Numerical Kinetic Model Research Articles

Transport kinetics of protium and deuterium in titanium: Experiments and modeling

We conducted absorption experiments on Ti using hydrogen isotopes, protium and deuterium, to gain insights into the kinetics of hydrogen atoms, particularly across the Ti surface. Rather than relying on various surface pretreatments, we identified the initial temperature of Ti in vacuum as the determining factor in achieving a high absorption rate and content. Specifically, we found that the initial Ti temperatures of approximately 900 and 980 °C are optimal for protium and deuterium, respectively, likely due to sufficient removal of the native surface oxide on Ti. The dependence of the absorption rate and amount of hydrogen isotopes on the temperature during absorption was partially explained by the phase transformation and exothermicity of the hydrogenation reaction. Moreover, this dependence strongly indicated the existence of a tunneling transport process. Additionally, we developed a kinetic model for hydrogen isotope transport in Ti to conduct numerical simulations. The absorption curves, calculated using the developed model, closely matched a series of experimental curves obtained at different temperatures. These curves were from an identical set of equations and kinetic parameters for both protium and deuterium. Our numerical kinetic model has the potential to serve as a valuable simulation tool for various applications, such as the design of high-performance hydrogen storage systems and maintenance strategies against hydrogen embrittlement of structural materials.

Evaluation of the function of polymeric bentonite adsorbent to retain strontium and cobalt radionuclides in OPC matrices

The effect of polyacrylamide-bentonite (PAAmB) as an adsorbent/cement-enhancement material was examined for the retention of strontium (Sr2+) and cobalt (Co2+) ions from aqueous system. PAAmB composite was synthesized and analyzed by diverse characterization techniques. The acquired experimental data revealed that the addition of bentonite to polyacrylamide polymer (PAAmP) enhanced the adsorption of strontium and cobalt ions capacities. To examine the adsorption mechanism onto PAAmB, the experimental data were fitted using hyperbolic and Langmuir equations at different temperatures. It was found that the adsorption nature was chemisorption and the adsorbed amount of the studied ions increased with increasing the temperature. Immobilization of spent polyacrylamide-bentonite composite loaded with 85Sr and 60Co radionuclides in different extents with Ordinary Portland Cement (OPC) was investigated. The results showed that the optimal compressive strength was attained at OPC blended with 5% PAAmB composite. The leaching patterns of the studied radionuclides from the immobilized waste form were compared with the standard static long-term leaching approach of International Atomic Energy Agency (IAEA). The cumulative leaching fraction (CLF) of the studied radionuclides from PAAmB-OPC was found to be < 5% in all scrutinized conditions, which suggests the applicability of the IAEA-recommended approach for assessing the diffusion coefficient. The acquired leaching data were nonlinearly regressed with numerous mathematical kinetic models to determine the leaching parameters and to evaluate the prevailing leaching mechanism. The results from the regression scrutiny showed that 85Sr and 60Co leaching resulted from three succeeding leaching mechanisms that were the first-order reaction exchange among the waste matrix surface and the leaching solution, diffusion and dissolution. Compliant with IAEA, the calculated leachability indices values implied that the studied matrices performance was within a suitable range and the immobilized spent PAAmB matrices had an adequate mechanical efficacy.

Experimental and numerical investigation on a solar-driven torrefaction reactor using woody waste (Ashe Juniper)

In this work, designs a novel solar-driven thermochemical conversion reactor to torrefy biomass waste (Ashe Juniper) for further pyrolysis applications. The effect of torrefaction temperature and residence time on the properties of biomass waste was investigated and results showed that torrefaction temperature dominates the properties of product compared to the effect of residence time. The highest energy yield (over 90%) was obtained at 210 ℃ while the highest energy densification (∼1.51) was achieved at 360 ℃. In addition, a two-step kinetic numerical model was used to analyze and predict the experimental process (kinetic rates) and results (C, H, and O contents) based on the experimental results. The analysis results showed that the predicted results are in good agreement with the practical results after torrefaction, indicating the feasibility of this numerical model for torrefaction and pyrolysis applications. The carbon footprint analysis showed that reduction effect of 1.3 ∼ 1.6 tCO2/ton-AJ can be obtained by torrefaction of Ashe Juniper. Finally, the prospects for future industrial applications of solar-driven torrefaction reactors discussed as one of affordable and clean energy.

