Diffusion-controlled Kinetic Model Research Articles

Synergistic effects of ferric sulfate addition and mechanical activation on leaching of Sarcheshmeh copper sulfide concentrate

In this paper, the leaching of a sulfide concentrate, from “Sarcheshmeh Copper Complex”, by sulfuric acid is studied. The influences of sulfuric acid concentration and leaching temperature were scrutinized to optimize the processing parameters and to disclose the kinetics of the extraction process. The leaching rate of copper was not significantly improved with enhancing the temperature and concentration of sulfuric acid. The formation of elemental sulfur was found as a reducer of the leaching rate. Only ~70% of copper was extracted by adding 1M ferric sulfate as the oxidant agent, as well as increasing the leaching temperature up to 85 °C. By leaching the mechanically activated concentrate in Fe2(SO4)3-doped H2SO4 at 85 °C, the amount of extracted copper was ~90% after 180 min. The experimental results were excellently fitted with the diffusion-controlled kinetic model as the activation energy of ~27 kJ/mol was estimated.

Synthesis, characterization and application of cross-linked chitosan/oxalic acid hydrogels to improve azo dye (Reactive Red 195) adsorption

Cross-linked oxalic acid/chitosan hydrogels (ChOxb) were synthesized, characterized and tested for the adsorption of azo-dyes (Reactive Red 195 RR195) in contaminated wastewater; this novel biodegradable material was highly efficient. SEM-EDS and N2 adsorption/desorption were used to analyze specific area; FTIR-ATR spectra evidenced electrostatic interactions between protonated amino groups of chitosan and oxalate ions (intensity decrease and shift of amide-II band). Adsorption performance in batch assays showed a maximum percentage of removal of 90.6%, at pH = 4 (initial dye concentration of 300 mg.L−1). The maximum adsorption capacity (Qm) at pH = 4 was 110.7 mg.g−1, positioning ChOxb as one of the most efficient adsorption materials. Oxalic acid (natural organic acid) is an eco-friendly cross-linking agent that reduced swelling and improved chemical stability of ChOxb at low pH = 2.5. Redlich-Peterson adsorption isotherm presented the best fit; adsorption thermodynamic parameters were evaluated. Mixed surface reaction and diffusion-controlled kinetic model was the equation that best fitted kinetic data. FTIR-ATR, SEM-EDS and Z-potential showed electrostatic interactions between dye and amino groups of ChOxb; ChOxd can be reused without losing adsorption capacity and competitive electrostatic interactions between ChOxb-nitrate were observed. This new bio-material is an excellent alternative for the removal of RR195, improving Qm with better structural and functional properties.

Kinetic modeling of high-temperature oxidation of pure Mg

Abstract A variety of experimental tracer diffusivities of Mg and O in magnesium oxide available in the literature were first assessed. Atomic mobilities including bulk and short-circuit diffusion of Mg and O were then obtained by means of the CALPHAD (Calculation of Phase Diagram) approach. Afterwards, the diffusion-controlled kinetic model of oxidation in a gas-MgO-Mg environment was developed based on the moving boundary model and Fick's law, coupling with the modified thermodynamic description of MgO. A mathematical expression for parabolic rate constant kp of the oxide scale was derived for magnesia and correlated with the thermodynamic and diffusion kinetic information. The evaluated kp results were in line with the experimental data. Finally, the oxidation process of pure magnesium at 673 K was model-predicted, and the predicted evolution of the oxide thicknesses agreed very well with the experimental data. It was indicated that the grain boundaries diffusion of magnesium cations predominated the high temperature oxidation process.

Nano-titania/light expanded clay aggregate fixed bed as an effective adsorbent for removal of organic pollutant from water: Equilibrium and kinetic studies

A constructed fixed bed of light expanded clay aggregate coated with nano-titania particles has been applied as an effective adsorbent fixed bed to remove an anionic azo dye, direct red 16, from aqueous solution. This process was carried out using a recycled batch system under environmental temperature. Initial pH of the adsorbate solution imposed a severe effect on the adsorption process so that the best and worst performances of the prepared beds belonged to the acidic and basic pHs of 3 and 10, respectively. Various equilibrium and kinetic models were applied for analyzing experimental data related to several initial concentrations of DR16. Langmuir-Freundlich isotherm and mixed surface reaction and diffusion-controlled kinetic model satisfactorily described equilibrium and kinetic adsorption data, respectively. The models suggested that there is heterogeneity in this system and diffusion step at the same time with surface reaction determines the overall rate of the adsorption process. Appropriate and considerably stable performance of the used nano-titania/light expanded clay aggregate fixed beds after regeneration is one of the outstanding characters of the prepared beds. It is noteworthy that based on tests, the removal efficiency of the pollutant with the initial concentration of 25 mg/L was about 95% after 25 min (under pH 3 and T = 25 °C). It is while the adsorbent beds still worked steadily after about 65 times of reuses which can keep approximately all the adsorption capacity remaining. Therefore, features such as the high and relatively fast removal of the adsorbate, the facility and high rate in the regeneration can candidate the prepared fixed beds as an effective adsorbent for wastewater treatment.

