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By Lan Li, Izaak Williamson

"The efficient separation and storage of CO2 from power plant flue gases can reduce the amount of CO2 released into the atmosphere and mitigate global warming. Potential candidates for industrial applications are solid sorbent materials. Crucial factors to control the efficiency of porous sorbent materials include the framework and pore structure, and the chemical and physical reactivity of CO2 within the pores. Computational modeling approaches, based on density functional theory (DFT) and van der Waals-DFT, have been applied to nanoporous solid – manganese dioxide a-MnO2. We found that the types and charges of cations as dopants in the a-MnO2 and the concentration of CO2 influence the structural features of a-MnO2, which control its CO2 selectivity performance within the flue gases.IntroductionCarbon capture and storage is a technique to separate large quantities of CO2 from power plant flue gases before being released into the atmosphere. Porous solids are a potential candidate as sorbents to “trap” CO2 through chemical or physical adsorption on their porous surfaces[1]. Such separation efficiency is determined by the size and shape of its pores and by the interaction between the porous surface and the gas adsorbates. The incorporation of cations into the pore can act as a means of structural support and alter the pore diameter to be comparable to the kinetic diameter of the gas adsorbate, such as CO2.A porous solid of particular interest for CCS is manganese dioxide a-MnO2, an octahedral molecular sieve (OMS) composed of edge-sharing MnO6 octahedra that are linked into a nanoporous framework[2]. The framework consists of (1×1) and (2×2) tunnels, referred to as OMS-2. Due to the larger tunnel size, cations and gas adsorbates prefer to reside along the (2×2) tunnel axis of the OMS-2. As seen in Figure 1, a potassium cation K+ is located in the (2×2) tunnel, known as cryptomelane-type MnO2. Its pore diameter of ~ 4.6 Å gives it a good CO2 selectivity performance, because the diameter is comparable to the kinetic diameter of 3.3 Å for CO2[3]. Alternatively, replacing potassium K+ with other cations, e.g. barium Ba2+, sodium Na+ or lithium Li+, in the OMS-2 tunnel is of great research interest, due to the effects of their concentrations, types and charges on the CO2 selectivity efficiency and sorption hysteresis phenomenon[2,4]."

Jan 1, 2014

By Yuanyuan Zhang, Patrick J. Masset

"The reduction of FexO in slag is one of the fundamental reactions in iron and steelmaking technology, including the blast furnace process (BF). Experiments on the reduction reaction of iron oxide using CaO-SiO2-Al2O3-FexO-C mixtures were carried out using thermogravimetric analysis (TGA) under reducing conditions at temperatures up to 1100°C. The composition of the primary slag was chosen so that the FexO concentration varied between 0 and 75 wt % and the CaO/SiO2 ratio being kept constant to 0.90. From the TGA curves recorded isothermally at different temperatures the kinetic parameters of the iron oxide reduction were determined.IntroductionIn blast furnace the iron ores and coke are charged in layers from the top. The reduction of iron oxide by coke is one of the fundamental reactions in the blast furnace process. Although a great amount of work has been done on the topic of reduction of composites [1, 2, 3], gasification of carbon [4, 5] and reduction of iron oxides by CO [4, 5, 6], the mechanism of reduction in iron oxide - carbon powder mixtures is not fully understood. Fruehan [1] and Rao [2] studied the reaction rate of the reduction of iron oxide by different types of carbon and concluded that the reaction mechanism is controlled by the oxidation of carbon at temperatures up to 1200°C. Rao [2] studied the reaction of hematite with graphite as carbon source up to 1080°C. An activation energy close to 300 kJ/mol was calculated within the temperature range of 950°C to 1087°C. In his study, Fruehan [1] determined the rate of reduction of Fe2O3 and FeO by coal, coke and coconut charcoal as carbon sources within the 900°C to 1200°C temperature range. He found that the reduction of Fe2O3 by carbon occurs in two stages and that the reduction of Fe2O3 to FeO is faster than that of FeO to Fe. This is due to the fact that the CO2/CO equilibrium ratio is higher, and hence, the rate of oxidation of carbon is faster. Fortini and Fruehan [3] have studied the reduction reaction of wustite by graphite and wood charcoal. They found that the wustite reduction can have a significant effect on the overall rate of reduction in composites at high temperatures or in the presence of a large excess of carbon. The calculated activation energy of the reduction reaction by wood charcoal was close to 368 kJ/mol, while the activation energy of the reduction reaction by graphite was 444 kJ/mol."

