Cylindrical Diffusion Research Articles

Effects of cross-linking degree and steric hindrance on the thermal degradation behavior of novel hybrid zirconium-silicone resin

Although silicone resins are commonly seen as popular candidates for heat-resistant applications, the severe weight loss at the temperature from 400 to 800 °C remains a challenge. Herein, we reported a strategy to enhance the thermal resistance by introducing Zr into the main chain. Molecular simulation shows the Zr atoms led to the formation of high energy Zr–O bonds and increased the cross-linking degree which in turn suppressed the formation of cyclic oligomers, the results was further supported by TG-IR. The degradation activation energy was increased from 75.26 (ZAS0) to 88.67 kJ/mol (ZAS5) for the major degradation stage. The degradation kinetics study shows the degradation of ZAS5 followed the cylindrical symmetrical three-dimensional diffusion mechanism (n = 1.5). This work could provide a systemic experimental and theoretical foundation for thermal properties enhancement through metal atoms incorporation.

Assessment of atomic mobilities in the Al-Li fcc_A1 phase

Diffusion is one of the key factors that controls the precipitation of Al3Li metastable phase in Al-Li alloys. In this work, the diffusivity data in fcc Al-Li binary alloys available in the literature were comprehensively reviewed and critically evaluated, the diffusion mobilities of Al and Li in the Al-Li fcc_A1 phase were then assessed based on the reliable experimental data and empirical equations in the literature. An early relationship that correlates the diffusion activation energy and the melting temperature was revisited for group I elements, Li, Na, and K, and was used to predict the diffusivity of fcc Li. One set of self-consistent atomic mobility parameters for the Al-Li fcc_A1 phase was obtained. The limited reliable experimental diffusivity data can be generally reproduced by the present model parameters. In combination with the related thermodynamic description, the atomic mobility parameters were further verified by simulating the diffusion profiles of ion implanted Al samples at different annealing times. The model parameters were also used to simulate the concentration profiles of a cylindrical diffusion couple and the solidification process of an Al-3.5 wt.% Li alloy.

Large eddy simulation of film cooling flow from diffusion slot hole with crossflow coolant configuration

A three-dimensional compressible large eddy simulation (LES) method was performed to explore the flow and heat transfer characteristics in the hole and mixing zone of a crossflow film cooling model. A traditional cylindrical hole and diffusion slot hole were selected as the cases for the film hole. The characteristics of the crossflow film flow-field and the influence of the internal crossflow on the film cooling of the diffusion slot hole were explained by the vortex flow in the hole and the instantaneous/time-averaged jet mixing. The results showed that helical motion is easily induced in the holes under the influence of crossflow. Asymmetric outlet flow behavior is the main reason for the asymmetric characteristics downstream of the hole. The difference in the blowing ratio results in the difference in the strength of the spiral vortex and the central vortex tube inside the hole. For the diffusion slot hole, the high-speed zone caused by the crossflow effect at the hole-inlet gradually evolves into strip shapes under the combined action of axial extrusion and spanwise diffusion. With the disappearance of the helical structure, the high-speed areas gradually converge on both sides of the hole exit in the span direction, and the streamline at the exit develops relatively smoothly. The inlet crossflow and the crossflow Reynolds number have little effect on the film cooling effectiveness of the diffusion slot hole. With an increase in the blowing ratio, the lateral diffusion capacity of the film is gradually enhanced. Furthermore, compared with the cylindrical hole, the instantaneous film fluctuation region of the diffusion slot hole case is smaller in range and more symmetrical in distribution. These findings advance the understanding of the film cooling of diffusion slot holes.

Acoustic field characteristics of seismic surveys in the shallow water environment of the Bohai Sea

AbstractAir gun arrays are designed to generate strong energy pulses of less than 100 Hz for offshore oil and gas exploration. In shallow seas, due to the directivity of air gun arrays, the complex propagation conditions and the limitations of acquisition methods, it is difficult to accurately evaluate the spatial time and frequency transmission characteristics of airguns. To alleviate the existing lack of knowledge about the transmission characteristics of air gun pulses in the shallow waters of the Bohai Sea, we analysed three‐dimensional ocean bottom cable seismic data collected during a seismic survey in the Bohai Sea, China, in June 2017, which were used to evaluate the reception level, frequency domain characteristics and spatial distribution characteristics within a 5.55 × 5.575 km area. The results showed that in shallow water, multipath propagation causes downfrequency chirplike sounds and an increased sound field. Within 0.3 km, the transmission model follows a cylindrical diffusion, and the sound loss rate decreases as the transmission distance increases until reaching 8 km. Signal capture by the sound channel results in a high transmission loss frequency band, whereas multimode interference weakens the transmission loss. The gun array directivity and the transmission channel are the two main factors affecting the acoustic field. This research provides an improved understanding of the acoustic field of airguns in the Bohai Sea, which can benefit the acoustic modelling of air gun arrays, the design of future seismic exploration projects and the conservation of marine life.

