Calculating models on surface tension of RE_2O_3-Mg O-SiO_2(RE=La, Nd, Sm, Gd and Y) melts

A thermodynamic model was developed for determining the surface tension of RE2O3-MgO-SiO2(RE=La, Nd, Sm, Gd and Y) melts considering the ionic radii of the components and Butler's equation. The temperature and composition dependence of the surface tensions in molten RE2O3-MgO-SiO2 slag systems was reproduced by the present model using surface tensions and molar volumes of pure oxides, as well as the anionic and cationic radii of the melt components. The iso-surface tension lines of La2O3-MgO-SiO2 slag melt at 1873 K were calculated and the effects of slag composition on the surface tension were also investigated. The surface tensions of La2O3, Gd2O3, Nd2O3 and Y2O3 at 1873 K were evaluated as 686, 677, 664 and 541 m N/m, respectively. The surface tension of pure rare earth oxide melts linearly decreases with increasing cationic field strength, except for Y2O3 oxide, while Y2O3 has a much weaker surface tension. The evaluated results of the surface tension show good agreements with literature data, and the mean deviation of the present model is found to be 1.05% at 1873 K.

Blast furnace ironmaking process with super high TiO_(2) in the slag:Density and surface tension of the slag

Aiming at the process of smelting ultra-high(>80%)or even full vanadium titanomagnetite in blast furnace,we are conducting a series of works on physics character of high TiO_(2) bearing blast furnace slag(BFS)for slag optimization.This work discussed the density and surface tension of high TiO_(2) bearing BFS using the Archimedean principle and the maximum bubble pressure method,respectively.The influence of TiO_(2) content and the MgO/CaO mass ratio on the density and surface tension of CaO-SiO_(2)-TiO_(2)-MgO-Al_(2)O_(3)slags were investigated Results indicated that the density of slags decreased with the TiO_(2) content increasing from 20wt%to 30wt%,but it increased slightly with the MgO/CaO mass ratio increasing from 0.32 to 0.73.In view of silicate network structure,the density and the degree of polymerization(DOP)of network structure have a consistent trend.The addition of TiO_(2) reduced(Q^(3))^(2)/(Q^(2)) ratio(Q^(2) and Q^(3) represent structural unit with bridge oxygen number of 2 and 3,respectively)and then decreased DOP,which led to the decrease of slag density.The surface tension of CaO-SiO_(2)-TiO_(2)-MgO-Al_(2)O_(3) slags decreased dramatically with the TiO_(2) content increasing from 20wt%to 30wt%.Conversely,it increased with the MgO/CaO mass ratio increasing from 0.32 to 0.73.Furthermore,the iso-surface tension lines were obtained under 1723 K using the Tanaka developed model in view of Butler formula.It may be useful for slag optimization of ultra-high proportion(>80%)or even full vanadium titanomagnetite under BF smelting.

Calculation Model for Surface Tension of Slag Melt

Based on the coexistence theory of slag melt structure and Butler’s equation,a new calculation model has been proposed for the calculation of surface tension of slag melt.This model establishes a specific correlation between surface tension and mass action concentrations(activities) in the melt and on its surface on the basis of inner and surficial structures of slag melt.Calculated surface tensions of CaO-SiOand MnO-SiOslag melts are consistent with those measured.Furthermore,iso-surface tension lines of CaO-MnO-SiOslag melt have also been calculated.

Densities and surface tensions of ionic liquids/sulfuric acid binary mixtures

The densities and surface tensions of [Bmim][TFO]/H2SO4, [Hmim][TFO]/H2SO4 and [Omim][TFO]/H2SO4 binary mixtures were measured by pycnometer and Wilhelmy plate method respectively. The results show that densities and surface tensions of the mixtures decreased monotonously with increasing temperatures and increasing ionic liquid （IL） molar fraction. IL with longer alkyl side-chain length brings a lower density and a smaller surface tension to the ILs/H2SO4 binary mixtures. The densities and surface tensions of the mixtures are fitted well by Jouyban-Acree （JAM） model and LWW model respectively. Redlich-Kister （R-K）equation and modified Redlich-Kister （R-K） equation describe the excess molar volumes and excess surface tensions of the mixtures well respectively. Adding a small amount of ILs （XIL 〈 0.1 ） into sulfuric acid brings an obvious decrease to the density and the surface tension. The results imply that the densities and surface tensions of IL5/H2SO4 binary mixtures can be modulated by changing the IL dosage or tailoring the IL structure.

Caffeine Crystallization Induction Time Measurements Using Laser Scattering Technique and Correlation to Surface Tension in Water and Ethanol

Caffeine nucleation induction times were measured at 30 °C and 40 °C in water and ethanol solvents employing laser light absorption technique. Supersaturation concentrations and liquid/solid phase surface tensions were calculated from crystallization induction times using classic homogeneous nucleation theory. Induction time and surface tension decreased at higher temperature.

