Contracting Sphere Research Articles

Oxidative leaching of rhenium from grinding waste of rhenium-containing superalloys

The study investigated the feasibility of oxidative leaching rhenium in the presence of hydrochloric acid from machining waste (grinding waste) derived from products made of ZhS-32VI, a nickel-based heat-resistant alloy containing rhenium. This was achieved through agitation leaching process. The grinding waste fraction size of –0.071 mm, which accounted for the highest yield (49.2 wt.%), was utilized in the experiments. The rhenium leaching process was conducted in two variations: in the first option, grinding waste was mixed with a hydrochloric acid solution at ~100 °C, followed by the addition of hydrogen peroxide to the leaching solution after it had cooled; in the second option, leaching was performed using a hydrochloric acid solution with the gradual addition of hydrogen peroxide solution. The highest degree of rhenium leaching (91.0 %) was achieved in the first option. In this case, the initial concentration of hydrochloric acid was 8 M, and the molar ratio of the added reagents was ν(HCl): ν(H2O2) = 2.7 : 1.0. The kinetics of nickel leaching using a 6 M hydrochloric acid solution at 70 °C, with a solid-to-liquid phase ratio of 1 g : 50 ml, was also examined. The analysis of the kinetic data, processed using the “contracting sphere,” Ginstling–Brounshtein, and Kazeev–Erofeev models, indicates that the nickel leaching process occurs within the kinetic region. Additionally, the kinetics of rhenium leaching from the solid residue obtained after the hydrochloric acid leaching of nickel from grinding waste was investigated. Employing the same kinetic models to analyze the data, it was determined that the limiting stage of this process involves the diffusion of hydrogen peroxide within the rhenium-containing solid residue.

Advanced isoconversional kinetic analysis of Fe2O3-2Al thermite reaction for plug and abandonment of oil wells

Moving from a carbon-based to a carbon-free economy has driven the development of groundbreaking new technologies for permanent plugged and abandoned (P&A) of mature oil wells, including the use of thermites as the energetic material for the so-called “Thermal P&A” technology. Better knowledge is then much needed on such chemical reactions. Accordingly, this research presents an in-depth kinetic study of the Fe2O3-2Al thermite reaction by analyzing differential scanning calorimetry (DSC) data at three heating rates. After an endothermic peak corresponding to the aluminum melting process (∼660.3 °C), two exothermic peaks were identified corresponding to thermal stages of the overall thermite reaction: the first stage at 800–1000 °C and second stage at 1000–1300 °C. The apparent activation energy of each reaction stage was calculated using several isoconversional kinetics methods. All methods revealed significant variation of activation energy with the extent of conversion. However, the differential method of Friedmann and the flexible-integral methods of Popescu and Vyazovkin identified higher variations than the rigid-integral methods, with EA values between 188 and 356 kJ/mol for the first reaction stage and 280 and 509 kJ/mol for the second one. These high variations indicated a multi-step mechanism that requires multiple kinetic triplets. The pre-exponential factor at each extent of conversion and the reaction mode of each reaction stage were estimated by an approach based on Popescu's equation and the compensation effect. A contracting sphere and a random nucleation mechanism were identified as suitable models to describe the first and second reaction stage, respectively. Modeled data showed an excellent agreement with the experimental data of the first reaction stage, with average deviations up to 1.2 %. However, modeled data of the second stage presented more notable variations with average deviations up to 9.5 %.

On the Kinetic Mechanisms of the Reduction and Oxidation Reactions of Iron Oxide/Iron Pellets for a Hydrogen Storage Process

