Spherical Particle Model Research Articles

Study on the characteristics particles of coarse grain material in high bench dump

Particle shape is an important factor affecting the strength and deformation of coarse materials in dumps. However, conducting research on particle shape in current laboratory experiments, and there exists no classification standard for the particle shape of the dump. Considering the project on high-bench dump in Jiangxi Province, based on the random particle construction method, this study determined the characteristic particles of coarse grain material in the dumping site by combining field investigation results, large-scale direct shear tests, and numerical analysis. Further, the influence mechanism of coarse grain content and characteristic particles on the mechanical characteristics of the dump were analyzed. The results showed that the increase in coarse grain content enhanced the irregularity of particle shape, increased the internal friction angle between particles, and reduced the cohesion of the dump. Moreover, with increase in the normal stress, the shear strength changed from insignificant to gradually enhanced, although the increasing trend slowed down. The constructed random particle model can well solve the effects of occlusion, nesting, and friction between particles that is neglected by the standard spherical particle model, and the fitting degree is better. The particle characteristics of coarse-grain materials in the dump were primarily block, strip, and flake. The three types of shape characteristics under low normal stress did not affect the mechanical properties of the dump. Further, with the increase in normal stress, the stress-strain curve reflected the shape characteristics and content of the dominant characteristics in the dump. Specifically, the block sample exhibited the dominant characteristics and the most content under the same normal stress, followed by the strip sample, with the flake sample exerting the least influence. The research results provide a theoretical basis for long-term safe operation, disaster monitoring, and early warning of high bench dump.

Deterministic drag modelling for spherical particles in Stokes regime using data-driven approaches

In this paper, we develop a deterministic drag model for stationary spherical particles in a Stokes flow using a cascade of data-driven approaches. The model accounts for the variation in drag experienced by each particle within fixed random arrangements. The developed model is a symbolic expression that offers explainability, ease of implementation, and computational efficiency. Firstly, we generate particle-resolved direct numerical simulation data of the flow past periodic random arrangements of stationary spherical particles with volume fractions between 0.05 and 0.4 using the method of regularized Stokeslets. Secondly, we train graph neural networks (GNs) on the generated data to learn the pairwise influence of neighbouring particles on a reference particle. The GNs are converted to symbolic expressions using genetic programming (GP), unveiling repeated subexpressions. Finally, these subexpressions constitute the foundation of the proposed algebraic model, further refined via non-linear regression. The proposed model can qualitatively mimic the pairwise influences as predicted by the GN and can capture the drag variations with accuracy from 74% and up to 84.7% when compared to the particle-resolved simulations. Due to the interpretability of the proposed model, we are able to explore how neighbour positions alter the drag of a particle in an assembly. The proposed model is a promising tool for studying the dynamics of particle assemblies in Stokes flow.

Uniform boundary conditions on models of spherical particles through alpha shape surface tracking and Laguerre–Voronoi diagrams

This study describes the adaptation of the alpha-shape three-dimensional surface reconstruction technique to boundaries of spherical particle packings, such as those modeled using Discrete Elements. The alpha shape technique is employed to reconstruct a boundary surface for a packing as well as to assemble a Laguerre–Voronoi Diagram of the packing's boundary. The reconstructed surface can be used to track the evolution of the packing surface, while the surface diagram can be used to directly obtain the discrete force vectors that result from applying a uniform stress tensor (Static Uniform Boundary Condition), as well as the discrete velocity vectors that result from applying a uniform velocity gradient tensor (Kinematic Uniform Boundary Condition) to a model of spherical discrete particles. Doing so continuously throughout a simulation allows for the application of uniform boundary conditions on spherical discrete particles, whilst enabling precise tracking of stress and deformation tensors of the packing. An implementation of this novel approach in the Yade open-source DEM code is detailed here. The power and versatility of the real-time boundary tracking approach is demonstrated using some boundary value problem simulations on polydisperse spherical particle models.

Numerical Simulations of the Epley Maneuver With Clinical Implications.

