Dilute Gas Limit Research Articles

Thermal Conductivity of Nitrogen-Methane Mixtures at Temperatures Between 300 and 425 K and at Pressures Up to 16 MPa

The thermal conductivities of nitrogen and three mixtures of nitrogen and methane at six nominal temperatures between 300 and 425 K have been measured as a function of pressure up to 16 MPa. The relative uncertainty of the thermal conductivity measurements at a 95% confidence level is estimated to be less then 1%. The data obtained and the results of the low-density analysis were used to test two prediction methods for the thermal conductivity of gas mixtures under pressure and for the thermal conductivity of dilute polyatomic gas mixtures. Reasonable agreement was found with expressions for predicting thermal conductivity of nonpolar mixtures in a dilute-gas limit developed by Schreiber et al. The scheme underestimates the experimental thermal conductivity with deviations not exceeding 3%. The prediction scheme for the thermal conductivity of gas mixtures under pressure suggested by Mason et al. and improved by Vesovic and Wakeham underestimates the experimental thermal conductivities throughout, likely due to its use of the Hirchsfelder–Eucken equation at the low-density limit.

Elliptic flow from two- and four-particle correlations in Au+Au collisions atsNN=130GeV

Elliptic flow holds much promise for studying the early-time thermalization attained in ultrarelativistic nuclear collisions. Flow measurements also provide a means of distinguishing between hydrodynamic models and calculations which approach the low density (dilute gas) limit. Among the effects that can complicate the interpretation of elliptic flow measurements are azimuthal correlations that are unrelated to the reaction plane (non-flow correlations). Using data for Au + Au collisions at sqrt{s_{NN}} = 130 GeV from the STAR TPC, it is found that four-particle correlation analyses can reliably separate flow and non-flow correlation signals. The latter account for on average about 15% of the observed second-harmonic azimuthal correlation, with the largest relative contribution for the most peripheral and the most central collisions. The results are also corrected for the effect of flow variations within centrality bins. This effect is negligible for all but the most central bin, where the correction to the elliptic flow is about a factor of two. A simple new method for two-particle flow analysis based on scalar products is described. An analysis based on the distribution of the magnitude of the flow vector is also described.

Calculation of the transport properties of carbon dioxide. I. Shear viscosity, viscomagnetic effects, and self-diffusion

Transport properties of pure carbon dioxide have been calculated from the intermolecular potential using the classical trajectory approach. Results are reported for shear viscosity, viscomagnetic coefficients, and self-diffusion in the dilute-gas limit and in the temperature range of 200–1500 K for the three recently proposed carbon dioxide potential energy hypersurfaces. Agreement with the measurements is, in general, within the experimental error. The calculations indicate that the corrections in the second-order approximation and those due to the angular-momentum polarization for the viscosity are small, <1% in the temperature range considered. The very good agreement of the calculated values for the Bukowski et al. potential energy hypersurface (1999) with the experimental viscosity data is consistent with the rigid-rotor assumption made in the calculations being reasonable for the three properties considered.

Prediction of the Thermal Conductivity of Gas Mixtures at Low Pressures

Three methods, namely, Mason–Saxena–Wassiljewa (MSW), Hirschfelder–Eucken (HE), and Schreiber–Vesovic–Wakeham (SVW), for predicting the thermal conductivity of nonpolar, multicomponent, molecular mixtures in the dilute-gas limit were tested against the available experimental data. Overall, the accuracy of the MSW method is judged to be of the order of ±6 to 8% while that of HE and SVW is ±2 to 3%. For the latter two methods this is a remarkably good agreement, considering the approximations made in deriving the prediction scheme from the kinetic theory results. The agreement achieved indicates that the HE and SVW methods can form the basis of accurate engineering estimation techniques for the thermal conductivity of gaseous mixtures at low pressures.

Cubic crossover equation of state for mixtures

In a preceding publication [S.B. Kiselev, Fluid Phase Equilibria 147 (1998) 7], a general procedure was proposed for transforming any classical equation of state (EOS) for pure fluids into a crossover EOS which incorporates the scaling laws asymptotically close to the critical point and is transformed into the original classical EOS far from the critical point. In the present paper, we extend this procedure and develop a cubic crossover equation of state for mixtures. A comparison is made with experimental data for pure methane, ethane, CO 2, and for the methane+ethane and CO 2+ethane mixtures in the one- and two-phase regions. The cubic crossover equation of state yields a satisfactory representation of the thermodynamic properties and the vapor–liquid equilibria of pure fluids and fluid mixtures in a large range of temperatures and densities, including the dilute gas limit, liquid densities, and the critical region.

