Kinetic Theory Of Polyatomic Gases Research Articles

Relativistic Kinetic Theory of Polyatomic Gases: Classical Limit of a New Hierarchy of Moments and Qualitative Analysis

A relativistic version of the Kinetic Theory for polyatomic gas is considered and a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal modes is presented. In the first part, we prove via classical limit that the truncated system of moments dictates a precise hierarchy of moments in the classical framework. In the second part, we consider the particular physical case of fifteen moments closed via maximum entropy principle in a neighborhood of equilibrium state. We prove that this symmetric hyperbolic system satisfies all the general assumptions of some theorems that guarantee the global existence of smooth solutions for initial data sufficiently small.

New International Formulation for the Thermal Conductivity of Heavy Water

The International Association for the Properties of Water and Steam has adopted new formulations for the thermodynamic and transport properties of heavy water. This manuscript describes the development of a formulation for the thermal conductivity of heavy water that was adopted as an international standard in 2021. It is consistent with the equation of state adopted in 2017, revised slightly in 2018, and is valid for fluid states up to 825 K and 250 MPa with uncertainties ranging from 1.5% to 6% depending on the state point. Comparisons with experimental data and with an earlier thermal-conductivity formulation are presented. The 2021 formulation accounts for the critical enhancement of the thermal conductivity, which was not incorporated in the previous formulation. Furthermore, in the zero-density limit, the 2021 formulation is based on thermal conductivity values at temperatures from 250 to 2500 K obtained from the kinetic theory of polyatomic gases. In addition, the 2021 formulation is applicable in a larger range of pressures than the previous formulation.

Reference Values for the Second Virial Coefficient and Three Dilute Gas Transport Properties of Ethane from a State-of-the-Art Intermolecular Potential Energy Surface

The second virial coefficient and the dilute gas shear viscosity, thermal conductivity, and self-diffusion coefficient of ethane (C2H6, R-170) were determined with high accuracy at temperatures from (90 to 1200) K using advanced computational approaches. The second virial coefficient was calculated semiclassically by means of the Mayer-sampling Monte Carlo technique, while the transport properties were obtained using the classical kinetic theory of polyatomic gases. The required intermolecular potential energy surface was developed as part of this work. It is based on high-level quantum-chemical ab initio calculations and was fine-tuned to reliable experimental data for the second virial coefficient. The computed thermophysical property values are in excellent agreement with the best available experimental data and are recommended as reference values. Correlations based entirely on the calculated values are proposed for practical applications in the low-density gas phase.

Transport properties of dilute D2O vapour from first principles

ABSTRACTThe classical kinetic theory of polyatomic gases has been applied to calculate the traditional transport properties of heavy water (D2O) in the dilute gas limit using two highly accurate ab initio pair potentials. Results are reported for shear viscosity, thermal conductivity and the product of molar density and self-diffusion coefficient at temperatures between 250 and 2500 K. The expanded uncertainty (coverage factor k = 2) of the computed values is estimated to be 2% for viscosity and self-diffusion and 2%–4%, depending on temperature, for thermal conductivity. For the most part, the agreement with the available experimental data is satisfactory.

Macroscopic descriptions of rarefied gases from the elimination of fast variables

The Boltzmann equation describing a dilute monatomic gas is equivalent to an infinite hierarchy of evolution equations for successive moments of the distribution function. The five moments giving the macroscopic mass, momentum, and energy densities are unaffected by collisions between atoms, while all other moments naturally evolve on a fast collisional time scale. We show that the macroscopic equations of Chen, Rao, and Spiegel [Phys. Lett. A 271, 87 (2000)], like the familiar Navier-Stokes-Fourier equations, emerge from using a systematic procedure to eliminate the higher moments, leaving closed evolution equations for the five moments unaffected by collisions. The two equation sets differ through their treatment of contributions from the temperature to the momentum and energy fluxes. Using moment equations offers a definitive treatment of the Prandtl number problem using model collision operators, greatly reduces the labor of deriving equations for different collision operators, and clarifies the role of solvability conditions applied to the distribution function. The original Chen-Rao-Spiegel approach offers greatly improved agreement with experiments for the phase speed of ultrasound, but when corrected to match the Navier-Stokes-Fourier equations at low frequencies, it then underestimates the phase speed at high frequencies. Our introduction of a translational temperature, as in the kinetic theory of polyatomic gases, motivates a distinction in the energy flux between advection of internal energy and the work done by the pressure. Exploiting this distinction yields macroscopic equations that offer further improvement in agreement with experimental data, and arise more naturally as an approximation to the infinite hierarchy of evolution equations for moments.