This work aims at investigating the kinetic mechanisms of the reduction/oxidation (redox) reactions of iron oxide/iron pellets under different operating conditions. The reaction principle is the basis of a thermochemical hydrogen storage system. To simulate the charging phase, a single pellet consisting of iron oxide (90% Fe2O3, 10% stabilising cement) is reduced with different hydrogen (H2) concentrations at temperatures between 600 and 800 °C. The discharge phase is initiated by the oxidation of the previously reduced pellet by water vapour (H2O) at different concentrations in the same temperature range. In both reactions, nitrogen (N2) is used as a carrier gas. The redox reactions have been experimentally measured in a thermogravimetric analyser (TGA) at a flow rate of 250 mL/min. An extensive literature review has been conducted on the existing reactions’ kinetic mechanisms along with their applicability to describe the obtained results. It turned out that the measured kinetic results can be excellently described with the so-called shrinking core model. Using the geometrical contracting sphere reaction mechanism model, the concentration- and temperature-dependent reduction and oxidation rates can be reproduced with a maximum deviation of less than 5%. In contrast to the reduction process, the temperature has a smaller effect on the oxidation reaction kinetics, which is attributed to 71% less activation energy (Ea,Re=56.9 kJ/mol versus Ea,Ox=16.0 kJ/mol). The concentration of the reacting gas showed, however, an opposite trend: namely, to have an almost twofold impact on the oxidation reaction rate constant compared to the reduction rate constant.

Degradation mechanism and oxidation kinetics of C60 fullerene

Despite a great deal of research on the basic properties of C60 to the present, no detailed and comprehensive reports are available concerning its degradation mechanism and oxidation kinetics. However, a deeper understanding of the oxidation mechanism of the most common fullerene broadens the horizons of potential applications, especially at high temperatures. Therefore, this study attempted to investigate the fullerene oxidation process using kinetic analysis under non-isothermal conditions. Initially, the powder was structurally and morphologically characterized accurately via XRD, Raman spectroscopy, FESEM, and TEM analyses. This was followed by simultaneous thermal analysis (STA) (i.e., TG and DSC) at four different heating rates (2.5, 5, 10, and 15 °C min−1) in airflow, and kinetic analysis was subsequently conducted to evaluate the thermal oxidation of C60. The activation energy as evaluated by model-free methods turned out to be almost invariant within the specified range of reaction fraction (α). Model-fitting methods were also employed to identify the oxidation mechanism involved, from which emerged two models (i.e., R3 (g(α) = 1-(1-α)1/3) and F1 (g(α) = −ln(1-α))) as possible reaction mechanisms. However, further investigation using the Z(α) master plot method revealed that the kinetic model R3, a phase-boundary process, is the controlling mechanism of C60 oxidation with E ≈ 96 kJ mol−1 and lnA ≈ 9.1 min−1. Further examinations were conducted in the neutral atmosphere, and the partial oxidation process based on TEM and FESEM images revealed that oxygen and heat applied during the process play a central role in the deagglomeration of C60 particles and the consequent oxidation. In fact, considering the spherical morphology and the agglomerates present in the C60 powder, the contracting sphere kinetic model (R3) was found to capture the oxidation process due to attacks by the oxygen molecules at the interface of C60 powder agglomerates.

Effects of Mustard Husk, Wheat Straw, and Flaxseed Residue Blending on Combustion Behavior of High Ash Coal and Petroleum Coke Blends

Abstract This present work reports the combustion studies of coal, petroleum coke (PC) and biomass blends to assess the effects of the mustard husk (MH), wheat straw (WS), and flaxseed residue (FR) blending toward improvement of coal combustion characteristics. Ignition temperature (TS), maximum temperature (TP), burnout temperature (TC), activation energy (AE), and thermodynamic parameters (ΔH, ΔG, and ΔS) were analyzed to evaluate the impact of biomass and PC blending on coal combustion. Experimental results indicate that coal and PC have inferior combustion characteristics compared to MH, WS, and FR. With the increase in WS content in blends from 10 to 30%, TS reduced from 371 to 258 °C and TP decreased from 487 to 481 °C, inferring substantial enhancements in combustion properties. Kinetic analysis inferred that blended fuel combustion could be explained mostly using reaction models, followed by diffusion-controlled and contracting sphere models. Overall, with the increase in FR mass in blends from 10 to 30%, AE decreased from 108.97 kJ/mol to 70.15 kJ/mol signifying ease of combustion. Analysis of synergistic effects infers that higher biomass addition improves coal and PC blends’ combustion behavior through catalytic effects of alkali mineral matters present in biomass. Calculation of thermodynamic parameters signified that combustion of coal and PC is challenging than biomasses; however, blending of biomass makes the combustion process easier.