Jan 1, 2011

By Kumar M. Lyer

The channel reactor for ferrous and nonferrous processing has been modeled as a combination of ideal reactors. Cold model studies simulated the counter-current flow of slag and matte (or metal) with high-strength submerged gas injection. A composite model has been developed which describes the mass transfer between the two liquid phases, including the transfer of minor elements. The residence time for the matte droplets in the matte/slag emulsion is compared with the settling rates for the matte droplets in the slag to determine their relative importance in the mass transfer between matte and slag. The governing equations for mass transfer have been developed using correlations for the mass-transfer coefficients in the continuous and dispersed phases. An application of this scheme to a typical copper smelting system is presented.

Jan 1, 1993

By K. Tozwa

The electrical conductivity of electrolytes for copper electrorefining and electrowinning processes has been reported by many researchers since 1911. The experimental results show that the conductivity increases with an increase in sulfuric acid concentration and decreascs with an increase in copper concentration. In pure copper sulfate solution, however, the conductivity increases with an increase in the copper concentration. After confirming the conductivity of pure and acidified copper sulfate solutions experimentally, the concentrations of hydrogen ion and free (not hydrated) water in the electrolytes were estimated and it was found that the relation between the conductivity of acidified copper sulfate electrolytes and the products of concentration of hydrogen ion and free water is linear. Accordingly, the conductivity of acidified copper sulfate electrolytes increases with an increase in sulfuric acid concentration and decreases with an increase in copper concentration.

Jan 1, 2003

By Kouichi Nakano

Austenitic stainless steel, which includes nickel for stabilizing austenitic structure, is used for various purposes, for example, for structural material, corrosion-resistant material, biomaterial etc. Nickel is set as one of the rare metals and economizing on nickel as the natural resources is required. On the other hand, nickel is one of the metals that cause metallic allergy frequently. Therefore, high nitrogen stainless steel, where nitrogen stabilizes austenitic structure instead of nickel, has been developed in Japan and some of the foreign countries for the above reason. When high nitrogen stainless steel is fused and bonded, dissolved nitrogen is released to the atmospheric area, and some of the material properties will change. In this study, we bonded high nitrogen stainless steel by stud welding process, which is able to bond at short time, and we evaluate joint performance. We have got some interesting results from the other tests and examinations.

Jan 1, 2016

By A. Jakobsson

Studies of the rate of interdissolution in oxide systems in the solid state are of importance in materials processing through the powder-metallurgical route. As there is a need for following the rate of the such reactions continuously, a new method based on high temperature X-ray diffraction was developed. Mechanical mixtures of the oxides were placed in a high-temperature X-ray diffraction unit and the changes in the intensity and position of the peaks with highest intensity for both the components were followed as functions of time. A suitable theoretical model has been developed in order to interpret the experimental data and evaluate the diffusion coefficients. The method was applied in the case of the system MgO-NiO. The results obtained are compared with those obtained by another new method, based on solid-state galvanic cell technique with calcia stabilized zirconia electrolyte, developed in the Department of Theoretical Metallurgy. The advantage of the present techniques to monitor the progress of the reaction continuously make them suitable for computer control of such processes.

Jan 1, 1995

By Warren J. Bruckard, Mark I. Pownceby, Sazzad Ahmad, M. Akbar Rhamdhani

Rutile is the preferred feedstock for producing high-grade TiO2 pigment but due to decreasing resources, alternative materials such as ilmenite is now used to produce a synthetic rutile (SR) feedstock. This requires removal of impurities (e.g. Fe, Mg, Mn) which, for a primary ilmenite is straightforward process. Processing of weathered ilmenite however, is complex, especially when chrome-bearing impurities are present since minor chromium downgrades the SR market value as it imparts color to the final TiO2 pigment, Chrome-bearing spinels are a problem in weathered ilmenites from the Murray Basin, Australia as their physical and chemical properties overlap with ilmenite making separation difficult. In this paper, different sulfidation process routes for weathered ilmenites are analyzed for their applicability to Murray Basin deposits as a mean of remove chrome spinel impurities. Thermodynamic and experimental studies indicated that selective sulfidation of chrome-bearing spinel can be achieved under controlled pO2 and pS2 processing conditions thereby making them amenable to separation.