The thermal conductivity of neon, methane and tetrafluoromethane

New, absolute measurements of the thermal conductivity of neon (Ne), methane (CH 4) and tetrafluoromethane (CF 4) are reported for the temperature range 308 to 428 K at pressures up to 10 MPa. The data have an estimated accuracy of ±0.3%. A statistical analysis of the density dependence of the thermal conductivity has been employed to deduce the thermal conductivity of the gases in the limit of zero density and the firt density coefficient. For methane the first density coefficient is well represented by a correlation based on data for monatomic gases whereas for tetrafluoromethane the same correlation greatly underestimates the same coefficient. The thermal conductivity in the limit of zero density has been used in conjuction with other transport property data to deduce a consistent set of effective cross-sections for the two gases over all the range of temperature studied, based entirely on experiment. Among other quantities the collision number for rotational relaxation has been deduced and is shown to be significantly different between the two gases. Although the Mason-Monchick approximation is inappropriate for the evaluation of some of the effective cross-sections for the gases, a recent, very simple formulation of the kinetic theory of polyatomic gases provides a satisfactory description of the thermal conductivity data.

The Viscosity of Normal Deuterium in the Limit of Zero Density

This paper contains a new representation of the viscosity of normal deuterium in the limit of zero density as a function of temperature. The correlation is based upon the semiclassical kinetic theory of polyatomic gases and a body of critically evaluated experimental data. The similarity of the intermolecular pair potentials of normal hydrogen and normal deuterium is employed to extrapolate the correlation for deuterium beyond the range of the experimental data. In the temperature range 250–350 K the accuracy of the representation of the viscosity is estimated to be ±1%, which deteriorates to ±2% at the lowest temperatures and to ±4% at the highest temperatures.

The Viscosity and Thermal Conductivity of Normal Hydrogen in the Limit of Zero Density

This paper contains a new representation of the viscosity and thermal conductivity coefficients of normal hydrogen in the limit of zero density as a function of temperature. The correlation is based upon the semiclassical kinetic theory of polyatomic gases and a body of critically evaluated experimental data. In the temperature range 200–400 K the accuracy of the representation of the viscosity is estimated to be ±0.5%. However, at the lowest temperature of 20 K and the highest temperature of 2200 K, the uncertainty rises to ±2.0%. The available thermal conductivity data of high accuracy cover the much more restricted temperature range from 100 to 400 K and the correlation of this property is limited to that range. Above room temperature, the uncertainty in the correlated values is no more than ±0.5%, but below room temperature it rises to one of ±1.5%. An attempt has also been made to represent the viscosity data by means of a correlation universal among several other polyatomic gases but it has proven unsatisfactory. An extension of the temperature range of the thermal conductivity correlation based upon the Wang Chang and Uhlenbeck kinetic theory also fails to produce acceptable results.

The Viscosity of Nitrogen, Oxygen, and Their Binary Mixtures in the Limit of Zero Density

The paper presents a concise and accurate representation of the viscosity of nitrogen, oxygen, and their binary mixtures at the limit of zero density and in the temperature range 110–2100 K, which can be programed easily on a computer. The correlation is founded upon the semiclassical kinetic theory of polyatomic gases and a body of critically evaluated experimental data. Use is also made of the principle of corresponding states to extend the correlation outside of the temperature range for which direct experimental results exist. The optimum correlation has an associated uncertainty of ±0.3% around room temperature, but it rises to a maximum of ±2% at either extreme of the temperature range. A secondary representation of the viscosity of the same gases, providing some saving in computational effort and a further extension of the temperature range at the expense of a small loss of accuracy, is also presented. The relationship of this second representation to similar correlations for other gases makes it attractive for some purposes.

The inelastic contributions to transport collision integrals in the infinite-order sudden approximation

The transport collision integrals of the Wang Chang and Uhlenbeck kinetic theory of polyatomic gases have been evaluated for an anisotropic intermolecular pair potential model for the He-CO2 interaction. The calculations have made use of the infinite-order sudden approximation to evaluate the state-to-state differential cross-sections, but otherwise involve no approximations. The results indicate that some earlier approximate methods for the evaluation of the collision integrals are quantiatively correct, although they are given a new interpretation. In particular, the simplifications introduced by Mason and Monchick are shown to yield essentially the same collision integral for viscosity as the more exact treatment. On the other hand, several long established procedures for treating the transport properties of polyatomic gases and gas mixtures are shown to be significantly in error. Specifically the diffusion coefficient for internal energy is some 10 per cent higher than the diffusion coefficient for ma...

Theoretical consistency test of steam transport properties

The kinetic theory of polyatomic gases is used to test the mutual consistency of the thermal conductivity, viscosity and specific heat of low-pressure steam from 100° to 700°C. No inconsistency exists within the cited tolerances of the skeleton tables recommended by the Sixth International Conference on the Properties of Steam, but there is some basis for suspecting that the high-temperature thermal conductivity values are slightly low. Methods for tightening the consistency bounds are suggested.

