Breakage Model Research Articles

Textural and Mineralogical Controls on Rock Strength Elucidated Using a Discrete Element Method Numerical Laboratory

Numerical modelling techniques such as the discrete element method are now well established and extensively used in many applications including solid earth geoscience, materials science, geotechnical engineering and rock mechanics. The potential for this technique in understanding comminution mechanisms has been identified as highly promising. This work utilizes the discrete element method as a numerical laboratory to conduct investigations relevant to comminution that would otherwise be costly or time-consuming to perform in the field or laboratory. A benchmark numerical model for impact breakage of rock specimens is first established and validated against results of controlled laboratory experiments. Thereafter, the model is utilized to systematically investigate the potential dependency of ore breakage properties upon the prevalence of pre-existing fractures, as well as the mineralogical composition of the ore. These numerical experiments serve to highlight the potential for quantitatively relating the mechanical response of ore to its textural and mineralogical characteristics. Tandem utilization of numerical and laboratory experimentation to formulate and test hypotheses is a promising avenue to illuminate such relationships.

A cone crusher model with a coupled energy- and breakage dependency

A cone crusher model is presented that uses the familiar “population balance” framework. The model was fitted so that the product particle size distribution can be predicted when operating at the minimum crusher gap CSS. A previously developed energy model is applied to the particle size distribution that is the output of the breakage model. This gives an estimate of the specific energy required, to generate that particle size distribution. The same quantity is calculated by dividing the crusher's available motor power by the tonnage at range of different CSS's assuming each of these are the minimum. The CSS that gives the same specific energy consumption as calculated by these two different techniques, corresponds to the minimum CSS that the crusher can reach. While the modeling approach is sound and gives realistic results, further validation against full scale test data is needed.

Role of Particle Breakage in Rockfill Materials: Investigated by Using Combined SBFEM/DEM with Two Different Breakage Models

This research will investigate the numerical simulation of rockfill materials using a combined scaled boundary finite–discrete element method (SBFEM/DEM) with two breakage models. Two rockfill specimens that are subjected to biaxial compaction will be simulated. The influence of breakage on the macroscopic stress–strain behaviors will be investigated by comparing the results obtained when breakage and no breakage were considered using two different models. Further investigations will be carried out to identify the effect of particle breakage on the stress–strain relationship, particle size distribution (PSD), and the force chain transmission of the rockfill specimens under different breakage models. The simulation with Breakage Model 2 (BM2) generated more small particles than when Breakage Model 1 (BM1) was used; therefore, it had the lowest shear strength, the most contractive behavior, and the lowest interparticle contact forces. Because one particle will be crushed into many small particles in practice, BM2 was recommended as the first option.

On the determination of particle impact breakage in selection function

This paper presents a thorough study of particle impact breakage in selection function with a unified breakage criterion. The impact mode and breakage pattern for particulate materials are classified based on a significant review of well-established impact testers. It was found that the lack of a unified breakage criterion to determine the breakage probability disables a direct comparison of particle breakage propensity from different impact loading testers. The literature breakage models to describe the breakage probability are reviewed where the advantage and drawback of these models are scrutinized. The sourced literature breakage models are compared with the zeolite breakage datasets in a unified breakage criterion to evaluate the model performance. A novel computational modelling workflow for a milling process is proposed to provide a guidance in implementing the digital twin in milling process prediction. The breakage probability models, i.e. the selection functions are comprehensively assessed in population balance model to examine the model serviceability. The model simplicity and fidelity in the model assessment are specifically discussed and the value of digital twin in substantially reducing the experimental trials is highlighted.

Direct Simulation Model for Fiber Motion and Breakage in the Processing of Discontinuous Fiber-reinforced Thermoplastics

Direct Simulation Model for Fiber Motion and Breakage in the Processing of Discontinuous Fiber-reinforced Thermoplastics

A breakage model for particulate solids under impact loading

This paper presents a breakage model of particulate solids under impact loading based on a mechanical approach. Existing breakage models are assessed using the experimental data from single particle impact tests, indicating a more general breakage model is required. Indentation fracture mechanics is used to account for surface damage under dynamic loading. The effect of impact angle is considered in the model, which rationalizes the contributions of both the normal and tangential impact velocity. A unified curve of breakage propensity is constructed using the equivalent velocity under oblique impact based on the experimental data from this study and the literature. This model provides a basis to evaluate breakage propensity of brittle/semi-brittle particles subject to oblique impact and the proposed equivalent velocity has a potential to improve the description of impact energy spectra for milling processes where oblique impact of particle is common and typically ignored.

