Breakage Model Research Articles

Prediction of zinc extraction from aqueous solution using iron oxide nanoparticles embedded formulation for tuning emulsion liquid membrane stability

The contamination of industrial wastewater with heavy metals poses a threat to both aquatic and human life. In this study, emulsion liquid membrane (ELM) as a great potential process was applied to remove and recover zinc (Zn) from industrial wastewater. However, the instability of ELM continues to hinder their commercialization. Consequently, this research focuses on studying the stability of water-in-oil-in-water (W/O/W) emulsion in ELM with the aid of nanoparticles in the formulation. The emulsion stability measurement based on volume and pH were applied. Additionally, a digital microscope with a camera is utilized to assess emulsion stability in terms of globule size. ELM formulation with incorporation of iron (III) oxide (Fe2O3) nanoparticles, and blended surfactant (Span 80 and Tween 80) were employed. The research investigates the optimal process parameters for W/O/W emulsion stability. This includes varying parameters such as nanoparticle concentration (0–0.08 % w/v), treat ratio (1:3 – 1:7), agitation speed (200–600 rpm), and time (1 – 5 min). The W/O/W emulsion with the highest stability was achieved at Fe2O3 concentration of 0.04 % (w/v), a treat ratio of 1:3, agitation speed, and time of 300 rpm and 3 min, respectively. Under these stable conditions, Zn extraction was predicted by simulation using a mathematical boundary breakage model of the process. The effects of the treat ratio, concentrations of synergist carrier (D2EHPA and Cyanex 302), stripping agent (acidic thiourea), and external feed phase were examined. The result showed that almost 100 % of Zn was extracted within 3 min at a 1:3 treat ratio, 0.03 M synergist carrier, and 1.37 M acidic thiourea for 50 ppm Zn concentration in the feed phase. This research highlights the tremendous potential of nanoparticle presence in enhancing emulsion stability and improving Zn extraction.

Evaluation of Mixing Effects and Particle Breakage on a Cross Flow Turbine with DEM

AbstractVarious effects during conveying and storage processes lead to size segregation of bulk material, but many applications require a mostly constant particle size distribution. Especially during bunker filling, segregation effects are noticed, which are further intensified by possible core flow effects. In order to reduce segregation effects during bunker filling, a cross flow turbine is installed at a bunker used for storage of blast furnace sinter. In this contribution, discrete element simulations were performed to analyze mixing effects and possible particle breakage due to the cross flow turbine. Significant mixing effects during bunker filling are noticed due to the cross flow turbine. The results show a more evenly distributed bunker outflow in terms of particle size.Particle breakage is analyzed by means of a newly developed breakage model for the Discrete Element Method (DEM). The model is based on a probabilistic particle replacement with voronoi-tessellated fragments. The validated breakage model allows high accuracy in prediction of fragment size distribution. Fragments are further breakable, which allows simulation of processes with several damaging effects. The breakage model was calibrated with a specially developed automated single particle impact tester for rapid analysis of breakage characteristics of bulk materials.

Applications of DEM particle breakage models in mineral industrial

Modeling processes are carried out in the mineral industry as well as in many areas depending on the development of computer technologies and software. Discrete Element Method (DEM) is used in modeling studies to explain the interaction of particles with other particles and communication equipment. The DEM provides the capability to simulate the movement of the granular media in a series of computational processes of each individual particle that consists of the granular media. It is becoming increasingly widely used to predict energy consumption, wear, particle breakage and particle size distribution in crushing and grinding processes that can be described in terms of granular materials using DEM. The selection of particle breakage models used by commercial software for modeling DEM particle breakage is important. In this study, it is summarized the studies have been carried out to understand the performance of particle breakage methods, which are Bonded Particle Model (BPM), Fast Breakage Model (FBM) and Particle Replacement Model (PRM), in the modeling of comminution equipment. In addition, the relationship between particle and breakage energies and theory of applied forces are described in detail for three breakage models existing in commercial DEM simulators.

