Corresponding states correlation for the thermal conductivity of molten alkali halides

The principle of corresponding states has been applied to the thermal-conductivity data for molten alkali halides which have been obtained by recent forced Rayleigh scattering measurements. The theory, which was developed by Harada et al. for the transport properties of uni-univalent molten salts, is based on the fluctuation-dissipation theorem with the pair interaction between ions composed of core repulsive and Coulombic potentials. Four characteristic parameters specific to each salt have been used to reduce the thermal conductivity and temperature. It has been found that the thermal conductivity of molten alkali halides is adequately correlated by the corresponding-states correlation ( ^* 1/T ^*) within experimental accuracy. By employing the correlation, the thermal conductivity of molten alkali fluorides, which could not be measured by the forced Rayleigh scattering method, is predicted.Paper dedicated to Professor Joseph Kestin.     

Self-diffusion at the melting point: From H2 and N2 to liquid metals

A nominal lower bound to the mean free diffusion time at the melting point T _m was obtained earlier which provided a factor-two type estimate for self-diffusion coefficients of the alkali halides, alkali metals, eight other metals, and Ar. The argument was based on the classical Uncertainty Principle applied to the solid crystal, whereby maximum-frequency phonons lose validity as collective excitations and degenerate into aperiodic, single-particle diffusive motion at the melting point. Because of the short time scale of this motion, the perfect-gas diffusion equation and true mass can be used to obtain the self-diffusion coefficient in the Debye approximation to the phonon spectrum. This result for the self-diffusion coefficient also yields the scale factor that determines the order of magnitude of liquid self-diffusion coefficients, which has long been an open question. The earlier theory is summarized and clarified, and the results extended to the more complex molecular liquids H₂ and N₂. It is also demonstrated that combining Lindemann's melting law with the perfect-gas diffusion equation estimate yields a well-known empirical expression for liquid-metal self-diffusion at T _m. Validity of the self-diffusion estimate over a melting temperature range from 14 to more than 1300 K and over a wide variety of crystals provides strong confirmation for the existence of the specialized diffusive motion at the melting point, as well as confirmation of a relation between the phonon spectrum of the solid crystal and diffusive motion in the melt.     

Experimental determination of the thermal diffusivity of molten alkali halides by the forced Rayleigh scattering method. II. Molten NaBr,KBr, RbBr,and CsBr

This is a companion to an earlier paper (on molten alkali metal chlorides) which gives experimental results for the thermal diffusivity of four molten alkali metal bromides: NaBr, KBr, RbBr, and CsBr. The measurements were performed with a forced Rayleigh scattering instrument at temperatures up to 1326 K. The overall uncertainty in the measured thermal diffusivity is estimated to be ±3 to ±11%, depending on the measured salts. The results converted to thermal conductivity show one of the smallest values among other earlier experimental data obtained mainly by the steady-state methods. It is also found that the temperature dependence of the thermal conductivity is weakly negative.     

Experimental determination of the thermal diffusivity of molten alkali halides by the forced Rayleigh scattering method. III. molten NaI,KI, RbI,and CsI

This paper is an addendum to two previous papers which contained data on the thermal diffusivity of molten alkali metal chlorides and bromides. The present salts are alkali metal iodides: NaI, KI, RbI, and CsI. The measurements were performed utilizing the forced Rayleigh scattering method at temperatures up to 1234 K. The accuracy of the reported data is estimated to be ±5 to ±10%. It is again found that our data show one of the smallest values and weakly negative temperature dependencies.     

Experimental determination of the thermal diffusivity of molten alkali halides by the forced Rayleigh scattering method. I. Molten LiCl,NaCl, KCl,RbCl, and CsCl

As a series of experimental determinations of the thermal diffusivity of molten alkali halides, this paper describes measurements on five molten alkali metal chlorides (LiCl, NaCl, KCl, RbCl, and CsCl) in the temperature range up to 1440 K by the forced Rayleigh scattering method. K₂Cr₂O₇ is employed as a dye substance to color the transparent molten salts. The accuracy is estimated to be ± 4 to ±11 % depending on the measured salts. In comparison with the present results converted into thermal conductivity, most of the previous experimental data obtained by steady-state methods show larger values, up to about five times, which may be due to the systematic error caused by the presence of convection and radiation. It is found that the thermal conductivity of these series of molten alkali metal chlorides decreases with increasing molecular weight, and their temperature coefficients are weakly negative.     

Vibrational entropy of polyatomic solids: Metal carbides,metal borides,and alkali halides

It is shown that in the high temperature vibrational entropy of polyatomic solids, the influence of the atomic masses is described by an effective mass , where c _i is the concentration of mass M _i . This mass effect explains almost all of the differences between TiC, ZrC, and HfC in the recommended entropy data of Hultgren et al. (1973). Analogous results are found for VC, NbC, and TaC and for TiB₂, ZrB₂, and HfB₂. Mass differences also explain a major part of the measured entropy differences between alkali halides AB, with A=Li, Na, or K and B=F, Cl, Br, or I. Finally, we discuss different methods, including one used in the JANAF Thermochemical Tables, to estimate standard entropies from data on chemically related compounds.     

