Entropy production and thermal conductivity of a dilute gas

It is known that the thermal conductivity of a dilute gas can be derived by using kinetic theory. We present here a new derivation by starting with two known entropy production principles: the steepest entropy ascent (SEA) principle and the maximum entropy production (MEP) principle. A remarkable feature of the new derivation is that it does not require the specification of the existence of the temperature gradient. The known result is reproduced in a similar form.     

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.     

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.     

The role of the dynamic pressure in stationary heat conduction of a rarefied polyatomic gas

The effect of the dynamic pressure (non-equilibrium pressure) on stationary heat conduction in a rarefied polyatomic gas at rest is elucidated by the theory of extended thermodynamics. It is shown that this effect is observable in a non-polytropic gas. Numerical studies are presented for a para-hydrogen gas as a typical example.     

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.     

Thermal electron capture in organic compound-carbon dioxide gas mixtures

The rates of free thermal electron capture were measured depending on the buffer gas (CO₂) pressure for 15 organic compounds in an ionization chamber with laser cathode photoionization. Procedures for preparing the tested gas mixtures and experimental data processing are described.     

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.     

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.     

Diffusion and thermal diffusion coefficients of a relativistic gas mixture

Values up to order c^-2 are given for the diffusion and thermal diffusion coefficients of binary relativistic gas mixtures of hard spheres and Israel particles.     

Second law of thermodynamics in volume diffusion hydrodynamics in multicomponent gas mixtures

We presented the thermodynamic structure of a new continuum flow model for multicomponent gas mixtures. The continuum model is based on a volume diffusion concept involving specific species. It is independent of the observer?s reference frame and enables a straightforward tracking of a selected species within a mixture composed of a large number of constituents. A method to derive the second law and constitutive equations accompanying the model is presented. Using the configuration of a rotating fluid we illustrated an example of non-classical flow physics predicted by new contributions in the entropy and constitutive equations.     

Relaxation and diffusion of perfluorocarbon gas mixtures with oxygen for lung MRI

We report measurements of free diffusivity D(0) and relaxation times T(1) and T(2) for pure C(2)F(6) and C(3)F(8) and their mixtures with oxygen. A simplified relaxation theory is presented and used to fit the data. The results enable spatially localized relaxation time measurements to determine the local gas concentration in lung MR images, so the free diffusivity D(0) is then known. Comparison of the measured diffusion to D(0) will express the extent of diffusion restriction and allow the local surface-to-volume ratio to be found.     

Thermal diffusion of hydrogen in zirconium with allowance for thermal stresses

The thermal diffusion of hydrogen atoms in zirconium is studied with allowance for thermal stresses. As a mathematical model, a steady-state temperature in a hollow cylinder is considered. The logarithmic coordinate dependence of this temperature allows an exact analytical solution to be obtained for a diffusion kinetics problem. The results of a theoretical analysis can serve as a test example for studying mass transfer in systems with a more complex coordinate dependence of temperature.     

Density and stability in ultracold dilute boson-fermion mixtures

We analyze in detail recent experiments on ultracold dilute ⁸⁷Rb–⁴⁰K mixtures in Hamburg and in Florence within a mean-field theory. To this end we determine how the stationary bosonic and fermionic density profiles in this mixture depend in the Thomas-Fermi limit on the respective particle numbers. Furthermore, we investigate how the observed stability of the Bose-Fermi mixture with respect to collapse is crucially related to the value of the interspecies s-wave scattering length.     

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.     

Magnetoresistance and conduction electron-impurity spin coupling in dilute silver alloys

From measurements of the magnetoresistance of silver containing both manganese and gadolinium, it is concluded that the s-d coupling and s-f coupling have opposite signs. As for gadolinium in silver the spin dependent part of the resistivity is small, a resistance anomaly at low temperatures can hardly be detected.     

Coarsening and self-organization in dilute diblock copolymer melts and mixtures

This paper explores the evolution of a sharp interface model for phase separation of copolymers in the limit of low volume fraction. Particles both exchange material as in usual Ostwald ripening, and migrate because of an effectively repulsive nonlocal energetic term. Coarsening via mass diffusion only occurs while particle radii are small, and they eventually approach a finite equilibrium size. Migration, on the other hand, is responsible for producing self-organized patterns.We construct approximations based upon an ansatz of spherical particles similar to the classical LSW theory to derive finite dimensional dynamics for particle positions and radii. For large systems, kinetic-type equations which describe the evolution of a probability density are constructed. For systems larger than the screening length, we obtain an analog of the homogenization result of Niethammer & Otto [B. Niethammer, F. Otto, Ostwald ripening: The screening length revisited, Calc. Var. Partial Differential Equations 13-1 (2001) 33-68]. A separation of timescales between particle growth and migration allows for a variational characterization of spatially inhomogeneous quasi-equilibrium states.     

Ion diffusion and momentum correlation functions in dilute electrolytes

The convergent cluster expansion of the ion-ion momentum time correlation functions in a dilute electrolyte, recently derived by Friedman, is applied here for the calculation of the limiting law for ion self-diffusion. Considering only the non-chain cluster terms leads to a result analogous to the Debye-Hückel limiting law for ionic conductivity. Taking into account the additional chain terms leads to exactly the Onsager result. We also use the cluster expansion to determine the long-time behaviour of the ion momentum time auto-correlation function, which we find goes as t ^-3/2, with a coefficient proportional to the square root of the solute concentration. Similar results are given for the associated memory function and the ion-ion momentum time correlation function.