Kinetics of Silicothermic Reduction of Manganese Oxide for Advanced High-Strength Steel Production

The kinetics of silicothermic reduction of manganese oxide from MnO–SiO₂–CaO–Al₂O₃ slags reacting with Fe-Si droplets were studied in the temperature range of 1823 K to 1923 K (1550 °C to 1650 °C). The effects of initial droplet mass, initial droplet silicon content, and initial slag manganese oxide content were studied. Data obtained for 15 pct silicon showed agreement with control by mass transport of MnO in the slag with a mass transfer coefficient (k _s) of 4.0 × 10^?5 m/s at 1873 K (1600 °C). However, when this rate-determining step was tested at different initial silicon contents, the agreement was lost, suggesting mixed control between silicon transport in the metal and manganese oxide transport in the slag. Increasing the temperature resulted in a decrease in the rate of reaction because of an increase in the favorability of SiO as a product. Significant gas generation was found during all experiments, as a result of silicon monoxide production. The ratio of silicon monoxide to silica formation was increased by factors favoring silicon transport over that of manganese, further supporting the conclusion that the reaction is under mixed control by transports of both silicon and manganese oxide.     

Formation of metallic phase by passing gaseous reducing agent through multicomponent oxide melt. Part 1. Theoretical principles

A model is proposed for the formation of metallic phase when gaseous reducing agent is bubbled through multicomponent oxide melt. The model includes the following stages: the formation of bubbles when gas is injected in the melt; the reduction of metal at the surface of the bubbles and its concentration in droplet form at the rear of the bubble; motion of the bubble–droplet system in a direction determined by the ratio of the uplift forces on the bubble and the gravitational forces on the droplet; entrainment of the droplets to the surface; and coalescence of the droplets and their descent on reaching a size such that the gravitational forces exceed the sum of the hydrostatic collision forces and the surface tension forces. Equations are presented for estimating the size of the gas bubble and the droplet moving in oxide melt without decrease in size; the direction of motion of the bubble–droplet system; its rate of ascent or descent; and the conditions in which the bubble–droplet system breaks down. The factors responsible for separation of the bubble and the droplet are identified: the surface properties of the oxide melt and the metallic melts and their interphase characteristics. By adjusting these parameters, the formation of metallic phase at the bottom of the vessel may be regulated.     

Composition and Mobility of Ionic Ensembles in Slags for Steel Refining in the Ladle–Furnace Unit