Notizen: Kinetic Theory of the Thermomagnetic Force

Abstract Results obtained within the framework of the kinetic theory of polyatomic gases, are reported for the influence of a magnetic field on the thermal force exerted on a solid sphere in a heat conducting gas.

A program for the extraction of bulk viscosities from sound absorption data

A review is given of the kinetic theory of polyatomic gases as based on the quantum mechanical Waldmann-Snider kinetic equation. The transport properties in the Navier-Stokes and Burnett regimes and their dependence on external electric and magnetic fields (Senftleben and Senftleben-Beenakker effects) as well as flow and heat-flow birefringence are discussed for gases consisting of linear, spherical top and symmetric top molecules. The relaxation phenomena associated with sound propagation, Rayleigh-Brillouin, depolarized Rayleigh and Raman light scattering are considered in some detail as well as nuclear magnetic and electron spin relaxation and pressure broadening of microwave spectral lines. Finally an overview is given of the quantum mechanical methods for the quantitative calculation of all these phenomena from the nonspherical intermolecular potential.

Kinetic Moment Equations for a Gas of Polyatomic Molecules with Many Internal Degrees of Freedom

The 17-moment approximation in the kinetic theory of polyatomic gases is extended to include gases whose molecules may possess many internal degrees of freedom. A closed set of moment equations is derived and their application to near equilibrium and relaxation type flows is considered. The role of complex collisions and the connection between the relaxation times and the volume viscosity are discussed.

628. Contribution to the kinetic theory of polyatomic gases: V M Zhdanov, Zh Eksper Teor Fiz, 53 (6), Dec 1967, 2099–2108 ( in Russian)

There are three types of installation in space research laboratories in which vacuum and low temperature are concerned. These are: 1.1. Space simulation chambers used to investigate the thermal balance of the satellite (solar simulation testing).2.2. Vacuum-temperature chambers in which the satellite or its component parts can be tested in the working condition for reliability under extreme temperatures (thermal-vacuum testing).3.3. Special installations for the study of particular phenomena or for the development of components.Only the first two types of installation are dealt with in this article. The two installation types can also be combined. In these installations, the test object is situated under vacuum in a chamber which is closed by a thermal wall. For the solar simulation testing, the thermal wall is cooled to a temperature of between 80 K and 100 K by means of LN2, in order to simulate the cold ambient conditions applying in space. A temperature range of from 100 to 370 K is covered during thermal-vacuum testing. The construction of a thermal wall is explained, together with the various systems of obtaining and maintaining definite temperatures. using LN2 and GN2.In the first generation of installations, simulation of the vacuum applying in space was obtained in the USA by a combination of 20 K cryopumps and diffusion pumps, whereas in Europe only diffusion pumps were used. During the past few years, new projects in space research have shown the provision of an ultra-clean vacuum in space simulation chambers to be an urgent necessity. Thus the original conception of a vacuum pump system has been changed in favour of the following combination of pumps: 1.1. Titanium sublimation pump with LN2-cooled getter surface,2.2. Sputter-ion pump and/or turbomolecular pump,3.3. 20 K cryopump. Installations built in the USA during recent years have used 20 K cryopumps as the main element providing the pumping action, whereas in the new installations in Europe, this function sublimation pump.The developments described are illustrated by means of examples, in particular by the IABG 4 m infrared space simulation and thermal-vacuum chamber in Ottobrunn, near Munich. This plant was completed a short time ago for use in connection with the research work on the Helios sun probe.

On a Gyro-Thermal Effect with Polyatomic Gases in a Magnetic Field

SCOTT, STURNER and WILLIAMSON observed that a polyatomic gas exerts a torque on a heated cylinder if a homogeneous magnetic field parallel to the axis is present. This effect is explained, for high enough pressure, by the kinetic theory of polyatomic gases. Decisive is the huge “amplification of spin” occurring when spin is transferred from molecules to cylinder in “cut tennis ball reflexion”. Phenomenologically this is manifested in the boundary condition (4): the gas shall have a slip velocity, tangential to the wall, which is proportional to the tangential component of its “azimuthal polarization”.

Kinetic Theory of Polyatomic Gases: Models for the Collision Processes

Models are developed for the collision term in the kinetic equation for polyatomic gases. Assumptions are made which imply that the translational degrees of freedom undergo violent changes in collisions, while the internal degrees of freedom undergo relatively small transitions. The models consist of a term for the translational degrees of freedom which is closely related to the Krook models for monatomic gases and a term for the internal degrees of freedom which has the character of a diffusion expression. An explicit model is constructed for a gas of eccentrically loaded spherical molecules. Disposable parameters appearing in the model are evaluated in the limits of impulsive and adiabatic collisions. The existence of characteristic rotational energy relaxation times in these limits is briefly examined.