Longitudinal force on a moving potential

We show a formal result of the longitudinal force acting on a moving potential. The potential can be velocity-dependent, which appears in various interesting physical systems, such as electrons in the presence of a magnetic flux-line, or phonons scattering off a moving vortex. By using the phase-shift analysis, we are able to show the equivalence between the adiabatic perturbation theory and the kinetic theory for the longitudinal force in the dilute gas limit.

Thermal conductivity of multicomponent polyatomic dilute gas mixtures

A new expression for the thermal conductivity of anN-component polyatomic gas mixture in the dilute-gas limit has been derived, based on the Thijsse approximation. The results are presented in terms of experimentally accessible quantities to allow for easier calculation of the thermal conductivity and easier interpretation of the experimentally available data. The resulting expression are much simpler than other formulae hitherto available. An additional new expression for the thermal conductivity of anN-component polyatomic gas mixture has been derived by replacing the effective cross-section by their spherical limits. These results are cast in a form which is analogous with, and no more complicated than, the corresponding expressions for purely monatomic mixtures.

Molecular Simulation Study of the Surface Barrier Effect. Dilute Gas Limit

The mass transfer resistance associated with penetrating the mouth of a very small pore is evaluated using classical molecular dynamics simulation techniques. The effects of temperature, pore size, and thermal motion of the adsorbent atoms are studied for a slit pore mouth model. Adsorption followed by surface diffusion to the pore mouth makes a significant contribution to the mass transfer when the temperature is low or, equivalently, when the adsorptive potential is strong. Thermal vibrations of the adsorbent atoms have little effect on the adsorption/surface diffusion mechanisms but cause fluctuations in the effective pore mouth area which can significantly affect transport rates. Perhaps the most important observation is that when the pore size approaches the kinetic diameter of the gas molecules, changes of a few percent in the pore size cause order-of-magnitude changes in the resistance. Therefore, it is possible that the surface barrier effect observed in zeolites and carbon molecular sieves is governed by highly localized (single atomic layer) structural details. 19 refs., 7 figs., 1 tab.

EXTREME TYPE II SUPERCONDUCTORS: UNIVERSAL PROPERTIES AND TRENDS

We review and analyze experiment results of the specific heat, the muon–spin rotation (μSR) relaxation rate and the fluctuation contributions to the magnetization and dc conductivity of extreme type II superconductors from the point of view of critical phenomena. Our estimates of critical exponents and amplitudes, the measured scaling behavior, the consistencies with the universal relations between the critical amplitudes and the decrease of the transition temperature (T c ) with decreasing thickness, which corresponds to a dimensional crossover from 3d and 2d xy critical behavior, provide considerable evidence for a three-dimensional xy critical point. The estimated volume of the critical correlation length amplitudes turns out to be comparable to that in super-fluid Helium and is several orders of magnitude smaller than in BCS superconductors. Moreover, motivated by the Uemura plot, which relates the measured T c to the zero temperature μSR relaxation rate, and by the hyperuniversal relation between T c and critical amplitudes of the London penetration depth and phase correlation length, we propose a simple "universal" scaling ansatz, where the plot of the rescaled transition temperature versus rescaled μSR relaxation rate should fall on a single parabola. Our analysis of the μSR data reveals excellent agreement with this scaling ansatz for a large class of cuprate and Chevrel-phase superconductors. The resulting dependence of T c on the zero-temperature "condensate density" is then used to explore universal trends in the pressure (α) and isotope (β) coefficients. In good agreement with experiment we find that α and β fall into common T c -α and T c -β regions, respectively, forming two branches, one for systems with positive and the other for compounds with negative pressure or isotope coefficient. The two branches merge at the maximum T c where the coefficients vanish and the magnitude of the coefficients increases with decreasing T c . The "universal" scaling ansatz also implies that the critical amplitudes of the penetration depth and phase correlation length are related to the zero temperature condensate density. This quantity is also related to the hole concentration. Finally we discuss the temperature dependence of the penetration depth. μSR measurements indicate that for various cuprates the temperature dependence for 0 < T < T c appears to be bounded by the two-fluid model and the dilute charged Bose gas behaviors, respectively. Consistent with the dependence of T c on the zero temperature condensate density, compounds with high T c 's turn out to be closer to two-fluid behavior, while compounds with decreasing T c and in turn with lower condensate density clearly reveal the crossover to the dilute gas limit. These trends combined with T → 0 point uniquely to Bose condensation of interacting and weakly charged pairs as the mechanism that drives the transition.