High-lime synthetic slags for refining steels in the ladle–furnace unit are investigated. The content of the slag mixtures is as follows: 60 wt % CaO, 7 and 8 wt % MgO, 7–23 wt % Al₂O₃, and 9–18 wt % SiO₂, with additions of 8 wt % CaF₃ and 5–15 wt % Na₂O. Polymer theory is used to calculate the composition of the anionic subsystem in the slag melts. The log-mean polymerization constants K _p ^* for multicomponent melts are calculated from the known polymerization constants in binary systems. It is found that K _p ^* ≈ 10^–3–10^–2 in the range 1500–1600°C. In that range, the melt’s degree of polymerization is 3 × 10^–4–8 × 10^–3. In the most polymerized melt, the ionic content of the dimers Si₂O ₇ ^6- and Al₂O ₇ ^8- is no more than 0.1 and 1.5% of the values for the corresponding monomers. Therefore, we assume, with an error of about 2%, that the structural units of the anionic subsystem are monomers AlO ₄ ^5- and SiO ₄ ^4- simple O^2– and F^– ions (slag 7). The cationic subsystem consists of Ca²⁺, Mg²⁺, Na⁺, and Al³⁺ ions in octahedral coordination with oxygen (less than 3% of all the Al atoms). In all the melts, the concentrations of free oxygen ions O^2– and Ca²⁺ ions are similar. In half the cases, the content of O^2– ions is greater than the content of Ca²⁺ ions. The mean mobility U and self-diffusion coefficient D for all the cations are calculated from data for the electrical conductivity and the density. With increase in temperature from 1500 to 1600°C, U and D increase by 50 and 60%, respectively, in all the slags. With increase in the mutual substitution of the components in the slag mixtures M = n(Na₂O, CaF₂)/n(Al₂O₃ + SiO₂), mol/mol, at 1600°C, U increases from 1.14 × 10^–8 to 1.46 × 10^–8 m²/(V s) for slags 1–6 (0 ≤ M ≤ 1.1) and from 1.01 × 10^–8 to 1.66 × 10^–8 m²/(V s) for slags 7–10 (0.25 ≤ M ≤ 0.65). Correspondingly, D increases from 9.2 × 10^–10 to 12.8 × 10^–10 m²/s for slags 1–6 and from 8.2 × 10^–10 to 14.3 × 10^–10 m²/s for slags 7–10. The temperature dependence of U and D may be approximated by an Arrhenius equation with activation energies E _U and E _D . With increase in M in the given ranges, E _U declines from 146 to 100 kJ/mol (slags 1–6) and from 124.5 to 109 kJ/mol (slags 7–10). Likewise, E _D declines from 159 to 116.5 kJ/mol (slags 1–6) and from 139.5 to 124 kJ/mol (slags 7–10). The mean values of E _U and E _D correlate with the mean distance between the cations in the melts. On the basis of the proposed alternative model of the conductivity, the O^2– ions may also transfer electric charge. Preliminary estimates show that the oxygen transport number at 1600°C may exceed 0.1 in some slags.     

Regularities of Metallurgical Reactions of Ti1 –n$${\text{Me}}_{n}^{{\text{V}}}$$C0.5N0.5 Carbonitrides with the Ni–Mo Melt

The influence of alloying TiC_0.5N_0.5 carbonitride by transition metals of Group V (V, Nb, and Ta) on the contact interaction mechanism with the Ni–25%Mo melt (T = 1450°C, τ = 1 h, rarefaction is 5 × 10^–2 Pa) is systematically studied by X-ray spectral microanalysis and scanning electron microscopy for the first time. It is established that the dissolution of single-type Ti_1 –n\({\text{Me}}_{n}^{{\text{V}}}\)C_0.5N_0.5 carbonitrides (n = 0.05) is an incongruent process (alloying metal and carbon preferentially transfer into the melt), and the relative rate and degree of incongruence of the dissolution process of carbonitrides in a series of alloying metals V–Nb–Ta vary nonmonotonically. An explanation for the discovered effects is proposed. The causal-effect relation between the initial composition of Ti_0.95\({\text{Me}}_{{0.05}}^{{\text{V}}}\)C_0.5N_0.5 carbonitride (the grade of the alloying metal) and composition of the Ti_{1 – n – m}Mo_n\({\text{Me}}_{m}^{{\text{V}}}\)C_x K-phase that is precipitated from the melt upon system cooling is analyzed. It is shown that the factor determining the composition of the forming K-phase is the ΔT factor (the degree of exceeding crystallization temperatures of carbide eutectics Ni/Me^VC over the crystallization temperature of the Ni/Mo₂C eutectic that is the lowest melting in these systems). The conclusion is argued that the interrelation between the initial carbonitride composition and the composition of the K-phase is a consequence of a microinhomogeneous structure of metallic alloys. It is shown that this interrelation is rather common and manifests itself in all studied systems irrespective of the type of alloying Group V metal and presence or absence of molybdenum in the melt.     