Canalith repositioning procedures to treat benign paroxysmal positional vertigo are often applied following standardized criteria, without considering the possible anatomical singularities of the membranous labyrinth for each individual. As a result, certain patients may become refractory to the treatment due to significant deviations from the ideal membranous labyrinth, that was considered when the maneuvers were designed. This study aims to understand the dynamics of the endolymphatic fluid and otoconia, within the membranous labyrinth geometry, which may contribute to the ineffectiveness of the Epley maneuver. Simultaneously, the study seeks to explore methods to avoid or reduce treatment failure. We conducted a study on the Epley maneuver using numerical simulations based on a three-dimensional medical image reconstruction of the human left membranous labyrinth. A high-quality micro-computed tomography of a human temporal bone specimen was utilized for the image reconstruction, and a mathematical model for the endolymphatic fluid was developed and coupled with a spherical particle model representing otoconia inside the fluid. This allowed us to measure the position and time of each particle throughout all the steps of the maneuver, using equations that describe the physics behind benign paroxysmal positional vertigo. Numerical simulations of the standard Epley maneuver applied to this membranous labyrinth model yielded unsatisfactory results, as otoconia do not reach the frontside of the utricle, which in this study is used as the measure of success. The resting times between subsequent steps indicated that longer intervals are required for smaller otoconia. Using different angles of rotation can prevent otoconia from entering the superior semicircular canal or the posterior ampulla. Steps 3, 4, and 5 exhibited a heightened susceptibility to failure, as otoconia could be accidentally displaced into these regions. We demonstrate that modifying the Epley maneuver based on the numerical results obtained in the membranous labyrinth of the human specimen under study can have a significant effect on the success or failure of the treatment. The use of numerical simulations appears to be a useful tool for future canalith repositioning procedures that aim to personalize the treatment by modifying the rotation planes currently defined as the standard criteria.

General aerosol Sauter mean diameter measurement for spherical and non-spherical particles based on low-complexity scattering algorithm

Sauter mean diameter (SMD) is a key microphysical indicator in aerosol measurements that rely on optical-scattering-related methods. However, owing to the lacking clear definition of non-spherical SMD and the complexity of scattering calculations for non-spherical particles, existing SMD measurement methods are only applicable to spherical particles. A general SMD measurement method for both spherical and non-spherical aerosols is thus proposed. In this method, the shape coefficients of non-spherical particles are defined and used to calculate SMD. The scattering models for spherical and non-spherical particles are unified into a low-complexity scattering algorithm (LCSA). Based on LCSA, SMD can be measured using only two light sources of different wavelengths. Compared with SMD measurement results without considering particle shape, the accuracy of the proposed method increased by an average of 11.31% and 11.37% for unimodal and bimodal aerosols, respectively, while its accuracies for spherical and non-spherical aerosols respectively reached 95.26% and 93.43%.

A texture inheritance model for spherical particles in particle replacement method (PRM) schemes for breakage in discrete element method (DEM) simulations

Various models have been developed in recent years to simulate particle breakage in discrete element method (DEM) simulations. However, texture inheritance of fragments is only available for certain complex particle shapes or bonded particle models, significantly increasing the computation time. We propose a spherical particle model coupled with a particle replacement method (PRM) scheme, which incorporates texture inheritance through an intermediate mapping step. In this way, the model benefits from the computational advantages of spherical particles without losing texture information during the breakage process.The model is evaluated by applying it to artificially generated particles incorporating texture information from a lithium-containing slag measured by X-ray microscopy (XRM) and an artificially generated magnetite iron ore. Comparisons of the liberation distributions with other models in the literature match with minor deviations. In addition, the liberation distributions calculated using the model are consistent with randomly sampled particles.

Nonlinear electrophoresis of nonspherical particles in a rectangular microchannel.

Nonlinear electrophoresis offers advantageous prospects in microfluidic manipulation of particles over linear electrophoresis. Existing theories established for this phenomenon are entirely based on spherical particle models, some of which have been experimentally verified. However, there is no knowledge on if and how the particle shape may affect the nonlinear electrophoretic behavior. This work presents an experimental study of the nonlinear electrophoretic velocities of rigid peanut- and pear-shaped particles in a rectangular microchannel, which are compared with rigid spherical particles of similar diameter and surface charge in terms of the particle slenderness. We observe a decrease in the nonlinear electrophoretic mobility, whereas an increase in the nonlinear index of electric field when the particle slenderness increases from the peanut- to pear-shaped and spherical particles. The values of the nonlinear index for the nonspherical particles are, however, still within the theoretically predicted range for spherical particles. We also observe an enhanced nonlinear electrophoretic behavior in a lower concentration buffer solution regardless of the particle shape.