Dependence of oxygen desorption kinetics on processing methods of SrCoO2.5

The effect of processing methods on oxygen storage and exchange kinetics of brownmillerite (BM) SrCoO2.5 is compared in terms of their reversible oxygen incorporation and desorption kinetics. BM SrCoO2.5 was synthesized through two different methods; solid-state synthesis and the nitrate–citrate gel method, both followed by Al foil pad quenching. Oxygen storage characteristics of synthesized samples were analysed using a home-built volumetric set-up. The maximum oxygenation achievable for BM SrCoO2.5 under prevailing conditions of O2 partial pressure (16 bar O2), temperature (673 K) and time (1 h) was unaltered, regardless of the synthesis method. Oxygen exchange kinetics of desorption was faster in the nitrate–citrate synthesized sample than in the solid-state synthesized sample. The kinetics of desorption correlated with the crystallite and particle sizes of the samples. The mechanism of desorption follows nucleation and growth model for nitrate–citrate synthesized sample, while it follows contracting sphere model for solid-state synthesized sample.

Pyrolysis kinetics and estimation of chemical composition of Quercus cerris cork

Pyrolysis kinetics of Quercus cerris cork was investigated using thermogravimetric analysis with heating rates of 10, 20, 50, and 100 °C min−1. The activation energies and chemical compositions of cork components were determined by different model-fitting methods, isoconversional Kissinger-Akahira-Sunose (KAS) method, and Lorentzian multi-peak fitting. Wet chemical analysis of cork was conducted to compare with the chemical compositions predicted by the kinetic models and Lorentzian multi-peak fitting. The results show that pyrolysis of Quercus cerris cork possibly follows nth-order kinetics, and best fits to the experimental data were obtained by three-halves kinetics followed by first-order and contracting sphere models. The fit qualities of the different models were close implying that the first order models could be used for practical applications. Six pseudo-components approximation used in these models suggested that while cork hemicelluloses and cellulose undergo thermal decompositions similar as in wood, cork suberin decomposes in two distinct steps, i.e., cellulose-like and lignin-like decompositions. Isoconversional KAS method showed that the average activation energy of Quercus cerris cork is approximately 298 kJ mol−1. The reconstructed mass loss curves after Lorentzian multi-peak fitting resulted in smaller activation energies for cork components.

Thermogravimetric and kinetic analysis of thermal decomposition characteristics of microbial calcites induced by cyanobacteria Synechocystis sp. PCC6803

Although various complicated methods have always been made attempts, it is still well difficult to efficiently distinguish between the biogenic and abiogenic minerals in geological area up to now. In present study, the thermal decomposition unique characteristics of microbial calcites (MC), induced by cyanobacteria Synechocystis sp. PCC6803, were compared with those of chemical calcites (CC) prepared by the reaction of sodium carbonate (Na2CO3) with calcium chloride (CaCl2). Two samples were firstly analyzed by scanning electron microscope and X-ray diffraction, and were further investigated thermal decomposition behaviors using a thermogravimetric analyzer at different heating rates of 278.15, 283.15, 293.15, and 303.15 K min−1 from 323.15 to 1273.15 K, respectively, then kinetic parameters were calculated via Popescu, Kissinger–Akahira–Sunose, and Flynn–Wall–Ozawa methods, and then the kinetics mechanism functions were deduced by Popescu method. The results showed that these two kinds of precipitates were actually both calcite crystals although the surface morphologies were quite different. Whereas thermal decomposition kinetics mechanism function of MC can be described as Avrami–Erofeev equation ([−ln(1 − α)]1/3), while CC corresponded to Contracting sphere (volume) ([1 − (1 − α)]1/3), the results also showed that the average activation energy of MC and CC was 217.9 and 170.5 kJ mol−1, respectively; that is, MC has higher thermal stability, which should be originated from the inducing effects and the different precipitation conditions provided by Synechocystis sp. PCC6803. These above results provided useful information not only for efficiently distinguishing between the biogenic and abiogenic minerals in geological area, and also for better understanding the microbial mineralization.