An effective sphere-based model for breakage simulation in DEM

Breakage occurs in several particulate systems that are simulated using the discrete element method (DEM), namely crushing and grinding as well as inadvertently in several others that include transportation, handling, mixing, separation and geotechnical applications. Different approaches may be used to describe particle breakage using DEM, but in cases in which particle breakage influences significantly the flow behaviour of the material, imbedding the breakage description in DEM provides the only valid alternative. This study describes the implementation of a detailed breakage model based on particle replacement with spheres in the commercial software EDEM. It accounts for variability and size-dependency in particle fracture energies, weakening of particles by unsuccessful stressing events, as well as addressing several reported shortcomings in sphere replacement schemes. The model is verified in great detail on the basis of single-particle breakage information and validated using measurements in unconfined particle beds of mineral ores.

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.

Theoretical approximation of hydrodynamic and fiber-fiber interaction forces for macroscopic simulations of polymer flow process with fiber orientation tensors

Flow processes of discontinuous fiber reinforced polymers (FRPs) are the essence of several polymer-based manufacturing processes. FRPs show a transient chemo-thermomechanical matrix behavior and fiber-induced anisotropic physical properties. Therefore, they are one of the most complex materials used in volume production. The general flow behavior is influenced by fibers and their interactions with the matrix and other fibers. The consideration of individual fibers is numerically not capable for process simulation of FRP parts. Therefore, orientation tensors are used in macroscopic simulations, leading to a loss of information about the fiber network. Within this work, novel approximation schemes are presented to determine hydrodynamic and fiber-fiber contact forces with information provided by the second order fiber orientation tensor. Approximation of these forces can henceforth facilitate fiber breakage modeling in macroscopic process simulations. The results are verified by numerical simulations with individual fibers of different orientation states and lengths, showing good agreement with the verification results.

Application of a drop breakage model using the full energy spectrum and a specific realisation of turbulence anisotropy

An anisotropic drop breakage model is applied to CFD–PBM simulations of turbulent emulsification in a high–pressure homogeniser. We compare the exponent of Sauter mean diameter – pressure drop correlations with published experimental results and with exponents obtained using existing drop breakage models. Its theoretical value assuming homogeneous isotropic turbulence is -0.6, while experiments have shown exponents of smaller magnitude. A breakage frequency model using the full spectrum of isotropic turbulence is found to produce a value of the exponent near -0.6. Our newly developed anisotropic breakage model predicts an exponent of smaller magnitude, closer to experiments. Breakage frequency based on isotropic turbulence exhibits non–monotonic behaviour (by predicting a maximum value for a certain drop size); the effect of turbulence anisotropy is to reduce non–monotonicity. It is shown that this reduction in non–monotonicity drives the decrease in the magnitude of the exponent.

The double wheel breakage test

The mining industry needs a low-cost and reliable breakage characterization test which can rapidly process a large number of samples for geometallurgical modelling. The more samples are tested, the better is the understanding of the ore hardness variability and lower the design or production risks. The proposed solution is a new testing device, herein named Geopyörä, which is a variation of a roll crusher with an adjustable gap and instrumentation to measure breakage forces and energy applied to rock particles during the breakage process. The principle utilises a controlled degree of crushing, with absorbed breakage energy being a response rather than an input. The new testing device is capable of rapidly testing rocks over a wide range of sizes and accurately measured energy levels. For a range of ores, the results were demonstrated to provide outputs that replicate the breakage modelling from full JK drop Weight tests. In addition to being suited to testing drill cores and small sample masses, the Geopyörä provides a distribution of particle strengths within every sample. This paper provides an introduction to the concept, development of the prototype device and breakage calibration results that indicate its potential to become a major player in geometallurgical ore testing.