Jan 1, 2015

By H. Saint-Raymond, F. Gruy, P. Gardin, M. Cournil

"The control of inclusion elimination is getting more and more important to obtain clean steel. This paper presents a methodology under development for predicting cluster growth and elimination in ladle - RH system. The first key point is to express the collision efficiency, which is very specific for alumina cluster due to the non-wetting fluid. Second, a description of the two-phase flow in the system is necessary. In our calculations with Fluent CFD package and Lagrangian approach for bubbles, bubble growth is implemented, which improves the predictions. Using global reactor decomposition makes possible the prediction of the time evolution of cluster distribution. Important effect of fractal dimension is demonstrated.IntroductionElaboration of new steel grades requires not only to have a high purity in terms of C, O and N content but also to eliminate particles such as alumina or slag droplets. Flow optimisation making easier inclusion elimination is then a key figure to satisfy cleanliness requirements. Mathematical models of flow and inclusion behaviour are widely used for this purpose (1, 2). But having a predictive tool is still a challenge, because the number of phases is important in steelmaking industry: liquid steel, slag layer, bubbles and inclusions (with a large range of composition and rheology). The paper presents the methodology which is developed at IRSID to predict oxygen content evolution during RH degassing.The main mechanisms which have to be considered are :-inclusion growth by turbulent aggregation of elementary inclusions (keeping in mind that liquid steel is a non-wetting medium for inclusions); the difficulty is to express collision efficiency for alumina particles,-inclusion removal by flotation; the difficulty for alumina clusters stems from the complex morphology of particle; fortunately, the use of fractal concept makes it possible to cope with this problem.The paper describes the general modelling of inclusion removal taking into account the previous mechanisms. Hydrodynamic parameters are obtained by means of Fluent CFD package and a specific coding is developed for cluster growth."

Jan 1, 2001

By E. A. van Dijk

Dusts from steel-making processes contain substantial amounts of zinc. Such dusts are also a hazardous waste and dumping them becomes unacceptable from environmental point of view. Therefore processes that can recover zinc and possibly other metals from steel-making dusts are being investigated. The aim of this paper is a contribution to the more fundamental kinetic aspects of zinc reduction from silica free calcium ferrite slags. The effects of alumina, lime and magnesium oxide contents of the slag, the COICO, ratio and the effect of initial Fe2O3/CaO ratio were studied experimentally at 1400°C The results indicated that the reduction of zinc from molten slag was possibly a first order reaction. As expected higher COICO, ratios increased both the extent and the rate of reduction. It was also observed that a higher iron content of slag improved the reduction of zinc from calcium ferrite slags. This fact seems to support the proposed mechanism that zinc is partly reduced by ferrous iron to zinc vapour and that ferric iron is reduced by carbon monoxide. The reduction rate of zinc in these slags was decreased by increasing alumina content of the slag. Alumina decreased the calculated optical basicity of the slag showing the fact that reduction of zinc oxide was more favorable in more basic slags. Probably the formation of complex ions by alumina and zinc oxide such as ZnAl2O32+ lowers the activity of Zn2+ ions in the slag and hence render them more difficult to reduce.

Jan 1, 1999

By Lev Levin, Sergei Lesokhin

"The formation of titanium carbide during hot filament assisted carburizing of NiTi alloy was investigated. Phase content and morphology of the diffusion zone were examined by X-ray diffraction, X-ray microanalysis, SEM, and Auger electron spectroscopy. The growth of stable and adherent TiC film was observed. A non-planarity of interphase boundary was noticed. The applicability of the chemical diffusion approach to the analysis of the experimentally observed interface instability is discussed. A criterion, taking into account the influence of growth stresses on the stability of the flat interface, is developed by means of linear perturbation analysis.Introduction.Equiatomic intermetallic NiTi belongs to a class of materials exhibiting the shape-memory effect. The unusual property of this compound promotes its application in many fields, from aerospace technologies to medicine. The relatively high ductility ofNiTi also permits its use as a matrix material in metal-ceramic composites. The objective of this work was to investigate the possible incorporation of a ceramic material (titanium carbide) into NiTi by gas carburizing.Free energy calculations indicate the potential to obtain TiC by carburizing Ni-Ti binary phases. The main obstacle to such a process is the high affinity of titanium to oxygen. At moderate temperatures the formation of TiC is preferable to titanium oxidation only if the partial pressure of oxygen is extremely low [1]. This problem was overcome in this work by the use of hot filament assisted gas carburizing. Due to chemical reactions occurring near the hot filament, the gas mixture, initially consisting of methane and molecular hydrogen, was enriched by atomic hydrogen [2], drastically decreasing the content of free oxygen in the carburizing atmosphere.The second part of this article concerns the theoretical analysis of reasons that lead to the development of the experimentally observed morphology of the diffusion zone. In particular, the influence of the growth stresses on the morphology of an interphase boundary is investigated."

