The surface tension of liquid silicon at high temperature

The measurement of the surface tension of liquid silicon has a long history with many results but no general agreement between them. Two values at the melting temperature are cited in reviews (749 and 827 mN/m [N. Eustathopoulos, E. Ricci, B. Drevet, Note Technique DEM No. 97/58, CEA, 1997]) but there are few arguments to determine the correct one. In the present study, new data for the surface tension obtained with the analysis of characteristic frequencies of a levitating drop are presented. The effect of oxygen and nitrogen are also considered. These data are compared with former data obtained with contactless techniques. The most recent surface tension values obtained with drop weights ranging on two orders of magnitude and environments of different natures (argon, hydrogen and vacuum) show excellent agreement (within a 1.5% margin) at temperatures between 1350 K and 2400 K. The comparison of these data to others obtained with different techniques, reveal a good agreement, except those obtained with the sessile drop technique on some supports like BN, SiO₂ and MgO. However, these special cases may be connected with the reactivity of silicon with these supports.     

A molecular dynamics simulation on surface tension of liquid Ni and Cu

Molecular dynamics simulations of liquid transition metals Ni and Cu have been performed with the tight-binding potential model. The surface tensions of the liquid metals at different temperatures are evaluated using both methods of calculating the work of cohesion and of using the mechanical expression for the surface stress. The calculated surface tension data are compared with available experimental values. The simulated results for Ni are in good agreement with experiment, but those for Cu show about 10–20% underestimation. Comparing with the mechanical method, the data of surface tension calculated using the method of cohesive work show remarkable dependence on temperature, and the estimated temperature coefficients of liquid Ni and Cu are consistent with the experimental data.     

A new variant for measuring the surface tension of liquid metals and alloys by the oscillating drop method

The theoretical background of the oscillating drop technique for measuring surface tension is briefly presented and the different analysis procedures are cited. A new method is described for obtaining oscillation frequencies by fast fourier transformation (FFT) of the pyrometer voltage signals from temperature measurements at the top of the levitated sample. The results on the first experiments on liquid nickel are in a good agreement with the hterature data.Paper presented at the Fourth International Workshop on Subsecond Thermophysics. June 27–29, 1995, Köln, Germany.     

Theoretical temperature-dependence surface tension of pure liquid gold

A calculation, based on statistical thermodynamics, of the surface tension of pure liquid gold, in the temperature range 1337-1653 K, is described. The calculated surface tension of liquid gold was found to be 1100 mJ/m² that agrees well with the reported experimental value (1149 mJ/m²). Results reveal that below 1480 K, the surface excess entropy changes by one order of magnitude (0.0151 mJ/m² K) as compared to the value above this temperature (0.1773 mJ/m² K), and thus predicting a structural changes at the surface of pure molten gold at high temperature.     

A dynamic technique for measuring surface tension at high temperatures in a microgravity environment

The feasibility of a dynamic technique for measuring surface tension of liquid metals at high temperatures in a microgravity environment is considered. The basic method involves heating a tubular specimen resistively from ambient temperature through its melting point in about l s by passing an electrical current pulse through it, while simultaneously recording the pertinent experimental quantities. Static equilibrium for the molten specimen may be achieved (at least for a short time) in a microgravity environment by splitting the current after it passes through the specimen tube and returning a fraction along the tube axis and the remaining fraction outside the specimen. Adjustments to the current split enable a balance between the magnetic and surface tension forces acting on the specimen. Values for surface tension are determined from measurements of the equilibrium dimensions of the molten specimen tube, and the magnitudes of the currents. Preliminary rapid melting experiments, performed during microgravity simulations with NASA's KC-135 aircraft, yield a value for the surface tension of copper at its melting point which is in reasonable agreement with literature data.Paper presented at the First Workshop on Subsecond Thermophysics, June 20–21, 1988, Gaithersburg, Maryland, U.S.A.Formerly National Bureau of Standards     

The determination of surface tension at elevated temperatures by drop image analysis

The advantages of image analysis as applied to surface tension measurements by the sessile drop technique are discussed. It is demonstrated that valuable effective improvements of dimensional resolution are obtained. Errors in surface tension arising from various unavoidable sources such as chemical reactions or optical distortions are shown to be the main difficulties in applying the sessile drop technique at high temperature. This suggests a limiting spatial resolution of the digitizer beyond which no further improvements to the accuracy of the surface tension results are possible.

