Influence of a magnetic field on diffusion and thermal diffusion in gaseous mixtures

The influence of a magnetic field on the transport properties of binary mixtures of a polyatomic and a noble gas is studied theoretically. Using an inverse operator technique, first thermal conductivity and viscosity are treated. Then diffusion and thermal diffusion are discussed in detail, with special emphasis on the composition dependence. A relation connecting the magnitudes of the field effects on thermal conductivity, diffusion, and thermal diffusion is derived. This relation is used to estimate the field effect on diffusion.     

Effects of dipolar forces on critical sound attenuation in uniaxial systems

Critical sound attenuation in uniaxial dipolar systems is investigated above and below T_c by using the dynamic renormalization-group analysis for an elastically coupled Ising-type model at d = 4. We predict a logarithmic crossover of the divergence of sound damping as $\text{t =}\text{|T ? T}{}_{\mathrm{c}}\text{|}\text{T}{}_{\mathrm{c}}\text{→ 0}$ and derive a universal, crossover-independent ratio R = 12.984|lnt| between the relaxation and the fluctuation damping below T_c. The effects of elastic anisotropy on the phase transition are discussed.     

Thermal conduction and thermal diffusion in dilute polyatomic gas mixtures

A novel theoretical basis for the evaluation of the thermal conductivity and the thermal diffusion ratios of dilute polyatomic gas mixtures is derived within the semi-classical isotropic kinetic theory. New expressions for species diffusion coefficients, thermal diffusion coefficients, and thermal diffusion ratios are also obtained by using an expansion vector based upon the total energy of the molecules. Finally, practical and accurate expressions for the thermal conductivity and the thermal diffusion ratios are derived by using the recent theory of iterative transport algorithms, as developed by the authors. The resulting expressions can be used in either theoretical calculations or computational models of multicomponent flows.     

Segregation by thermal diffusion in moderately dense granular mixtures

A theory based on a solution of the inelastic Enskog equation that goes beyond the weak dissipation limit is used to determine the thermal diffusion factor of a binary granular mixture under gravity. The Enskog equation that aims to describe moderate densities neglects velocity correlations but retains spatial correlations arising from volume exclusion effects. As expected, the thermal diffusion factor provides a segregation criterion that shows the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the system (masses, sizes, composition, density and coefficients of restitution). The form of the phase diagrams for the BNE/RBNE transition is illustrated in detail in the tracer limit case, showing that the phase diagrams depend sensitively on the value of gravity relative to the thermal gradient. Two specific situations are considered: i) absence of gravity, and ii) homogeneous temperature. In the latter case, after some approximations, our results are consistent with previous theoretical results derived from the Enskog equation. Our results also indicate that the influence of dissipation on thermal diffusion is more important in the absence of gravity than in the opposite limit. The present analysis, which is based on a preliminary short report of the author (Phys. Rev. E 78, 020301(R) (2008)), extends previous theoretical results derived in the dilute limit case.     

Molecular origin of thermal diffusion in benzene + cyclohexane mixtures

The isotope effect in thermal diffusion (Soret effect) of benzene+cyclohexane mixtures has been investigated by a holographic grating technique. The Soret coefficient can be split into additive contributions. One contribution, the isotope effect, stems from the differences of both mass and moment of inertia, and is independent of composition. An additional "chemical" contribution depends on concentration and even changes its sign at a benzene mole fraction x(benz) approximately 0.7. The mass effect is in agreement with molecular dynamics calculations: the heavier component migrates to the cold side.     

Effects of porous covering on sound attenuation by periodic arrays of cylinders

The acoustic transmission loss of a finite periodic array of long rigid cylinders, without and with porous absorbent covering, is studied both theoretically and in the laboratory. A multiple scattering model is extended to allow for the covering and its acoustical properties are described by a single parameter semi-empirical model. Data from laboratory measurements and numerical results are found to be in reasonable agreement. These data and predictions show that porous covering reduces the variation of transmission loss with frequency due to the stop/pass band structure observed with an array of rigid cylinders with similar overall radius and improves the overall attenuation in the higher frequency range. The predicted sensitivities to covering thickness and effective flow resistivity are explored. It is predicted that a random covered array also gives better attenuation than a random array of rigid cylinders with the same overall radius and volume fraction.     