DEM simulation and optimization of crushing chamber shape of gyratory crusher based on Ab-t10 model

To study and optimize the crushing chamber performance of the gyratory crusher, the impact of the crushing chamber shape on the gyratory crusher performance is explored in this paper. The discrete element method (DEM) analysis model of ore particle and gyratory crusher is established, where ore particle crushing is realized based on the Ab-t10 breakage model, and its validity is verified based on actual working conditions. On this basis, the performance of the gyratory crusher under different crushing chamber shapes is studied by combining the DEM simulation with the response surface method (RSM), and the performance prediction model is obtained based on multiple nonlinear regression. Further, the productivity is considered as the main optimization objective, the mass percentage of effective particles and the crushing force are used as auxiliary optimization objectives. The multi-objective optimization is implemented and the optimized effects are analysed by DEM simulation, and the optimized quartic equation coefficients of the concave curve are obtained. Finally, the results show that the productivity, mass percentage of effective particles, and crushing force are increased to varying degrees. Meanwhile, the clogged layer area increases to some extent, which promotes the crushing of ore particles.

Three-dimensional simulation of the influence of different flotation media in the dissolved air flotation tank through the population balance model.

Gas-liquid flow in the dissolved air flotation (DAF) tank was studied through computational fluid dynamics through the realizable k-ε model and the population balance model (PBM) to predict the gas content of different flotation mediums (air, carbon dioxide, and chlorine) at different heights of the separation zone in the DAF tank. Simultaneously, a particular focus was placed on studying the effects of bubble aggregation and breakage on gas content. The results indicated that there were virtually no bubbles present in the region below 0.1 m of the separation zone. The gas content in the separation zone could meet the needs for gas content in the DAF tank when all these three gases were adopted as flotation medium. The introduction of models for bubble aggregation and breakage resulted in lower gas content at the bottom of the separation zone and higher gas content at the top, aligning more closely with experimental data. Due to the structural similarity and similar physicochemical characteristics of carbon dioxide and water molecules, the impact of bubble aggregation and breakage on the gas content is minimal.

Breakage behavior of corn kernels subjected to repeated loadings

Studying the breakage behavior of corn kernels subjected to repeated compressive events, including at low frequency and low strain rate, are important for the development of breakage models for prediction of kernel breakage in handling and processing machines. The main purpose of this study was to identify the breakage behavior and mechanism of weakening of corn kernels under repeated loadings as affected by their moisture content and kernel thickness. Corn kernels at four moisture content levels (8.20%, 11.95%, 16.00%, 20.02%) and in four thickness ranges were subjected to repeated compressive loading between two parallel steel plates in quasi-static regime at a constant loading rate of 2 mm/min (strain rates from 4.7 × 10−3 to 1.0 × 10−2). Conducted experiments allow to observe the different grain breakage patterns, identify the crack initiation and its development, describe the weakening of kernels by changes in the total specific energy, plastic and elastic deformation energies, and the number of loading cycles to break (breakage probability) the kernels. The results indicate that the breakage models describing the damage and weakening of grains in terms of changes in the total and strain energy or changes in the stiffness can be used for understanding the effect of moisture content and thickness on breakage of corn kernels.

Evaluating the grinding performance of cutter-type disk mills using DEM-CFD simulations with a breakage model

In the recycling process of plastics, grinding is commonly employed as a pre-treatment method to facilitate molding by increasing the specific surface area. A cutter-type disk mill that mainly causes shear forces is expected to be the most efficient for grinding plastics. However, it is necessary to optimize the geometry and operating conditions of the mill. This study aimed to evaluate the grinding performance of different blade geometries in the cutter-type disk mill. To optimize the blade geometry, the discrete element method (DEM) coupled with the computational fluid dynamics (CFD) and a breakage model was employed to simulate plastic particle breakage. The simulations showed that the highest grinding performance was achieved with a grinding blade angle of 45°. Depending on the angle of the grinding blade, the effects of the power acting on the grinding blade and the force acting on the particles varied. According to these results, an appropriate blade geometry in the cutter-type disk mill can be proposed for grinding plastic. This study demonstrated that the DEM-CFD simulations are effective for evaluating the grinding performance and optimizing the blade geometry of the cutter-type disk mill.

Is It Possible to Use Breakage Models to Predict Particle Deformation?

Is It Possible to Use Breakage Models to Predict Particle Deformation?

Population balance modeling of formation and breakage of nanoparticle agglomerates in a spouted bed

A population balance framework for fluidization of Al2O3 nano-agglomerates in a ProCell-type spouted bed considering agglomeration and breakage phenomena is developed. An equipartition of kinetic energy (EKE kernel) is used to model the agglomeration phenomena. For breakage, two different fragment distribution functions are considered, the Dirac delta function and a function with confined uniform binary breakage. The fractal dimension property is incorporated in both the agglomeration and breakage models. The model parameters are extracted from batch fluidization experiments conducted by varying the air pressure of the top nozzle. The developed model shows a good agreement with experimental observation in regard of the temporal change in the area and volume-weighted average size of nano-agglomerates and of their final size distribution. The developed population balance model is simulated to study the influence of model parameters on the evolution of average size and coefficient of variation of the nano-agglomerates.

