Thermophysical properties of liquid metals

The viscosities of liquid metals vary by a factor of about 10 between the empty metals, and the full metals, and typical values are 0.54 x 10 2 poise for liquid potassium, and 4.1 x 10 2 poise for liquid copper, at their respective melting points. Empty metals are those in which the ionic radius is small compared to the metallic radius, and full metals are those in which the ionic radius is approximately the same as the metallic radius. The process was described by Andrade as an activated process following an Arrhenius expression 

In connection with the earlier consideration of diffusion in liquids using the Stokes-Einstein equation, it can be concluded that the temperature dependence of the diffusion coefficient on the temperature should be T(exp(—Qvls/RT)) according to this equation, if the activation energy for viscous flow is included. 

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It should be noted that it is difficult to obtain models that can accurately predict thermal contact resistance and rapid solidification parameters, in addition to the difficulties in obtaining thermophysical properties of liquid metals/alloys, especially refractory metals/al-loys. These make the precise numerical modeling of flattening processes of molten metal droplets extremely difficult. Therefore, experimental studies are required. However, the scaling of the experimental results for millimeter-sized droplets to micrometer-sized droplets under rapid solidification conditions seems to be questionable if not impossible,13901 while experimental studies of micrometer-sized droplets under rapid solidification conditions are very difficult, and only inconclusive, sparse and scattered data are available. 

Not much is known about the thermophysical properties of liquid metals, especially the transport properties such as chemical and thermal diffusivities. The existing data are sparse and the scatter makes it difficult to make an accurate determination of the temperature dependency of these properties. This situation was the motivation for Froberg s experiment on Space-lab-1 in which he measured the temperature dependence of the self-diffusion of Sn from 240°C to 1250°C. He found that the diffusion coefficients were 30-50% lower than the accepted values and seemed to follow a 7 dependence as opposed to the Arrhenius behavior observed in solid state diffusion. ... 

Known existing experiments The first us of a microsecond device for reporting the thermophysical properties of liquid metals were Lebedev et al. in 1971 [9] from the Russian In tute of High Temperature. Similar e eriments have been constructed and used ftiroughout ftie world by different groups, namely Martynyuk and Gerrero 1972 [23] at Patrice Lumumba University in Moscow, Russia, Henry et al. 1972 [24] and later continued by Gathers et al. 

To summarize the above, the thermophysical properties of liquid metals and gases experience only minor linear changes with increasing temperature. However, all the properties of water at pseudocritical conditions go through very rapid changes. The basic properties of He, CO2, and water are summarized in Table A2.5. Basic properties of Pb, molten salt (FLiNaK), and Na are summarized in Table A2.6. 

The thermophysical properties of liquid metals and gases show only small linear changes with temperamre. However, all the properties of SCW go through very rapid changes in the pseudocritical range. 

Tepper, F., A. Murchison, J. Zelenak, and F. Roehlich, 1964, Thermophysical Properties of Rubidium and Cesium, Proc. 1963 High Temperature Liquid Metal Technology Meeting Vol. 1, 26-65, US AEC Rep. ORNL-3605. (5)... 

Fl, -, 2 8, Metier Diagram for Sodium Drawn from the Vargaftik et al. values in Ohse, R. W Handbook of Thermodynamic and Transport Froperties of Alkali Metals Blackwel Set Pubs. Oxford, UK, 1985. These values are identical with those of Vargaftik, N. B Handbook of Thermophysical Properties of Gases and Liquids, Moscow, 197 and the Hemisphere translation, p. 19. An apparent discontinuity exists between the superheat values and the saturation values not reproduced here. For a Mol her diagram in f.p.s. units from 0.1 to 150 psia, 1500 to 2700°R, see Fig. 3-36, p. 3-232 of the 6th edition of this handbook. An extensive review oi properties of the solid and the saturated liquid was given by Alcock, C. B., Chase, M. W et al., /. Phys. Chem. Ref Data, 23(3), 385-497,... 

DYNAMIC PULSE CALORIMETRY - THERMOPHYSICAL PROPERTIES OF SOLID AND LIQUID METALS AND ALLOYS... 