Recovery of nickel from spent multilayer ceramic capacitors: A novel and sustainable route based on sequential hydrometallurgical and photocatalytic stages

The depletion of primary metal sources and the extensive use of nickel necessitate its extraction from secondary resources. In this study, we employed a chloride-based solution containing cupric ions (NaCl/CuCl2) to enable a straightforward recovery process for nickel from Ni-containing waste materials. Prior to application in real systems, we evaluated different operating conditions using metallic nickel particles, including chloride and cupric ion concentrations, system temperature, and pH. Optimal efficiency was achieved at T = 60 °C, pH = 5.0, [Cu(II)]0 = 5.0 × 10−3 M, and [Cl]0 = 6.0 M, resulting in complete dissolution of metallic Ni (58 ppm) within 180 min. This optimized leaching system was then applied to exhausted nickel-containing multilayer ceramic capacitors (MLCCs) matrixes, leading to 80% Ni recovery. FESEM-EDX and XRD analysis characterized both synthetic and real matrixes. Additionally, we proposed a viable route for selective metal recovery through precipitation and photodeposition on titanium dioxide. Complete copper photodeposition occurred after 150 min, while Ni precipitation as Ni(OH)2 was achieved by adjusting the solution pH to 10. Experimental data from runs with the synthetic matrix were analyzed using a shrinking spherical particle model.

Impacts of Shape Assumptions on Z–R Relationship and Satellite Remote Sensing Clouds Based on Model Simulations and GPM Observations

In this study, the spherical particle model and ten nonspherical particle models describing the scattering properties of snow are evaluated for potential use in precipitation estimation from spaceborne dual-frequency precipitation radar. The single scattering properties of nonspherical snow particles are computed using discrete dipole approximation (DDA), while those of spherical particles are determined using Mie theory. The precipitation profiles from WRF output are then input to a forward radiative transfer model to simulate the radar reflectivity at Ka-band and Ku-band. The results are validated with Global Precipitation Mission Dual-Frequency Precipitation Radar measurements. Greater consistency between the simulated and observed reflectivity is obtained when using the sector- and dendrite-shape assumptions. For the case in this study, when using the spherical-shape assumption, radar underestimates the error of the cloud’s top by about 300 m and underestimates the error of the cloud’s area by about 15%. As snowflake shapes change with temperature, we use the range between −40 °C and −5 °C to define three temperature layers. The relationships between reflectivity (Z) and precipitation rate (R) are fitted separately for the three layers, resulting in Z=134.59·R1.184 (sector) and Z=127.35·R1.221 (dendrite) below −40 °C.

Shear thickening in dense bidisperse suspensions

Discrete-particle simulations of bidisperse shear thickening suspensions are reported. The work considers two packing parameters, the large-to-small particle radius ratio ranging from δ=1.4 (nearly monodisperse) to δ=4, and the large particle fraction of the total solid loading with values ζ=0.15, 0.5, and 0.85. Particle-scale simulations are performed over a broad range of shear stresses using a simulation model for spherical particles accounting for short-range lubrication forces, frictional interaction, and repulsion between particles. The variation of rheological properties and the maximum packing fraction ϕJ with shear stress σ are reported. At a fixed volume fraction ϕ, bidispersity decreases the suspension relative viscosity ηr=ηs/η0, where ηs is the suspension viscosity and η0 is the suspending fluid viscosity, over the entire range of shear stresses studied. However, under low shear stress conditions, the suspension exhibits an unusual rheological behavior: the minimum viscosity does not occur as expected at ζ≈0.5, but instead decreases with further increase of ζ to 0.85. The second normal stress difference N2 acts similarly. This behavior is caused by particles ordering into a layered structure, as is also reflected by the zero slope with respect to time of the mean-square displacement in the velocity gradient direction. The relative viscosity ηr of bidisperse rate-dependent suspensions can be predicted by a power law linking it to ϕJ, ηr=(1−ϕ/ϕJ)−2 in both low and high shear stress regimes. The agreement between the power law and experimental data from literature demonstrates that the model captures well the effect of particle size distribution, showing that viscosity roughly collapses onto a single master curve when plotted against the reduced volume fraction ϕ/ϕJ.