Surface tension of lithium bromide aqueous solution/ammonia with additives and nano-particles

In order to investigate the effect of additives and nano-particle on the surface tensions of lithium bromide(Li Br) aqueous solution/ammonia, many experiments were carried out based on Wilhelmy plate method. Firstly, the surface tension of Li Br aqueous solution with 1-octanol was measured and then the comparison between the measured results and previous experimental results was given to verify the measuring accuracy. Some new additives, such as cationic surfactants cetyltrimethyl ammonium chloride(CTAC), and cetyltrimethyl ammonium bromide(CTAB) were chosen in the experiments. The experimental results show that CTAC and CTAB can obviously reduce the surface tension of Li Br aqueous solution/ammonia. In addition, it is found that nano-particles cannot remarkably decrease the surface tension of Li Br aqueous solution/ammonia. However, the mixed addition of additives and nano-particles can remarkably affect the surface tension of Li Br aqueous solution/ammonia. That is to say, additives play more important role in reducing the surface tension of Li Br aqueous solution/ammonia. But nano-particles may enhance the heat transfer in the absorption refrigeration process.

Phase field investigation on the initial planar instability with surface tension anisotropy during directional solidification of binary alloys

Phase field investigation reveals that the stability of the planar interface is related to the anisotropic intensity of surface tension and the misorientation of preferred crystallographic orientation with respect to the heat flow direction. The large anisotropic intensity may compete to determine the stability of the planar interface. The destabilizing effect or the stabilizing effect depends on the misorientation. Moreover, the interface morphology of initial instability is also affected by the surface tension anisotropy.

SURFACE TENSION OF MOLTEN IF STEEL CONTAINING Ti AND ITS INTERFACIAL PROPERTIES WITH SOLID ALUMINA

Surface tension of molten IF steel containing Ti and contact angle between the liquid steel and solid alumina were measured with sessile droplet method under Ar gas atmosphere at 1500, 1575 and 1600°C. The results show that titanium decreases the surface tension of the molten IF steel and the contact angle. The interfacial tension between the molten IF steel containing Ti and solid alumina decreases with increase in titanium content. The work of adhesion between molten IF steel containing Ti and solid alumina decreases slightly at 1550°C, but increases at 1600°C with increasing titanium content. It can be deduced that fine bubbles and fine alumina inclusions are easily entrapped in solidifying interface for IF steel containing Ti.

Surface tension of liquid Au-Bi-Sn alloys

The surface tension of a promising lead-free solder Au-Bi-Sn alloys was investigated both by the sessile-drop method and calculation. Experimental measurements were carried out for two cross-sections with the constant gold to bismuth ration of 1:1 and 1:2. For all the investigated compositions, decrease of the surface tension is observed with increasing temperature. Meanwhile, the surface tension values were also calculated based on Butler’s equation, with using the newest research on thermodynamics data of Au-Bi-Sn ternary system. Compared with the experimental results, a good agreement was obtained.

Heat Transfer in a Liquid-Solid Circulating Fluidized Bed Reactor with Low Surface Tension Media

Heat transfer characteristics between the immersed heater and the bed content were studied in the riser of a liquid-solid circulating fluidized bed, whose diameter and height were 0.102 m (ID) and 2.5 m, respectively. Effects of liquid velocity, particle size, surface tension of liquid phase and solid circulation rate on the overall heat transfer coefficient were examined. The heat transfer coefficient increased with increasing particle size or solid circulation rate due to the higher potential of particles to contact with the heater surface and promote turbulence near the heater surface. The value of heat transfer coefficient increased gradually with increase in the surface tension of liquid phase, due to the slight increase of solid holdup. The heat transfer coefficient increased with the liquid velocity even in the higher range, due to the solid circulation prevented the decrease in solid holdup, in contrast to that in the conventional liquid-solid fluidized beds. The values of heat transfer coefficient were well correlated in terms of dimensionless groups as well as operating variables.

Roughness-dependent wetting and surface tension of molten lead on alumina

Surface roughness is an important factor that affects the wetting of molten metal on ceramics.The effect of surface roughness of the alumina substrate on the contact angle,contact diameter,drop height and surface tension of molten lead was investigated in the temperature range of 923-1123 K.The microstructure of the lead/substrate interface was observed by SEM.The surface free energy of alumina substrates was calculated by the geometrical average method.When the surface roughness of the substrate increased from 0.092 to 2.23μm,the surface free energy increased gradually,ranging from 13.356 to 39.998 mJ/m^(2).The contact diameter of lead droplets decreased from 9.111 to 7.19 mm.The lead drop height increased from 3.41 to 3.85 mm.The contact angle increased from 113.05°to 137.15°.Moreover,the surface depression of the alumina substrate was filled with lead,and no obvious change was observed.The results demonstrated that the wetting of lead drop on alumina substrates was consistent with the Wenzel state.