Jan 1, 1996

By F. Shahbazian

attempt to systematize the knowledge on slag viscosities, the present work was carried out. The Among the physical properties of slags, viscosity is very important in understanding the mass out in the temperature range 1438-1762 Q The rotating cylinder method was used in the viscosity measurements. Crucibles and spindles made out of pure iron were employed. The transfer phenomena in metallurgical processes. The viscosities of fayalitic slags are of great interest in the non-ferrous metal industry, with special reference to copper production. In an slags were prefused before the measurements. In order to take into account the vaporization reactions involving CaF2, pre- and post measurement samples of the slags were chemically analysed and the compositions were ascertained. The results show that in the case of the CaO-SiO2 system, CaF2 additions tend to decrease the viscosity, in accordance with the expectations. In the case of the "FeO"-SiO2 system, at higher "FeO" / SiO2 ratios in the slags, a reverse trend was observed. The results are discussed on the basis of a viscosity model for silicate melts developed in the present laboratory as well as the structural considerations of silicates.

Jan 1, 2000

By Gaballah Djona M.

Spent hydrorefining catalysts contain about 5 % of CoO and/or NiO, 12 % of MoO3 and up to 10 % of V205. They are generally supported by alumina and contain up to 25 percent of C, S and hydrocarbons. Such materials are potentially hazardous to the soil and to water resources. Selective chlorination of raw unroasted samples with Cl2 + air gas mixture had been investigated. At temperatures lower than 600 °C, it was possible to recover more than 90 % of nickel and cobalt chlorides, about 99 % of the molybdenum and up to 75 % of vanadium chlorinated compounds. CoCl2 and Ni/Cl2 were extracted from the chlorination residues by their dissolution with acidified water. Molybdenum and vanadium chlorinated compounds were recovered by selective condensation from the vapor phase. The chlorination of Al2O3 could be limited to less than 6 %. The scale up of this treatment was successful and a flow-sheet is proposed.

Jan 1, 1995

By D. Doungdeethaveeratana

The extraction kinetics in a novel solvent extraction process have been investigated. In this process, the liquid-liquid emulsion is generated by bottom gas injection into countercurrently flowing aqueous and organic phases. This process has a number of advantages over the mixer-settler unit or the spray column in terms of simple equipment configuration, without any mechanical moving parts, and the ease of cleaning and process control, while providing a sufficiently large interfacial area for rapid mass transfer. The overall rate increased with increasing gas injection rate and height of the aqueous phase but decreased with increasing injector diameter at the same gas injection rate. The variation of the overall rate constant was correlated against a set of dimensionless numbers, representing the operating conditions. Extraction rates and efficiencies comparable to those in a mechanically generated emulsion were attained in this new process.

Jan 1, 1998

By Shengqin Zhang, Yousef Mohassab, Feng Chen, Hong Yong Sohn, Mohamed Elzohiery, Amr Abdelghany

The kinetics of hematite concentrate reduction by mixtures of hydrogen and CO of various compositions has been investigated as part of the development of a flash ironmaking process at the University of Utah. This process produces iron directly from iron oxides concentrates by the gas-solid flash reaction based on the partial oxidation of natural gas, resulting in a significant reduction in energy consumption and greenhouse gas emission. The reduction kinetics of hematite concentrate of an average particle size 21.3 μm by the above mentioned gases in the temperature range 1423 to 1623 K (1150 to 1350 ºC) was investigated. Hematite concentrate particles can be reduced to > 90% by any of these reductants in several seconds of residence time typically available in a flash reactor. The activation energy ranged from 214 kJ/mol for hydrogen to 231 kJ/mol for CO.