Reactive RED 195 dye removal using chitosan coacervated particles as bio-sorbent: Analysis of kinetics, equilibrium and adsorption mechanisms

Chitosan particles (CP) prepared by coacervation technique were used as bio-sorbent material to remove the azo RR-195 dye; removal percentage (%RM) and adsorption capacity (Q) in batch adsorption experiments under different conditions of bio-sorbent doses, agitation speed and pH medium were determined; the maximum pH of dye removal was 4. Different adsorption equilibrium isotherms were tested and Redlich-Peterson was the model that best fitted experimental results. From the adsorption thermodynamic parameters, it was concluded that the adsorption process of RR-195 onto CP is spontaneous, favorable (ΔG<0), endothermic (ΔH>0) and the dye molecules show affinity for the bio-sorbent (ΔS>0). The maximum monolayer adsorption capacity (Qm) of CP was 82.1 mg.g−1 at pH = 4 and 318 K; therefore coacervated chitosan particles are among the top three adsorbent agents for this dye. The %RM was 84.2% in 10 h when the initial concentration of the dye was 300 mg.L−1. The mixed surface reaction and diffusion-controlled kinetic model (MSR-DCK), fitted satisfactorily experimental results, by considering simultaneous mechanisms of diffusion and adsorption process in the active sites. Fourier transform infrared spectroscopy (FTIR) with attenuated total reflection (ATR), scanning electron microscope-energy dispersion spectrometry X-ray (SEM-EDS) and Zeta potential analysis revealed that the interaction between dye molecules and the bio-sorbent are of an electrostatic nature. Desorption/regeneration experiments indicated that CP can be used in adsorptions/desorption cycles for the removal of wastewater containing RR-195. The information presented in this work demonstrates that CP can be a potent eco-friendly bio-adsorbent for the remediation of industrial wastewater.

Experimental and modeling study on controlling factor of methane hydrate formation in silica gels

In order to study the mechanism of methane hydrate formation in porous media, the formation experiments of methane hydrate in porous media at the constant pressure were performed in the temperature range of 274.15–276.15 K and the pressure range of 5–8 MPa. The silica gels with the average pore diameters of 129.5, 179.6, and 332 Å were used as the porous media for the experiments. The experimental results indicate that the final gas consumption increases with the increase of the formation pressure and the decrease of the formation temperature. Based on the shrinking core model, the reaction-controlled kinetic model and the diffusion-controlled kinetic model for hydrate formation in silica gels were built, respectively. The reaction-controlled kinetic model well fits the kinetic data in 129.5 Å and 179.6 Å silica gels, and the diffusion-controlled model well fits the kinetic data in 332 Å silica gels with a relatively high regression coefficient (R2 > 0.99). The formation rate of the methane hydrate is controlled by the gas diffusion process in 129.5 Å and 179.6 Å silica gels, and is controlled by the reaction process in 332 Å silica gels.

Heap bioleaching of uranium from low-grade granite-type ore by mixed acidophilic microbes

We evaluated uranium bioleaching from low-grade, granite-type uranium ore using mixed acidophilic microbes from uranium mine leachate. A 4854-ton plant-scale heap bioleaching process achieved sustained leaching with a uranium leaching efficiency of 88.3% using a pH of 1.0–2.0 and an Fe3+ dosage of 3.0–5.5 g/L. Acid consumption amounted to 25.8 g H2SO4 kg−1 ore. Uranium bioleaching follows a diffusion-controlled kinetic model with a correlation coefficient of 0.9136. Almost all uranium was dissolved in aqueous solution, except those encapsulated in quartz particles. Therefore, heap bioleaching by mixed acidophilic microbes enables efficient, economical, large-scale recovery of uranium from low-grade ores.