Oxidation of Aluminum Melts with Rare-Earth Metals

Thermogravimetry studies show that the oxidation of aluminum–rare-earth metal (R) melts obeys a parabolic law. The true oxidation rate of the melts is on the order of 10^–4–10^–3 kg/(m² s). In the Al–R systems, the minimum oxidation rate corresponds to the compositions of intermetallic compounds. The oxidation rate of a melt is shown to increase with temperature. It is found by IRS (infrared spectroscopy) and XRD (X-ray diffraction) that the melt oxidation products consist of γ-Al₂O₃, R₂O₃ (R = La, Ce, Pr, Nd, Y, Sc), CeO₂, and rare-earth metal monoaluminates RAlO₃ (CeAlO₃, LaAlO₃, NdAlO₃).     

Solubility of oxygen in Fe–Co melts containing titanium

Solutions of oxygen in Fe–Co melts containing titanium are subjected to thermodynamic analysis. The first step is to determine the equilibrium reaction constants of titanium and oxygen, the activity coefficients at infinite dilution, and the interaction parameters in melts of different composition at 1873 K. With increase in cobalt content, the equilibrium reaction constants of titanium and oxygen decline from iron (logK(FeO · TiO₂) =–7.194; logK(TiO₂) =–6.125; logK(Ti₃O₅) =–16.793; logK(Ti₂O₃) =–10.224) to cobalt (logK(CoO · TiO₂) =–8.580; logK(TiO₅) =–7.625; logK(Ti₃O₅) =–20.073; logK(Ti₂O₃) =–12.005). The titanium concentrations at the equilibrium points between the oxide phases (Fe, Co)O · TiO₂, TiO₂, Ti₃O₅, and Ti₂O₃ are determined. The titanium content at the equilibrium point (Fe, Co)O · TiO₂ ? TiO₂ decreases from 1.0 × 10^–4% Ti in iron to 1.9 × 10^–6% Ti in cobalt. The titanium content at the equilibrium point TiO₂?Ti₃O₅ increases from 0.0011% Ti in iron to 0.0095% Ti in cobalt. The titanium content at the equilibrium point Ti₃O₅ ? Ti₂O₃ decreases from 0.181%Ti in iron to 1.570% Ti in cobalt. The solubility of oxygen in the given melts is calculated as a function of the cobalt and titanium content. The deoxidizing ability of titanium decline with increase in Co content to 20% and then rise at higher Co content. In iron and its alloys with 20% and 40% Co, the deoxidizing ability of titanium are practically the same. The solubility curves of oxygen in iron-cobalt melts containing titanium pass through a minimum, whose position shifts to lower Ti content with increase in the Co content. Further addition of titanium increases the oxygen content in the melt. With higher Co content in the melt, the oxygen content in the melt increases more sharply beyond the minimum, as further titanium is added.     

Formation of metallic phase on reducing-gas injection in multicomponent oxide melt. Part 2. Density and surface properties

The density and surface tension of melts of ferronickel (0–100% Ni) and oxidized nickel ore are measured by the sessile-drop method, as well as the interface tension at their boundary in the temperature range 1550–1750°C. The composition of the nickel ore is as follows: 14.8 wt % Fetot, 7.1 wt % FeO, 13.2 wt % Fe₂O₃, 1.4 wt % CaO, 16.2 wt % MgO, 54.5 wt % SiO₂, 4.8 wt % Al₂O₃, 1.5 wt % NiO, and 1.2 wt % Cr₂O₃. In the given temperature range, the density of the alloys varies from 7700 to 6900 kg/m³; the surface tension from 1770 to 1570 mJ/m²; the interface tension from 1650 to 1450 mJ/m², the density of the oxide melt from 2250 to 1750 kg/m³; and its surface tension from 310 to 290 mJ/m². The results are in good agreement with literature data. Functional relationships of the density, surface tension, and interphase tension with the melt temperature and composition are derived. The dependence of the alloy density on the temperature and nickel content corresponds to a first-order equation. The temperature dependence of the surface tension and interphase tension is similar, whereas the dependence on the nickel content corresponds to a second-order equation. The density and surface tension of the oxide melt depend linearly on the temperature. The results may be used to describe the formation of metallic phase when carbon monoxide is bubbled into oxide melt.     