Jan 1, 2016

By Du Sichen, S. Seetharaman, Wei Liu

"The viscosities of two-phase mixtures are of great importance in the modelling of the fluid flow in metallurgical processes. For example, in steel making and refining, the intimate mixing of metal droplets in the slag phase requires a consideration of the effective viscosities for the mixture. The present work was aimed at an understanding the phenomena underlying the viscous flow in a two-phase mixture with widely differing viscosities.Emulsions of silicone oils of known viscosities (345mPa.S and 1010mPa.S at 293K) with small amounts of water evenly distributed in the same were prepared by subjecting the mixture to uniform stirring using a magnetic stirrer. The viscosities of these emulsions were measured at constant temperature by rotating cylinder method using Brookfield Digital Rheometer. The uniformity of the preparation of the emulsions was confirmed by the reproducibility of the results. Th7 measured viscosities were generally found to be independent of the torque under the experimental conditions so that the two-phase mixture could be considered as a Newtonian liquid. The variation of viscosities with temperature and the effect of addition of a surface-active substance were also studied in this work.The measured viscosities were found to be· higher than those of both pure water and silicone oil. The experimental viscosities were found to increase with increasing concentration of water. The influence of surface tension on the viscosities was examined by adding surfaceactive agent to the mixtures. The result is discussed and compared with theoretical models developed by Einstein, Taylor and Oldroyd."

Jan 1, 2000

By George E. Cook, Peter C. Levick, Francis M. Wells

"Relationships are established between the peak current of a pulsed, rectangular current waveform and the pulse current duty cycle under conditions of constant arc power. By appropriate choice of these interrelated parameters, it is shown that the arc pressure may be varied over a wide range even though the arc power is held constant. The methodology is suggested as a means of countering the effect of gravity in 5-G welding, while maintaining constant heat input to the weld. Combined with appropriate penetration sensors, the methodology is additionally suggested as a means of controlling penetration. IntroductionBoth low frequency pulsation (typically 0.1 - 20 Hz) and high frequency pulsation (> 100 Hz) are often used with GTA welding. Benefits derived from pulsing include improved weld quality and better process control.Advantages cited for low frequency pulsation include claims that the total heat input to the weld is reduced, the weld bead size is reduced, weld penetration is increased, grain size is reduced, porosity is reduced, weld distortion is reduced, thinner materials can be welded successfully, and the tolerance of the welding process to material and production variations is improved (1-16). With respect to the latter, pulsing aids control of weld bead penetration by increasing the tolerance to component dimensions and joint fit-up. It also reduces the sensitivity to disparities in heat sink, and it helps to reduce distortion in thin section material or distortion attributable to poor clamping. In certain materials it can reduce the sensitivity to surface oxides and to cast to cast compositional variations (16). Low frequency pulsation is also useful in welding thick materials mated by a prepared groove. In these applications the low frequency pulsation is used to obtain proper sidewall fusion as the tungsten electrode is weaved from one side of the groove to the other. In this case the weld current pulsation is synchronized with the cross seam weave pattern, such that the high current pulses occur at each sidewall. This type of low frequency pulsation has proven particularly useful in welding with narrow width groove designs (17-21). Finally, Ecer (22) has shown that the pulsed current arc is more stable against magnetic disturbances than an equivalent constant current arc."

Jan 1, 1986

By Zhenyang Wang, Xingle Liu, Xiangdong Xing, Shan Ren, Hongen Xie, Jianliang Zhang

