Mixed Control Model Research Articles

SIMULATION OF LEDGEWISE GROWTH KINETICS OF PROEUTECTIOD FERRITE UNDER INTERFACIAL REACTION–DIFFUSION MIXED CONTROL MODEL

A mixed control model considering both carbon diffusion and interfacial reaction is es- tablished for ledgewise growth kinetics of proeutectiod ferrite during → � isothermal transformation in low carbon steels. In this model, the growth rate of ledgewise ferrite and the carbon concentration at the ledge riser are determined by both carbon diffusion at ledge riser in austenite and interfacial reaction rate of → � transformation, which is different from the traditional local equilibrium(LE) model. Simulation is done by utlizing this model to analyze the ledgewise growth kinetics of proeu- tectiod ferrite. And based on analysis of the characteristics of growth kinetics of proeutectiod ferrite obtained by the simulation, a factor S, which includes the effects of carbon diffusion, interface migra- tion, temperature and composition, is proposed to characterize the control mode of growth kinetics. By judging this factor S, we can predict that if the carbon diffusion or interfacial reaction dominates the growth kinetics of proeutectiod ferrite. In the case that the value S is relatively small, the growth kinetics is mainly controlled by interfacial reaction. In the case that the value of S is quite large, the growth kinetics is controlled by carbon diffusion, which returns to the traditional local equilibrium model. The mixed control simulation results for ledgewise growth of proeutectoid ferrite at 720 in Fe-1%C (atomic fraction) alloy show a good agreement with the experimental results previously reported.

How are eye fixation durations controlled during scene viewing? Further evidence from a scene onset delay paradigm

Recent research on eye movements during scene viewing has focused on where the eyes fixate. But eye fixations also differ in their durations. Here we investigated whether fixation durations in scene viewing are under the direct and immediate control of the current visual input. In two scene memorization and one visual search experiments, the scene was removed from view during critical fixations for a predetermined delay, and then restored following the delay. Experiment 1 compared filled (pattern mask) and unfilled (grey field) delays. Experiment 2 compared random to blocked delays. Experiment 3 extended the results to a visual search task. The results demonstrate that fixation durations in scene viewing comprise two fixation populations. One population remains relatively constant across delay, and the second population increases with scene onset delay. The results are consistent with a mixed eye movement control model that incorporates an autonomous control mechanism with process monitoring. The results suggest that a complete gaze control model will have to account for both fixation location and fixation duration.

Eye movements during scene viewing: Evidence for mixed control of fixation durations

Recent behavioral and computational research on eye movement control during scene viewing has focused on where the eyes move. However, fixations also differ in their durations, and when the eyes move may be another important indicator of perceptual and cognitive activity. Here we used a scene onset delay paradigm to investigate the degree to which individual fixation durations are under direct moment-to-moment control of the viewer's current visual scene. During saccades just prior to critical fixations, the scene was removed from view so that when the eyes landed, no scene was present. Following a manipulated delay period, the scene was restored to view. We found that one population of fixations was under the direct control of the current scene, increasing in duration as delay increased. A second population of fixations was relatively constant across delay. The pattern of data did not change whether delay duration was random or blocked, suggesting that the effects were not under the strategic control of the viewer. The results support a mixed control model in which the durations of some fixations proceed regardless of scene presence, whereas others are under the direct moment-to-moment control of ongoing scene analysis.

Leaching of zinc sulfide concentrate from the ganesh-himal deposit of nepal

The leaching of zinc concentrate obtained from the zinc ore located in the Ganesh-Himal region of Nepal has been carried out in the presence of ammonium persulfate (APS) as an oxidant. Leaching variables such as time, temperature, acid, and oxidant concentration, E h , and particle size of sphalerite concentrate were studied to optimize the condition and to understand the mechanism of the reaction. The zinc extraction increased up to a temperature of 333 K and a further rise in the temperature to 343 K resulted in lowering of metal extraction. A decrease in particle size and increase in oxidant concentration enhanced the dissolution rate of zinc. The leaching data best fitted to the mixed controlled kinetic model. An activation energy of 43 kJ/mol was obtained for the dissolution of zinc in the temperature range 303 to 333 K with APS. The leaching mechanism was further established by characterizing the original concentrate and the leach residue by X-ray diffraction (XRD) phase identification and scanning electron microscopy (SEM) studies.