Development and in vitro assessment of Analgesic and Anti-inflammatory Mefenamic acid Nanosponge Loaded Topical Formulation

The present research work was done with the objective of topical formulation development of poorly water-soluble drug Mefenamic acid. The drug was firstly incorporated in nanosponge of ethyl cellulose. Then Mefenamic acid nanosponge-loaded topical gel formulations were developed by using Carbopol 934 as a gel-forming polymer. The Mefenamic acid-loaded nanosponges were tested for various quality parameters such as particle size distribution, polydispersity.index(PI),. Surface morphology and drug entrapment efficiency etc. Gel formulations were tested for viscosity, pH, in vitro diffusion and other parameters. The average size of developed nanosponge preparations was found between 250nm to 894nm. Scanning electron microscopy photographs of developed formulations clearly reveal the spongy and porous nature of particles along with spherical shape. The PI was. found in. the range. of 0.206 to 0.934. It was found that formulation N3 with a drug-to-polymer ratio of 1:4 has the highest drug loading. Further nanosponge were characterized for different parameters and results revealed acceptable characteristics of N3 formulation. These prepared nanosponges were loaded in topical Carbopol gel (Formulation G3) and evaluated for in vitro diffusion release. Obtained in vitro data was applied to numerous kinetic models which reveal typical zero order in vitro drug diffusion with prolonged release of Mefenamic acid and therefore it can be effectively used as analgesic and anti-inflammatory formulation.

Study of temporal dissociation and atomic excitation rates in a flowing N2 DC discharge and post-discharge

In this work, we experimentally and theoretically study mechanisms of molecular dissociation and atomic excitation occurring in a flowing nitrogen DC discharge and its post-discharge. A specific discharge experimental condition for the pink afterglow plasma occurrence in the post-discharge tube is analyzed. We employ optical emission spectroscopy (OES) and Langmuir probes to measure the reduced electric field (E/N), electron density (n e), gas temperature (T g) and N2(X1Σ+ g) vibrational temperature (T v) in the positive column. OES was also employed in the post-discharge for measurements of relative densities of N(4S) and N(2D) atoms in the pink afterglow. Two well-established numerical kinetic models, one for the positive column and another one for the post-discharge, were used to calculate the rates of molecular dissociation and atomic excitation as a function of gas residence time in the positive column and also in the nitrogen post-discharge. We analyzed the role of 13 molecular dissociation mechanisms, and 8 atomic excitation mechanisms in the positive column and pink afterglow. Results demonstrate that the positive column dissociation processes are dominated by the direct electron impact mechanism in the earlier discharge gas residence times and that, for longer times, reactions between electronically excited states and N2(X1Σ+ g, v) vibrational states become the dominant dissociation mechanisms. It is also observed that dissociation processes occurring in the pink afterglow present relevant rates as compared to the same processes occurring in the positive column, demonstrating the high effectiveness of such processes in the post-discharge. The N(2D) and N(2P) excitation mechanisms are also examined. We observe that molecular dissociation and atomic excitation mechanisms strongly depend on the N2(X1Σ+ g) vibrational distribution function of the discharge and post-discharge.

Optimization of operating conditions on ultra-fine coal grinding through kinetic stirred milling and numerical modeling

This study investigated ultra-fine coal grinding performance of four low- to moderate-cost grinding media in a laboratory stirred mill. Kinetic grinding tests showed that silica beads generated the finest product size with a P80 of 5.9 μm from a feed size of 24.4 μm while having a specific energy (SE) input of 309 kWh/ton. Nonetheless, the least energy consumption of 109 kWh/ton was achieved by alumina beads; however, yielding a coarser product size of 15.5 μm. In addition, test results indicate that optimizing media sizes, solids concentration, and using viscosity modifiers enhance coal ultra-fine grinding performance. Under the optimized testing conditions, a P80 of 2.7 μm was produced with a corresponding SE input of 270 kWh/ton using silica beads ranging from 420 to 850 μm and a dispersant dosage of 14 kg/ton. Moreover, the mathematical models generated based on population balance modeling provided an accurate forecast of the particle-size distribution.