Thermodynamics of oxygen solutions in nickel melts containing aluminum and titanium

Thermodynamic analysis of oxygen solutions in nickel melt shows that, as aluminum and titanium are added to the melt, the solubility of oxygen decreases. However, after reaching 0.205% Al and 0.565% Ti, the oxygen concentration in the melt begins to rise with increase in the Al and Ti content. The minimum oxygen concentrations in the reduction of nickel melt by aluminum (1.44 × 10^–4% O) and titanium (2.98 × 10^–4% O) are determined. On that basis, we may propose the optimal approach to alloying nickel melts with aluminum and titanium. First, the melt is reduced by adding sufficient aluminum to minimize the oxygen concentration in the melt (~0.2% Al). Then the oxide formed is removed, so as to prevent repeated oxidation of the melt. Finally, the melt is alloyed with aluminum and titanium to obtain the required alloy composition.     

Evaluation of Thermal Stability of Multilayered Nanostructured Coatings Based on Analysis of Diffusion Mobility of Components of the Layers

The thermal stability of multilayered nanostructured coatings is evaluated by analyzing the diffusion mobility of layer components. The possibility of increasing the thermal stability of multilayered coatings based on mutually soluble Ti–Al–N and Cr–N layers due to the introduction of an additional barrier layer based on Zr–N into a multilayered nanostructure is investigated in detail. Calculated diffusivities of basic metallic elements of the coating into corresponding nitride layers upon heating in a temperature range of 800–1000°C evidence the absence of noticeable diffusion spread of layer boundaries in the presence of the Zr–N-based barrier layer. For example, their values lower upon its introduction (it is found at t = 1000°C, cm²/s: D_Cr/TiN = 5 × 10^–17, D_cr/ZrN = 2 × 10¹⁸, \({D_{Ti/C{r_2}N}}\) = 9 × 10^–18, and D_Ti/ZrN = 3 × 10^–18). The physicomechanical properties of coatings do not vary upon their vacuum annealing at t < 900°C; however, they noticeably lower with a further increase in temperature due to the degradation of a multilayered coating structure during annealing.     

Dephosphorization Kinetics between Bloated Metal Droplets and Slag Containing FeO: The Influence of CO Bubbles on the Mass Transfer of Phosphorus in the Metal

Dephosphorization kinetics of bloated metal droplets was investigated in the temperature range from 1813 K to 1913 K (1540 °C to 1640 °C). The experimental results showed that the overall mass transfer coefficient, \( {k_{\text{o}}} \), decreased with increasing temperature because of decreasing phosphorus partition ratio, \( {L_{\text{P}}} \). It was also found that the mass transfer coefficient for phosphorus in the metal, \( {k_{\text{m}}} \), had the highest value at the lowest temperature [i.e., 1813 K (1540 °C)] because the formation of smaller CO bubbles increased the rate of surface renewal, leading to faster mass transport. Meanwhile, metal droplets without carbon were also employed to study the effect of decarburization on dephosphorization. The results show that although decarburization lowers the driving force significantly, \( {k_{\text{m}}} \) (6.2 × 10^?2 cm/s) for a carbon containing droplet is two orders of magnitude higher than that for carbon free droplets (5.3 × 10^?4 cm/s) because of the stirring effect provided by CO bubbles. This stirring offers a faster surface renewal rate, which surpasses the loss of driving force and then leads to a faster dephosphorization rate.     