Short-time behavior of mixed diffusion-barrier controlled adsorption

This paper focuses on the short-time adsorption kinetics of nonionic surfactants onto water/air surfaces, analyzed in the context of the mixed diffusion-barrier controlled adsorption modeling framework. Specifically, we reconcile the apparent contradiction between theoretical prediction and experimental observations on the adsorption kinetics mechanism at short times: while the mixed diffusion-barrier controlled model predicts a barrier-controlled adsorption, as well as the impossibility of a diffusion-controlled adsorption at asymptotic short times, the short-time experimental dynamic surface tension (DST) behavior of many nonionic surfactants has been interpreted to result from diffusion-controlled adsorption at asymptotic short times. This is because the short-time experimental DST of these surfactants displays a t variation, which is considered as a fingerprint for the existence of diffusion-controlled adsorption, based on the short-time asymptotic behavior of the diffusion-controlled adsorption model. As a result of this interpretation, the fundamental physical nature of the energy barrier has been proposed to be associated with high surfactant surface concentrations. In this paper, we derive a new nonasymptotic short-time formalism of the mixed diffusion-barrier controlled model to describe surfactant adsorption onto a spherical pendant-bubble surface, including determining the ranges of time and surfactant surface concentration values where the short-time formalism is applicable. Based on this formalism, we find that one can expect to observe an apparent t variation of the DST at short times even for the mixed diffusion-barrier controlled adsorption model. We analyze the consequence of this finding by re-evaluating the existing notions of the energy barrier. We conclude that the energy barrier is associated with the adsorption of a single surfactant molecule onto a clean surface.

Dissolution kinetics of smithsonite ore in ammonium chloride solution

The results of a dissolution kinetics study of smithsonite ore in ammonium chloride are presented. Effect of stirring speed, ore particle size, reaction temperature, and the concentration of ammonium chloride on zinc dissolution rate are determined. The results obtained show that leaching of about 91.2% of zinc is achieved using 84–110 μm ore particle size at a reaction temperature of 90 °C for 240 min reaction time with 5 mol/L ammonium chloride. The solid/liquid ratio was maintained constant at 1:10 g/mL. Leaching kinetics indicates that chemical reaction at the new particle surface and the diffusion through the inert particle pores together are the rate control steps. A corresponding mixed control model is found suitable to explain the relationship between the reaction time and the fraction of zinc leached. The apparent activation energy of this process is determined to be 21.3 kJ/mol.

Effects of SiO2 and Al2O3 on the Lattice Parameter and CO Gas Reduction of CaO-containing Dense Wustite.

The effects of SiO2 and Al2O3 on the lattice parameter and the initial reduction rate of CaO-containing wustite were studied at 1 273 K. Wustite plates containing 0.5-2 mass% CaO, 0.2-2 mass% SiO2 and 1 mass% Al2O3 were prepared at the mass fractions of CaO/SiO2=0.5-5. The lattice parameter of CaO–SiO2- containing wustite decreased with decreasing CaO/SiO2 ratio at a constant CaO content. This corresponded to a decrease of the dissolved content of CaO in the wustite due to a formation of CaO-FeO-SiO2 compounds. Similarly, the dissolved content of CaO decreased in CaO-SiO2-Al2O3-containing wustite. The process of CO gas reduction within the wustite phase field was traced with the lattice parameter measurement of the partially reduced samples and was analyzed with a mixed-control model of chemical reaction at the surface and the solid state diffusion in the wustite. The chemical reaction rate constant, k´, decreased with increasing the amount of SiO2 addition at a constant CaO content. The dependence of k´ on SiO2 (and Al2O3) addition was in good accordance with the change in the dissolved content of CaO in the wustite owing to the formation of the compounds containing CaO. The inter-diffusion coefficient, D, tended to decrease slightly with increasing the amount of compound.