"Non-isothermal combustion experiments of different additive amount of bituminous (0, 20, 40, 60, 80, 100 wt%) were conducted by synthesized thermogravimetry analyzer(STA409PC) from room temperature to 900°C in air. The changes of combustion characteristic parameters o f pulverized coals in different atmospheres are analyzed. The results show that DTG curves of coal combustion move to low temperature zones when the amount of bituminous increases. It indicates that both ignition and burnout temperature are lower, burnout time decreases, combustion characteristic index obviously increases, and combustion performance of blending coal are improved. The iso-conversional method involving Kissinger-Akah-Sunose (KAS) method was used for the kinetic analysis of the main combustion process. The results indicated that, when the additive amount of bituminous varied from 0 to 100 wt%, the value of activation energy which would sharply reduce if the additive amount of bituminous was under 60% increased from 133.94 kJ•mol-1 to 78.03 kJ•mol-1by using KAS method.IntroductionPulverized coal injection (PCI) to blast furnace (BF) is an important way for saving energy and reducing resource consumption during the ironmaking process. In order to acquire higher coal injection quantity, the relevant research topics in the field of pulverized coal combustion technology such as enhancing the efficiency of pulverized coal combustion, improving the combustion characteristics and reducing the harmful gas emissions and so on received extensive attention in recent years [1,2]. The combustion of blending coal when the appropriate proportion is selected for coal and also mixed well- distributed could give full play to the advantages of various types to make up the defects of single coal which is widely used throughout the world. So the blending coal injection to BF could produce a good impact on safety and economy for productive process. Therefore, a large amount of experimental researches on the combustion characteristic of blending coal for anthracite and bituminous were carried out by experts and scholars around the world [2-7].Nevertheless, the systematic research on the combustion behavior of anthracite with different content of bitumite in a thermogravimetric analyzer (TGA) is less. So in this paper, using the method of multiple scanning rate of conversion method, bituminous to promote the pulverized coal combustion reaction was studied to analyze its promotion mechanism of pulverized coal combustion reaction process, and the kinetic parameters of activation energy was also calculated, which to provide theoretical basis for the rationalization of resource utilization."

Jan 1, 2014

An EAF dust generated in a Swedish steel mill has been leached in hydrochloric acid at The solution obtained has been subjected to purification by cementation followed by precipitation of zinc with sodium carbonate. The thermal decomposition of the precipitate was studied using thermal analysis and X-ray diffraction. The results show that during the calcination of the precipitate three different reactions occur. The decomposition of the solid phases Zn5(CO3) (OH)6, CaZn(CO3)2 and CaCO3 occur completely at 370°C, 560°C and 940°C respectively, yielding a final product containing 61.9% ZnO and 38.1% CaO. Methods to minimize calcium and manganese in the final product are discussed.

Jan 1, 2003

By James A. Voigt

"The efficient separation of metal species from aqueous streams by precipitation techniques requires a fundamental understanding of the various processes that occur during precipitation. These processes include particle nucleation, particle growth by solute deposition, agglomerate formation, and agglomerate break-up. The application of the population balance approach has been used to develop a kinetic model that accounts for these competing kinetic processes. The usefulness of the model is illustrated through its application to the precipitation of yttrium hydroxynitrate, YHN. The kinetic parameters calculated from the model equations and system specific solution chemistry are used to describe several aspects of the effect of pH on the precipitation of the YHN. Implications with respect to the simultaneous precipitation of more than one cation type are also discussed through use of example systems. The effects of solution chemistry, precipitator design, and solvent choice are considered.IntroductionThe application of precipitation technologies to the separation of metals from solution is widely used. Regardless of its application, be it in such diverse areas as the preparation of metal oxide powders for use in commercial products or as a unit operation in the removal of trace metals during wastewater clean up, the fundamental processes involved are the same. These processes include: nucleation from solution, either homogeneous or heterogeneous; growth from solution with chemical reaction either in solution or at the precipitate/solution interface; growth by particle agglomeration; and particle break-up by collisional or shear forces. The effectiveness of the operation and the properties of the precipitate formed, or ""quality"" of the product, are determined by the competing kinetics of the different processes. The kinetics of the processes, in tum, are determined by system-specific solution chemistries and the conditions used to carry out the precipitation operation. For example, generally, when system conditions are such that the supersaturation driving force for precipitation is very high, growth species normally do not have the time to organize themselves with a high degree of crystallographic order and the precipitate is amorphous. In this case nucleation rates are invariably extremely high and the primary mechanism for growth is the agglomeration of nuclei. Conversely, when the supersaturation levels for the same system are reduced, the kinetics of the nucleation and growth processes also are greatly reduced, and a crystalline precipitate can be formed, since the growth species have time to order on particle surfaces."

Jan 1, 1996

By Guo Xian Jian

In this paper, the effects of matte grade, flux grain size, blast flowrate and blast O2 content on the process of silica flux melting in a copper converter were investigated. The results showed that the blast flowrate and the blast 02 content were not significant factors in the melting process. However, with an increase in grain size of flux and grade of matte, the amount of the flux molten decreased. The data on the melt rate of process correspond well with the mathematical model which simulates the chemical reactions occurring at the interface. The kinetic equations of melting are as follow:

Jan 1, 1996