A solution to the focusing 3d NLS that blows up on a contracting sphere

We rigorously construct radial H 1 H^1 solutions to the 3d cubic focusing NLS equation i ∂ t ψ + Δ ψ + 2 | ψ | 2 ψ = 0 i\partial _t \psi + \Delta \psi + 2 |\psi |^2\psi =0 that blow-up along a contracting sphere. With blow-up time set to t = 0 t=0 , the solutions concentrate on a sphere at radius ∼ t 1 / 3 \sim t^{1/3} but focus towards this sphere at the faster rate ∼ t 2 / 3 \sim t^{2/3} . Such dynamics were originally proposed heuristically by Degtyarev-Zakharov-Rudakov in 1975 and independently later by Holmer-Roudenko in 2007, where it was demonstrated to be consistent with all conservation laws of this equation. In the latter paper, it was proposed as a solution that would yield divergence of the L x 3 L_x^3 norm within the “wide” radius ∼ ‖ ∇ u ( t ) ‖ L x 2 − 1 / 2 \sim \|\nabla u(t)\|_{L_x^2}^{-1/2} but not within the “tight” radius ∼ ‖ ∇ u ( t ) ‖ L x 2 − 2 \sim \|\nabla u(t)\|_{L_x^2}^{-2} , the second being the rate of contraction of self-similar blow-up solutions observed numerically and described in detail by Sulem-Sulem in 1999.

Thermal decomposition mechanism of ammonium sulfate catalyzed by ferric oxide

The decomposition mechanism of ammonium sulfate catalyzed by ferric oxide was investigated in this paper. The decomposition kinetics parameters were determined via a global optimization of the Kissinger iterative method using the non-isothermal thermogravimetric analysis data. The products and intermediates were synchronously characterized by X-ray diffraction and mass spectrometry. The obtained results indicate that the decomposition process of ammonium sulfate catalyzed by ferric oxide can be divided into four stages of which the activation energies are 123.64, 126.58, 178.77 and 216.99 kJ·mol−1 respectively. The decomposition mechanisms at the first and the fourth stage both belong to Mample power theorem, the second stage belongs to Avrami-Erofeev equation and the third belongs to contracting sphere (volume) equation. The corresponding pre-exponential factors (A) are calculated simultaneously.

Thermal degradation kinetics of poly(trimethylol propane triacrylate)/poly(hexane diol diacrylate) interpenetrating polymer network

Interpenetrating polymer networks (IPNs) of trimethylol propane triacrylate (TMPTA) and 1,6-hexane diol diacrylate (HDDA) at different weight ratios were synthesized. Temperature modulated differential scanning calorimetry (TMDSC) was used to determine whether the formation resulted in a copolymer or interpenetrating polymer network (IPN). These polymers are used as binders for microstereolithography (MSL) based ceramic microfabrication. The kinetics of thermal degradation of these polymers are important to optimize the debinding process for fabricating 3D shaped ceramic objects by MSL based rapid prototyping technique. Therefore, thermal and thermo-oxidative degradation of these IPNs have been studied by dynamic and isothermal thermogravimetry (TGA). Non-isothermal model-free kinetic methods have been adopted (isoconversional differential and KAS) to calculate the apparent activation energy (Ea) as a function of conversion (α) in N2 and air. The degradation of these polymers in N2 atmosphere occurs via two mechanisms. Chain end scission plays a dominant role at lower temperature while the kinetics is governed by random chain scission at higher temperature. Oxidative degradation shows multiple degradation steps having higher activation energy than in N2. Isothermal degradation was also carried out to predict the reaction model which is found to be decelerating. It was shown that the degradation of PTMPTA follows a contracting sphere reaction model in N2. However, as the HDDA content increases in the IPNs, the degradation reaction follows Avrami–Erofeev model and diffusion governed mechanisms. The intermediate IPN compositions show both type of mechanism. Based on the above study, debinding strategy for MSL based microfabricated ceramic structure has been proposed.

THERMAL BEHAVIOR OF EUCLIDEAN STARS

A recent study of dissipative collapse considered a contracting sphere in which the areal and proper radii are equal throughout its evolution. The interior space–time was matched to the exterior Vaidya space–time which generated a temporal evolution equation at the boundary of the collapsing sphere. We present a solution of the boundary condition which allows the study of the gravitational and thermodynamical behavior of this particular radiating model.