Effect of Mass Transfer and Bulk Flow on the Zinc Oxide Reduction by Methane

Zinc oxide reduction with methane can introduce a new zinc-producing technology. The advantages of this method with respect to conventional carbothermic furnaces are lower operating temperatures, a simple indirect condenser, and copreparation of synthesis gas. The kinetics of ZnO reduction by CH4 at the chemical control regime has been studied on the thermogravimetric (TG) scale and at moderate temperatures extensively (Ale Ebrahim, H.; Jamshidi, E. Trans. Inst. Chem. Eng. 2001, 79A, 62−70). On the industrial scale with large ZnO pellets, mass transfer and bulk flow will be effective even at moderate temperatures. Therefore, a successful mathematical model for the design of such industrial plants is needed. In this work the ZnO + CH4 reaction at high temperature (1000 °C) was studied, where the kinetic resistance decreased considerably. Thus, the effect of mass transfer and bulk flow can be considered in on the TG scale. Then a mixed control model was developed which contains the effects of external mass ...

Photomineralisation kinetics of aqueous chlorophenols at a supported TiO 2 surface studied by the channel-flow method with electrochemical detection

The channel flow method with electrochemical detection (CFMED) of Cl − ion product has been applied to the photodegradation kinetics of four chlorophenols (CPs) undergoing photolysis ( λ>300 nm) at a TiO 2 film. The effects on the rate of photomineralisation of (i) varying CP concentration, (ii) O 2 concentration, (iii) flow rate, (iv) light intensity and (v) supporting electrolyte, have been examined. Of particular note are the accelerative effects of increasing [O 2] and removing background electrolyte. The kinetics have been shown to fit models derived from Langmuir–Hinshelwood kinetics; at high [CP], the rates fit a surface-limited model, but at low [CP], this model proves inadequate and a mixed-control model, incorporating mass transfer as an additional parameter, is shown to be necessary. The approach developed allows the conditions under which mass transfer is important in controlling photomineralisation rates to be identified.

Dissolution kinetics of potassium from glauconitic sandstone in acid lixiviant

Laboratory studies have been conducted for dissolution of potassium from glauconitic sandstone in diluted hydrochloric acid, nitric acid and sulphuric acid at different temperatures. The dissolution of potassium was analysed with different kinetic models. The dissolution of potassium follows a mixed control model embodying chemical control model at the initial stages of dissolution and diffusion control model at the later stages of dissolution for all the three lixiviants. The activation energy for dissolution of potassium in hydrochloric acid varies from 79.03 to 99.41 kJ/mol, whereas in nitric acid and sulphuric acid, it varies from 56.93 to 95.18 and 37.43 to 56.24 kJ/mol, respectively.

Mathematical model for nitrogen control in oxygen steelmaking

A mathematical model was developed to quantify the effects of different operational parameters on the nitrogen content of steel produced during oxygen steelmaking. The model predicts nitrogen removal by the CO produced during decarburization and how the final nitrogen content is affected by different process variables. These variables include the type of coolants used (scrap, direct reduced iron (DRI), etc.), the sulfur content of the metal, combined gas blowing practices, and the nitrogen content in the hot metal, scrap and oxygen blown. The model is a mixed control model that incorporates mass transfer and chemical kinetics. It requires a single parameter that reflects the surface area and mass-transfer coefficient that is determined from the rate of decarburization. The model also computes the rate of decarburization and the change in surface active elements, such as sulfur and oxygen, that affect the rate of the nitrogen reaction. Nitrogenization of steel in the converter is also predicted with the model. The computed results are in good agreement with plant data and observations.