A one-dimensional combined multifluid-population balance model for the simulation of batch bubble columns

Bubble columns are widely used as multiphase reactors for gas–liquid reactions in industrial applications. For the sensitivity and usability analysis of the bubble column in the process development, a model is needed that incorporates couplings between the fluid dynamics, the population balance equation (PBE) and the thermodynamics. Thereby the model should be as fast and reliable as possible. A suitable candidate is the kinetic theory approach with size resolution (KTAWSR), as one of the most rigorous combined multifluid-PBE models.A steady-state and one-dimensional version of the KTAWSR model was used and extended to batch bubble columns. For this purpose, a new approach for the determination of the integral gas holdup was developed which does not require additional empirical correlations. The spectral orthogonal collocation method was used to solve the model equations. Different breakage and coalescence model combinations were calibrated, compared and investigated on the basis of measured bubble size distributions. To validate the model, the integral gas holdup and the bubble size distribution were measured at four axial positions at three gas volume fluxes reaching the transition flow regime in a batch water–air bubble column. The novel integral gas holdup calculation approach could be predictively confirmed with measured data.

A model for the carbon fiber breakage along the twin‐screw extruder

AbstractCarbon fiber‐reinforced plastics (CFRP) are widely used in the plastics industry. The production of CFRP is mostly carried out on the twin‐screw extruder. Many different process variables change the process ability and the final fiber length in the product. In the literature, some models for fiber length decrease along the extruder with glass fibers can be found. The effects of the processing conditions on the final length for glass fiber are determined. In comparison, the incorporation behavior of the carbon fibers are not sufficiently analyzed. The purpose of this paper is to predict the fiber breakage along the screw for carbon fibers. First of all, the buckling case must be determined. The basis of the modeling is a fragmentation equation, for which a break probability and a break rate are defined. A comparison with experimental data shows satisfactory results.

Emulsion liquid membrane modeling for chromium removal from electroplating wastewater using TOMAC as a carrier.

Hexavalent chromium, emanating primarily from the electroplating industries, can be reduced to the less toxic trivalent variety by several methods, including emulsion liquid membrane (ELM). In this work, studies on the continuous removal of chromium from authentic electroplating wastewater by ELM are reported. The effects of treat ratio, external feed phase, and stripping agent concentration were examined. A mathematical boundary breakage model was used to study the extraction efficiency of chromium through the ELM process. The model representing the prediction of ELM extraction performance for chromium was validated through the comparison between the simulation and experimental results. The result showed the simulation model is found to be in good agreement with the experimental result. Almost 100% of 40ppm chromium in the external feed phase was extracted within 3 to 5min using 0.022M TOMAC as extractant, 1.0M acidic thiourea in the internal phase, and 1 to 5 of treat ratio. PRACTITIONER POINTS: Hexavalent chromium, emanating primarily from electroplating industries, can be reduced to the less toxic trivalent using ELM process. The developed method was tested for its applicability with predominant species of Cr2 O7 2- in real rinse electroplating wastewater. The extraction efficiency (%) of Cr (VI) was almost 100% for 40ppm Cr in the external feed phase within 3 to 5min. The result showed the simulation model is found to be in good agreement with the experimental result.

Simulation of High-Strain-Rate Comminution through a Breakage Model with Adaptive Rate Dependence

AbstractWhile laboratory evidence suggests that particle crushing generates nonnegligible rate-dependence in granular materials, few constitutive laws reproduce such effects in light of grain-scale...

Modeling drop breakage using the full energy spectrum and a specific realization of turbulence anisotropy

AbstractThe assumption of homogeneous isotropic turbulence when modeling drop breakage in industrially relevant geometries is questionable. We describe the development of an anisotropic breakage model, where the anisotropy is introduced via the inclusion of a perturbed turbulence spectrum. The selection of the perturbed spectrum is itself motivated by our previous large‐eddy simulations of high‐pressure homogenizers. The model redistributes energy from small to large scales, and assumes that the anisotropic part of the Reynolds stresses is confined to the energy‐containing range. The second‐order structure function arising from the perturbed spectrum is used in the standard framework of Coulaloglou and Tavlarides to calculate breakage frequency. While the base model exhibits non‐monotonic behavior (by predicting a maximum value for a certain drop size), the effect of anisotropy is shown to increase breakage frequency in length scales larger than this peak, thereby reducing non‐monotonicity. This effect is more pronounced for small turbulence Reynolds numbers.