The technique has been applied to determine the surface tension of liquid Cu, Bi and Ag as well as a series of sodium borosilicate glasses.     

The surface tension of liquid aluminium-based alloys

In a systematic study, the surface tensions of the binary alloys Al–Fe and Al–Ni were investigated over a wide temperature and concentration range using electromagnetic levitation and the oscillating drop technique. Surface tensions were derived from the oscillation frequencies applying the formalism of Cummings and Blackburn. Temperature was measured by single-color pyrometry. Of particular interest in these alloys are melts corresponding to compositions of intermetallic phases, because potential ordering phenomena may influence all thermophysical properties. In both systems, an increase of the surface tension is observed at such concentrations. On the basis of partial excess Gibbs enthalpies, surface tensions can be calculated via the Butler equation and compared with experimental results. The agreement with our experimental data depends crucially on the quality of the thermodynamic potentials used. In addition, phenomenological models are also discussed, which describe the general trend correctly.     

A generalized equation for the surface tension of refrigerants

This work presents a literature survey of the available data of the experimental surface tension data for refrigerants. The experimental data were collected for the following pure fluids: R11, R12, R13, R13B1, R14, R21, R22, R23, R32, R113, R114, R115, R123, R123a, R124, R125, R134, R134a, R141b, R143a, R152a, R218, R225ca, R225cb, R227ea, R236ea, R236fa, R245ca, R245fa, R365mfc, R846, and R1234yf. Experimental data were regressed with the most reliable semi-empirical correlating methods based on the corresponding state theory existing in the literature.To minimize the deviation between the predicted data and the experimental data and to find the optimal equation for data representation, a design of experiment procedure coupled with the Yates algorithm and the steepest ascent method was adopted. Finally, the influence of the dipole moment on the refrigerant surface tension prediction was discussed and a new equation to represent the surface tension of refrigerants was presented.     

The surface tension meniscus of liquid helium

A technique is described for calculating the shape of the surface tension meniscus at a vertical wall, in the presence of Van der Waals forces. The method of analytic continuation is used to compute a solution of the relevant differential equation. Results (believed accurate to better than 0.5%) are presented for He³ and for He⁴ at a variety of film flow rates. It is found that the shape of the classical meniscus remains unaltered over most of its length, but it is displaced horizontally relative to the wall by a flow dependent amount. The results are contrasted with those from a previous calculation.     

A quasi-containerless pendant drop method for surface tension measurements on molten metals and alloys

A quasi-containerles pendant drop method for measuring the surface tension of molten metals and alloys is being developed. The technique involves melting the end of a high-purity metal rod by bombardment with an electron beam to form a pendant drop under ultra-high-vacuum conditions to minimize surface contamination. The magnified image of the drop is captured from a high-resolution CCD camera. The digitized image of the drop is then analyzed to compute the surface tension. A computer program has been developed that reads the pixel intensities from a graphics file containing the digital image. The code searches for the edge of the drop along rows and columns of pixels and stores the edge coordinates in an array. It then computes an optimized theoretical drop shape by solving the Young-Lapface differential equation from which the quantity of surface tension is deduced. This technique has been demonstrated with the surface tension measurement of molten zirconium metal.Paper presented at the Twelfth Symposium on Thermophysical Properties. June 19–24, 1994, Boulder, Colorado, U.S.A.     

强反射复杂表面随机缺陷自动检测系统

系统采用分光照明方式,设计均匀散射光源,通过图像增强预处理,灰度分析,图像二值化,特征提取与图像识别, 自动分选出表面有缺陷的工件。硬软件包括:光学系统;接收系统;控制电路和Visual C 、汇编语言程序等。系统有效解决了强反射光、复杂表面和随机缺陷带来的检测困难,检测精度可达97.3%。     

Automatic technique for measuring interfacial properties of liquid metals

Abstract

An improved technique for calculating the interfacial characteristics of liquids in the sessile drop configuration has been developed. The procedure, based on grabbing of the observed shape of the sessile drop followed by computer analysis, has acceptable accuracy and good productivity.

