Relations Between Transport Coefficients in Lennard–Jones Fluids and in Liquid Metals

Several simple approximate hard-sphere relations for transport coefficients are compared with the results of molecular dynamics (MD) simulations performed on Lennard–Jones (LJ) fluids. Typically the individual transport coefficients: self-diffusion coefficients, D, shear viscosity, _s, bulk viscosity, _B, and thermal conductivity, , agree within a factor of two of the exact results over the fluid and liquid parts of the phase diagram, which seems reasonable in view of the approximations involved in the models. We have also considered the ratio, /_s, and the product, D_s, for which simple analytic expressions exist in the hardsphere models. These two quantities also agree within a factor of two of the simulation values and hard sphere analytic expressions. Using time correlation functions, Tankeshwar has recently related the ratio /D to thermodynamic quantities, in particular, to the differences in specific heats, C _p – C _V, and to the isothermal compressibility, T. Using D and thermodynamic values taken solely from LJ MD simulations, his relation was tested and found to give typically better than ~20% agreement at liquid densities, deteriorating somewhat as density decreases into the gas phase. Finally liquid metals are considered. In this case, is dominated by its electronic contribution, which is related approximately to the electrical conductivity by the Wiedemann–Franz Law. Some theoretical results for the electrical conductivity of Na are referenced, which allow a semiquantitative understanding of the measured thermal conductivity of the liquid metal. Shear viscosity is also discussed and, following the work of Tosi, is found to be dominated by ionic contributions; Nevertheless, at the melting temperature of Na, a relation emerges between thermal conductivity, electrical resistivity and shear viscosity.     

Magnetic penetration depth measurements with the microstrip resonator technique

The microstrip resonator technique is a convenient way to sensitively measure the temperature dependence of the magnetic penetration depth (T) in superconducting thin films. Because the method relies on measuring the resonant frequency of a high-Q transmission line resonator at microwave frequencies, one can very precisely measure small changes in (T). This technique is applied to studying the low-temperature dependence of (T), since that is in principle a measure of the low-lying pair-breaking excitations of the superconductor. We find that the penetration depth in niobium films is consistent with the predictions of weak coupled BCS theory. The low-temperature dependence of (T) inc-axis YBa₂Cu₃O_7– films can be interpreted as either a weak exponential or as a power law. In addition, the measured value of (0) is found to be strongly dependent on the form of the temperature dependence for (T) used in fitting the data. Best fits over the entire temperature range are obtained with a BCS temperature dependence having values for 2(0)/k _BT_c strictly less than 3.5, consistent with our measurements of the temperature dependence of (T) at low temperatures in YBa₂Cu₃O_7– .     

The Thermal Conductivity and Thermal Diffusivity of Liquid n-Alkanes: C n H2n+2 (n=5 to 10) and Toluene

Experimental values of the thermal conductivity and the thermal diffusivity of six pure liquid n-alkanes (C _n H_2n+2; n=5 to 10) and toluene are presented in the temperature range of –20 to 70°C under atmospheric or saturation pressure. Measurements were made with the transient hot-wire method, and in the analysis, the temperatures T and T (associated with both and ) were used. In the present work, the values of thermal diffusivity were corrected by the factors k _f (=1.0076 to 0.9892) for data sets obtained with different configurations of the experiment, in which the factors were determined by reference to the thermal diffusivity of n-heptane [= _s/(c _p )_s] at 298.15 K calculated from the volumic heat capacity (c _p )_s as a reference material for heat capacity and the experimentally obtained thermal conductivity _s. The uncertainty of the data is estimated to be 0.48% for the thermal conductivity (absolutely measured) and about 1.8% for the thermal diffusivity (with a coverage factor of k _p =2; p=95%).     

Thermal diffusivity of inhomogeneous systems

The possibility of analyzing the nonsteady temperature fields of inhomogeneous systems using the quasi-homogeneous-body model is investigated.Notation t, t_I, t_i temperature of quasi-homogeneous body inhomogeneous system, and i-th component of system - a, , c thermal diffusivity and conductivity and volume specific heat of quasi-homogeneous body - a_{i i}, c_i same quantities for the i-th component - q heat flux - S, V system surface and volume - x, y coordinates - macrodimension of system - dimensionless temperature Fo=a/² - Bi=/ Fourier and Biot numbers - N number of plates - =h/ ratio of micro- and macrodimensions - _V, volumeaveraged and mean-square error of dimensionless-temperature determination - time - m_i i-th component concentration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 126–133, July, 1980.     