Thermodynamic description of the interaction processes in the Cu–Ce–O system in the temperature range 1100–1300°C

A thermodynamic simulation and an experimental study of the interaction between cerium and oxygen in liquid copper have been performed. The thermodynamic analysis of the interaction processes in the Cu–Ce–O system is carried out using the technique of constructing the surface of solubility of components in a metal in the temperature range 1100–1300°C. As a result of simulation, data on changes in the Gibbs energy ΔG _T ° and the equilibrium constants of formation of cerium oxides Ce₂O₃ and CeO₂ from the components of a copper-based metallic melt are obtained. The first-order interaction parameters (according to Wagner) of cerium and oxygen dissolved in liquid copper, namely, e _Ce ^Ce, e _O ^Ce, and e _Ce ^O, are evaluated. Experimental studies of the Cu–Ce–O system have been performed. The morphological features, the size, and the composition of nonmetallic inclusions formed as a result of interaction in the Cu–Ce–O system are studied using scanning electron microscopy and electron-probe microanalysis.     

Thermodynamics of carbon and oxygen solutions in manganese melts

The thermodynamics of carbon and oxygen solutions in manganese melts is studied. An equation for the temperature dependence of the activity coefficient of carbon in liquid manganese is obtained (γ _C(Mn) ⁰ = ?1.5966 + (1.0735 × 10^?3)T). The temperature dependence of the Gibbs energy of the reaction of carbon dissolved in liquid manganese with the oxygen of manganese oxide is shown to be described by the equation ΔG _T ⁰ = 375264 ? 184.66T(J/mol). This reaction can noticeably be developed depending on the carbon content at temperatures of 1700–1800°C. The deoxidation ability of carbon in manganese melts is shown to be much lower than that in iron and nickel melts due to the higher affinity of manganese to both oxygen and carbon. Although the deoxidation ability of carbon in manganese melts increases with temperature, the process develops at rather high carbon contents in all cases.     

Microstructural Analysis of Multi-phase Ultra-Thin Oxide Overgrowth on Al–Mg Alloy by High Resolution Transmission Electron Microscopy

High-resolution transmission electron microscopy analyses are carried out to understand the microstructure of the ultra-thin oxide-film grown on a (native) amorphous Al₂O₃-coated Al-0.8 at.% Mg alloy substrate at T = 600 K for t = 2 h and at pO₂ of 1 × 10^?2 Pa. This oxide-film is found to be non-uniformly thick with thicknesses varying from 1.50 to 4.60 nm. Occasionally, this oxide is found to diffuse into the Al–Mg alloy substrate, forming oxide thicknesses up to 10.5 nm. Overall, this oxide-film is found to consist of a mixed amorphous, (poly) crystalline and an intermediate amorphous-to-crystalline transition regions, with crystalline regions consisting mostly of MgO and the diffused oxide regions into the Al–Mg alloy substrate coated with γ-Al₂O₃. These observations are then compared with the experimental results obtained using angle-resolved X-ray Photoelectron Spectroscopy analysis and thermodynamic predictions for the growth of an ultra-thin oxide-film due to dry, thermal oxidation of Al–Mg alloy substrates.     

Phase Equilibria of a Pb–Sb–Ag Alloy during Vacuum Distillation

The saturated vapor pressures of lead, silver, and antimony are calculated for Pb–Ag and Pb–Sb alloys at temperatures of 1073–1773 and 823–1073 K, respectively. High ratios (p_Sb*/p_Pb*) × 10³ = 15.0–1.8 and p_Pb*/p_Ag* = 2.9 × 10³–74.0 create theoretical possibilities for sequential selective separation of these metals by vacuum distillation, during which the vapor is enriched in antimony and then lead and the liquid is enriched in silver. For vapor–liquid equilibrium (VLE) diagram, the lever rule (the rule of line segments) can be used to predict the amounts of substance, residue, and sublimate at a given temperature. Calculations of the ternary-alloy parameters can be performed by the Wilson equation using parameters obtained for the binary systems. The fractional Gibbs free energy (–ΔG_Pb/Sb/Ag = (2.1–22.4)/(1.9–25.5)/(18.1–50.0)), the enthalpy (ΔH_Pb/Sb/Ag = ±(0.2–16.9)/–(0.2–1.8)/(105–140) J/(K mol)), and the entropy (ΔS_Pb/Sb/Ag = (2.4–13.4)/(2.2–15.2)/(20.8–30.0) J/(K mol)) of the components of the Pb–Sb–Ag melts are calculated. As the fractions of metals in a starting alloy increase, the thermodynamic parameters decrease. The negative and positive values of the enthalpy indicate exothermic and endothermic processes in the melt during distillation of components, respectively. The calculated and experimental thermodynamic parameters are shown to agree satisfactorily: the standard relative deviation is 1.9% and the root-mean square deviation is 0.1 kJ/mol.     