Kinetics of inclusion precipitation during steel solidification

The precipitation of non‐metallic inclusions (complex oxides, sulphides, nitrides …) during steel solidification is analysed using the multiphase equilibrium code CEQCSI and a nucleation and growth model. The CEQCSI code is based in part on the Irsid slag model, and it provides an evaluation of the composition of inclusions formed at equilibrium, as well as guidelines for industrial treatments in order to reach desirable compositions in semi‐killed steel grades. The nucleation and growth model can be applied to the formation, during steel solidification, of stoichiometric compounds or liquid oxide inclusions. Two particularities of this kinetic model are that nucleation and growth are treated simultaneously, and they compete in consuming the supersaturation at each moment, and that a mixed controlled growth model transport/interfacial kinetics at the precipitate/liquid steel interface is considered. The predicted size distribution of TiN precipitates formed in two steel grades is in good agreement with the results of laboratory experiments. In the case of liquid oxide precipitation, the first calculations indicate that the composition of inclusions can be significantly different from that of inclusions assumed to precipitate under equilibrium conditions.

On optimization of the powder plasma arc surfacing process

METALLURGICAL AND MATERIALS TRANSACTIONS B In summary, a re-examination of the influence of the gascarbon reaction on the reaction kinetics of FeO by solid carbon using recently available data has shown that this reaction may have a significant effect on the observed rates. A comprehensive mixed control model was used to evaluate the influence of the gas-carbon reaction on the observed reduction rate, and the predictions agree well with the measured data. In general, the overall rate is controlled by the various steps in a series. The predominant step will depend on the stirring condition and type of carbon. The rates observed in graphite are probably not strongly affected by the gas-carbon reaction, the rate limiting steps are liquid phase mass transfer in combination with the slag-gas reaction. On the other hand, when coke is used, the considerably lower reactivity of this carbonaceous material to CO2 at high temperatures appears to cause this reaction to have significant influence on the rate of reduction.

Decarburization Kinetics of Fe-C-S Droplets with H2O.

Decarburization of liquid Fe-C-S droplets with HO vapour was investigated using the electromagnetic levitation technique. The results indicated that the decarburization of liquid iron droplets by HO vapour can be adequately described by the mixed control of the gas phase mass transport and the dissociative chemisorption of HO at the melt surface. The Steinberger-Treybal correlation equation was found to correctly represent the gas phase mass transfer in the present system geometry and experimental conditions. The rate of decarburization decreased significantly with increase in sulphur content in the melt, and this effect was quantitatively represented by the mixed control model. There exists a residual rate of decarburization at high sulphur contents in the melt. The extent of the residual rate observed can be interpreted as implying that, even at the melt surface of apparent saturation with sulphur, 8-9% of the surface sites are still available for HO molecules to react with carbon. The activation energy of dissociative chemisorption of HO was 95 kJ mol-1.

Reduction of FeO in smelting slags by solid carbon: Experimental results

The reduction of CaO-SiO2-Al2O3-FeO slags containing less than 10 wt pct FeO by solid carbonaceous materials such as graphite, coke, and coal char was investigated at reaction temperatures of 1400 °C to 1450 °C. The carbon monoxide evolution rate from the system was measured using stationary and rotating carbon rods, stationary horizontal carbon surfaces, and pinned stationary spheres as the reductants. The measured reaction rate ranged from 3.25 × 10−7 mol cm−2 s−1 at 2.1 pct FeO under static conditions to 3.6 × 10−6 mol cm−2 s−1 at 9.5 pct FeO for a rotating rod experiment. Visualization of the experiment using X-ray fluoroscopy showed that gas evolution from the reduction reaction caused the slag to foam during the experiment and that a gas film formed between the carbon surface and the slag at all times during experimentation. The reaction rate increased with increased slag FeO contents under all experimental conditions; however, this variation was not linear with FeO content. The reaction rate also increased with the rotation speed of the carbon rod at a given FeO content. A small increase in the reaction rate, at a given FeO content, was found when horizontal coke surfaces and coke spheres were used as the reductant as compared to graphite and coal char. The results of these experiments do not fit the traditional mass transfer correlations due to the evolution of gas during the experiment. The experimental results are consistent, however, with the hypothesis that liquid phase mass transfer of iron oxide is a major factor in the rate of reduction of iron oxide from slags by carbonaceous materials. In a second article, the individual rates of the possible limiting steps will be compared and a mixed control model will be used to explain the measured reaction rates.