Adsorption of picloram herbicide on montmorillonite: Kinetic and equilibrium studies

The kinetics of the adsorption of picloram (PCM) onto montmorillonite (Mt) was studied in situ by attenuated total reflectance Fourier-transform infrared spectra (ATR-FTIR). Pseudo-first-order, pseudo-second-order, intra-particle diffusion and mixed surface reaction intra-particle diffusion-controlled kinetic models were applied to the experimental results. The latter was the model that best represented the experimental results. The adsorption equilibrium isotherms revealed the presence of two independent adsorption processes on different surface sites. The adsorption isotherms normalized by the surface area were fitted with the Langmuir and Freundlich models to obtain the respective parameters.Due to the anionic form of PCM, the adsorption onto the external clay mineral surface sites followed by the entrance of the PCM molecule into the Mt basal space in a less energetically favorable pathway was proposed. The interaction of PCM with montmorillonite surface sites through nitrogen of the pyridine ring and carboxylic group by forming an inner sphere complex was confirmed by ATR-FTIR.

Mixed Surface Reaction and Diffusion-Controlled Kinetic Model for Adsorption at the Solid/Solution Interface

The effects of diffusion and surface reaction mechanisms have been considered conjointly to investigate the kinetics of adsorption. A new model has been proposed for the modeling of adsorption kinetics at the solid/solution interface in batch systems. Based on generated data points (t, q) by using of the new model, it was found that there is a deviation from linearity as a downward curvature at initial times of adsorption in usual t/q vs time plot, when diffusion contributes to the rate-controlling step of adsorption. Moreover, results of nonlinear fitting to the different experimental data show that the mixed surface reaction and diffusion-controlled model can be useful for kinetics modeling of adsorption in which pure surface reaction or mixed surface reaction and diffusion contribute to the rate-controlling step of adsorption.

CeO2–Al2O3, CeO2–SiO2, CeO2–TiO2 core-shell spheres: formation mechanisms and UV absorption

In this work, a general colloid synthesis method for CeO2–Al2O3, CeO2–SiO2, and CeO2–TiO2 core-shell spheres was reported. The properties of these CeO2-based composites were greatly dependent on the additive species. A diffusion-controlled kinetic model was applied to explore the morphology and crystallinity evolution of these core-shell spheres. CeO2–Al2O3 spheres undergo a significant morphology evolution when the Ce/Al molar ratio is varied from 1 : 0.2 to 1 : 1. It also provided an effective way to observe the diffusion channel for mass transport in the diffusion process by dissolving the Al2O3 in CeO2–Al2O3 spheres in alkaline solution. Moreover, a significant composition and structure dependent nature was observed from the UV-vis absorption spectra of these CeO2–Al2O3, CeO2–SiO2, and CeO2–TiO2 core-shell spheres.

Comparison of activated carbon and iron impregnated activated carbon derived from Gölbaşı lignite to remove cyanide from water

The ability of lignite-activated carbon (LAC) and iron-impregnated activated carbon (FeAC) obtained from Gölbaşı lignite to remove cyanide ions from aqueous solution by adsorption was researched and compared with each other. The same process was applied also with commercial activated carbons which are in both granular (CAC-1) and powder forms (CAC-2). The morphologies, structures and properties of the activated carbons were determined by BET, XRD, XRF, SEM, zeta meter and magnetometer, respectively. The effects of various experimental parameters, such as initial cyanide concentration, pH, adsorbent type and particle size were researched in a batch adsorption technique at a temperature of 25°C. BET surface area of LAC is determined as 921m2/g. The obtained magnetic activated carbon has high surface area of 667m2/g with 19wt.% Fe3O4 coated and perfect magnetic separation performance. Langmuir model was found to be the best representative for cyanide-adsorption. The maximum monolayer adsorption capacities of LAC and FeAC are 60.18mg/g and 67.82mg/g at pH values of 7–7.5 and 64.10mg/g and 68.02mg/g at pH values of 10–10.5, respectively. Kinetic evaluation indicated that the cyanide adsorption onto the obtained activated carbons followed the pseudo-second order rate reaction. The diffusion-controlled kinetic models on the cyanide-adsorbent system showed that the removal rate was controlled not only by intraparticle diffusion but also by film diffusion. All experimental results point out that the LAC and FeAC are viable candidates for the removal of cyanide from water and wastewater.

Combined kinetic analysis of thermal degradation of polymeric materials under any thermal pathway

Combined kinetic analysis has been applied for the first time to the thermal degradation of polymeric materials. The combined kinetic analysis allows the determination of the kinetic parameters from the simultaneous analysis of a set of experimental curves recorded under any thermal schedule. The method does not make any assumptions about the kinetic model or activation energy and allows analysis even when the process does not follow one of the ideal kinetic models already proposed in the literature. In the present paper the kinetics of the thermal degradation of both polytetrafluoroethylene (PTFE) and polyethylene (PE) have been analysed. It has been concluded, without previous assumptions on the kinetic model, that the thermal degradation of PTFE obeys a first order kinetic law, while the thermal degradation of PE follows a diffusion-controlled kinetic model.