DEM contact model for spherical and polyhedral particles based on energy conservation

The mechanical behaviors of granular materials are greatly influenced by the geometric shapes, which is widely investigated using the discrete element method (DEM). Accurate contact detection is a critical issue in modelling complicated contact types, especially for arbitrary shaped particles. In this study, the contact detection algorithms for spherical and polyhedral particles based on energy conservation are classified into polyhedron-polyhedron and sphere-polyhedron contacts. The polyhedron-polyhedron and sphere-polyhedron contact detection algorithms are developed under the DEM framework of Coupling Simulator (CoSim-DEM). Geometric dualization theory is used in the polyhedron-polyhedron contact detection algorithm to construct the overlapping volume of polyhedral particles. For the sphere-polyhedron contact detection, the algorithm can transfer into the contact between sphere and triangles composed of polyhedron, and the contact forces between arbitrary shaped particles can be calculated based on calculated contact characteristics. Particle collision tests with different particle shapes and contact types are used to validate the aforementioned algorithms. Experiments and simulation studies of deposition tests are conducted to validate the effectiveness and stability of algorithms. Furthermore, the rotating drum tests are used to analyze the influence of particle shapes on the calculation efficiency. Finally, a large-scale rotating drum test involving different kinds of particles with random sizes is performed, demonstrating the robustness of algorithms based on CoSim-DEM.

Dust adhesion and deposition behavior in internal cooling duct with pin fins

The collision-adhesion and deposition of micron-sized dust particles in the internal cooling duct with pin fin arrays are investigated, integrating the energy dissipation collision model of spherical particles and gas-solid two-phase theory. The effects of particle Stokes number (Stk = 0.12, 0.48, and 3), particle temperature (Tp = 1173, 1223, 1273, and 1343 K), and streamwise pin spacing (S = 2.5, 3, and 3.75D) on the collision ratio, sticking ratio and deposition ratio of particles on pin fins and endwalls are investigated when the inlet Reynold number is 36,575. The results show that the pin collision ratio rises drastically with the increase of particle size, while the sticking ratio decreases. The particle temperature has a minimal impact on the collision ratio, sticking ratio, and deposition ratio when particle temperature is below 1273 K. However, the collision ratio of particles on the pins decreases appreciably when the particle temperature increases further up to 1343 K, while the sticking ratio increases significantly. The pin fin arrays with the streamwise spacing of 3D and 3.75D reduce the number of endwall deposition of particles with Stokes number of 0.12, compared to the pin fin array with a streamwise spacing of 2.5D. The windward region of the pin shows the largest potential for dust deposition and the maximum deposition height occurs at the junction of the pin-endwall. Moreover, the deposits on the pin fin grows and tends to be more uniform with the increase of particle temperature, according to the deposition profile on the pin.

The Nonlinear Dynamic Behavior of a Particle on a Vibrating Screen Based on the Elastoplastic Contact Model

The dynamic response of particles is closely related to screening efficiency. To study the dynamic response of particles, the dynamic equations of a particle on a screening surface are established based on the elastoplastic contact model of spherical particles and are solved for the coal particle. Then, the trajectories of the particles are given with different falling heights and particle radii. The completely different trajectories with slight changes in the falling height and particle radius indicate strong nonlinearity. Second, the nonlinear dynamic behavior under different amplitudes and frequencies is discussed, and the route of transition from quasiperiodic motion to chaotic motion is revealed. Finally, we discuss the average speed along the screening surface considering the frequency, amplitude, friction coefficient, inclination angle, and vibration direction angle. In addition, the convergence conditions of particle motion are proposed, and they are only affected by the inclination angle and friction angle. The results show that in the normal direction of the vibrating screen, the particle motion is quasiperiodic at low frequencies. With increasing frequency, the motion of the particle becomes chaotic, and its Poincaré map becomes petal-shaped. In addition, the number of petals increases at the mutation of the bifurcation diagram. The increase in frequency, amplitude and inclination angle and the decrease in friction coefficient lead to an increase in particle speed along the screen surface. In addition, the particle speed reaches a maximum when the vibration direction angle is 65°. This work provides a theoretical basis for controlling the thickness of granular material flow on a vibrating screen and selecting screening process parameters.