A breakage model with different liquid properties for pressurized bubble columns in a homogeneous regime

The bubble breakage rate in gas-liquid bubble columns increases for organic liquid and at high pressure. This study developed a breakage model that accounts for different liquid properties in gas-liquid pressurized bubble columns in the homogeneous regime. The Luo (1996), Lehr (2002), and Wang (2003) breakage models, which are widely used for the population balance equation (PBE) of bubble columns, were compared in terms of the total breakage rate, daughter size distribution, and computational time. The model with two empirical equations, modified from Luo’s breakage kernel, was proposed. One represented bubble deformation behavior in different liquid properties in terms of buoyancy, surface tension, and viscosity. The other considered the effect of operating pressure (or gas density) on the breakage rate. The modified model was compared with experimental data and a rigorous breakage model from the literature. The proposed breakage model shows good agreement with experimental data and computational efficiency. This breakage model is applicable for computational fluid dynamics with PBE in pressurized bubble columns with organic liquids.

Existence and NonExistence for the Collision-Induced Breakage Equation

A mathematical model for collision-induced breakage is considered. Existence of weak solutions to the continuous nonlinear collision-induced breakage equation is shown for a large class of unbounde...

Impact mechanism of gas temperature in metal powder production via gas atomization* *Project supported by the Open Fund of State Key Laboratory of Advanced Forming Technology and Equipment (Grant No. SKL2019006) and the National Natural Science Foundation of China (Grant No. 51975240).

This paper aims at studying the influence mechanism of gas temperatures (300 K, 400 K, 500 K, and 600 K) on gas atomization by simulating the integral atomization process of the close-coupled nozzle in vacuum induction gas atomization (VIGA). The primary atomization is simulated by the volume of fluid (VOF) approach, and the second atomization is studied by the discrete phase model (DPM) combined with the instability breakage model. The results show that, at an increased gas temperature, the influences of gas–liquid contact angle and gas temperature in the recirculation zone on the primary atomization are virtually negligible. However, increasing the gas temperature will increase the gas–liquid relative velocity near the recirculation zone and decrease the melt film thickness, which are the main reasons for the reduced mass median diameter (MMD, d 50) of primary atomized droplets. During the secondary atomization, increasing the gas temperature from 300 K to 600 K results in an increase in the droplet dispersion angle, which is beneficial to the formation of spherical metal powder. In addition, increasing the gas temperature, the positive effect of gas–liquid relative velocity increase on droplets refinement overweighs the negative influence of the GMR decrease, resulting in the reduced MMD and diameter distribution interval. From the analysis of the atomization mechanism, the increase in atomization efficiency caused by increasing the temperature of the atomizing gas, including primary atomization and secondary atomization, is mainly due to the increase in the gas drag force difference between the inner and outer sides of the annular liquid film.

Mechanisms Generating Cancer Genome Complexity: Back to the Future.

Simple SummaryIn the 1990s, fluorescent in situ hybridization approaches made it possible to analyze the early stages of gene amplification in mammalian cells. These studies established breakage-fusion-bridge cycles as a major mechanism of intrachromosomal gene amplification. They also revealed that the amplified DNA perturbed nuclear architecture and led to micronucleation, which suggested a mechanism for the shortening of amplified units. The “interphase breakage model” postulated that the tremendous genomic instability occurring at early stages of gene amplification resulted from the interweaving of an amplification mechanism (breakage-fusion-bridge cycles) and of a deletion mechanism (micronucleation and stitching of DNA fragments retained in the nucleus). This model is strikingly consistent with recent data and conclusions obtained from live-cell imaging and single cell genome sequencing. The comparison of both sets of data suggests new questions to explore.Understanding the mechanisms underlying cancer genome evolution has been a major goal for decades. A recent study combining live cell imaging and single-cell genome sequencing suggested that interwoven chromosome breakage-fusion-bridge cycles, micronucleation events and chromothripsis episodes drive cancer genome evolution. Here, I discuss the “interphase breakage model,” suggested from prior fluorescent in situ hybridization data that led to a similar conclusion. In this model, the rapid genome evolution observed at early stages of gene amplification was proposed to result from the interweaving of an amplification mechanism (breakage-fusion-bridge cycles) and of a deletion mechanism (micronucleation and stitching of DNA fragments retained in the nucleus).