Integrating glass breakage models into CFD simulation to investigate realistic compartment fire behaviour

Glass failure affects the ventilation conditions in compartments, which particularly varies the fire development history in large compartments as the initial ventilation may become insufficient due to the existence of window glass. This paper proposes a ‘criterion-controlled’ model to simulate the interaction between glass failure and fire behaviour in CFD fire models. The proposed modelling approach has shown good performance in simulating the Shield Test, where the predicted cracking points and timeline of glass failure are almost identical to the test records. By implementing the glass failure model in the large compartment fire models adapted from the Kirby Test and the Malveira Test models, the influence of glass failure on the large compartment fires has been revealed. In the adapted Kirby Test model with glass panes, the case with window glass exhibits a much faster fire growth compared to the case with initially opened windows of no glass. When considering the window glass failure in Malveira Test model, the slow ‘travelling fire’ behaviour found in the full-scale test is changed to a fast spread fire and the window glass panels fail to provide the desired ventilation, which suggests the inadequacy of assuming complete openings at windows and it is necessary to consider the effect of window glass to large open-plan compartment fires in real modern buildings.

Modelling of droplet multiple breakage accounting for entire energy spectrum bottleneck effect and eddy-droplet discrepancy

This work focused on the contribution of the two aspects of entire energy spectrum bottleneck effect and eddy-droplet discrepancy to droplet multiple breakage simulation. The droplet breakage mechanism model was closured by more accurate turbulent parameters determined by accounting for the bottleneck effect and a formula was proposed to consider the effect of the eddy-droplet discrepancy. The influences of the two aspects on collision/interaction frequency density, breakage probability, breakage frequency and daughter size distribution (DSD) were analyzed. The proposed model agreed well with the measured breakage frequency, relative proportion of multiple breakage modes and DSDs from single droplet experiments and drop swarm experiments. The predicted size distribution evolution also exhibited a better agreement with experimental data by comparing with other models. An obvious quantitative prediction difference on whether to consider the two aspects proved the necessity and advantage of model development.The bottleneck effect represents a physical phenomenon fully validated by experimental data and direct numerical simulation results. Ignoring bottleneck effect hinders the acceptable reproduction of longitudinal velocity gradient skewness, while considering it obviously increases the quantitative prediction accuracy of turbulence parameters. Considering the physical fact that turbulent eddies will disappear, the eddy-droplet discrepancy neglected by existing mechanism model is used to characterize the impact of eddy lifetime on eddy-droplet collision/interaction. To summarize, the improvements of this work are beneficial for consolidating the breakage model physical foundation.

Oblique impact breakage unification of nonspherical particles using discrete element method

Particle breakage commonly occurs during processing of particulate materials, but a mechanistic model of particle impact breakage is not fully established. This article presents oblique impact breakage characteristics of nonspherical particles using discrete element method (DEM) simulations. Three different particle shapes, i.e. spherical, cuboidal and cylindrical, are investigated. Constituent spheres are agglomerated with bridging bonds to model the breakage characteristics under impact conditions. The effect of agglomerate shapes on the breakage pattern, damage ratio, and fragment size distribution is fully investigated. By using a newly proposed oblique impact model, unified breakage master surfaces are theoretically constructed for all the particle shapes under oblique impact conditions. The developed approach can be applied to modelling particulate processes where nonspherical particles and oblique impact breakage are prevailing.

Study on productivity of eccentric roll crusher based on theory and experiment

Productivity, as one of the key indicators for assessing the performance of a crusher, holds significant importance in guiding production practices. It refers to the quantity of materials processed or the quality of output materials within a given time frame. However, there is currently limited research on eccentric roller crushers, and the calculation method for productivity is unclear, failing to consider the motion characteristics between the roller and the materials. To address these issues, this study analyses the motion mode of the crushing roller and establishes a dynamic model for the roll and a flow model for the material. Furthermore, a particle size distribution at the choke level has been established using the breakage model. Based on these models, a productivity calculation method for eccentric roll crushers is proposed. Then, the effectiveness of the method is verified through laboratory experiment. The results indicate that the proposed calculation method can effectively estimate the productivity of eccentric roll crushers.