Density dependence of the effective mass of excess electrons in fluid methane

We report the calculation of the effective mass (m*) of excess electrons injected in fluid methane as a function of number density (n). The calculation is performed within the framework of the Wigner–Seitz model for nonpolar fluids, using an accurate molecular potential which satisfactorily describes the scattering of low-energy electrons in the gas phase. Our calculated m*(n) values are found to decrease monotonically from the free-electron mass (m0) in the dilute gas limit to 0.72 m0 in the high-density liquid near the triple point. Comparison is made with available data in the literature.

The Minimum in the Mobility-Density Curve for Electrons Injected into Insulating Dense Gases

Abstract Average force and force-force correlation formulae both point to the same result that the mobility μ of electrons injected into dense gases like Ar, Xe, CH4 and C2H6 ought to exhibit at least gross regularities with respect to changes in gas density n. This is the motivation for focussing here on the mobility minimum characterized by dμ/dn = 0. At this minimum, a formula for μmin is obtained from which the scattering length a has been eliminated in favour of its density derivative (da/dn). This density derivative, it is argued, must have the form a gasωt, where ωt, is a ‘characteristic volume for transport’ while a gas is the scattering length in the dilute gas limit. The Onsager continuum model, plus the Bottcher-Onsager formula for the dielectric constant, can be used as a first estimate of ωt, which is shown to be proportional to the cube of the ‘cavity radius’ in this model. The formula for μmin is finally brought into direct contact with experiment.

Nonlinear transport processes and fluid dynamics: Effects of thermoviscous coupling and nonlinear transport coefficients on plane Couette flow of Lennard-Jones fluids.

To examine the effects of nonlinear transport processes on the flow properties of a real fluid, we study the plane Couette flow under a temperature gradient in a Lennard-Jones fluid over a range of gas pressure. The analysis is based on the nonlinear transport coefficients derived in the modified moment method. The linear transport coefficients appearing in the theory are those constructed by Ashurst and Hoover from the nonequilibrium molecular-dynamics simulations, while for the equation of state for the Lennard-Jones fluid we use the empirical form proposed by Ree. Examples for the flow characteristics at two extreme conditions when either the gas is very dilute, or when it is very dense, are presented. It is shown that the temperature and velocity profiles for nonlinear transport processes are significantly different from the ones obtained with the linear transport coefficients. In the dilute-gas limit, slip boundary conditions are used which are derived by applying the Langmuir theory of gas-surface interaction. Flow profiles show pronounced boundary-layer structures near the wall when the product of the Knudsen number and the Mach number is sufficiently large.

Transport properties of diatomic gases

The coefficients of shear viscosity and self-diffusion for nitrogen in the dilute gas limit have been calculated within the Mason-Monchick approximation using the intermolecular potential surfaces of Berns and van der Avoird and van Hemert and Berns. The same potentials had previously been used in transport property calculations using the classical limit of the Wang Chang, Uhlenbeck and de Boer theory. Comparisons between the results for each potential surface using the different transport theories reveal surprising discrepancies which increase with increasing temperature. Possible causes of this behaviour are considered.

Dual transformations: An equivalence between the continuum and lattice versions of the two-dimensional Abelian Higgs model

The topological excitations in the two-dimensional Abelian Higgs model are studied in both the continuum and the Villain lattice version, and the results are compared. Using a singular gauge transformation, it is shown that there is an exact equivalence between the dual form of both versions. A fermion form of the theory is useful in studying its confinement properties beyond the dilute-gas limit. Also, the correct measure factor for the continuum version is derived.