Cylindrical diffusion model and parameter optimization for NaOH solution reinforcement of collapsible loess

The diffusion distance and grouting effect of alkaline solution in collapsible loess are greatly influenced by pore tortuosity. In this study, the fractal dimensions of pore area and tortuosity that characterized the permeation path were included in a cylindrical diffusion model for NaOH solution grouting in collapsible loess. Ten sets of field test data were employed in model verification. The tortuosity-based model shows better agreement with the test data than the conventional model. X-ray powder diffraction (XRD) tests, scanning electron microscopy (SEM) tests, and unconfined compressive strength (UCS) tests were conducted to reveal the reinforcement mechanism of the above method. Spherical colloids formed from calcium silicate and aluminum silicate complexes were present in the treated loess, which enhanced the cementation between the soil particles and increased the UCS. Six factors for grouting design were targeted in sensitivity analysis and could be ranked by sensitivity as grouting time t > grouting pressure p > porosity ϕ > solution viscosity ratio β > permeability coefficient K > grouting pipe radius r0. The response surface methodology (RSM) was employed to optimize the sensitive factors. Results show that the design diffusion radius is 40 cm, and the optimized factors are t = 58 min, p = 0.05 MPa, ϕ = 0.4, β = 1.1, K = 0.0006 cm/s, r0 = 1 cm.

Blockage coefficient of cylindrical blocker and diffusion resistance of membrane channels.

This study deals with potential flow of ideal fluid in an infinite cylindrical tube in the presence of a blocking object. The blockage effect of the object on the flow can be characterized by a lump parameter, blockage coefficient, which accounts for the object shape and size. For a cylindrical blocking object, analytical results for the blockage coefficient are known only in three limiting cases: for a long thin cylinder and for small and large blocking disks. We propose a simple analytical expression for the blockage coefficient of a cylindrical blocker of arbitrary length and radius that reduces to the known asymptotic results in the corresponding limits.

Pre-Reinforcement Mechanism and Effect Analysis of Surface Infiltration Grouting in Shallow Buried Section of Long-Span Tunnel

In order to solve the problem that the hole-forming rate of boreholes is low and it is difficult to reach the designed length when supporting a long pipe shed in loose stratum in a shallow buried section of a long-span tunnel, it is necessary to pre-reinforce the loose stratum in order to improve the strength and integrity of the surrounding rock. Relying on the grouting project of the shallow buried section at the exit of Botanggou tunnel, it is assumed that the grouting material is Newtonian fluid and the steel floral tube shows cylindrical infiltration and diffusion. Through the analysis of the structural characteristics of the injected stratum, the conceptual model of infiltration grouting is established. Twelve groups of test slurry were prepared with ordinary Portland cement and ultra-fine cement, and through the analysis of the slurry parameters of each group, ordinary Portland cement slurry was selected with a water–cement ratio of 1:1 plus 3% water glass to strengthen the gravel layer, and ultra-fine cement slurry with a water–cement ratio of 1:1 plus 3% water glass and 0.3% polycarboxylate superplasticizer to strengthen the fully and strongly weathered porphyritic granite layer. Through the on-site single-hole grouting test and combining with the empirical formula, the maximum diffusion radius of single-hole infiltration grouting is calculated, and the sliding width of the sidewall is deduced using Terzaghi theory. To ensure the grouting effect, the 5 m expansion of the excavation profile is taken as the grouting range. Grouting construction adopts the overall order of periphery and then interior, and three-sequence opening and grouting are adopted in the same row of grouting holes, which can effectively prevent grouting running and grouting. For the strata treated by surface grouting, the construction of the long pipe shed is smooth and reaches the designed length, and there is no large deformation of the surrounding rock when excavated using the CD method. The treatment effect is analyzed by the P-Q-t control method, excavation observation method, and deformation monitoring method. The results show that the injected stratum is fully infiltrated and gelled, forms an obvious grouting stone body, the integrity and strength of surrounding rock are obviously improved, and the convergence values of the tunnel surface, vault subsidence, and clearance do not exceed the alarm value of 60 mm. The research results provide some awareness and understanding of the grouting pre-reinforcement of loose stratum in a shallow buried section of a long-span tunnel in the future.