Energetic pickup proton population downstream of the termination shock as revealed by IBEX-Hi data

ABSTRACT Pickup protons originate as a result of the ionization of hydrogen atoms in the supersonic solar wind, forming the suprathermal component of protons in the heliosphere. While they are being picked by the heliospheric magnetic field and convected into the heliosheath, the pickup protons may suffer stochastic acceleration from the solar wind turbulence in the region from the Sun up to the heliospheric termination shock, where they can also experience shock-drift acceleration or reflection from the cross-shock potential. These processes create a high-energy tail in the pickup ion energy distribution. The properties of this energetic pickup proton population are still not well defined, in spite of the fact that they are vital for models that simulate energetic neutral atom fluxes. We consider two scenarios for the pickup proton velocity distribution downstream of the heliospheric termination shock (a filled shell with an energetic power-law tail, and bi-Maxwellian). Based on a numerical kinetic model and observations of the energetic neutral atom fluxes from the inner heliosheath by the IBEX-Hi instrument, we characterize the pickup proton distribution and provide estimations of the properties of the energetic pickup proton population downstream of the termination shock.

Study of ionization and ion transfer rates in flowing N2 DC discharges and post-discharges

In this work, we studied the ionization and ion transfer rates in flowing nitrogen DC discharges and post-discharges. Two different experimental set-ups and conditions for the flowing nitrogen discharges were analyzed. The first experimental set-up includes a post-discharge tube where the pink afterglow phenomenon was detected. Two well-established discharge and post-discharge kinetic numerical models we had previously developed to study the nitrogen flowing DC discharges and post-discharges were employed to calculate the rates for our experimental conditions. We analyzed 18 ionization and nine ion transfer mechanisms for N+, N2 +, N3 +, and N4 + ions in the discharges and post-discharges. We observed that the electron density of the discharges, which varies by one order of magnitude, plays a major role in the rates behavior for the two experimental set-ups. Moreover, we observed that the rates found in the pink afterglow phenomenon are relevant when compared to rates found in the discharges. The important role of molecular metastable Penning ionization and atoms and molecules associative ionization appear in the ionization rates of the discharges. It is also shown that ion transfer mechanisms play a crucial role in the ions densities distribution found in the discharges and post-discharges. This work brings an original comparative study of ionization and ion transfer rates for experimental flowing nitrogen DC positive columns and pink afterglow post-discharge. This is the first time that a detailed combined experimental and theoretical analysis on the ionization and ion transfer rates is carried out for nitrogen flowing DC positive columns and pink afterglow plasma.

Electro-activated persulfate oxidation (EC/PS) for the treatment of real oilfield produced water: Optimization, developed numerical kinetic model, and comparison with thermal/EC/PS and EC systems

In this study, the performance and efficiency of electrocoagulation (EC), electro-activation of persulfate (EC/PS), and thermal activated-EC/PS for the treatment of two real produced water (PW) samples using iron electrodes were studied. To optimize and find out the effect of operating conditions on the different responses for EC and EC/PS, response surface methodology (RSM) was implemented. The results showed that EC process had considerable performance in the removal of H2S (96 %), oil and grease (O&G) (98–99 %), turbidity (91–97 %), phosphate phosphors (94 %), and heavy metals (92 %). EC/PS was introduced as an effective and a compact method for the removal of soluble hydrocarbons and nitrogen-ammonium (N-NH4+). The results indicated that at the current density of 35 A/m2, PS of 30 mM, reaction time of 30 min, N-NH4+ and chemical oxygen demand (COD) removal efficiency increased to 37 % and 71–94 %, respectively. To further increase the ammonia removal, EC/PS was integrated into thermal-PS activation at 65 °C, and the results showed that the ammonia removal by thermal/EC/PS reached about 69 %. According to gas chromatography/mass spectrometry (GC/MS), EC/PS was able to effectively eliminate most of the hydrocarbons. Moreover, a new kinetic model based on a novel algorithm and the main reactions occurring during EC/PS was developed to predict the COD removal efficiency, and the results indicated that it could predict COD removal efficiency with the acceptable accuracy. The estimated operating costs and energy consumption for EC/PS demonstrated that this process was more economical and efficient than other advanced oxidation processes (AOPs).