Quantum fluctuations in the one-instanton sector of the CP n−1 model

Within the two-dimensional CP n−1 model we calculate the instanton density function in the dilute-gas limit by studying the quantum fluctuations in the one-instanton sector in the one-loop approximation. The result disagrees with the 1 n expansion. Green functions in the one-instanton background are displayed.

General self-dual Yang-Mills solutions

The recent work of Atiyah, Hitchin, Drinfeld, and Manin is used to discuss self-dual Yang-Mills solutions for the compact gauge groups $O(n)$, $\mathrm{SU}(n)$, and $\mathrm{Sp}(n)$. It is shown that the resulting solutions contain the correct number of parameters for all values of the topological charge. Although explicit construction of a general self-dual field requires the solution of a finite-dimensional, nonlinear matrix equation, we show that for widely separated instantons this equation can be solved perturbatively, providing a systematic expansion about the dilute-gas limit and a physical interpretation of the independent parameters in this limit. Further, closed-form expressions can be obtained for the general SU(2) solutions with topological charge 2 or 3. Finally, explicit isospin-1/2 and isospin-1 propagators are derived for a massless scalar field in the presence of the general self-dual SU(2) solution.

Instantons - how significant numerically at short distances?

It is attempted to calculate the instanton effects in the hadronic cross section of e +e − annihilation, the magnetic form factor of quark, and the potential of heavy quark-antiquark by expanding the quark-instanton interaction in the dilute gas limit.

On transient relativistic thermodynamics and kinetic theory

In the conventional Onsager formulation of non-equilibrium thermodynamics the Fourier heat conduction law is parabolic, and permits arbitrarily large propagation velocities for temperature discontinuities. While embarassing in a non-relativistic theory, this is unacceptable in a relativistic one. This paper presents a detailed discussion of the thermodynamics and (in the dilute gas limit) kinetic theory of such transients. When proper account of the two length scales involved is taken into account, the theory becomes hyperbolic; propagation velocities for a dilute gas never exceed √3/5 c = 0.775 c , where c is the speed of light.

Inelastic light scattering from density fluctuations in dilute gases. The kinetic-hydrodynamic transition in a monatomic gas

The number-density fluctuation spectrum, ${S}_{n}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}, \ensuremath{\omega})$, of xenon has been studied in the dilute-gas limit. Spectra of He-Ne laser light scattered through an angle of 10.58\ifmmode^\circ\else\textdegree\fi{} at room temperature were measured for pressures ranging from 0.02 to 0.6 atm. Over this range ${S}_{n}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}, \ensuremath{\omega})$ evolves from the Gaussian kinetic form to three peaked hydrodynamic form. Measured spectra were used to evaluate various kinetic and hydrodynamic calculations of ${S}_{n}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}, \ensuremath{\omega})$ through this transition. Spectra obtained from the Boltzmann equation using the Gross-Jackson kinetic modeling procedure, for both Maxwell and hard-sphere intermolecular potentials, are in excellent agreement with the measurements. Among the hydrodynamic theories tested only the generalized hydrodynamics of Selwyn and Oppenheim satisfactorily provides the initial nonhydrodynamic corrections to the Navier-Stokes equations.

ChemInform Abstract: REORIENTATIONAL AND ANGULAR MOMENTUM CORRELATION TIMES IN GASEOUS TETRAFLUOROMETHANE AT MODERATE DENSITIES

NMR 19F spin‐lattice relaxation times and Raman 435 cm−1 doubly degenerate [ν2(e)] vibrational‐rotation band shapes have been measured in gaseous carbon tetrafluoride at 25 °C and densities of 9 to 120 amagat. NMR spin‐lattice relaxation times have also been measured over the temperature range of −60 to 40 °C for the above densities. The Fourier transform analysis of the Raman band shapes has allowed us to calculate the reorientational correlation time τθ,2. Since spin rotation interactions provide the dominant relaxation mechanism for fluorine in CF4, then the angular momentum correlation time τJ is obtained directly from the 19F T1 relaxation times with the assumption that the anisotropy of the spin‐rotation interaction tensor is small. A comparison of our experimental τθ,2 and τJ relationship agrees well with that predicted by the dilute gas limit of Gordon's J ‐ and M ‐diffusion model as extended to classical spherical molecules by McClung.