Study of deep transportation and plugging performance of deformable gel particles in porous media

Deformable gel particles (DGPs) possess the capability of deep profile control and flooding. However, the deep migration behavior and plugging mechanism along their path remain unclear. Breakage, an inevitable phenomenon during particle migration, significantly impacts the deep plugging effect. Due to the complexity of the process, few studies have been conducted on this subject. In this paper, we conducted DGP flow experiments using a physical model of a multi-point sandpack under various injection rates and particle sizes. Particle size and concentration tests were performed at each measurement point to investigate the transportation behavior of particles in the deep part of the reservoir. The residual resistance coefficient and concentration changes along the porous media were combined to analyze the plugging performance of DGPs. Furthermore, the particle breakage along their path was revealed by analyzing the changes in particle size along the way. A mathematical model of breakage and concentration changes along the path was established. The results showed that the passage after breakage is a significant migration behavior of particles in porous media. The particles were reduced to less than half of their initial size at the front of the porous media. Breakage is an essential reason for the continuous decreases in particle concentration, size, and residual resistance coefficient. However, the particles can remain in porous media after breakage and play a significant role in deep plugging. Higher injection rates or larger particle sizes resulted in faster breakage along the injection direction, higher degrees of breakage, and faster decreases in residual resistance coefficient along the path. These conditions also led to a weaker deep plugging ability. Smaller particles were more evenly retained along the path, but more particles flowed out of the porous media, resulting in a poor deep plugging effect. The particle size is a function of particle size before injection, transport distance, and different injection parameters (injection rate or the diameter ratio of DGP to throat). Likewise, the particle concentration is a function of initial concentration, transport distance, and different injection parameters. These models can be utilized to optimize particle injection parameters, thereby achieving the goal of fine-tuning oil displacement.

Novel experimental data-driven bubble breakage model for universal application in Euler-Lagrange multiphase frameworks

An experimental data driven model for the prediction of bubble breakage in gas–liquid multiphase reactors was developed which fulfills requirements of the Euler-Lagrangian (EL) framework for the analysis of individual bubbles. The critical Weber number (Wecrit) serves as the breakage criterion in combination with the minimum time between two consecutive breakage events. Wecrit indicates when the hydrodynamic forces acting on an individual bubble surmount its surface tension. Once the threshold is passed a binary bubble breakup event occurs, which results in the formation of daughter bubbles assigned to an M−shaped daughter size distribution (DSD). Optimum Wecrit values were obtained by minimizing the difference between simulated and measured Sauter mean diameters d32. The latter were derived from bubble size distributions (BSDs) measurements that cover about 11 – 89 W m−3 power inputs. Using deionized water and a minimum timespan of 30 ms between two consecutive breakages Wecrit = 6.1 was determined. To extend the scope of the model, characteristic media compositions for so-called syngas fermentations with Clostridium ljungdahlii were investigated. To match surface tension and viscosity with those of fresh medium (FM) and late phase medium (LPM), two aqueous solutions containing sodium dodecyl sulfate (SDS) and glycerol were prepared. Notably, the breakage model managed to well predict the impact of altered fluid properties of FM and LPM without requiring further calibration. The sum of Sauter diameter deviation between simulations and experiments was only 0.21 and 0.40 mm for FM and LPM, respectively.

CFD-DEM investigation of particle breakage in spout-fluidized beds

In a fluidized bed, particles undergo mechanical stress resulting from collisions with other particles, the bed walls, or internal equipment. Particle breakage exerts a significant impact on the hydrodynamics and overall performance of the fluidized bed by modifying the particle size distribution. This study explores this phenomenon through the application of an enhanced computational fluid dynamics-discrete element method (CFD-DEM) coupled with a particle breakage model in three distinct flow regimes: spouted bed, jet-in-fluidized bed, and spouting-with-aeration bed. The simulations revealed various aspects related to particle breakage, encompassing the spatial and temporal distribution of particle sizes, the location of breakages, breakage rates, solid particle fraction, and the height of the bed. The findings establish a pronounced correlation between the breakage rate and the velocity of the jet, with the spouting-with-aeration bed displaying the highest level of particle breakage. Furthermore, it is noteworthy that nearly 98% of the breakages occur within the distributor zone.