Thermal conductivity of hydrocarbons in the naphthene group under high pressures

The thermal conductivity of hydrocarbons in the naphthene group has been experimentally determined. An equation is now proposed for calculating the thermal conductivity over the given temperature and pressure ranges.Notation thermal conductivity - ₂₀ and ₃₀ values of the thermal conductivity at 20 and 30°C, respectively - t₀,P₀ thermal conductivity at t₀, p₀ - _t p thermal conductivity at temperature t and under pressure P - change in thermal conductivity - P pressure - P_melt melting pressure - P₀ atmospheric pressure - t₀ 20°C temperature - T, t temperature - T_cr critical temperature - temperature coefficient of thermal conductivity - ₂₀ temperature coefficient of density - density - ₂₀ density at 20°C - _cr critical density - M molar mass - =T/T_cr referred temperature - v specific volume - v₀ specific volume at 20°C - v change in specific volume - _{3 0} a coefficient - B (t) a function of the temperature - S a quadratic functional - W_i, weight of the i-th experimental point - _i error of the i-th experimental value of thermal conductivity - B _{y, =0.6} value of B (t) at T = 0.6T_cr - B = B (t)/B_{, =0.6} referred value of coefficient B (t) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 491–499, September, 1981.     

A method of determining the thermal conductivity of powdered and fibrous insulation as a function of filler gas pressure

An examination is made of the theoretical basis and implementation of a nonstationary method of rapid measurement of the thermal conductivity of powdered and fibrous insulation under conditions of monotonic change of filler gas pressure.Notation t temperature - ,a thermal conductivity and diffusivity of test material - k, k_a relative temperature coefficients of anda - thickness of test layer - x variable layer coordinate reckoned from shell - =(x), _c excess temperature of material at section x and of core over shell - b_c, b_v rate of cooling of core and of variation of volume-mean temperature of layer - c_c, c total heat capacity of core and material - f_s, F_c area of working surfaces of shell and core - d diameter of particles of bulk material - p material porosity - volume density of material     

Dependence of the contact heat conductivity of granular systems on the external load

An examination has been made of the dependence of the contact heat conductivity of granular systems on the external load. The calculation formulas proposed for contact heat conduction are applicable over a wide range of materials.Notation s_a area of actual contact of two particles in a granular material - _c conductivity of the contact between two particles - h_r height of a micro-roughness - _s thermal conductivity of the material of the particles - d=2r particle diameter - _c contact thermal conductivity of the granular material - p porosity of the system - S_a1, S_a2 area of contact of two particles in the freely poured state and under the action of a load - f thermal conductivity of the granular system in the freely poured state - () portion of the thermal conductivity of a granular material that depends on the external load - relative area of contact - s_n nominal area of contact of the two particles - external specific load - E modulus of elasticity of the particle material - E₀ effective modulus of elasticity of the granular material - k₁, k₂, k₃, k_m, k_b empirical coefficients     

Investigation of the thermophysical properties of fireclay ceramics in the temperature range 80°–1200° K

The thermal conductivity, diffusivity, and specific heat of fireclay ceramics have been investigated over a wide temperature range in various gases. A method of calculating the thermophysical properties of the materials is given, whose use is fully justified by experiment. A method is described of theoretically determining the thermophysical properties of ceramics in various gases on the basis of investigations of these materials in air.Notation _eff effective thermal conductivity of porous material - _sk thermal conductivity of skeleton - _c thermal conductivity of continuous phase of skeleton - _d thermal conductivity of dispersed phase of skeleton - V_d volume fractions of disperse phase of skeleton - P) volume porosity, h/L=f(P) [5] - c) Stefan-Boltzmann constant - T) absolute temperature, °K - d) pore diameter - a thermal diffusivity     

Relationship between thermal conductivity,speed of sound,and isobaric heat capacity of liquids

Using two liquids-water and toluene — as an example, the author determines the dependence of the coefficient of thermal conductivity on the speed of sound and isobaric molar heat capacity for high state parameters.Notation coefficient of thermal conductivity - u speed of sound - _S same for a saturated liquid - c isobaric molar heat capacity - density - p_s same, for a saturated liquid - p pressure - p_s same, for a saturated liquid - R gas constant - T absolute temperature - x coefficient of thermal activity - x _s same, for a saturated liquid - L, constants in Eqs. (1) and (2) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 311–314, August, 1980.     