The Interplay Between Ambipolar Electric Field and Coulomb Collisions in the Solar Wind Acceleration Region

AbstractThe solar wind protons are accelerated to supersonic velocities within the distance of 10 solar radii from the Sun, as a consequence of a complex physical mechanism including particle kinetic effects as well as the field‐particle energy and momentum exchange. We use a numerical kinetic model of the solar wind, accounting for Coulomb collisions (BiCoP), and model a solar wind accelerated only by the ambipolar electrostatic filed (E) arising due to the difference in mass between electron and proton, and assuring quasi‐neutrality and zero current. We study the effect E, which was found to be on the order of Dreicer electric field (ED) (Dreicer, 1959), has on the resulting electron velocity distribution functions. The strahl electron radial evolution is represented by means of its pitch‐angle width (PAW), and the strahl parallel temperature (Ts,‖). A continuous transition between collisional and weakly collisional regime results in broader PAW, compared to the single‐exobase prediction imposed by the exospheric models. Collisions were found to scatter strahl electrons below 250 eV, which in turn has an effect on the measured Ts,‖. A slight increase was found in Ts,‖ with radial distance, and was stronger for the more collisional run. We estimate that the coronal electron temperature inferred from the observations of Ts,‖ in the solar wind, would be overestimated for between 8% and 15%.

Analysis of the IBEX-Lo interstellar hydrogen fluxes collected in 2009–2018 as a tool for sensing of the solar radiation pressure and the hydrogen ionization rate

ABSTRACT The Interstellar Boundary Explorer (IBEX) has been measuring interstellar hydrogen fluxes at 1 au since 2009. In this paper, we analysed all available data obtained with the IBEX-Lo instrument at energies 11–41 eV using our numerical kinetic model of the interstellar hydrogen distribution in the heliosphere. We performed a fitting of the data to find independently the model parameters: the ratio of the solar radiation pressure to the solar gravitation (μ0), ionization rate of hydrogen atoms at 1 au (β0), parameters of the secondary interstellar atoms at 70 au from the Sun, which provide the best agreement with the data by minimization of metric χ2. We also analysed temporal variations of the ratio of the fluxes measured in a fixed direction at energy bin 1 and energy bin 2. It is found that in 2009–2011 and 2017–2016 the ratio provided by the model is smaller than in the IBEX-Lo data, while in 2012–2015, oppositely, the model ratio is larger compared to the data. This might be caused by the incorrect separation of the measured fluxes between energy channels in the data, or by some additional physical factors that are omitted in the model. Understanding this issue may be important for the preparation of future Interstellar Mapping and Acceleration Probe mission. At this stage, we relied on the sum of the fluxes measured in energy bins 1 and 2 for comparison to model predictions.