Kinetics and mechanisms of converting bioactive borate glasses to hydroxyapatite in aqueous phosphate solution

Borate bioactive glasses are receiving increasing attention as scaffold materials for bone repair and regeneration. In this study, the kinetics and mechanisms of converting three groups of sodium–calcium–borate glasses with varying CaO:B2O3 ratio to hydroxyapatite (HA) in 0.25 M K2HPO4 solution were investigated at 10–70 °C. Glass disks with the composition 2Na2O·(2 − x)CaO·(6 + x)B2O3 (x = 0, 0.5, and 1.0) were immersed for up to 8 days in the potassium phosphate solution. The conversion kinetics to HA were monitored by measuring the weight loss of the glass, while X-ray diffraction, scanning electron microscopy, and Fourier transform infrared spectroscopy were used to study structural and compositional changes. All three groups of glasses formed HA on their surfaces, showing that the glasses were bioactive. At 10–37 °C, the conversion kinetics was well fitted by the contracting sphere model. Also, the contracting sphere model has a good fit for the early stage of conversion at 70 °C, whereas a three-dimensional (3D) diffusion model provided a good fit to the data of the later stage. The results of this study provide kinetic and structural data for the design of borate bioactive glasses for potential applications in bone tissue engineering.

Thermal degradation behaviors of polyethylene and polypropylene. Part I: Pyrolysis kinetics and mechanisms

Study of the decomposition kinetics is an important tool for the development of polymer recycling in industrial scale. In this work, the activation energy and the reaction model of the pyrolysis of high density polyethylene (HDPE), low density polyethylene (LDPE) and polypropylene (PP) have been estimated from non-isothermal kinetic results. Firstly, the activation energy values obtained by Friedman, Kissinger–Akahira–Sunose and Flynn–Wall–Ozawa isoconversional methods, are 238–247 kJ/mol for HDPE, 215–221 kJ/mol for LDPE and 179–188 kJ/mol for PP. Secondly, the appropriate conversion model of the process was determined by Coats–Redfern and Criado methods. The pyrolysis reaction models of HDPE and LDPE are accounted for by “Contracting Sphere” model, whereas that of PP by “Contracting Cylinder” model.

Non-isothermal decomposition kinetics of magnesite

Kinetics of thermal decomposition of Indian magnesite was studied by thermo-gravimetric analysis under non-isothermal condition. Coats and Redfern Integral approximation method was used to determine the kinetic parameters. Using the kinetic parameters different kinetic functions were analyzed with the experimental data to ascertain the decomposition mechanism of magnesium carbonate and it was observed that the decomposition reaction followed a contracting sphere kinetic mechanism.

Growth, characterization and thermal behaviour of gel grown mixed Gd–Sr–molybdate crystals

The growth of mixed Gd–Sr–molybdate crystals, bearing stoichiometric composition Gd 2Sr 7Mo 9O 37·14H 2O, is achieved by gel encapsulation technique, using the system RCl 3(NH 4) 6Mo 7O 24NH 4NO 3HNO 3Na 2SiO 3 (where R=Gd:Sr). Addition of Sr in the lattice of pure Gd-heptamolybdate (reported elsewhere) influences the morphological development of grown crystals. While pure Gd-heptamolybdate assumes spherulitic morphology under all conditions of growth, addition of Sr modifies the morphology of mixed crystals drastically and develops them as agglomerations of stacked hexagonal crystal platelets. The mixed crystals carry water of hydration and are thermally unstable. Various physico-chemical techniques, which include optical and scanning electron microscopy/XRD/energy dispersive analysis of X-rays and FT-IR were used to characterize the grown crystals. Thermal behaviour of these crystals using the thermoanalytical techniques, including TG/DTA and DSC is discussed. Thermal analysis suggests decomposition of the material in different temperature intervals. Results obtained on application of TG based models viz., Horowitz–Metzger, Coats–Redfern and Piloyan–Novikova are reported. The results of the kinetics of thermal decomposition suggest contracting sphere model as the one that is relevant to the decomposition of mixed Gd–Sr–molybdate. The kinetic parameters, viz. the order of reaction, frequency factor and energy of activation using above-mentioned models, are computed.