Hydrogen Uptake Kinetics of 1,4-Bis(phenylethynyl)benzene Rubberized O-Rings: Measurements, Modeling, and Comparison with Additional Forms of Organic Getters

A class of molecules called “hydrogen getters” can react with, or scavenge, H2 in applications where the hydrogen presence and/or buildup are not desirable. One such “getter”, 1,4-bis(phenylethynyl)benzene or DEB, can be incorporated into a silicone matrix in the form of an O-ring for added flexibility, environmental resiliency, and convenient use as a gasket in sealed applications. However, the performance and kinetics of this DEB-loaded rubberized O-ring have not yet been characterized. In this work, the hydrogen uptake kinetics of the rubberized DEB O-ring were extracted by the isoconversional analysis from isothermal isobaric data under conditions of 13,332 Pa H2 and 305–325 K. The isoconversional and cylindrical diffusion approximations were then used to predict and model the hydrogen uptake of rubberized DEB O-rings under any arbitrary condition, as illustrated in this work for the simple case of a constant rate of hydrogen generation/input. In comparison with other Pd/carbon-based/organic getter systems, these rubberized DEB O-rings provide a type of hydrogen getter material with enhanced flexibility and catalyst protection in applications where an O-ring seal is needed.

Analytical Sensitivity Analysis of a Spent Nuclear Fuel Cask

Abstract Nuclear science and engineering is a field increasingly dominated by computational studies resulting from increasingly powerful computational tools. As a result, analytical studies, which previously pioneered nuclear engineering, are increasingly viewed as secondary or unnecessary. However, analytical solutions to reduced-fidelity models can provide important information concerning the underlying physics of a problem and aid in guiding computational studies. Similarly, there is increased interest in sensitivity analysis studies. These studies commonly use computational tools. However, providing a complementary sensitivity study of relevant analytical models can lead to a deeper analysis of a problem. This work provides the analytical sensitivity analysis of the one-dimensional (1D) cylindrical mono-energetic neutron diffusion equation using the forward sensitivity analysis procedure (FSAP) developed by Cacuci. Further, these results are applied to a reduced-fidelity model of a spent nuclear fuel cask, demonstrating how computational analysis might be improved with a complementary analytic sensitivity analysis.

Theoretical Research on Grouting in Deep Loose Layers Based on the Cylindrical Diffusion Model of Radial Tube Flow

Grouting in deep, loose layers are a complex process in which many modes such as infiltration, splitting, and compaction coexist. It is of great significance to establish a realistic, simplified physical model to study the law of slurry diffusion. Herein, a cylindrical diffusion model of radial tube flow is established, and the control differential equations of both the Bingham slurry diffusion velocity in a single tube and the diffusion velocity of the radial tube flow are deduced. Additionally, the calculation formulas for the diffusion radius and slurry pressure distribution function are obtained. The rationality of the theory is verified by combining our results with those of the field grouting test of the Guotun coal mine. The results show that the cylindrical diffusion model of radial tube flow can successfully characterize the slurry diffusion law of grouting in a deep, loose layer. The slurry pressure attenuation shows distinguishable stages: within the first 30% of the diffusion radius, the slurry pressure decreased sharply by approximately 70%, and the slurry pressure decreases slowly in the later stages. Furthermore, the diffusion radius has a nonlinear, negative correlation with the height of the grouting section and the comprehensive injection rate of formation; the change rate is relatively more gradual, and there are no distinguishable stages. The research results provide a theoretical basis for reasonably determining the grouting parameters of deep, loose layers in the future.