Experimental determination of the volume change of pure salts and salt mixtures at their melting point

Measurements of the melting temperature as a function of pressure for some pure salts (NaNO₃, LiOH) and salt mixtures (Na₂SO₄-NaCl, NaNO₂-NaNO₃- KNO₃, Li₂SO₄-NaCl, NaCl-MgCl₂) are reported. The experiments were performed up to 250 MPa. From the melting curves, the slopes (dP/dT) _m ⁰ at atmospheric pressure were determined. Finally, using the Clapeyron equation, with the enthalpy of melting taken from the literature, the volume change on melting at atmospheric pressure was determined for each compound.     

Reduction of lattice thermal conductivity by point defects at intermediate temperatures

The lattice thermal conductivity is reduced by point defects because they scatter phonons. An analytic expression can be derived only in the limit of high temperatures; at lower temperatures one must have recourse to numerical calculations. Because the conductivity is due mainly to phonons of low frequencies when point-defect scattering is strong, the high-temperature approximation can be used at temperatures above half the Debye temperature. Numerical calculations, using the Ge-Si system as an example, show that the error incurred by using the high-temperature approximation is less than 10%.     

Correlation of dense fluid self-diffusion,shear viscosity,and thermal conductivity coefficients

A general procedure has been developed for simultaneously fitting any two of the self-diffusion coefficient, the viscosity (as the fluidity), and the thermal conductivity (as its reciprocal) as Dymond reduced coefficients, (D*,*,*), to a simple function of the volume and the temperature for dense fluids. For example,D*=₁+₂ V _r/(1+₃,/V _r), whereV _r=V[1-₁(T–T _r)-₂(T–T _r)²].T _r is any convenient temperature, here 273.15 K. AsV _r is common to the two properties, only eight coefficients, _j and _k are required. Such reduced transport-coefficient curves are geometrically similar for members of groups of closely related compounds. The procedure has been extended to give family curves for such groups by fitting a pair of transport properties for three substances from the group in a single regression. Overall, fewer coefficients are required than for other schemes in the literature, and the fitting functions used are simpler. The curves so constructed can be used for the correlation of data obtained from different sources, as well as interpolation and, to a limited extent, extrapolation. A comparison is made for a number of compotmd groups between simultaneous fits of the pairs (D– ), (D–), and (–)Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Electrical Conductance, Density, and Viscosity in Mixtures of Alkali-Metal Halides and Glycerol

This paper presents the results of density, viscosity, and electrical conductivity measurements for glycerol solutions of some alkali-metal halides at 25°C. The apparent and partial molar volumes (V and V ₁) in mixtures of KCl, NaCl, KBr, KI, and glycerol were calculated from the density data. The Debye–Hückel limiting law was assumed to be valid at low concentrations, and values of the molar volumes at infinite dilution were obtained by extrapolation. The viscosity data were analyzed by means of the Jones–Dole equation. The Kaminsky method, based on reference electrolyte (on B_K+ = B_Cl-), was used in glycerol. Viscosity B-coefficients are compared with those calculated applying existing theories based on the model of hard-charged spheres moving in a solvent continuum. Specific agreement between theory and experiment was not generally good. The electrical conductivities of solutions of salts (KCl, NaCl, KBr, NaBr, NaI, KI, and LiBr) in glycerol have been measured at three concentrations (approximately 0.01, 0.1, and 0.3 M) at 25°C. Values of the molar conductivity at infinite dilution were obtained by extrapolation using the conductance equation of Onsager. Using previously measured transference numbers for KCl and NaCl in glycerol, values of limiting Walden products for the individual alkali-metal and halide ions in glycerol have been derived and compared with those in aqueous and other alcohol solutions.     

原位膨胀法制备PMMA/EG复合材料及其导电和流变性能的研究

使用低温可膨胀石墨,通过"原位膨胀-机械剥离"的方法制备了PMMA/EG复合材料,研究了可膨胀石墨含量对其电导率的影响。电导率、SEM、动态流变等测试表明膨胀后的石墨片层在树脂基体中分散良好;从10~20 phr开始,石墨鳞片相互接触形成网络结构显著地提高电导率,最高达12个数量级。采用原位膨胀法可以制备逾渗阈值较小的导电复合材料,填充少量低温可膨胀石墨就可以大幅度提高PMMA电导率。     

Improving the performance of the boundary element method with time-dependent fundamental solutions by the use of a wavelet expansion in the time domain