Simultaneous Decarburization and Denitrogenization of Molten Iron with Vacuum Suction Degassing Method.

A kinetic study has been made on simultaneous decarburization and denitrogenization of molten iron in low content ranges by using Vacuum Suction Degassing method (VSD method). A porous Al2O3-SiO2 tube was immersed into molten iron. Internal pressure of the tube was reduced to remove gaseous products from the tube-molten iron interface. The initial carbon and nitrogen contents were in the ranges of 0-1000 ppm and 50-100 ppm, respectively. The initial oxygen content was below 50 ppm. The atmosphere of the bath surface was Ar (1.01×105 Pa). The experimental temperature was 1853 K. The VSD method can greatly increase the rate of denitrogenization as well as decarburization, and the carbon and nitrogen contents can be decreased to very low values. The decarburization rate constant increases with increasing gas permeability of the porous tube and with decreasing its internal pressure. The decarburization at higher carbon content is largely affected by the dissociation reaction of solid oxide of the tube. The decarburization enhances the denitrogenization considerably. The denitrogenization reaction rate is strongly dependent on gas permeability of the porous tube. A mixed control model is applied to explain the denitrogenization at the porous tube-melt interface. It is found that the denitrogenization rate is controlled by the mass transfer in the porous tube wall at lower permeability and mainly by the chemical reaction at the tube-melt interface at higher permeability.

金属鉄生成以前におけるウスタイトのCOガス還元の混合律速モデルによる速度解析

金属鉄生成以前におけるウスタイトのCOガス還元の混合律速モデルによる速度解析

Oscillating Bubble Tensiometry: A Method for Measuring the Surfactant Adsorptive-Desorptive Kinetics and the Surface Dilatational Viscosity

Mobilities of surfactant laden interfaces are determined by both surfactant-mass-transfer kinetics and surface viscosities. In this paper, a theoretical framework for measuring these parameters by analyzing forced radial oscillations of a spherical pendant bubble about an equilibrium, quiescent base state is developed. Because of the Gibbs-Marangoni elasticity caused by hindered surfactant mass transfer, and the surface viscosities, oscillations in the gas phase pressure and bubble radius are out of phase. Using a linear analysis of the governing fluid mechanical and mass-transfer equations, the phase lag (θ) and the amplitude ratio of these two quantities (Λ) are derived. Three cases are considered for the surfactant mass transfer: a mixed-controlled model in which diffusion and sorption kinetics play a role, along with the limiting cases of diffusion-control and sorption-control, respectively. Both θ and Λ depend upon the bulk diffusivity, the equilibrium physicochemical constants, and two unknowns: the sorption kinetic constant and the surface dilatational viscosity. In this paper, by varying these unknowns, theoretical families of curves for both θ and Λ vs forcing frequency, ω′, are generated using values for the bulk diffusivity and the equilibrium physicochemical constants for decanol at aqueous-air interfaces from Lin et al. (Langmuir 7, 1055, 1991). These curves indicate the potential of the oscillating bubble as a measurement tool, i.e., that experiments in which θ and Λ are measured vs ω′ can be used to determine the adsorption-desorption kinetic constants and the surface dilatational viscosity and to differentiate them from each other.

The influence of oxygen pressure on the kinetics of the thermal decomposition of Co3O4

The kinetics of the thermal decomposition of Co3O4 has been examined in the 1123–1200 K temperature and 2.66–20.73 kPa oxygen pressure range. The kinetics of this process has been deseribed in terms of a mixed-control model of reaction. The values of activation energies of diffusion and chemical reaction as well as the observed activation energy have been given. The strong dependence of the decomposition rate on temperature and oxygen pressure has been explained.

Mixed control kinetics of copper dissolution for copper ore using ferric chloride

Mixed control kinetics of copper dissolution using ferric chloride were investigated in the temperature range of 30–90°C, together with the rate-controlling steps during the initial as well as the final stages of the reaction. It was observed that chemical reaction at the mineral surface is rate controlling in the initial stages and, during later stages, diffusion through the product layer is rate controlling. The overall reaction is described by the mixed control model.