Theoretical Research on Sand Penetration Grouting Based on Cylindrical Diffusion Model of Tortuous Tubes

The penetration paths of grouts in sand layers are tortuous, and there is no reasonable penetration grouting theory at present. By employing tortuous circular tubes as the internal penetration pore channels of the sand layer, the cylindrical diffusion model is established for sand-layer penetration grouting. First, the permeability of porous media and average penetration velocity of Bingham slurry were deduced by considering tortuosity. Second, based on the penetration continuity equation, the active steady-state penetration differential equation of Bingham slurry and the pressure distribution function of slurry in the diffusion region were obtained. Finally, combined with the indoor penetration grouting test results, the attenuation law of slurry pressure and the influencing factors of diffusion radius were discussed. The results show that the cylindrical diffusion model of tortuous tubes can better characterize the diffusion process of penetration grouting in the sand layer. The stop condition for diffusion during penetration grouting is the reduction of the pressure gradient of the slurry to its starting value. The slurry pressure attenuation has obvious stages. The slurry pressure attenuation is faster in the area close to the grouting tube. At 50% of the maximum diffusion radius, the pressure attenuation is 70.01~75.41% of the total pressure attenuation within the diffusion region. Increasing the grouting pressure and permeability coefficient and reducing the slurry viscosity ratio can greatly increase the slurry diffusion radius. These results provide a theoretical basis for determining sand grouting parameters in the future.

Permeation grouting diffusion mechanism of quick setting grout

Quick setting grout is used in permeation grouting projects to control the grouting diffusion range effectively and reduce the waste of grout. Owing to the double-component injection method and quick setting property of the grout, the viscosity of the quick setting grout is non-uniformly distributed in the grouted region, which has a significant influence on the grouting diffusion process. In this study, the permeation grouting process of a quick setting grout was studied. A 2-D cylindrical permeation grouting diffusion model was developed considering the non-uniform distribution of grout viscosity. A visible permeation grouting diffusion simulation test system was designed and established. A series of tests were carried out to verify the correctness of the theoretical model, in which cement–sodium silicate grout, a typical quick setting grout, with two water–cement ratios (W/C = 1, 2) and gravel sand with two different ranges of particle size (2–5 mm, 5–20 mm) were used. The results show that (1) when the size of the void space in the sand stratum exceeds a certain value, the permeation diffusion of grout is completely controlled by grout gravity, and the influence of the quick setting characteristics can be ignored. Otherwise, the quick setting characteristics have the most important effect on permeation diffusion. (2) The calculated results agree well with the test results. The calculated injection pressure result is 1.0–1.4 times the experimental result, and the calculated diffusion radius is 95.7% –98.5% of the test value with the same final injection pressure. (3) It is necessary to consider the non-uniform distribution of viscosity in the calculation of the permeation grouting process of a quick setting grout. For a quick setting grout, if the non-uniform distribution of viscosity is not considered, the injection pressure would be overestimated by more than 10 times the actual value, and the diffusion radius would be underestimated by 30%–50% of the actual value.

Alpha track distribution on lateral wall of cylindrical radon diffusion chamber

Cylindrical diffusion chamber with solid state nuclear track detector placed at the bottom of the chamber is frequently used device for measuring radon concentration in dwellings. In this work, the diffusion chamber with CR-39 detector was modeled to determine track distribution on the lateral (cylinder) wall of the chamber and compare track density between cylinder wall and bottom. Model is based on the diffusion, deposition and decay of radon and its progeny in diffusion chamber. Equations for criteria of track visibility and track density were derived. Along with theoretical model, measurements were performed to verify the theoretical results. Three different chambers with CR-39 detectors slabs attached along the cylinder wall were investigated. It was found that alpha track density on cylinder wall is not uniform and depends on the shape and size of the chamber. Deviation of track density along cylinder wall was up to 30% for chambers used in this work. Sensitivity of the cylinder wall was found to be almost the same as the sensitivity of the bottom. In comparison with the experiment, theoretical results give good predictions. Along with previous results of the authors where bottom track density was modeled, presented model can be used for calibration and optimization of the diffusion chambers used for radon measurements.