Optimization of mixing chamber parameters of pavement recycling machine under engineered particle model analysis

ABSTRACT The structural parameters of the mixing chamber of a pavement recycling machine affect the mixing behavior of an asphalt mixture. Most of the existing studies have used spherical particle models to analyze the mixing behavior, and it is difficult to truly understand the mechanical properties of asphalt mixtures in the mixing chamber. In this study, the discrete element similarity theory and dimensional analysis method were used to establish an engineered asphalt mixture particle model, and the validity of the model was verified by conducting a slump test. Based on these test results, the discrete element method was used to analyze the mixing behavior of the asphalt mixture, and the effect of the structural parameters of the mixing chamber on the mixing time of the asphalt mixture was investigated. The experiment was designed using the orthogonal test method, and a regression model was established based on the experimental data. The PSO algorithm was used to optimize the structural parameters of the mixing chamber. The results show that the mixing time of the coarse aggregate is reduced by 19.31%, the mixing time of the fine aggregate is reduced by 36.36%, and the mixing time of the powder is reduced by 33.33%.

Optimization of Steam Distillation Process and Chemical Constituents of Volatile Oil from Angelicaesinensis Radix

In this study, the steam distillation process of volatile oil from Angelicaesinensis Radix was optimized according to the concept of quality-by-design. A homemade glass volatile oil extractor was used to achieve better cooling of the volatile oil. First, the soaking time, distillation time, and liquid–material ratio were identified as potential critical process parameters by consulting the literature. Then, the three parameters were investigated by single factor experiments. The volatile oil yield increased with the extension in the distillation time, and first increased and then decreased with the increase in soaking time and liquid–material ratio. The results confirmed that soaking time, distillation time, and liquid–material ratio were all critical process parameters. The kinetics models of volatile oil distillation from Angelicaesinensis Radix were established. The diffusion model of spherical particle was found to be the best model and indicated that the major resistance of mass transfer was the diffusion of volatile oil from the inside to the surface of the medicinal herb. Furthermore, the Box–Behnken experimental design was used to study the relationship between the three parameters and volatile oil yield. A second-order polynomial model was established, with R2 exceeding 0.99. The design space of the volatile oil yield was calculated by a probability-based method. In the verification experiments, the average volatile oil yield reached 0.711%. The results showed that the model was accurate and the design space was reliable. In this study, 21 chemical constituents of volatile oil from Angelicaesinensis Radix were identified by gas chromatograph-mass spectrometer(GC-MS), accounting for 99.4% of the total volatile oil. It was found that the content of Z-ligustilide was the highest, accounting for 85.4%.

Acid dissolution of jarosite-type compounds: Effect of the incorporation of divalent cations into the structure on the reaction rate

The present study analyzes the effect of the incorporation of divalent cations (Cu2+ and Zn2+) in the structure of a synthetic sodium jarosite on the dissolution rate in acid medium (H2SO4). Four syntheses of sodium jarosite with different amounts of Zn and Cu were performed using the hydrothermal method. The precipitates were characterized in detail using different analytical techniques. The feasibility of substituting Cu2+ and Zn2+ in the synthetized jarosites and in other previously reported jarosites was also analyzed by considering the Hume-Rothery rules for substitutional solid solutions. The variables investigated to determine the dissolution kinetics were temperature, pH and particle size. The rate-controlling step was the chemical reaction on the jarosite particle surface, which occurred according to the shrinking core kinetic model for spherical particles without the formation of a solid byproduct layer. In addition, the decomposition curves showed that the concentrations of Cu, Zn and Fe in the leach liquor increased as the reaction progressed. The reaction rate was affected by the presence of Cu in the structure of the sodium jarosite; the rate constant of dissolution for the Zn-incorporated jarosite (0.0035 min−1) was very similar to that obtained for the nonsubstituted jarosite (0.0034 min−1), but these values were higher than that determined for the Cu-incorporated jarosite (0.0026 min−1). This difference might be related to the difference between the atomic radii of Cu and Fe, which may cause a distortion of the jarosite crystal lattice due to the variation in the a parameter. Finally, a global kinetic equation was proposed that considers the kinetic parameters determined from the induction and progressive periods; this model was able to satisfactorily describe the leaching behavior of Cu-incorporated sodium jarosite under acidic conditions.