Influence of alloying the TiC<Subscript>0.5</Subscript>N<Subscript>0.5</Subscript> carbonitride with zirconium on an interaction mechanism with the Ni–Mo melt

The influence of alloying the TiC_0.5N_0.5 titanium carbonitride with zirconium on the mechanism and kinetic features of the contact interaction with the Ni–25%Mo melt (t = 1450°C, rarefaction 5 × 10^–2 Pa) is investigated for the first time by electron probe microanalysis and scanning electron microscopy. The main effects of the modifying influence of zirconium on the dissolution, phase formation, and structure formation processes which occur during the interaction of the Ti_1–n Zr _n C_0.5N_0.5 carbonitride (n = 0.05 and 0.20) with the Ni–Mo melt are revealed and the factors promoting their manifestation are analyzed. The practical absence of zirconium and nitrogen in the composition of the K-phase (the Ti_{1 – n} Mo _n C _x metastable solid solution, where n ≤ 0.65 and x = 0.7 ± 0.1) is confirmed experimentally. It is shown that the zirconiumenriched Ti_0.80Zr_0.20C_0.5N_0.5 carbonitride cannot be recommended as a refractory component of cermet because of the limitations of the chemical character.     

Electrocapillary motion of copper and nickel matte droplets on fayalite-based slag surfaces

The electrocapillary motion of Cu₂S and Ni₃S₂ droplets on the surface of fayalite-based slags under 50% Ar-CO atmosphere has been studied for the effects of droplet size, temperature, electric field strength. Cu content m Cu₂S-FeS droplets, Ni content in Ni₃S₂ FeS droplets and slag composition. The copper matte droplets migrate to the anode (positive electrode) while the nickel matte droplets migrate to the cathode (negative electrode). Typical speeds encountered are of the order of 0.05–0.80 cm/s (Cu) and 0.16–0.62 cm^−s (Ni) with droplet diameters between 0.10 and 0.28 cm, applied potentials between 0.17 and 2.0 V/cm (Cu) and 0.75 and 3.3 V cm (Ni) and for temperatures between 1473 and 1573 K. The migration rate appears to be independent of droplet size for droplet diameters between 0.10 and 0.28 cm, but it increases with applied potential field and temperature.The effects of matte and slag contents on the migratory behavior are complex. As the Cu content in the Cu₂S-FeS matte droplet increases above 40% Cu. the migration rates also increase. Below 40% Cu matte grade, the migration rates are not significantly different. As the Ni content in the Ni₃S₂-FeS matte droplet increases, the migration rates decrease. These migration rates are also affected by the slag composition. As the Cu and Ni matte droplets migrate in opposite directions under the influence of the electric field, electrocapillary phenomena may be used to enhance metal recovery in slag cleaning operations using electric furnaces.     