Neutral and Excited Molecules and Atoms Densities in the Positive Column of Flowing N2 DC Discharges

We investigated flowing N2 DC discharges both experimentally and theoretically. The discharge gas and N2(X1Σ+g) vibrational temperatures, electron density (ne), reduced electric field (E/N), and radiative state densities were measured by optical emission spectrometry (OES) and Langmuir double probes. We formulated a discharge kinetic numerical model to calculate the densities of nitrogen species as functions of the gas residence time. We combine the experimental parameters measured in the discharge with the kinetic model to analyze different discharge conditions where E/N varies significantly. First, we analyzed the measured and calculated radiative states densities and N2(X1Σ+g) vibrational distributions at the end of the positive column. Results show good agreement between calculated and measured parameters. Then, we studied the excited molecular species densities, and neutral and excited atoms densities as functions of the discharge gas residence time. This work presents for the first time the temporal densities of excited molecular and atomic states from 10−9 to 10−1 s discharge residence times, calculated for experimental conditions where ne presents a low variation and E/N varies from high (94 Td) to relatively low values (48 Td). The discharge experimental conditions are discharge current of 60 mA, gas pressure of 230–530 Pa, and gas flow rate of 0.9 Slm−1.

Kinetic investigation of N2 flowing DC discharges

Nitrogen flowing DC discharges were generated between two side-armed electrodes in a drift tube. The discharges operated at gas residence times (t) of ∼4 × 10−4 s, reduced electric fields (E/N) between 90 and 118 Td, and electron densities (ne) between 1010 and 1011 cm−3. A kinetic numerical model was elaborated to study the discharge kinetics. The model calculates the densities of 18 electronic states of nitrogen in the discharge, including the 45 vibrational levels of the N2(X1Σ+g) molecules, as functions of the gas residence time. The model is employed to describe the density profiles of neutral and excited atomic and molecular species, and nitrogen ions, along with the N2(X1Σ+g) vibrational distributions for our experimental conditions. The N2(X1Σ+g) vibrational and gas temperatures, E/N, ne, and the N2(B3Πg), N2(C3Πu), and N2+(B2Σ+u) relative densities were measured in the discharge by optical emission spectroscopy and double probes. The experimental determined gas temperature (Tg), electron density, and reduced electric field were used in the calculations of the electron energy distribution function and reaction rate constants. The vibrational temperature (Tv) and excited species densities measured were compared to the calculated values from the model. Although much attention has been devoted to the study of nitrogen DC discharges in the last few years, this work presents for the first time the N+ – N4+ and N2+(B2Σ+u) ion density distribution together with the densities of 13 atomic and molecular nitrogen states as functions of the discharge gas residence time and N2(X1Σ+g) vibrational distributions calculated for experimental conditions of low pressure DC discharges operating at short residence times.

Advanced numerical kinetic model for predicting COD removal and optimisation of pulp and paper wastewater treatment by Fenton process

ABSTRACT In the present study, a kinetic model has been developed to predict the chemical oxygen demand (COD) removal efficiency of Fenton process for the treatment of pulp and paper mill (P&P) wastewater. In order to investigate the effects of main parameters including Fe(II) dosage, H2O2 dosage, and pH, 45 experiments have been carried out at three levels for each parameter, and thus COD removal efficiency has been obtained. The Fenton process was simulated by using 10main reactions, and the model was solved numerically according to a specific algorithm. All the pollutants in the P&P wastewater were assumed to be a pseudo-material, andapparent kinetic constant (k**)was calculated using a developed iterative method. The results of the numerical model indicated that the proposed model had a great potential to predict COD removal efficiency for P&P wastewater by Fenton in comparison to the first and second-order kinetic models. Accordingly, R-squared (R 2), Root Mean Square Error (RMSE), and Mean Relative Error (MRE) of the numerical kinetic model were 0.93, 4.296 × 10−7, and 0.035, respectively, implying remarkable accuracy of the numerical model. Furthermore, at the optimum point of Fenton process,which was pH: 3,[H2O2]:0.015 Molar, and [Fe(II)]: 0.015 Molar, the COD removal efficiency of P&P wastewater reached 78%. As the basis of the numerical model was established according to mechanisms of Fenton process, the results demonstrated the great performance of the advanced kinetic model in the estimation of the COD removal efficiency, the behaviour of effective parameters such as pH, H2O2, and Fe(II) along with their effects on k**, and Fe(III) accumulation during Fenton process.