Estimation of surface tension of organic compounds using quantitative structure-property relationship

A novel quantitative structure-property relationship （QSPR） model for estimating the solution surface tension of 92 organic compounds at 20℃ was developed based on newly introduced atom-type topological indices. The data set contained non-polar and polar liquids, and saturated and unsaturated compounds. The regression analysis shows that excellent result is obtained with multiple linear regression. The predictive power of the proposed model was discussed using the leave-one-out （LOO） cross-validated （CV） method. The correlation coefficient （R） and the leave-one-out cross-validation correlation coefficient （Rcv） of multiple linear regression model are 0.991 4 and 0.991 3, respectively. The new model gives the average absolute relative deviation of 1.81% for 92 substances. The result demonstrates that novel topological indices based on the equilibrium electro-negativity of atom and the relative bond length are useful model parameters for QSPR analysis of compounds.

Surface Tension Calculation of Undercooled Alloys

Based on the Butler equation and extrapolated thermodynamic data of undercooled alloys from those of liquid stable alloys, a method for surface tension calculation of undercooled alloys is proposed. The surface tensions of liquid stable and undercooled Ni-Cu (x(Ni)=0.42) and Ni-Fe (x(Ni)=0.3 and 0.7) alloys are calculated using STCBE (Surface Tension Calculation based on Butler Equation) program. The agreement between calculated values and experimental data is good enough, and the temperature dependence of the surface tension can be reasonable down to 150-200 K under the liquid temperature of the alloys.

Modeling of Surface Tension and Viscosity for Non-electrolyte Systems by Means of the Equation of State for Square-well Chain Fluids with Variable Interaction Range

The equation of state(EOS)for square-well chain fluid with variable range(SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids(ILs).A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures.The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation(AAD)of 0.36%.A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring’s rate theory of viscosity and the SWCF-VR EOS.The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases.The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT,vapor-liquid equilibrium,caloric properties,surface tension,and viscosity.

3D numerical investigation of effects of density and surface tension on mixing time in bottom-blown gas-stirred ladles

In molten phase metallurgical processes,mixing via gas injection has a vital role in obtaining a homogeneous product.The efficiency of mixing depends on operational variables such as gas flow rate and slag height as well as physical properties of the molten phases.A numerical simulation is conducted to study the above parameters in the flow behavior of a bottom-blown bath.The molten metal and the slag are modeled by water and oil,respectively.The numerical results,particularly the mixing time,are validated against experimental data.The results show that mixing time increases as the slag height increases and decreases as the density of the slag material increases.The mixing time decreases with an increase in the density of the primary phase;however,it increases as the surface tension between air and water increases.A case with properties close to a real molten metal is also modeled.The performance of the system is influenced by the momentum rather than the dissipative forces.Thus,the effect of the density of the molten phase on the mixing process is more pronounced compared to the effect of the surface tension between the air and the molten phase.

A Surface Tension Model for Liquid Mixtures Based on NRTL Equation

A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59% and 1.55% respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.

Key Role of Some Specific Occupied Molecular Orbitals of Short Chain n-Alkanes in Their Surface Tension and Reaction Rate Constants with Hydroxyl Radicals: DFT Study

Basing on the DFT calculations we propose the new theoretical model which describes both the surface tension σ of the short chain n-alkanes at their normal boiling points and their reaction rate constants with hydroxyl radicals OH• (at 297 ± 2 K) on the basis of their molecular orbital electronic characteristics. It has been shown that intermolecular dispersion attraction within the surface liquid monolayer of these compounds, as well as their reaction rate constants k with OH• radicals are determined by the energies Eorb of the specific occupied molecular orbitals which are the same in the determination of both the above physico-chemical characteristics of the studied n-alkanes. The received regression equations confirm the theoretically found dependences between the quantities of σ and k and the module |Eorb|. For the compounds under study this fact indicates the key role of their electronic structure particularities in determination of both the physical (surface tension) and the chemical (reaction rate constants) properties.

A Home-made Simple Set-up for Measurement of Electrochemical Surface Tension Spectrum on a Mercury Drop Electrode

A setup for recording surface tension curves at a mercury drop during potential scanning is designed based on photo-sensitive detection system. Surface tension spectrum at Hg drop can be recorded by voltam0metdc study. A Yb（Ⅲ）-NO2 catalytic reduction system was used for characterization. The simple, sensitive technique can be expected to provide fresh information on molecular interactions at electrode surfaces.

Mechanical effects of circular liquid inclusions inside soft matrix:role of internal pressure change and surface tension

The mechanical effects of dilute liquid inclusions on the solid-liquid composite are explored,based on an analytical circular inclusion model incorporating the internal pressure change of the liquid and the surface tension of the interface.Several simple explicit dependences of the stress field and effective stiffness on the bulk modulus and the size of the liquid,the surface tension,and Poisson’s ratio of the matrix are derived.The results show that the stresses in the matrix are reduced,and the stiffness of the solid-liquid composite is enhanced with the consideration of either the surface tension or the internal pressure change.Particularly,the effective Young’s modulus predicted by the present model for either soft or stiff matrices agrees well with the known experimental data.In addition,according to the theoretical results,it is possible to stiffen a soft solid by pressured gas with the presence of the surface tension of the solid-gas interface.