Calculation model for drag coefficient and multi-phase flow characteristics in dust removal process: Comparison between flake aluminum powder and spherical aluminum powder

It is of great significance to study the force model of flake and spherical particles in a two-phase flow system for reducing dust hazards. In present work, the correspondence between drag coefficient Cd and Re for spherical particle is specified by a new CFD method. Moreover, 144 kinds distribution states for flake particle with equal probability are summarized into 7 kinds stress state models with different occurrence probabilities, and the corresponding relationship between the equivalent drag coefficient Cd and the equivalent Reynolds number Re is further obtained. A series of ventilation and dust removal experiments and full-scale numerical simulation in a large space are carried out, and the maximum error of peak dust concentration between the simulation results and the experimental results for flake powder is 17.4%. In addition, the size effect of flake powder is more obvious than that of spherical powder, and the fluidity of flake powder with equal particle size is obviously better than that of spherical powder, so flake powder can be removed from the production workshop faster. However, in the process of ventilation and dust removal, the diffusion risk of spherical dust larger than 100 μm do not change much during the ventilation process.

A Hybrid Particle/Finite Element Model with Surface Roughness for Stone Masonry Analysis

Circular and spherical particle models are a class of discrete elements (DEM) that have been increasingly applied to fracture studies of quasi-brittle materials, such as rock and concrete, due to their proven ability to simulate fracture processes through random particle assemblies representing quasi-brittle materials at the grain scale. More recently, DEM models have been applied to old stone masonry fracture studies. In order to extend its applicability to structures of larger dimensions, an enhanced hybrid particle model is proposed here that allows finite elements with a given surface roughness, provided by the discretization of the element boundary with particles, to interact with the particulate media in which they are embedded. The performance of the hybrid model is compared with that of a traditional all-particle model under uniaxial testing. It is shown that similar results are obtained, namely, in the elastic phase, figures of rupture and pre-peak and post-peak behavior, while the hybrid model allows for a significant computational run time reduction of 20% to 25% in the coarse particle assemblies. Finally, the proposed hybrid model is applied in the simulation of shear tests of stone masonry walls and dry and mortared joints, providing reasonably good agreement with both the experimental results and predictions. For the rubble masonry tests, the hybrid model allows for a computation run time reduction of around 40% when compared with an all-particle model.

Experimental and modeling investigation on char combustion and char-nitrogen evolution characteristics under different conditions

The proper description of char combustion and char-nitrogen (char-N) evolution characteristics are imperative to analyze the operating performance of decoupling combustion systems. The char-O2 combustion and char-CO2 gasification reactivity of three typical coal chars, including lignite, bituminous, and anthracite, was tested in a lab-scale fixed-bed reactor in the temperature range of 1023 K–1223 K. The relevant chemical kinetic parameters were determined by applying a one-dimensional packed-bed reactor model embedded with a lumped particle model. Meanwhile, a 1-dimensional spherical particle model is necessary for describing the char-N conversion behaviors. Experimental results show that the conversion rate of char-N in the entire bed to NO (XNO, bed) gradually decreases with increasing temperature, and the decrease of coal rank leads to a decline in the NOx emission. Further simulation results indicate that for a single char particle in the initial combustion stage, if the char particle size increases (0–1000 μm), the external gas mass transfer coefficient decreases (0–5 m·s−1), or the oxygen content decreases (0–20%), the char-N conversion to NO (XNO, p) will gradually decrease. However, due to the complicated effects of temperature on multiple factors, involving reactivity, CO/CO2 ratio in products, and dual nature of CO influence on char-NO reaction, the relationship between char-N conversion and temperature for a single particle is not fixed. When the oxygen concentration is low, the XNO, p increases as temperature rising; while, an opposite trend may be formed under high oxygen conditions.

Leaching of Copper Contained in Waste Printed Circuit Boards, Using the Thiosulfate-Oxygen System: A Kinetic Approach.

The present work is related to the treatment of crushed waste of printed circuit boards (WPCBs) from electrical and electronic devices (WEEE), carrying out the recovery of copper in solution. In the first stage, the studied material was characterized by AAS, SEM-EDS, and XRD. The results revealed significantly high amounts of copper (744.42 mg/g), compared with the rest of the metals present in the sample, mainly iron and zinc. In the second stage of the work, alkali dynamic leaching experiments were carried out in the medium, evaluating important kinetic variables in order to verify the controlling step of the system and adjust the data to a kinetic model. According to the results obtained from the various experimental tests executed, it was found that in the studied system of , the leaching of copper was preferably adjusted to the model of spherical particles with a shrinking core finding a mixed chemical–diffusive control, with values of Ea = 25.78 kJ/mol and n = 0.22 (for the leaching reagent), indicating that the reaction was controlled by the oxygen transport to the solid–liquid interface and also by the chemical reaction in the surface of particles, obtaining up to 99.82% copper in solution.