Decomposition of Dolomite Monitored by Neutron Thermodiffractometry

Dolomite powder from Coín (Spain) was heated in air at a constant rate of 2°C/min to 1000°C, while neutron diffraction patterns were collected every 150 s. Rietveld refinement was applied and raw intensity data were used to monitor decomposition. The full process happened in two stages: dolomite decomposition to give calcite and periclase, and calcite breakup. The first stage activation energy was 47 kcal·mol−1 from fitting to a contracting sphere model. The dolomite mean thermal expansion coefficients were (6.7 ± 0.4) × 10−6 and (2.7 ± 0.2) × 10−5 K−1 along the a and c axes, respectively. Changes in the Ca–O and Mg–O bond distances were also measured.

Zircon formation from amorphous silica and tetragonal zirconia: kinetic study and modelling

The kinetics of the reaction, a-SiO 2+t-ZrO 2→ZrSiO 4, were monitored by isothermal HTXRD experiments. A series of diffractograms were recorded at constant temperature (1250°C, 1300°C, 1350°C, 1400°C), after heating the precursor powder. Integrated intensities of the peaks relating respectively to the ZrSiO 4 (200) and tetragonal t-ZrO 2 (101) planes, were used to obtain the conversion rate. According to the shape of the curves, λ= f( t), the limiting step of the zircon formation is not the nucleation process, but, in fact, diffusion of silicon species through a zircon layer, from an external continuous or granular silica phase to the surface of zirconia grains. To account for the results obtained, a model of a contracting sphere is proposed: the system is described as either a series of spherical t-zirconia grains surrounded by a shell of zircon, which is covered by amorphous silica, or as spherical t-zirconia grains surrounded by a shell of zircon, which is in contact with spherical amorphous a-SiO 2 particles. In the latter case, fast superficial diffusion of Si 4+ and electrons originating from silica grains on the external surface of the zircon layer produce a homogenisation of the silicon concentration. The validity of this model is confirmed by the fact that the experimental data, λ= f( t), fit the kinetic law of Valensi and Carter, considering chemical diffusion through the reaction product (oxide layer) as the rate limiting step. Consequently, the apparent diffusion coefficient of silicon can be estimated.

Constraints on cardiac hypertrophy imposed by myocardial viscosity.

Laplace's law constrains how thin the ventricular wall may be without experiencing excessive stress. The present study investigated constraints, imposed by myocardial viscosity (resistance to internal rearrangement), on how thick the wall may be. The ventricle was modeled as a contracting, spherical shell. The analysis demonstrated that viscosity generates stress and energy dissipation with inverse fourth- and eighth-power dependence, respectively, on distance from the cavity center. This result derives from the combination of squared dependence of viscous forces on shearing velocity gradients and the greater shear rearrangement required for inner layers of a contracting sphere. These predictions are based solely on geometry and fundamentals of viscosity and are independent of material properties, cytoskeletal structure, and internal structural forces. Calculated values of energy and force required to overcome viscosity were clearly large enough to affect the extent of thickening of the left ventricle. It is concluded that load-independent viscous resistance to contraction is an important factor in cardiac mechanics, especially of the thickened ventricles of concentric hypertrophy.

Dynamics and topochemistry of the thermal formation of cadmium telluride from the constituent elements: a differential scanning calorimetry study

The kinetics and topochemical details of the condensed-phase Cd + Te = CdTe reaction system were studied by differential scanning calorimetry (DSC) in conjunction with scanning electron microscopy (SEM) and energy-dispersive X-ray analysis (EDX). Measurable rates in this reaction system were sustained only after fusion of the Cd reactant particles. The exothermic reaction heat-release profiles were analyzed by DSC as a function of the scan rate. A new kinetics measurement protocol was developed that combines isothermal DSC operation with dynamic heat-cool probe' cycles for the Cd content of the reaction mixture. When the starting reaction components were in fine powder form, the reaction rate initially was very rapid, leading to the formation of a passivating CdTe outer skin. The activation energy of 7.2 {plus minus} 0.8 kJ/mol measured from these data was consistent with a model involving physical diffusion of the reactants through the CdTe layer as the rate-determining step. Accordingly, the use of larger size Te reactant particles in the 575-875-{mu}m range enabled a quantitative fit of the kinetics data to a contracting sphere model. Finally, the use of SEM and EDX permitted unambiguous verification of the proposed model for the reaction topochemistry.