Hybrid modeling of drop breakage in pulsed sieve tray extraction columns

Accurate models for pulsed sieve tray extraction columns (PSEs) depend on the correct prediction of the drop diameter to estimate extractive mass transfer across the phase boundary. Phenomenologically, the drop diameter is determined by a balance of drop breakage and coalescence. While for most industrial solvent systems, coalescence plays a minor role; breakage is mostly the dominant phenomenon determining the drop diameter. However, most modeling approaches for drop breakage in PSEs are characterized by a trade-off between a broad validity range and good prediction accuracy. To overcome this limitation, we developed a hybrid breakage model for drop breakage in PSEs in which a physical-empirical model basis is enhanced by data-driven parameter estimator models (PEMs). The hybrid model is based on a revised form of Garthe’s breakage model, for which we developed a linear PEM for the model parameters and two data-driven PEMs for dstab and d100, respectively. The hybrid breakage model was validated on 743 experimental data sets and evaluated based on the pull metric. In a sensitivity analysis, the model correctly predicted the breakage probability over a wide range of solvent properties, operating conditions, and sieve tray geometries. In future studies, the hybrid breakage model can be incorporated into extraction column models without an initial parametrization.

Detection of breakage and impurity ratios for raw sugarcane based on estimation model and MDSC-DeepLabv3.

Broken cane and impurities such as top, leaf in harvested raw sugarcane significantly influence the yield of the sugar manufacturing process. It is crucial to determine the breakage and impurity ratios for assessing the quality and price of raw sugarcane in sugar refineries. However, the traditional manual sampling approach for detecting breakage and impurity ratios suffers from subjectivity, low efficiency, and result discrepancies. To address this problem, a novel approach combining an estimation model and semantic segmentation method for breakage and impurity ratios detection was developed. A machine vision-based image acquisition platform was designed, and custom image and mass datasets of cane, broken cane, top, and leaf were created. For cane, broken cane, top, and leaf, normal fitting of mean surface densities based on pixel information and measured mass was conducted. An estimation model for the mass of each class and the breakage and impurity ratios was established using the mean surface density and pixels. Furthermore, the MDSC-DeepLabv3+ model was developed to accurately and efficiently segment pixels of the four classes of objects. This model integrates improved MobileNetv2, atrous spatial pyramid pooling with deepwise separable convolution and strip pooling module, and coordinate attention mechanism to achieve high segmentation accuracy, deployability, and efficiency simultaneously. Experimental results based on the custom image and mass datasets showed that the estimation model achieved high accuracy for breakage and impurity ratios between estimated and measured value with R2 values of 0.976 and 0.968, respectively. MDSC-DeepLabv3+ outperformed the compared models with mPA and mIoU of 97.55% and 94.84%, respectively. Compared to the baseline DeepLabv3+, MDSC-DeepLabv3+ demonstrated significant improvements in mPA and mIoU and reduced Params, FLOPs, and inference time, making it suitable for deployment on edge devices and real-time inference. The average relative errors of breakage and impurity ratios between estimated and measured values were 11.3% and 6.5%, respectively. Overall, this novel approach enables high-precision, efficient, and intelligent detection of breakage and impurity ratios for raw sugarcane.

An improved breakage model with a fast-cutting method for simulating the breakage of polyhedral particles

In order to accurately describe the breakage of a large number of particles while ensuring computational efficiency, a particle breakage model based on the particle replacement scheme is proposed within the DEM framework in this work, in which the particles are described by the polyhedral model. Furthermore, a fast-cutting algorithm for polyhedral particles is proposed to accurately reproduce the size distribution of the progeny particles determined by the breakage model. The validation of the algorithm indicates that the number of faces and progeny particles will affect the performance of the algorithm, and the accuracy, efficiency and stability of the algorithm are satisfactory. The breakage probability of a single particle described by the breakage model is validated by an impact test on a single particle. To verify the breakage model as well as the fast-cutting algorithm well describes the fragmentation of not only a single particle but also a large number of particles under the impact, a simulation of particle bed test is carried out, and the passing rates of different size classes of particles are consistent with the experimental results.

A Thermodynamically Consistent 3D Breakage Model Considering Intermediate Principal Stress for Granular Crushing Problems

A Thermodynamically Consistent 3D Breakage Model Considering Intermediate Principal Stress for Granular Crushing Problems