated in the discrete element models by the use of clumps. The results show that a preferred orientation of approximate ellipsoidal sedimentary particles has only a minor effect on the number and the position of particle contacts but leads to a significant load transfer from the rim to the centre of the oblate sides of the ellipsoidal particles, in comparison to an assembly of arbitrarily oriented particles. The comparison of the different particle size models indicates that the influence of the particle size distribution on the loading condition is relatively low. The results have significant implications for the breakage rate of non-spherical particles in sediments under load.     

Effects of main particle diameter on improving particle flowability for compressed packing fraction in a smaller particle admixing system

Particle flowability can be improved by admixing particles smaller than the original particles (main particles). However, the mechanisms by which this technique improves flowability are not yet fully understood. In this study, we examined compressed packing in a particle bed, which is affected by particle flowability. To estimate the mechanism of improvement, we investigated the effects of the main particle diameter on the improvement of compressed packing fractions experimentally.The main particles were 397 and 1460 nm in diameter and the admixed particles were 8, 21, 62, and 104 nm in diameter. The main and admixed particles were mixed in various mass ratios, and the compressed packing fractions of the mixtures were measured. SEM images were used to analyze the coverage diameter and the surface coverage ratio of the admixed particles on the main particles. The main particle packing fraction was improved as the diameter ratio (=main particles/admixed particles) increased. This was explained by a linked rigid-3-bodies model with leverage. Furthermore, the actual surface coverage ratio at which the most improved packing fraction was obtained decreased with increasing main particle diameter. This was explained by the difference in the curvature of the main particle surface.     

The role of particle size on the performance of pumice as a supplementary cementitious material

A critical area overlooked in previous research on pumice is understanding how its physical characteristics influence its behavior as a supplementary cementitious material (SCM). This study investigated three pumices with different particle size distributions to observe whether these porous materials exhibit enhanced nucleation and growth of hydration products, in the same way as non-porous materials, and whether the rate of pozzolanic reaction can be changed through particle size. The effect of particle size on compressive strength, rheology and resistance to alkali silica reaction (ASR) was also evaluated. Results showed that reducing particle size increased the rates of cement hydration, pozzolanic reaction, and compressive strength gain, while also increasing mixture viscosity. Interestingly, particle size did not impact the yield stress of the mixture or the resistance to ASR. These new findings give insight about how the particle size of pumice can be used to overcome drawbacks reported in previous literature.     

Multi-resolution fuzzy clustering approach for image-based particle characterization for particle systems

Online characterization of particles is an important step for maintaining desired product quality in particulate processes. Direct real-time image analysis is a promising method for monitoring particle systems, and is becoming increasingly more attractive due to availability of high speed imaging devices and equally powerful computers. Performing image segmentation (separation of objects (particles) within one image) accurately becomes a key issue in particle image analysis. This paper presents a novel technique based on combining wavelet transform and Fuzzy C-means Clustering (FCM) for particle image segmentation. Through performing wavelet transform on images, the noise and high frequency components of images can be eliminated and the textures and features can be obtained. FCM is then used to divide data into two clusters to separate touching objects. To quantitatively evaluate this method, a case study involving a particle image is investigated. The procedure of selecting optimum wavelet function and decomposition level for this image is presented. ‘Fuzzy range’ is used as a derived feature for segmentation. The number of particles, particle equivalent diameters, and size distribution before and after partition are discussed. The results show that this method is effective and reliable.     

Direct tensile tests on particulate agglomerates for the determination of tensile strength and interparticle bond forces

The importance of direct tensile tests on solid and capillary bonded particulate agglomerates is investigated and compared to compression test measurements. The properties of wet agglomerates are varied by changing the contact angle by means of functionalization of the particle surface. Process conditions are considered by variation of ambient humidity. A qualitative evaluation of the results is performed by analyzing the measured force distance curves of different tensile tests. The results are quantitatively evaluated by calculating the breakage strength, mass related breakage energy and breakage probability showing that the ratio between tensile and compressive tests is highly dependent on the adjusted parameters. Next to the process parameter effect, also the influence of agglomerate size is considered. Tensile strength data are used to estimate the single bond forces between the primary particles of the agglomerates. Tensile and compressive test results are compared to numerical results (DEM) of agglomerate breakage using an elastic stiff bond model.