Diffusion of Cosmic Antiprotons Generated throughout the Dark Matter Halo—A Semianalytical Solution for a Linear Galactic Wind Model

Abstract The public GALPROP code gives a fully numerical solution for the spectrum of cosmic rays propagating through a linear Galactic wind directed outward from the Galactic plane in the framework of a cylindrical diffusion model. Alternatively, for the linear Galactic wind case, we present a semianalytical solution of the two-zone cylindrical model that describes the spectrum of cosmic-ray antiprotons produced from the primary sources throughout the dark matter (DM) halo. While the secondary antiprotons can be generated by, e.g., the GALPROP WebRun, consistently using this semianalytical solution for the primary ones would be helpful to build a suited DM model, which may be sophisticated, and then to perform a statistical analysis when comparing it with data. As an example, using the obtained formula, we study the possible DM signal through the channel DM DM → b ¯ b and its constraint from the measurement of the AMS-02 antiproton-to-proton ratio. The indication of the DM signal is discussed. The advantages of the semianalytical approach and its comparison with the GALPROP model are presented.

Structural dependence of effective mass transport properties in lithium battery electrodes

Scanning electrochemical microscopy (SECM) has recently been reported as a convenient technique to characterize the apparent diffusion coefficients in porous media (D⋆) such as lithium-ion battery electrodes. The technique relies on hemispherical diffusion at the probe in the presence and absence of porous media. However, transition towards cylindrical diffusion follows as the diffusion layer becomes comparable to the media thickness, gradually limiting direct correlation between D⋆ and the SECM probe steady state current. In this work, we examine the experimental parameters that define this transitional frontier using simulations. A best practice thickness criterium is derived that ensures that the measured steady state current is ≳ 90% of that found in the ideal hemispherical case. Below this thickness limit the response was found to follow an empirical formulation with only two variables. Fundamentally, this quantifies diffusion in the transition regime between hemispherical and cylindrical transport. Practically, this correction formulation may be included into standard steady-state current expression to account for the deviation from hemispherical transport in “thin” electrodes. The analysis consolidates SECM as a reliable tool to characterize liquid phase mass transport within porous films over wide range of thicknesses, including films supported on blocking substrates, like lithium-ion battery electrodes.

Overlapping correction suitable for an LR-115 detector located inside a diffusion chamber

A simulation program based on Monte Carlo methods was developed to study the behaviour of the overlapping effect in the LR-115 nuclear track detectors located inside a diffusion chamber. The relation between the non-overlapped tracks and the radon exposure level that the detector was exposed was adopted. This study focuses on very high radon concentration levels found in soil gas, uranium mines, or underground places. These anomalous levels can influence the radiological risk related to inhalation of indoor radon or the spontaneous increases in thermal neutron background. LR-115 detector exposed to anomalous levels can register a large number of latent tracks on its surface. After an etching treatment, some visible tracks can be placed covering one or more visible tracks altering the LR-115 response. In order to develop this work and be more realistic, visible tracks were simulated taking into account radon exposure level, geometry and dimensions of the diffusion chamber, dimensions of the detector, the V function, the etching process and the reading process. Results show that the overlapping effect in the LR-115 inside a cylindrical diffusion chamber exposed to very high levels can be solved with an uncertainty of 5%. The same methodology can also be applied when considering other detectors and geometry and dimensions of a diffusion chamber.

Simultaneous Determination of Gaseous Ammonia and Particulate Ammonium in Ambient Air Using a Cylindrical Wet Effluent Diffusion Denuder and a Continuous Aerosol Sampler.

A sensitive and fast method for simultaneous determination of gaseous ammonia (NH3) and particulate ammonium (NH4+) in ambient air is presented. NH3 is sampled in a cylindrical wet effluent diffusion denuder (CWEDD) and analyzed online by a continuous flow system with a fluorescence detector (FLD), while NH4+ bound to aerosol particles is sampled in parallel by a condensation growth unit-the aerosol counterflow two-jet unit (CGU-ACTJU) sampler-and analyzed online with another FLD. The sensitive fluorescence detection of ammonium in concentrates of the CWEDD and the ACTJU is based on its reaction with ortho-phthaldialdehyde and sulfite to form isoindol-1-sulfonate. The calibration curve of ammonium is linear in the concentration range of 5 × 10-9 to 2 × 10-6 M. The limit of detection (LOD = 3 s/n) values of NH3 and NH4+ are 3.52 ng m-3 (5.05 ppt) and 1.04 ng m-3, respectively. The developed method enables online measuring of distribution of NH3/NH4+ in ambient air with a time resolution of 1 s. The optimized method was used for the determination of NH3/NH4+ in urban air in Brno in two campaigns during the winter and summer of 2018. The results obtained by the developed method were compared with a reference method based on the sampling on filters and "dry" diffusion denuders coated by phosphoric acid.