Wall effects on sound propagation in tubes

Numerical solutions have been obtained for the exact equations describing the propagation of periodic axisymmetric waves in a rigid cylindrical tube. Results were obtained for air over a range of conditions corresponding to shear wave numbers (s = R √?ω/μ) from 0·2 to 5000 and reduced frequencies (k = ωR/a) from 0·01 to 6. For conciseness and convenient application, the results for the attenuation and phase shift coefficients are given in the form of simple polynomials for the ranges 5 ? s ? 5000 and 0·01 ? k ? 6. This range covers virtually all values of tube diameter and sound frequency likely to be met in practical situations that are consistent with a continuum gas model.     

Diffusion and thermal diffusion in binary mixtures of sulphur hexafluoride with noble gases

Diffusion coefficients and thermal diffusion factors are reported for binary mixtures of sulphur hexafluoride with noble gases. The results are compared with theoretical values calculated by means of the Chapman-Enskog theory, spherical potentials for the like interactions and multi-parameter anisotropic potentials for the unlike interactions.     

Frustration and sound attenuation in structural glasses

Three classes of harmonic disorder systems (Lennard-Jones-like glasses, percolators above threshold, and spring disordered lattices) have been numerically investigated in order to clarify the effect of different types of disorder on the mechanism of high frequency sound attenuation. We introduce the concept of frustration in structural glasses as a measure of the internal stress, and find a strong correlation between the degree of frustration and the exponent alpha that characterizes the momentum dependence of the sound attenuation gamma(Q) approximately Qalpha. In particular, alpha decreases from approximately d+1 in low-frustration systems (where d is the spectral dimension) to approximately 2 for high-frustration systems such as the realistic glasses examined.     

On thermal diffusion in binary and ternary Lennard-Jones mixtures by non-equilibrium molecular dynamics

Molecular simulation appears to be an alternative to experiment for the estimation of transport and thermodynamics properties of fluid mixtures, which is of primary importance in the evaluation of the initial state of a petroleum reservoir. In this study, a non-equilibrium molecular dynamics algorithm has been applied to mixtures of Lennard-Jones spheres in order to compute the thermal diffusion process. The pertinence of such an approach to simple alkane mixtures is shown. The separate influences on the thermal diffusion of the molecular features in binary equimolar mixtures are then summarized. Simulations on binary non-equimolar mixtures have been performed as well. The results indicate an increase in the thermal diffusion process with increasing molar fraction of the lightest component. Moreover, this increase is enhanced with increasing difference in the number of carbons between the two alkanes. Then, a simple method, which yields results consistent with simulations, is proposed to predict thermal diffusion for the whole range of molar fractions starting only from the equimolar value. Finally, for ternary mixtures, the law of the corresponding states is shown to be valid when the appropriate mixing rules are applied, which allows the estimation of thermal diffusion in such mixtures from equivalent binary mixtures.     

Benchmark values for the Soret,thermal diffusion and diffusion coefficients of three binary organic liquid mixtures

With the aim of providing reliable benchmark values, we have measured the Soret, diffusion and thermal diffusion coefficients of the three binary mixtures of dodecane, isobutylbenzene and 1,2,3,4 tetrahydronaphthalene for a concentration of 50 wt% at a temperature of 25C. The experimental techniques applied by the five participating laboratories are transient holographic gratings, annular and parallelepipedic thermogravitational columns, and vertical parallelepipedic columns with velocity amplitude determination by laser doppler velocimetry. The systems have also been studied in a annular thermogravitational column filled with a porous medium in the gap. There is a good agreement between the different experiments with deviations of the order of a few per cent in most cases (8.5% at most). The numerical values are tabulated in the paper.     