The Prandtl number depends on the thermophysical properties of the fluid only. Typical values of the Prandtl number are 0.001-0.03 for liquid metals, 0.2-1 for gases, 1-10 for water. 

Frenkel J1 (1926) Thermal movement in solid and liquid bodies. Z Phys 35 652-669 Wagner C, Schottky W (1930) Theory of controlled mixed phases. Z phys Chem 11 163-210 Kraftmakher Y (1998) Equilibrium vacancies and thermophysical properties of metals. Phys Rep 299 80-188... 

Kaschnitz, E., Pottlacher, G., and Jager, H. (1992) A new microsecond pulse-heating system to investigate thermophysical properties of solid and liquid metals. Int. ]. Thermophys., 13, 699-710. 

The NFE theory describes a simple metal as a collection of ions that are weakly coupled through the electron gas. The potential energy is volume-dependent but is independent of the position of the electrons. This is valid for both solids and dense liquids. At densities well above that of the MNM transition, we can use effective pair potentials and find the thermophysical properties of metallic liquids with the thermodynamic variational methods usually employed in theoretical treatments of normal insulating liquids. One approach is a variational method based on hard sphere reference systems (Shimoji, 1977 Ashcroft and Stroud, 1978). The electron system is assumed to be a nearly-free-electron gas in which electrons interact weakly with the ions via a suitable pseudopotential. It is also assumed that the Helmholtz free energy per atom can be expressed in terms of the following contributions ... 

Mercury has the lowest known critical temperature (1478 °C) of any fluid metal. It is therefore particularly attractive to experimentalists. Mercury is also considerably less corrosive than many metals, especially the alkali metals discussed in the preceding chapter. These relatively favorable circumstances permit precise measurement of the electrical, optical, magnetic, and thermophysical properties of fluid mercury. With care, one can control temperatures accurately enough to determine the asymptotic behavior of physical properties as the liquid-vapor critical point is approached. Such truly critical data are especially valuable for exploring the relationship between the liquid-vapor and MNM transitions. Of the expanded metals exhibiting MNM transitions, mercury is therefore the most extensively investigated. It is the only expanded divalent metal whose critical region has proven to be experimentally accessible. 

The Prandtl number depends on the thermophysical properties of the fluid only. Typical values of the Prandtl number are 0.001-0.03 for liquid metals, 0.2-1 for gases, 1-10 for water, 5-50 for organic liquids and 50 - 2000 for oils. The Prandlt number depends on the bulk temperature of the fluid since the viscosity is a strong function of temperature for this reason, especially in very narrow microchannels in which the viscous heating effects are not negligible (see viscous heating and viscous dissipation), the Prandlt number cannot be considered as a constant along the channel. 

The solution of the gas flow and temperature fields in the nearnozzle region (as described in the previous subsection), along with process parameters, thermophysical properties, and atomizer geometry parameters, were used as inputs for this liquid metal breakup model to calculate the liquid film and sheet characteristics, primary and secondary breakup, as well as droplet dynamics and cooling. The trajectories and temperatures of droplets were calculated until the onset of secondary breakup, the onset of solidification, or the attainment of the computational domain boundary. This procedure was repeated for all droplet size classes. Finally, the droplets were numerically sieved and the droplet size distribution was determined. 

This technique based on a hot wire thermal probe with AC excitation and 3 CO lock-in detection. Since the principle and procedures of the technique have been described in details previously [51] only a brief description is given here. We consider a thermal probe (ThP) consisting of a metallic wire of length 21 and radius r immersed in a liquid sample, acting simultaneously as a heater and as a thermometer. The sample and probe thermophysical properties are the volume specific heat pc and the thermal conductivity k, with the respective subscripts (5) and (p). The wire is excited by ac current... 

With the development of tools and techniques for computer-assisted calculations and simulations, knowledge of thermophysical properties at elevated temperatures up into the liquid phase has become even more important for the metal-working industry and related fields. Advances in computer-based simulations allow simulations of heat transport, solidification shrinkage, residual stress, or even predictions of microstructures, to name a few. 

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