A diffusion-controlled kinetic model for growth of Au-catalyzed ZnO nanorods: Theory and experiment

A kinetic model for growth of ZnO nanorods via vapor–liquid–solid (VLS) mechanism based on the bulk diffusion of Zn atoms through the Au–Zn droplet is presented. The dependences of the growth rate on size are given quantitatively. A general expression for the growth rate of nanorods during VLS process is derived. The derived formula shows the dependences of growth rate on lateral size of nanorods, concentration and supersaturation of Zn atoms in the liquid droplet. Based on the presented kinetic model the smaller nanorods have faster growth rate. Au-catalyzed ZnO nanorods are grown by chemical vapor transport and condensation (CVTC) process experimentally. Theoretical and experimental rate/radius curves are compared to each other. Theoretical predictions are in good agreement with the experimental results.

A diffusion-controlled kinetic model for binder burnout in a powder compact

Many powder metallurgy processes involve the use of a polymeric binder as a carrier for easy manufacture of product pre-forms. Complete and clean removal of the binder before consolidation or firing is essential to achieve high quality materials or products. A diffusion-controlled numerical model was established here for the prediction of binder burnout kinetics within powder compacts. It considers the degradation of a polymeric binder into a monomer, liquid state diffusion of the monomer in a core region, and gaseous transport of the monomer in a gas-filled annulus. The rate-controlling mechanism is identified as the diffusion of the monomer in the liquid core, while gaseous transport in the porous annulus poses minor influence. The model is able to predict the remaining weight fraction of polymer during debinding and the total burnout time under different geometric and processing conditions. It is noted that the burnout time increases markedly with compact size, but varies insignificantly with powder particle size. The rate of binder removal increases sharply with temperature. The theoretical predictions of the burnout-out kinetics are in line with experimental findings.

Kinetics and rheology characterization during curing of dicyanates

Reaction kinetics and viscosity rise of a liquid dicyanate ester monomer, 1,1-bis(4-cyana-tophenol)ethane, are characterized and fitted several models. Fourier transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC) are used to obtain the isothermal reaction kinetic data. The liquid dicyanate resin shows second-order reaction kinetics in the early stage and approaches a plateau conversion at longer times with each curing temperature. Experimental data show that the diffusion limitation for dicyanate resin occurs well before the vitrification point. A two-step kinetic model and a Williams-Landel-Ferry-(WLF-) type diffusion-controlled kinetic model are developed to describe the entire range of curing. For the temperature range we studied (140°C–200°C), the WLF-type diffusion-controlled kinetic model gives a better prediction than the two-step kinetic model does. The viscosity rise during isothermal curing is characterized using disposable parallel plates. A Castro-Macosko type of equation is used to describe the isothermal viscosity rise. © 1996 John Wiley & Sons, Inc.

Kinetics and rheology characterization during curing of dicyanates

Reaction kinetics and viscosity rise of a liquid dicyanate ester monomer, 1,1-bis(4-cyana-tophenol)ethane, are characterized and fitted several models. Fourier transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC) are used to obtain the isothermal reaction kinetic data. The liquid dicyanate resin shows second-order reaction kinetics in the early stage and approaches a plateau conversion at longer times with each curing temperature. Experimental data show that the diffusion limitation for dicyanate resin occurs well before the vitrification point. A two-step kinetic model and a Williams-Landel-Ferry-(WLF-) type diffusion-controlled kinetic model are developed to describe the entire range of curing. For the temperature range we studied (140°C–200°C), the WLF-type diffusion-controlled kinetic model gives a better prediction than the two-step kinetic model does. The viscosity rise during isothermal curing is characterized using disposable parallel plates. A Castro-Macosko type of equation is used to describe the isothermal viscosity rise. © 1996 John Wiley & Sons, Inc.

Diffusion phenomena during cyanate resin cure

The diffusion phenomena, including the molecular diffusion processes and the effect of diffusion on the cure kinetics and molecular size distribution, during the curing of a zinc-catalysed cyanate ester resin have been studied. The average diffusivity, which was estimated using the dielectric analysis-based approach, decreased by several orders of magnitude during the curing process. The molecular size distribution measured with size exclusion chromatography was found to deviate from the mean-field prediction at relatively high conversions. By using the Rabinowitch model, a diffusion-controlled kinetic model was formulated, which adequately predicted the experimental cyanate conversion profiles over the entire range of cure.