Low-frequency sound absorption and attenuation in marine medium

Original experimental data are analyzed on the low-frequency sound attenuation in the Mediterranean, Black, and Baltic Seas, Sea of Japan, and the north-western region of the Pacific Ocean. In these regions, waters significantly differ in their temperatures and salinities. The analysis is aimed at obtaining an expression for calculating the low-frequency absorption coefficient in sea water. The analysis uses the previously published data on the measured (by the temperature discontinuity method) low-frequency relaxation times associated with boron present in sea water. The dependence of the absorption on the pH value (which was revealed in the 1970s) and the experimental data on sound absorption at frequencies higher than 5–10 kHz are also taken into account. As a result of the analysis based on the assumption that low-frequency relaxation takes place, an expression is proposed that relates the low-frequency absorption to the temperature, salinity, and pH value and equally well describes the experimental frequency dependences of attenuation for the four regions at hand (except for the Baltic Sea). Increased attenuation coefficients are noticed for shallow seas and deep-water regions where waters are influenced by intense currents, strait zones, and zones of mixing waters of different origin, i.e., for the ocean areas where, in addition to the attenuation, sound scattering by inhomogeneities of the marine medium and sound energy leakage into the sea floor are significant.     

Non-linear effect of wall linings on sound attenuation in ducts

The equivalent surface source method is extended to the analysis of high intensity sound propagation in a duct whose wall is partially treated with a sound absorbing material. The propagation of sound in the gas is assumed to be linear, but the acoustic resistance of the sound absorbing material is assumed to be a function of the normal acoustic velocity. The problem is reduced to a non-linear integro-differential equation for the fluid particle displacement at the lined wall surface, which can be solved by a successive approximation method. Numerical examples show that the non-linear effect decreases or increases the peak sound attenuation rate of the lowest mode depending upon the linear component of the resistance. The dependence of the attenuation spectrum on modal phase difference of multi-mode incident waves is heavily affected by the non-linear effect. In the case of incident waves of multi-circumferential modes, different circumferential modes are generated by the non-linear effect.     

X-ray attenuation coefficients of elements and mixtures

This paper is concerned with X-ray attenuation in samples of pure elements and mixtures of elements. The emphasis is on the energy range 30–150 keV although the energy regions 10–30 and 150–1000 keV are also discussed. The approximations involved in deriving several well known formulae for the photoelectric and scattering cross-sections are described and the accuracy of these formulae is assessed. More accurate formulae are derived by reference to fundamental theory. It is shown that definitions of such quantities as effective atomic number cannot be justified from fundamental theory. The consequences of this result are explored in relation to various experimental conditions and the physical parameters of a complex medium which can be determined by X-ray transmission measurements are identified. Connections with related areas of interest in atomic physics and low energy X-ray scattering are made.     

Non-linear attenuation of sound in circular lined ducts

The attenuation of high intensity sound in circular ducts lined with fibrous material has been investigated. With no mean flow, the sound pressure levels are varied to illustrate the linear and non-linear absorption characteristics of the liner. Effects of liner thickness, perforation ratio of the duct wall and the $\text{d}\text{t}$ ratio are analysed.Optimum combinations of the perforation geometry and liner thickness are found to be of stable attenuation characteristics over a wide frequency range and at high sound levels.     

Anomalous attenuation of transverse sound in 3He

We present the first measurements of the attenuation of transverse sound in superfluid 3He-B. We use fixed path length interferometry combined with the magnetoacoustic Faraday effect to vary the effective path length by a factor of 2, resulting in absolute values of the attenuation. We find that attenuation is significantly larger than expected from the theoretical dispersion relation, in contrast with the phase velocity of transverse sound. We suggest that the anomalous attenuation can be explained by surface Andreev bound states.     

有限振幅脉冲波在管道中的传播

本文分析有限振幅声波在刚性管道中的传播.首先讨论忽略管壁阻尼影响时Burgers方程的解,以反对称N波解为基础,获得了非对称的N波解,能更好地适配实际产生的N波。然后把管壁阻尼的影响作为小量进行修正,获得了广义Burgers方程的近似解.文中对实验测试作了扼要介绍,表明理论预测与实验结果良好相符。     

The theory of the sound attenuation in one-dimensional metals

The elasticity theory equations are obtained for a 1d conductor. The frequency dependence of the sound attenuation is analysed, the spatial dispersion being strong or weak. The effect of oscillations of the attenuation is predicted which is due to a jumping nature of electronic motion in a non-uniform field of the sound wave, with a fixed jumping length. That is why the oscillations are of the geometric resonance type. Because of absence of Landau's damping, the frequency dependence of attenuation in a region of strong spatial dispersion is quadratic rather than linear one, as in 3d metals. This dependence is determined by a quantum nature of electronic scattering on separate impurities which move with an oscillating lattice.