Displacement infiltration diffusion model of power-law grout as backfill grouting of a shield tunnel

Shield tunnel is widely adopted in the metro construction, and backfill grouting is the significant part. With power-law fluid grouts as the study object, a cylindrical infiltration diffusion model and spherical infiltration diffusion model are developed by applying the generalized Darcy law and theories of seepage mechanics based on the displacement effect of grout on groundwater. Through examples, the impact of factors including grouting pressure and formation permeability coefficient in the spherical displacement infiltration diffusion model on diffusion radius, flow rate, total pressure of grout in segments, and uniform equivalent pressure in grout diffusion area (grout pressure per unit area in a segment) is analyzed. The result shows that, the diffusion speed, injection flow rate and the pressure received in segments increase with an increase of the grouting pressure. Meanwhile, as the injection time increases, the flow rate of grout under conditions of different grouting pressure all decreases, and a sharp decrease exists. The diffusion speed and grouting pressure are positively correlated to the permeability coefficient, and with the increasement of the injection time, the diffusion displacement of grout in different permeability coefficient varies increasingly, the increase amplitude of the pressure acting on the segment by grout increases gradually.

Influence of Liver Intoxication by Carbon Tetrachloride or D-Galactosamine on Absorption of Fluorescein Isothiocyanate-Dextran-10 and Other Marker Compounds with Different Molecular Weights from the Rat Liver Surface.

We examined the influence of liver disease on the absorption from the liver surface of fluorescein isothiocyanate (FITC)-dextran 10 (FD-10, MW: 11000) and several marker compounds with different molecular weights. The purpose of this study was to determine the feasibility of liver surface application of macromolecular compounds in the disease state. We used male Wistar rats treated with carbon tetrachloride (CCl4) or D-galactosamine (GAL). FD-10 and other marker compounds were applied to the liver surface using a cylindrical diffusion cell in liver-intoxicated rats. The blood, bile, urine, and the remaining solution in the diffusion cell were collected for assay. FD-10 was absorbed by first-order kinetics from the liver surface in the liver-intoxicated rat models. The calculated rate constant ka values in the normal, CCl4 and GAL groups were 0.000965, 0.00125 and 0.00104 min-1, respectively. Increased absorption of FITC-dextrans in the liver-intoxicated rats was observed. In both CCl4 and GAL groups, an inverse relationship was observed between the molecular weight and ka from the rat liver surface of the marker compounds. The limits of the molecular weight absorbed from the liver surface were extrapolated to be 71200, 135000, and 105000 in the normal, CCl4, and GAL groups, respectively. In conclusion, increased absorbability from the rat liver surface indicates that liver surface application for liver targeting of macromolecules in the diseased state is indeed feasible. Therefore, our findings can support further research on liver surface application of drugs under liver disease.

Physicochemical study of the sustainable preparation of nano-Fe2O3 from ferrous sulfate with coke

A route to produce nano-Fe2O3 by reduction of ferrous sulfate with coke to was proposed to improve the utilization of waste residues from TiO2 production. The effects of thermodynamic factors on the reaction were analyzed via Factsage 6.0 software, which showed that SO2 and O2 atmospheres have a significant inhibition effect on the decomposition of ferrous sulfate. Then, the optimal reaction condition (heating at 600 °C for 40 min with ferrous sulfate to coke ratio of 4:8) was obtained by single-factor and orthogonal experiments. Under the optimal reaction condition, the average desulfurization rate was found to reach 99.92%. Moreover, scanning electron microscopy images showed that the products were nanopowders with a porous structure and particle sizes between 40 and 70 nm. Finally, the non-isothermal decomposition kinetic parameters and mechanism of the reaction were determined. Two reaction stages, which were named “random nucleation and then growth” and “symmetric cylindrical diffusion (3D),” were determined. Using the Coats–Redfern, Flynn–Wall Ozawa (FWO), and Kissinger–Akahira–Sunose (KAS) methods, the apparent activation energy and pre-factor of the first reaction stage were determined to be 291.10 kJ mol−1 and 1.41 × 1016 s−1, while those of the second reaction stage were determined to be 285.94 kJ mol−1 and 3.27 × 1014 s−1. The most probable mechanism functions of the two stages were also determined. This process can make use of ferrous sulfate not only highly valuable, but also to improve the recycling of sulfur and iron resources after the production of white titanium.