Transport properties of helium near the liquid-vapor critical point. II. Thermal conductivity of a3He-4He mixture

Measurements of the thermal conductivity are reported for an 80%³He-20%⁴He mixture above the critical point along several isotherms and near-critical isochores, using the same techniques and apparatus described for a study of³He. Using again the assumption that the observed conductivity can be decomposed into a sum of a regular and a singular contribution _reg and _sing, it is shown that along two near-critical isochores, _sing diverges. In particular, along the isochore showing the largest at the phase transition, the divergence is nearly the same as for³He and can be roughly characterized by a simple power law (T-T_c)^– with 0.58. This observation is contrary to predictions that foresee _sing0 asT _c is approached. The relaxation times characterizing the attainment of steady state conditions after switching the heat flux on and off show a similar behaviour as a function of reduced temperature as do those for pure³He. This result might indicate a substantial coupling between concentration and entropy diffusion. In the Appendix, the correlation length for³He nearT _c is calculated from heat conductivity, viscosity, and specific heat data.Work supported by Grant DMR 8024056 of the National Science Foundation.     

Pressure dependence of T c for lead

The superconducting transition temperature T _c for Pb has been determined as a function of hydrostatic pressure up to 26 kbar. T _c is found to more closely follow a linear pressure dependence, with T _c/P = –(3.61 ± 0.05)× 10^–5K/bar, than a linear volume dependence, as previously reported. The volume dependence of the electron-phonon parameter derived from these measurements, d(ln )/d(ln V) = 4.2 ± 0.1, is in good agreement with theoretical calculations by Ott and Sorbello and by Carbotte and Vashishta. The variation of for larger volume changes is discussed.Supported by the Australian Research Grant Committee.     

On intrinsic and extrinsic effects in the surface impedance of cuprate superconductors

Surface impedance measurements in the normal and superconducting state are an excellent method to study conduction electron dynamics and extended defects. Electron dynamics show up most clearly in the relaxation range, i.e., for distances traveled in one rf periods= _F/ ( _F Fermi velocity) being smaller or of the order of the penetration depth and mean free pathl. For materials with _F10⁷ cm/sec the relaxation range is easily accessible forf0.1 THz. Then, in the normal state, relaxation defines the surface impedance with an intrinsic penetration depth _I approaching the London penetration depth _L andR _{I 0 L}/ 2 as surface resistance, allowing measurement of _L and relaxation time(T, ). In the superconducting state the photon interaction scales with _L/ _L=1/( _F dimension of Cooper pairs forl) and causes at low frequencies an absorption rate growing with, which is decreasing with _F/l. The rate increase proportional to turns to a decrease above 0.1 THz, which is accompanied by a decrease ofA with frequency which is stronger for large and small _F/l. These characteristic dependences allow measurement of material parameters, anisotropy, and dynamics of electrons, especially the relaxation rate. But presently, the rf surface impedanceZ is still shrinking with material improvements, which shows, clearly, that theZ=Z _I+Z _res is still dominated by extrinsic properties summarized inZ _res. We present evidence thatZ _res is due to the large leakage currentj _bl and the smallj _cJ of weak links where the latter destroys the intrinsic shielding from a _I-thin seam _J deep into the bulk. This causes rf residual lossesR _res( ₀)² _J ³ _bl/2.R _res stays finite atT-0 due to _bl(T0) _bl(j _bl) being amplified by ( _J/ _I)³>10³ as a weighting factor. The appropriate measure of weak links are the grain-boundary resistanceR _bn((0)) enhancing _JR _bn andR _resR _bn ² . Thus,Z _res is minimal for minimal extrapolated resistivity(T0).To identify the weak links as a new entity, the H-field dependence is most helpful, because at very low fieldsH _c 1J1/ _J Josephson fluxons penetrate into the weak links. These Josephson fluxons show negligible flux flow or flux creep, and enhanceZ _res by _J(H, T) . The measuredj _cJ(H, T) andj _bl values explainZ _res quantitatively as well as in temperature (a+T ⁿ ) (n1,T<T _c /2) and in field (b+H ⁿ ) (n1,H>H _c1J) dependence. The strength of the field dependencedZ _res/dHZ _res(H _c1J )/H _c2J(T) is not only a measure ofZ _res andH _c2J(T) but is crucial for nonlinear effects and (fluxon) noise also, which limit the performance of rf devices.     