Temporal electron collisions and adjunct ionization mechanisms in the positive column of a flowing N2 DC discharge

We studied a flowing nitrogen DC discharge by Langmuir double probes and optical emission spectroscopy (OES). We measured the reduced electric field (E/N) and electron density (ne) with the double probes. The gas (Tg) and N2(X1Σ+g) vibrational temperature (θ) were measured by OES from the nitrogen first and second positive systems transitions. We constructed a kinetic numerical model accounting for N2(X1Σ+g, 0 ≤ v ≤ 45), N2(A3Σ+u), N2(B3Πg), N2(a1Πg), N2(a′1Σ−u), N2(w1Δu), N2(a″1Σ+g), N2(W3Δu), N2(E3Σ+g), N2(C3Πu), N2+(X2Σ+g), N2+(B2Σ+u), N+, N3+, N4+, N(4S), N(2D), and N(2P) states. The species densities are calculated as functions of the discharge gas residence time in pure nitrogen for our experimental conditions. The kinetic model assumes as input parameters the experimental discharge gas pressure (p), tube radius (R), electron density (ne), gas temperature (Tg), reduced electric field (E/N). In this Letter, the kinetic model is applied to calculations of the fractional contribution of each ionization mechanism to the total ionization generated in the discharge. We compute 24 different ionization mechanisms to the five ions species. We have observed that ionization is generated by different physical-chemical reactions depending on the discharge gas residence time. It changes from dominant electron impact ionization process in the earlier times of the discharge to adjunct ionization mechanisms depending on the pooling of N2(a′1Σ−u) and N2(A3Σ+u) metastable molecules and associative ionization of N2(a′1Σ−u), N(2D) and N(2P) metastable atoms and molecules. Moreover, we have observed the occurrence of approximate charge neutrality for our studied experimental condition: discharge current of 30 mA, gas flow rate of 1 Slm−1, and gas pressure of 230 Pa. Also, the kinetic model fits quite well the measured N2(X1Σ+g) vibrational temperature at the end of the positive column.

Numerical Modeling of Leaching of Aluminophosphate Glass in the Batch Mode in the Presence of Bentonite

A numerical kinetic model of leaching of aluminophosphate glass, an analog of a glass matrix for radioactive waste, in the batch mode in the presence of bentonite, taking into account the sorption processes, was constructed on the basis of the experimental data. The model describes the glass dissolution kinetics within the framework of the concept of approach to the equilibrium, taking into account shielding of the surface with glass corrosion products. The sorption is described within the framework of the ion exchange model. Modeling was performed using PhreeqC code.

Optimal production of tires through an integrated experimental, kinetic and finite element Fe modelling approach

An integrated three-step approach for the optimization of tires mechanical properties based on experimental characterization, kinetic steady-state model and Finite Element FE heat transmission modelling is presented. The first experimental characterization is needed to calibrate a kinetic numerical model (second step), directly nested in the last step into a FE software for the simulation of 3D heat transmission problems. The kinetic model is a phenomenological approach based on 3 kinetic constants, which allows predicting the initial curing rate, maximum crosslinking and reversion. Kinetic constants are deduced fitting normalized experimental rheometer curves. FE transient curing computations are carried out on a real car tire, discretizing the geometry through a refined mesh. All element of the tire (e.g. belts, carcass, core etc.) can be separately meshed, so the exact vulcanization process in different phases can be eventually accounted for.