MST/3017     

A unified model for the cohesive enthalpy, critical temperature, surface tension and volume thermal expansion coefficient of liquid metals of bcc, fcc and hcp crystals

First the cohesive enthalpy of pure liquid metals is modeled, based on experimental critical temperatures of alkali metals. The cohesive enthalpies are scaled to the melting points of pure metals. The temperature coefficient of cohesive enthalpy is the heat capacity of the liquid metal. The surface tension and its temperature coefficient for pure liquid metals are modeled through the excess surface enthalpy, excess surface entropy and molar surface area supposing that the outer two surface layers of liquid metals are similar to the {1 1 1} plane of fcc crystals. The volumetric thermal expansion coefficient of liquid metals is scaled to the ratio of the heat capacity and cohesion enthalpy. From known values of melting point, heat capacity and molar volume the following calculated properties of liquid metals are tabulated: (i) cohesive enthalpy at melting point, (ii) cohesive energy of the solid metal at 0 K, (iii) critical temperature, (iv) surface tension at melting point, (v) volume thermal expansion coefficient, and (vi) temperature coefficient of surface tension. The present models are valid only for liquid metals of bcc, fcc or hcp crystals as only their structure and nature of bonding are similar enough to be treated together.     

Investigation of technique for measuring liquid volume under micro-gravity conditions

Measurement of liquid volume under the micro-gravity condition is an important aspect of space technology. In an attempt to create an effective and low-cost measurement system, a Helmholtz resonance technique was applied. Two different liquids were tested. We used water and liquid nitrogen as test liquids, the latter to confirm the applicability of this measurement technique to cryogens. It was found that the measurement technique using Helmholtz resonance is applicable under micro-gravity conditions. However, it was also found that obtaining accurate velocity of sound is important for the measurement. The measurement of spatial temperature distribution in the container is necessary to apply this measurement technique to cryogens because the velocity of sound has strong temperature dependency.     

Surface tension of pure liquid bismuth and its temperature dependence: Theoretical calculations

A theoretical method for calculating the surface tension of liquid metals as a function of temperature is proposed. A mathematical equation, based on statistical thermodynamics, is applied to calculate the surface tension of pure liquid bismuth, in the temperature range 545-620 K. The calculated surface tension of liquid bismuth was found to be 388 mJ/m², which is in excellent agreement with the reported experimental values (374-417 mJ/m²). The surface tension of bismuth decreases linearly with temperature, confirming a negative slope.     

On finite element modelling of surface tension: Variational formulation and applications – Part II: Dynamic problems

In Part I, a finite element model of surface tension has been discussed and used to solve some quasi-static problems. The quasi-static analysis is often required to find not only the initial shape of the liquid but also the static equilibrium state of a liquid body before a dynamic analysis can be carried out. In general, natural and industrial processes in which surface tension force is dominant are of dynamic nature. In this second part of this work, the dynamic effects will be included in the finite element model described in Part I.A fully Lagrangian finite element method is used to solve the free surface flow problem and Newtonian constitutive equations describing the fluid behaviour are approximated over a finite time interval. As a result the momentum equations are function of nodal position instead of velocities. The resulting ordinary differential equation is integrated using Newmark algorithm. To avoid overly distorted elements an adaptive remeshing strategy is adopted. The adaptive strategy employs a remeshing indicator based on viscous dissipation functional and incorporates an appropriate transfer operator.The validation of the model is performed by comparing the finite element solutions to available analytical solutions of a droplet oscillations and experimental results pertaining to stretching of a liquid bridge.     

An alternative process for refining dore liquid metals

A novel method for refining gold-containing ores is reported. The method is based on impingement of a controlled oxygen flow on the liquid metal so as to oxidize the impurities. The experiments were carried out both at laboratory scale and pilot-plant scale. The thermodynamics involved, discussed in the light of the experimental results, are quite complex. The oxidation rate of a specific impurity depends on interaction with other constituents of the system. Received: 28 November 1999 / Reviewed and accepted: 29 November 1999