Effect of sample density on magnetic penetration depth in YBaCuO ceramic superconductors

We have measured magnetic penetration depth(0) of high-T _c YBCO samples of different density by the cavity resonant frequency shift method at 10, 16.65, and 22.3 GHz microwave frequencies. The value of(0) at 10 GHz is found to decrease from 5850 Å to 2550 Å as the density of the sample increases from 4.4 to 5.3 g/cm³. The results of the frequency response of the penetration depth show a fairly constant value of(0) for all the three samples in the frequency range 10–22.3 GHz. The wide variation observed in the value of(0) for different density samples has been explained in terms of varying Josephson coupling strength in these ceramics.     

Electron-phonon coupling as a mechanism for high-temperature superconductivity

We have solved the Eliashberg gap equations which are valid for arbitrary phonon frequency, (_ph), electron-phonon coupling constant, (), and screened Coulomb interaction, ( ^*). We have used values of (_ph),, and ( ^*) appropriate to the cuprate superconductors, and calculated the density of states, the pair potential., and the value of the gap at T=0 K. Using the linearized Eliashberg equations in the matrix representation, we have calculatedT _c and 2/k T _c . We have found that we can account for the highT _c 's in the cuprates with reasonable values for, ^*, and _ph.     

Correlation and prediction of dense fluid transport coefficients. V. Aromatic hydrocarbons

A previously described method, based on consideration of hard-sphere theory, is used for the simultaneous correlation of the coefficients of self-diffusion, viscosity, and thermal conductivity for benzene, toluene, o-, m-, and p-xylene, mesitylene, and ethylbenzene in excellent agreement with experiment, over extended temperature and pressure ranges. Values are given for the roughness factors R _D , R , and R , and the characteristic volume, V ₀, is expressed as a function of both carbon number and temperature.     

A method of joint determination of the effective coefficients of horizontal mixing of large particles and of external heat exchange in an organized fluidized bed

A method is proposed for the joint determination of the coefficients of horizontal particle diffusion and external heat exchange in a stagnant fluidized bed.Notation c_f, c_s, c_n specific heat capacities of gas, particles, and nozzle material, respectively, at constant pressure - D effective coefficient of particle diffusion horizontally (coefficient of horizontal thermal diffusivity of the bed) - d equivalent particle diameter - d_t tube diameter - H₀, H heights of bed at gas filtration velocities u₀ and u, respectively - H_a height of active section - l width of bed - L tube length - l _o width of heating chamber - N number of partition intervals - p=H/H₀ expansion of bed - s_n surface area of nozzle per unit volume of bed - S_h, S_v horizontal and vertical spacings between tubes - t_c, t₀, t_s, t_n, t_w initial temperature of heating chamber, entrance temperature of gas, particle temperature, nozzle temperature, and temperature of apparatus walls, respectively - u₀, u velocity of start of fluidization and gas filtration velocity - y horizontal coordinate - ^*, coefficient of external heat exchange between bed and walls of apparatus and nozzle - ₁, ₁, ₂, ... coefficients in (4) - thickness of tube wall - _b bubble concentration in bed - ₀ porosity of emulsion phase of bed - _n porosity of nozzle - =(t_s – t₀)/(t_c – t₀) dimensionless relative temperature of particles - _n coefficient of thermal conductivity of nozzle material - f, _s, _n densities of gas, particles, and nozzle material, respectively - _be=_s(1 – ₀) (1 – _b) average density of bed - time - _max time of onset of temperature maximum at a selected point of the bed - R =l _o/l Fourier number - Pe = ₁ l ²/D Péclet number - Bi = /_n Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 457–464, September, 1981.     