SWAN/SOHO Lyman‐α Mapping: The Hydrogen Geocorona Extends Well Beyond the Moon

AbstractThe Earth's hydrogen exosphere Lyman‐α radiation was mapped with the Solar Wind Anisotropies/Solar and Heliospheric Observatory (SWAN/SOHO) instrument in January 1996, 1997, and 1998 (low solar activity). The use of a hydrogen absorption cell allowed to disentangle the interplanetary emission from the geocoronal one and to assign the absorbed signal almost entirely to the geocorona. The geocorona was found to extend at least up to 100 Earth radii (RE) with an intensity of 5 Rayleigh, an unprecedented distance well exceeding the recent results of Lyman Alpha Imaging Camera (LAICA) imager (∼50 RE), and encompassing the orbit of the Moon (∼60 RE). We developed a numerical kinetic model of the hydrogen atoms distribution in the exosphere, which includes the solar Lyman‐α radiation pressure and the ionization. The radiation pressure compresses the H exosphere on the dayside, producing a bulge of H density between 3 and 20 RE, which fits observed intensities very well. The SWAN Lyman‐α distribution of intensity was compared both to LAICA (2015) and to Orbiting Geophysical Observatory number 5 (1968) measurements. Integrated H densities of SWAN at a tangent distance of 7 RE are larger than LAICA/Orbiting Geophysical Observatory number 5 by factors 1.1–2.5, while we should expect a stronger effect of the radiation pressure at solar max. We discuss the possible role of H atoms in satellite orbits to explain this apparent contradiction. An onion‐peeling technique is used to retrieve hydrogen number density in the exosphere for the three SWAN observations. They show an excess of density versus models at large distances, which is likely due to nonthermal atoms (not in the model).

Numerical kinetic model with regularization for NR–PB natural and poly-butadiene rubber blends: implementation and validation against experimental data

A simple and versatile numerical approach of experimental data regularization plus a kinetic model to predict the vulcanization behavior in a rheometer for natural rubber (NR) and poly-butadiene (PB) blends is presented. The numerical model proposed uses generic rheometer experimental curves to estimate kinetic constants of the cure reactions, preliminarily regularizing input data through Cn continuous polynomial splines of degree n, with spline knots equally spaced or placed at user’s discretion. Splines coefficients are efficiently evaluated through a standard non-linear least squares optimization procedure. In this way a set of meta-data fitting optimally experimental values is obtained, with a smooth prediction of the local curing rate. The kinetic approach adopted is classic but adaptable to a wide class of cases and characterized by only three kinetic constants, describing two reactions occurring in parallel and two in series (reversion phenomenon). The determination of the three kinetic constants characterizing the model is performed graphically in quasi analytical form. The model is benchmarked by means of an ad-hoc conducted experimental campaign carried out with different typologies of rubber blends constituted by NR and PB at 70–30% and 50–50% concentrations, with sulfur at 1 phr and two accelerants (TBSS and DPG) at 1 and 3 phr, under standard vulcanization conditions (rheometer) at 150 °C, 170 °C and 180 °C.

Investigation of the kinetic energy transformation pattern of gangue particles in a buffer system

A suspended buffer system reduces the out-of-pipe speed of gangue particles to a reasonable value, which prevents damage to the gangue storage silo. During the buffering process, the kinetics energy of gangue particles is dissipated by particle collision and structural damping of the suspended buffer, with the remaining energy being the residual kinetics energy of gangue particles. The ratios of these energies are important indicators of the buffering effect and are the basis for feeding safety judgment. Therefore, it is necessary to reveal the kinetic energy transformation pattern of gangue particles during the collision process. This paper established a numerical kinetic energy transformation model for gangue particles by combining Solidworks and Femap. The simulation results showed that kinetics energy of gangue particles is mainly consumed by the collision between particles and the suspended buffer, while the energy consumed by structural damping of the suspended buffer is relatively small. At the same time, the ratio of energy consumed by particle collision decreases with the increase of gangue particle size, which corresponds to the increasing particle residual kinetic energy. Origin was then employed to fit ratio of energy consumed by collision, particle residual kinetic energy and velocity as functions of particle size: E1 = 57.19 + 34.48/(1 + e(D-48.89)/7.19), E2 = 40.57–33.59/(1 + e(D-49.16)/8.14) and v´ = 52.34–51.93/(1 + e(D-50.50)/18.75). Based on the requirement of particle kinetic energy transformation, the reasonable particle size was determined to below 50 mm according to the aforementioned functional relationships. Industrial testing of the simulation result was performed in the Dongping coal mine, which showed good buffering effect while damage of the storage silo was not observed.