Rheological Properties of the EP742-ID Alloy in the Context of Integrated Computational Materials Science and Engineering: Part I. Results of Experimental Investigations

Rheological properties of the EP742-ID alloy are investigated during high-temperature compression tests of cylindrical samples with various ratios of homological initial sizes of diameter and height (d₀/h₀). It is shown by the results of tests in ranges of temperature t = 1000–1150°C and initial deformation rates ε?₀= 3 × 10^–2–3 × 10^–4 s^–1 that an increase in the compression flow tension manifests itself at all temperatures and deformation rates with an increase in ratio d₀/h₀ with the linear dependence on the magnitude of ε?₀ and ratio d₀/h₀. The procedure of recalculating characteristics of the deformation resistance for the specified ratio of homological parameters is proposed. An increase in the compression flow tension is associated with an increase in the rigidity coefficient of the samples and their specific contact surfaces. The temperature dependence of the apparent activation energy of the plastic deformation (Q_def) of the alloy and its relation with the phase composition and running conditions of the dynamic recrystallization of the γ-solid solution are established. The magnitude of Q_def in temperature conditions of the development onset of the dynamic recrystallization of the γ-solid solution (1000–1050°C) is 959 kJ/mol for samples with d₀/h₀ = 0.75. The largest values of Q_def for the samples with d₀/h₀ = 0.75 equal to 1248 and 1790 kJ/mol are observed in a temperature region of the intense dissolution and coagulation of the grain-boundary γ′-phase (1050–1100°C). The value of Q_def for the samples with d₀/h₀ = 3.0 increases to 2277 kJ/mol in this temperature range. The apparent activation energy of the plastic deformation lowers to 869 kJ/mol in the temperature region of the γ-solid solution with grain-boundary primary and secondary carbides (1100–1150°C). The results of compression of alloy samples during single and repeated sequential loading with various durations of pauses between deformation actions are presented. It is shown that no metadynamic recrystallization occurs in the experimental conditions in the γ + γ′-region, while it runs slowly in the γ-region.     

Regularities of the contact interaction of double carbides (Ti<Subscript>1 –<Emphasis Type="Italic">n</Emphasis></Subscript>Me<Stack><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><Superscript>IV,V</Superscript></Stack>)C with the Ni–Mo melt

Regularities of dissolution, phase formation, and structure formation during the interaction of double carbides (Ti_1–n Me _n ^{IV, V} )C with the Ni–25%Mo melt (t = 1450°C, τ = 1 h, vacuum 10^–1 Pa) are investigated for the first time by electron probe microanalysis and scanning electron microscopy. The role of each alloying metal in the composition and microstructure formation of studied compositions is revealed. It is established that Group IV alloying metals (Zr and Hf) almost do not enter the composition of the forming K-phase (carbide Ti_1–n Mo _n C _x ); therefore, its composition is independent of their concentration in double carbide. In contrast with zirconium and hafnium, Group V alloying metals (V and Nb) actively participate in the formation of the K-phase; however, the dependences of the composition of the K-phase and metallic matrix on the vanadium and niobium content are the opposite in this case. An interpretation of the causes of these distinctions is proposed.     

The influence of the capillary pressure in nanobubbles on their attachment to particles during froth flotation: Part IV. Spreading nanobubbles as natural fractals

The specific property of nanobubbles with spontaneous spreading over the solid hydrophobic particle substrate adhered to them, which is caused by a high capillary gas pressure in nanobubbles (P _c > 10⁶ N/m²), is considered. The computational principle of bubble spreading curves is considered and parameter X characterizing the intensity is introduced. Dependence X(a) (a is the bubble base diameter) is presented by a bimodal curve, which confirms that the nanobubble spreading is energetically provided by two sequentially acting independent sources. The first source is conditioned by the reduction (approximately by 11%) of the nanobubble curvilinear surface area at the initial spreading stage, and the second source is conditioned by the work of gas expansion caused by the drop of P _c when the bubble is spreading. Parameter X is characterized by a considerably larger slope of dependence X(a) at the first spreading stage compared to the second one. It now turned out that the revealed property, which determines the efficiency of industrial flotation processes in past, finds prospects for application again after its recognition. Since it manifests itself in a limited range of bubble sizes, it is proposed to attribute it to the proper or natural fractal by analogy with the Brownian motion, which manifests itself in a definite range of particle sizes. The influence of the surface activity of flotation reagents on the shape of bubble spreading curves is shown.