The effect of molecular orientation and acetylene-enhanced crosslinking on the wear of UHMWPE in total artificial joints

This paper investigates the benefits of combining roll-drawing and acetylene-enhanced crosslinking to alter the mechanical properties of the ultra high molecular weight polyethylene (UHMWPE) used in total hip and knee replacements, with the aim of improving its resistance to wear. UHMWPE was processed via crosslinking, roll-drawing and a combination of crosslinking and roll-drawing and subjected to gel content analysis, tensile tests, X-ray diffraction and wear tests using different types of motion and smooth and rough counterfaces.Purely roll-drawn materials with length and width draw ratios of _l × _w = 1.3 × 1.0 and _l × _w = 1.6 × 0.9 respectively, were found to have lower wear factors in a unidirectional motion test with a rough counterface when compared to the virgin material.The crosslinked roll-drawn material, with length and width draw ratios of _l × _w = 1.6 × 0.9, was seen to possess five crosslinks per initial number average molecule. This crosslinked and roll-drawn material showed 5.5 times less wear than the virgin material in a multidirectional motion test with a smooth counterface and 1.4 times more wear than the virgin material in a unidirectional motion test with a rough counterface. Hence this study supports previous work by the authors that acetylene-enhanced crosslinked materials may show benefits for a total hip replacement, but only where the femoral head remains smooth. The improvements in wear with the roll-drawn material in unidirectional tests were smaller, but may prove to have some benefits in the knee. © 2001 Kluwer Academic Publishers     

Heat transfer in a “pseudoturbulent” bed of dispersed material

A two-phase model is proposed for the steady heat exchange between a surface and a pseudoturbulent bed of dispersed material. Expressions are obtained for the temperature fields of the gaseous and solid phases.Notation _g effective thermal conductivity of gaseous phase - _s effective thermal conductivity of the mixed solid phase - porosity - _m molecular thermal conductivity - d particle diameter - temperature of dispersed bed at a large distance from heat source - , g gas temperature - _p particle temperature - _w wall temperature - x current coordinate in the direction perpendicular to the wall - l bed thickness - q heat flux - coefficient of heat exchange between wall and pseudoturbulent bed of dispersed material - ^* coefficient of interphase heat exchange - _g=_g/_w dimensionless gas temperature - _p = _p/_w dimensionless particle temperature - Y = x/d dimensionless coordinate - L =l/d dimensionless bed thickness - A_h dimensionless coefficient of interphase heat exchange - Nu_g = d/_s Nusselt number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 465–469, September, 1981.     

Eliashberg Spectral Functions for Some High-Tc Superconductors

We used a simplified but more realistic form of a model spectral functions for some high-T _c superconductors (e.g., LSCO, YBCO, BSCCO), avoiding the elaborate process of solving the Eliashberg equations numerically. The resulting spectral functions, constructed using the phonon density of states (PDOS), obtained from INS experiments with the easy use of available expressions, reproduce the observed critical temperature, gap ratio, and several other parameters. T _c is found to have a stronger increase with the electron–phonon coupling constant compared to those obtained from several equations, constructed from numerical solution of the Eliashberg equations for lower values. The obtained functions show widely spreading spectra that inhibit lattice instability by yielding not too large values of (< 2.95).     

Effect of growth rate and lamellar spacing on microhardness in the directionally solidified Pb-Cd, Sn-Zn and Bi-Cd eutectic alloys

Lead-cadmium, Zinc-tin and Bismuth-cadmium of (99.99%) high purity eutectic alloys were melted in a graphite crucible under vacuum atmosphere. These eutectic alloys were directionally solidified upward with a constant temperature gradient G and different growth rates V in the Bridgman type directional solidification furnace. The lamellar spacings and microhardness H _V were measured from both transverse section and longitudinal section of the specimen. The variations of H _V with respect to V and have been determined by using the linear regression analysis method. H _V values increase with the increasing values of V and decrease with the increasing values. The Hall-petch type relationships obtained in this work have been compared with the previous works.