The object of this paper is a wavelet-based formulation of the boundary element method (BEM) for diffusion problems, characterized by time-dependent fundamental solution. While the BEM is a well known and often used technique, its time-dependent formulation for diffusion problems is very rarely used in practical applications, due to the high computational cost which characterizes it. Here, a new formulation is proposed, which, through the use of the wavelet expansion of the time behaviour of the boundary elements, is characterized by a lower CPU time consumption when compared with the standard BEM diffusion formulation. The problem to be solved is transformed into an algebraic system (of higher dimension) and its solution gives the time domain behaviour of the desired quantities; in this way, the time stepping procedure is avoided. Together with the formulation, the analysis of the computational cost, and two examples are given in the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Viscosity and thermal conductivity of binary eutectics of alkali metals in the vapor phase

Values calculated for the dynamic viscosity and thermal conductivity are presented for vapors of binary eutectics of the alkali metals at temperatures from 800 to 1500 K and at pressures from 100 to 8×10⁵ Pa. Data are presented for the vapors of the systems Li + Na, Na + Rb, Na + Cs, K + Rb, K + Cs, Na + K, and Rb + Cs. The values of the concentrations of the five components in the vapor phase of each binary eutectic are also presented. The accuracy of the calculated viscosities is estimated to be within 4–5% and the accuracy of the calculated thermal conductivities is estimated to be within 8–10%.     

Thermal conductivity and thermal expansion of stainless steels D9 and HT9

Renewed interest in the use of metallic fuel in a liquid-metal fast breeder reactor has prompted study of the thermodynamic and transport properties of fuel and cladding materials. Two stainless steels are of particular interest because of their good performance under irradiation. These are D9, an austenitic steel, and HT9, a ferritic steel. Thermal conductivity and thermal expansion data for these cladding alloys are of particular interest in assessing in-reactor behavior. These two properties were measured for the two steels at temperatures to 1200 K. Of particular interest is the influence on these properties of a phase transition in HT9.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Experimental study of thermal conductivity of solid and liquid phases at the phase transition

An experimental method for the determination of the thermal conductivity of a pure material at its freezing melting point has been developed. In the present investigation. this method is discussed further by studying the effective thermal conductivity of the frozen as well as the thawed state of a wet porous material. and of solid and liquid benzene at the interface. The method involves the study of the transient propagation of the freezing or melting zone through the specimen as well as the steady state of the freezing melting process. The method makes use of the heat of transition as the heat flow, and it enables the interlace to act as a heat transfer surface, thus incorporating realistic features of the phase change process. Compared with data from the literature. the experimental results for benzene agree within 2% for the solid phase and within 3% for the liquid phase. when some precautions are made to avoid free convection. The experimental effective thermal conductivity of the packed bed is compared with data from a numerical analysis: the results agree within 4%, indicating that the method is applicable also for measurements on heterogeneous materials.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.On leave from Central South University of Technology, 410083 Changsha, P.R. China.     

Effect of package size and temperature on the volume expansion of flexible permeable packages of Kimchi,a Korean fermented vegetable

The effect of package size and temperature on package volume expansion was investigated when P71197, a high CO₂ permeability film of amorphous nylon laminate structure, was applied to packaging kimchi, a Korean ethnic fermented vegetable. The volume expansion, after an initial lag period, rapidly reached a maximum and then either decreased or stayed constant. A higher temperature and a larger package caused greater volume expansion within the experimental time span. Based on the criterion of ≤0.8 ml/g as a tolerable volume change, the appropriate window of package size and temperature has been suggested. The expanded volume was found to consist mainly of CO₂ produced from kimchi, resulting in higher CO₂ concentrations for higher temperatures and larger package sizes. The effect of package size on the volume expansion and gas composition can be explained by the differences in the ratio of surface area to filled weight among the packages. The effect of storage temperature can be explained by the difference in activation energy between CO₂ production from the kimchi and gas permeation through the film. Copyright © 2001 John Wiley & Sons, Ltd.     

Theoretical considerations of the effects of rapid heating of solids on their apparent thermal properties

The conditions are investigated for thermal properties to change from their normal values when solids are heated very rapidly. The properties considered are specific heat, thermal expansion, thermal conductivity, and thermal diffusivity. Over times which may be as long as a microsecond, the heated solid is unable to expand: the appropriate values of specific heat and thermal conductivity are then those at constant volume rather than constant pressure. In those alloys where thermal equilibrium requires diffusion, its establishment is delayed, and if solids do not have time to expand, the diffusion coefficient is reduced. For heating times below nanoseconds, the electrons and the lattice may be at different temperatures, particularly if the energy is initially imparted to the electrons. The temperature of the electron gas of metals may then approach the degenerary temperature. The apparent specific heat of a decoupled system departs from the steady-state value in a manner which depends on how temperature is measured. In such a decoupled system the concepts of thermal conductivity and thermal diffusivity must be used with care.Paper presented at the First Workshop on Subsecond Thermophysics, June 20–21, 1988, Gaithersburg, Maryland, U.S.A.